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Faraday Discuss., 1997, 108, 1»22 Spiers Memorial Lecture On Dynamics From isolated molecules to biomolecules Joshua Jortner School of Chemistry, T el Aviv University, Ramat Aviv, 69978 T el Aviv, Israel We address the dynamics of electronic»vibrational excited states in isolated molecules, clusters, condensed phase and biosystems, which pertain to the phenomena of energy acquisition, storage and disposal as explored from the microscopic point of view.The advent of femtosecond dynamics opened up new horizons in the exploration of chemical and biophysical processes on the timescale of nuclear motion. These ultrafast radiationless processes involve isolated molecules, where ultrafast ìnonreactiveœ intramolecular internal conversion can occur on the timescale of vibrational motion, while ì reactive œ dissociation and Coulomb explosion manifest the sliding down on the repulsive nuclear surface.In some cluster and condensed phase systems ultrafast energy dissipation processes, manifesting collective large nuclear con–gurational changes, bear analogy to the molecular ì reactive œ dynamics, but can concurrently maintain vibrational phase coherence induced by nuclear impact.For ultrafast dynamics in clusters, in the condensed phase and in the protein medium, separation of timescales for nuclear dynamics may prevail. Interstate and energy relaxation are understood, while the interplay between relaxation and dephasing is of considerable interest. The ubiquity of vibrational and electronic coherence eÜects, ranging from small to huge systems, raises the conceptual question of the distinction between the experimental conditions of the preparation and interrogation, and the intrinsic aspects of relaxation and dephasing dynamics.These are some of the central aspects of the novel and fascinating area of femtosecond chemistry, whose conceptual framework rests on a uni–ed theory and simulation of intramolecular, cluster, condensed phase and biophysical dynamics.It is an honor to deliver the 1997 Spiers Memorial Lecture. Frederick S. Spiers left his mark on the scienti–c infrastructure of physical chemistry, as secretary of the Faraday Society, which he helped to found in 1902. Essentially, he has determined the character of these scienti–c discussions by which the Faraday Society and later the Faraday Division of the Royal Society of Chemistry became famous throughout the world.The interests of Spiers transcended pure and applied chemistry, encompasing music and culture. He was a –ne Hebrew and Talmudic scholar. At the onset of the Spiers Memorial Lecture on Dynamics, it may be appropriate to quote from an old Hebrew scholarship : ìYou should know where you are coming from and where you are going toœ, Proceedings of the Sage Fathers, 2nd Century AD.This quotation captures the essence of dynamics from isolated molecules to biomolecules, pertaining to the elucidation of the phenomena of energy acquisition, storage and disposal in large molecules, clusters, condensed phase and biophysical systems, as explored from the microscopic point of view.The genesis of intramolecular nonradiative dynamics dates back to the origins of quantum mechanics. In 1928 BonhoeÜer and Farkas1 observed that predissociation of 12 Spiers Memorial L ecture Fig. 1 A molecular energy-level model used to describe coupling and nonreactive relaxation in a bound-level structure in excited states of large molecules. This model was introduced by Bixon and Jortner18,19 to describe interstate coupling and relaxation, and is adequate to describe intrastate coupling and intramolecular vibrational energy redistribution.the ammonia molecule is manifested by spectral line broadening (line width C). This observation established experimental veri–cation of the Heisenberg energy»time uncertainty relation with the decay lifetime of the metastable state being given by the CqBÅ, golden rule2 q~1PoHo2(dn/dE), where H is the matrix element of the perturbation causing the transition, and dn/dE is the energy density of states.The same formalism was concurrently applied for atomic and molecular autoionization.2 The studies of predissociation and autoionization established the conceptual framework of the dynamics and the dynamic»spectroscopic relations for the decay of a metastable state into a (dissociative or ionizative) continuum.Important developments in the realm of intermolecular dynamics were pioneered by Wigner, Polanyi and Eyring in the 1930s,3 for kinetics in the gas phase, in molecular beams and in solution.4 In the 1950s and 1960s the conceptual framework was advanced for two novel classes of nonradiative process, i.e., dynamics in the condensed phase and intramolecular radiationless transitions in large molecules. The –eld of nonradiative dynamics in the condensed phase was pioneered by Huang and Rhys,5 Kubo,6 Lax,7 and Kubo and Toyozawa8 in the context of the theory of electron»hole recombination in semiconductors.Conceptually and physically isomorphous classes of radiationless phenomena pertain to the theoretical foundations of electron transfer (ET) processes in solution, whose exploration was pioneered by Marcus,9 and electronic energy transfer (EET) processes, which were elucidated by Foé rster.10 When this signi–cant progress was accomplished in the 1950s, no one realized the interrelationship between condensed-matter relaxation, e.g., electron»hole recombination, electron transfer and energy transfer, and intramolecular radiationless transitions, e.g., intersystem crossing and internal conversion in large molecules.At that time some experimental information was already available on intramolecular relaxation in large molecules embedded in a condensed medium, i.e., a solution or a glass.Kasha formulated his (approximate) rules to characterize internal conversion and intersystem crossing of solvated organic molecules,11 while Beer and Longuet-Higgins provided striking experimental evidence for the internal conversion of the –rst singlet excited state of azulene in solution.12 Guided by the experimental background, the –rst theories of relaxation of large molecules focused on the coupling to the medium as an essential ingredient inducing electronic»vibrational conversion.Robinson and Frosch13 proposed sequential interstate electronic coupling and medium-induced vibrational relaxation, Gouterman14 alluded to medium phonon emission, while Lin15 and Lin and Bersohn16 considered medium and intramolecular multiphonon processes. A central ingredient of electronic relaxation in large molecules originated from the seminal experiments ofJ.Jortner 3 Fig. 2 The application of the eÜective Hamiltonian formalism for interstate and intrastate intramolecular coupling and dynamics. The zero-order states o sT and Mo lTN are characterized by the energies and respectively, and by the decay widths and represents the Es MElN, cs MclN.Vsl intramolecular (interstate or intrastate) coupling between the doorway state o sT and the Mo lTN manifold, which is characterized by the density of states Diagonalization of the eÜective ol . Hamiltonian results in a set of independently decaying levels MomTN, i.e., generalized molecular eigenstates, characterized by energies decay widths and density of states MEmN, McmN, om .Kistiakowski and Parmenter, which demonstrated the occurrence of intersystem crossing in the ì isolated œ collision-free benzene molecule.17 The iconoclastic implications of the occurrence of irreversible relaxation in a bound level structure were fully realized by Kistikowski and Parmenter, who stated that their results may be incompatible with the laws of quantum mechanics.17 The intramolecular nature of radiationless transitions in a bound level structure was established by the Bixon»Jortner model,18h25 which rests on near-resonance coupling, the dynamics of wavepackets of mixed bound states, –nite time evolution, and practical irreversibility in a dense bound level structure of a vibrational quasicontinuum (Fig. 1). This general conceptual framework is applicable both for interstate coupling,18h36 which involves two electronic con–gurations coupled by nuclear momenta (i.e., the breakdown of the Born»Oppenheimer separability), and/or spin»orbit interaction, as well as for intrastate coupling, which involves intramolecular vibrational energy redistribution (IVR) within a single electronic con–guration with rotational» vibrational states coupled by anharmonic or Coriolis interactions.35,36 This theoretical framework is of wide applicability for the exploration of the dynamics of electronically excited states of ì isolated œ molecules in the gas phase, of clusters, and in condensed media.Femtosecond dynamics opened up new horizons in the exploration of ultrafast radiationless processes. In the realm of chemical and biological dynamics ultrafast relaxation can prevail on the timescale of nuclear motion.The exploration of ultrafast chemical and biological dynamics stems from concurrent progress in theory and experiment. The advent of fs lasers allows for the real-time interrogation of the intramolecular and intermolecular nuclear motion during chemical and biophysical transformation.37h39 On the theoretical front, the theory and simulations of radiationless processes,40,41 wavepacket dynamics,42 coherence eÜects,42 cluster dynamic size eÜects,43 nonadiabatic condensed phase dynamics40,41 and nonlinear optical interactions44 provide the conceptual framework for ultrafast intramolecular, cluster, condensed phase and biophysical dynamics.4 Spiers Memorial L ecture Fig. 3 Classi–cation of the intramolecular level structure. The relevant energetic and dynamic parameters are : the (interstate and intrastate) coupling V , the density of the independently decaying levels o and their decay widths c. The spectra exhibit the energy dependent lineshapes L (E) vs. E. Intramolecular dynamics in a bound level structure The central ingredients of the theory of intramolecular dynamics in a bound level structure, developed by Bixon, Nitzan, Mukamel and Jortner,26h36,45,46 are as follows : (1) The characterization of the level structure.This requires the characterization of the appropriate zero-order states and their (small) couplings. (2) The accessibility of the zero-order states, leading to the speci–cation of the doorway state(s) of the system.(3) The decay channels of the zero-order states, specifying their decay to genuine (radiative decay, predissociation, autoionization) continuum channels, which are characterized by appropriate decay widths. (4) The initial excitation conditions, which are governed by the (optical) excitation modes. Ingredients (1) and (3) allow for the construction of the (complex) molecular eigenstates, i.e., the independently decaying molecular levels MomTN, which are obtained from the diagonalization of the eÜective Hamiltonian26h36,45,46 Hå eff\Hå M[(i/2)C å (1) where is the molecular Hamiltonian and is the decay matrix (Fig. 2). The MomTN Hå M C å states are characterized by the complex energies em\Em[(i/2)cm (2)J. Jortner 5 where are the energy levels, while represents the decay widths.Relevant time- MEmN Mcm N resolved observables for a broad-band excitation, which are based on ingredients (1) and (2), involve the population probability of the doorway state P(D)(t)\K;m oAm o2 expA[iEm t Å [ cm t 2Å BK2 (3) where are the excitation amplitudes of the MomTN manifold, and the Am\Sg o k� omT energy-resolved (radiative) decay probability to a vibrational level o gvT of the ground electronic state P(v)(t)\K;m AmBm v expA[iEm t Å [ cm t 2Å BK2 (4) where are the transition amplitudes.These probabilities constitute Bmv \Smo k� o gvT Fourier sums damped by real decay exponents, and may involve either a superposition of exponentials (for a sparse or intermediate level structure) or an exponential decay of a giant resonance (in the statistical limit), while eqn.(4) may also result in quantum beats (in the intermediate level structure). The character and dynamical manifestations of the sparse, intermediate and statistical level structure (Fig. 3) can be inferred in a transparent way from the lineshapes L (E)\[ImG(E), where the Greenœs function is G(E)\ The classi–cation of the level structures (Fig. 3) is speci–ed by the coarse (E[Heff)~1. grained interstate or intrastate coupling V , by the density of states of the proper symmetry o, and by the decay widths c. The limit of isolated states, with Vo\1, constitutes the spectroscopistœs paradise, when distinct ìpureœ rotational»vibrational levels can be observed. For the strongly coupled situation, with Vo[1, the sparse (co\1), the intermediate (coB1) and the statistical level structures (Fig. 3), can be realized. (coA1) The statistical limit, mode selectivity and vibronic and electronic chemistry Some aspects of the theory and experiment relevant to dynamics in isolated molecules will now be addressed. A Ultrafast intramolecular relaxation in the statistical limit The statistical limit corresponds to the extreme situation of overlapping resonances, where the whole structure in the spectrum is washed out (Fig. 3). The absorption lineshape is Lorentzian with the width and the nonradiative life- C\2p ;l o Vsl o2 d(Es[El) time These predictions were con–rmed in the 1980s by the experimental q\Å/C. observation of a Lorentzian absorption lineshape due to internal conversion from the electronic origin (which precludes IVR) of some intravalence excitations of large isolated jet-cooled molecules,47h51 e.g., the origin of azulene (Fig. 4) and the origin S1 S2 (Qy band) of free base porphin (Fig. 5), as well as of the extravalence Rydberg excitations (principal quantum number n\3»5) of benzene (Fig. 6). The observation of a Lorentzian lineshape for a highly congested bound level structure constitutes the victory of dynamics over spectroscopy.The spectroscopic information (Table 1) on ultrafast dynamics (q\3000»10 fs) reveals that the timescale for internal conversion of high intravalence excitations of benzene and anthracene (10»20 fs) corresponds to the highest molecular vibrational frequencies 1500»3000 cm~1. Only recently the –rst time-resolved lifetime of ca. 40 fs for the state of isolated benzene was reported by Hertel and S2 co-workers.52a It is an open question whether these ultrafast relaxation times in high electronic excitations of large, rigid aromatics correspond to the weak coupling limit or to the strong coupling limit, according to the Englman»Jortner classi–cation.53 The6 Spiers Memorial L ecture Fig. 4 The absorption spectrum of the 0»0 electronic origin of the of the isolated S0 ]S1 jet-cooled azulene molecule K, K).The Lorentzian line broadening (–tted (Trot\20 Tvib\30 by a solid line) re—ects intramolecular coupling and statistical limit relaxation in S1(0»0)]S0* a bound level structure (ref. 47). strong coupling limit, where the two potential energy surfaces cross in the vicinity of the minimum of the higher surface, and which may also include the situation of conical intersection under proper symmetry representation,54 can be realized for some intramolecular isomerization processes and for some cases of intermolecular coupling to exterior medium modes. In the weak coupling limit the displacement of the minima of the two surfaces is small so that the dynamics occurs in the region where no surface crossing prevails.This state of aÜairs bears analogy to nuclear tunneling. Fig. 5 Absorption of the 0»0 electronic origins of the band) of isolated jet-cooled S0 ]S2 (Qy free base porphin. The linewidth (D\1.0 cm~1) of the origin originated from rotational S1 structure, while the Lorentzian line broadening (–tted by open circles) of the origin orig- S2 inates from intramolecular coupling and statistical limit relaxation in a bound S2(0&r;0)]S1* level structure (ref. 48).J. Jortner 7 Fig. 6 Absorption spectrum of isolated jet-cooled benzene. Note the sharp feature, which corresponds to the n\3 Rydberg. The upper panel shows the lineshape analysis of the Ru (3Ru) Rydberg, which is Lorentzian (–tted by a solid line) with a lifetime of q\154 fs for (and C6H6 q\188 fs for exhibiting a small deuterium eÜect.Note that the Rydberg relaxation is C6D6), considerably slower than the intravalence pp* excitation in the same energy domain (ref. 24 and 51). Also note the lack of resonance Rydberg-pp* background interference eÜects (ref. 51). Table 1 Electronic relaxation lifetimes in isolated jet-cooled moleculesa molecule channels q/fs footnotes azulene S1 S1 ]S0 800^200 b, c *E\14 400 cm~1 phenanthrene S2 S2 ]S1 500^100 b, c *E\4684 cm~1 free-base porphyrin S2(Qy) S2 ]S1 450^50 b, c *E\3540 cm~1 Zn-tetraphenyl porphyrin S2 ]S1 3200^300 b, c benzene (H6) 3nRy]MSnN]S0 160 b, c benzene (D6) 190 n\3 Rydberg benzene S3(1E1u) S3 ]MSnN]S0 (20) b, d benzene S2(1B1u) S2 ]S1 S0 40 d, e anthracene n\3 Rydberg 3nRy]MSnN]S1 ]S0 180 b, c anthracene S3(1B3u `) S3 ]S1 ]S0 (7) b, c —uoranthene S4 S4 ]S3 ] 60 b, f 1,2-benzanthracene S3 S3 ]S2 ] 136 b, g a Electronic origin of electronic transition.b From Lorentzian line broadening. c Tel Aviv work (ref. 47»51). d Lifetime data. e Ref. 52a. f Ref. 52b. g Ref. 52c.8 Spiers Memorial L ecture B Mode selectivity Current experimental and theoretical progress allows for the control of intramolecular and intermolecular dynamics via passive control of energy acquisition when the system envolves under its own Hamiltonian, as well as by active control of energy storage and disposal by the modi–cation of the equations of motion by an external laser –eld.55 The characteristics of interstate coupling and intramolecular relaxation in a large isolated molecule can be more complex and interesting due to resonance eÜects, providing means for mode-selective dynamics.56,57 Mediated intersystem crossing from an vibronic S1 state to the dense lowest triplet manifold can be induced by the sequential coupling MT1N via a sparse manifold of vibronic states corresponding to a higher triplet state.The MTxN Vso Vvib theory of mediated coupling and relaxation29,56,57 predicts the S1»»MTx kN»»MT1N occurrence of resonances originating from vibronic coupling which MTxN»MT1N (Vvib), mediate the decay of the doorway state induced by spin»orbit coupling.Dra- S1 (Vso) matic vibrational mode-selective eÜects are revealed in the absolute —uorescence quantum yields from photoselected vibronic levels in the manifold of 9,10- S1 dibromoanthracene56,57 (Fig. 7), where the irregular variance of the nonradiative lifetimes spans about three orders of magnitude. These resonance eÜects for the decay of the S1 state span the excess vibrational energy range cm~1 above the elec- Evib\0»800 tronic origin of the electronic manifold, while at higher mode selectivity is eroded S1 Evib due to intramolecular vibrational energy distribution.C Towards chemistry. Long-range electron transfer in isolated supermolecules Electron transfer (ET) reactions in chemistry, physics and biology have been almost exclusively explored in donor (D)»acceptor (A) systems embedded in a medium, e.g., solvent, glass or protein. The seminal Marcus theory of ET9,58 encompasses a broad spectrum of systems, e.g., ion in solution, supermolecules and biomolecules, with the solvent coupling playing a central role in dynamics.Intramolecular ET can be realised as an interstate radiationless transition, with the vibronic quasicontinuum acting as a dissipative channel.59h62 We have challenged the conventional wisdom regarding the dominating role of medium coupling in ET, proposed long-range ET which occurs in an isolated solvent-free supermolecule DBA (where B is a molecular bridge), and analyzed Fig. 7 Absolute —uorescence quantum yields (Y ) and lifetimes (q) of the photoselected vibronic level of jet-cooled 9,10-dibromoanthracene, which exhibit a marked mode selectivity in the vibrational energy range cm~1 above the electronic origin (ref. 63) 0OEvibO800J.Jortner 9 the structural and energetic constraints for the occurrence of this radiationless transition. 59,60 The order of the singlet electronic states of an isolated supermolecule exhibiting ET should involve the ground state the charge transfer state S0(DBA), and the localized excitation A single vibronic level of S1(D`BA~) S2(DBA*). S2(DBA*) can act as a doorway state for internal conversion to the quasicontinuum.S1(D`BA~) The ladder diagrams for intramolecular ET are isomorphous to Fig. 1 and 2. It is gratifying that resonance Raman63 and optical lineshape data64 will allow for the quanti –cation of these ladder diagrams. The realization of the molecular limit for ET59,60 in a (neutral) DBA requires an appropriate electronic level structure, being subjected to the structural»energetic constraints for the D»A (center-to-center) distance65,66 RDAO i.e., where I(D), E(A) and denote the ionization e2/[I(D)[E(A)[E00], RDAO7A, E00 potential of D, the electron affinity of A and the electronic origin of the (DBA)* transition.For small polaron transfer in D~BA and hole transfer in D`BA there are no constraints on The prediction for structural constraint in DBA was borne out by RDA .59 Wegewijs and Verhoeven65 for ET in isolated jet-cooled rigid supermolecules, with D\dimethoxynaphthalene, A\dicarboxymethyoxy ethylene or dicyanoethylene and B\norbornyl-like bridge with N bonds (denoted as DBNA). S2(DBA*)]S1(D`BA~) ET was observed for N\3 with as expected.The theory provides dynamic RDA\5.8 ”, rules for ET in isolated supermolecules.The theory59 also predicts the formation of giant D`BA~ dipoles, with dipole moment O35 D§ in molecular beams. Microscopic (state-selective) ET rates are given in the statistical limit in the form59h62 ks\ in terms of a product of an electronic coupling (V ) and the nuclear (2p/Å)V 2AFD(Es) Franck»Condon overlap density Isolated molecule ET rates exhibit the energy AFD(Es).gap (*E) dependence (Fig. 8), with typical ET rates in the range (V / ks\107»3]108 cm~1)2 s~1 for charge separation from the electronic origin of the state. For S2(DBA*) the molecules (N\3) s~1 (ref. 65) in accord with our estimate with DBNA ksP1014 V B1000 cm~1. Another, more complex and interesting, isolated-molecule ET pertains to the DBA molecule with D\aniline and A\cyanonaphthalene, held together by a semirigid bridge60 (Fig. 9). Long-range ET in the extended structure, followed by Fig. 8 ET dynamics in isolated supermolecules. The energy gap ([*E) dependence of the averaged Franck»Condon density (AFD) and the rate for the electronic k\(2p/Å)V 2AFD origin. Calculations for a four intramolecular vibrational level system (u/cm~1)\(200, 500, 1200, 1500) with couplings S\(6, 3, 1, 1).Note the exponential energy gap for charge separation at large [*E (ref. 99). § 1 D (debye)B3.335 64]10~30 C m.10 Spiers Memorial L ecture Fig. 9 Sequential long-range electron transfer and electrostatically driven conformational folding in an isolated semirigid DBA molecule. Isolated-molecule ET dynamics is described by a mediated intramolecular radiationless transition (ref. 60). electrostatically driven conformational folding (Fig. 9),66,67 was described60 in terms of mediated nonradiative ET. This analysis builds a bridge between ET and intramolecular radiationless transitions. Unifying features of intramolecular dynamics can be applied to predict and describe other nonadiabatic processes, e.g., electronic energy transfer and spin-conversion in isolated supermolecules, opening up new areas of intramolecular chemistry.D Electronic quasicontinuum Up to this point we were concerned with intramolecular dynamics within a vibrational quasicontinuum, manifesting nuclear motion. Very high n (equal to 50»250, where n is the principal quantum number) molecular Rydberg states are characterized by a high density (oPn3/Ry, where Ry is the Rydberg constant) of electronic states and by unique intramolecular nl»n@l@ coupling which involves core»multipole interactions in the absence of an external (weak) electric –eld.70h72 A generalization and uni–cation of the theory of intramolecular coupling and dynamics for a Rydberg manifold was provided, establishing the conditions for strong coupling of a doorway Rydberg state and the attainment of the statistical limit within an electronic quasicontinuum.72 Another interesting aspect of the dynamics of a Rydberg manifold pertains to the preparation and interrogation of a wavepacket of electronic states.72 Correlations in continua and quasicontinua determining dynamics on the timescale of nuclear motion Radiationless processes in molecular and cluster systems involve the following decay channels (Fig. 10). (1) ìReactiveœ nonradiative channels for molecular (rotational, vibrational or electronic) autoionization or predissociation. (2) ìNonreactiveœ channel for electronic»vibrational relaxation or IVR within a bound level structure involving the vibronic quasicontinuum. (3) The electronic quasicontinuum of an ultrahigh Rydberg manifold.The dissipative channels for intramolecular dynamics can be characterized in terms of the state speci–city of the matrix elements of the Hamiltonian (H), i.e., Vsl\Ss oHo lT, for the coupling of the doorway states o sT, o s@T, o sAT. . . , with the Mo lTN states of the continuum or quasicontinuum. The state dependence of the couplings is quanti–ed byJ.Jortner 11 Fig. 10 Intramolecular dynamics in isolated molecules the correlation parameter68,69,73 gss{\SVsl Vls{T/[SV sl 2TSV s{l 2 T]1@2 (5) where ST denotes average products over the energy range which includes and Es Es{ . The continua and quasicontinua can be segregated into : (i) ìsmoothœ decay channels, involving slow energy dependence of with for i.e., dissociative and (El) Vsl , gss{\1 sDs@, ionizative continua and the electronic quasicontinuum, and (ii) ìnonsmoothœ decay channels, where exhibits a large and irregular energy variation, where Vsl (El) gss{@1, sDs@, i.e., the vibrational Franck»Condon quasicontinuum.The distinction between ìsmoothœ and ìnonsmoothœ channels does not aÜect the level structure and dynamics of molecular eigenstates which have their parentage in a single doorway state coupled to a single quasicontinuum. This distinction is of central importance for interference eÜects between several doorway states, which exhibit a profound in—uence on femtosecond intramolecular dynamics in electronically»vibrationally excited wavepackets of states of large isolated molecules and in the condensed phase.The correlation parameters determine gss{ vibrational coherence in nonradiative dynamics73 and determine the upper temporal limits for relaxation.69 For intramolecular relaxation processes involving a ìsmoothœ correlated (gss{B1), dissipative channel, the temporal constraints on the dynamics can be inferred from the theory of overlapping resonances74,75 which sets an upper limit on k.For the population of a set of equally spaced (nearest neighbor separation of u) resonances (of widths C\2pV 2o for an isolated resonance), interference eÜects set in when CBu. The intramolecular relaxation rate is The rate exhibits a transition from k\(C/Å)/[1](pC/u]. for an isolated resonance to k\u/h for overlapping resonances k\(C/Å) (C@u)12 Spiers Memorial L ecture The overlapping resonance domain provides an upper limit for the nonradi- (CAu).ative rates, i.e., kOu/h, which is determined by the level spacing, i.e., the vibrational frequency (timescale tBk~1B10»1000 fs). This situation prevails for intramolecular dynamics in a ìsmoothœ nuclear continuum, i.e., electronic and vibrational predissociation. The experimental ultrafast fs electronic predissociation times of diatomics76 are limited by the overlapping resonances constraint.For dynamics in the ìsmoothœ electronic Rydberg quasicontinuum the upper limit for the rate is (i.e., k for kO2Ry/n3Å n\50 being in the ps~1 domain). For the decay of weakly correlated overlapping resonances into a (gss{@1) ìnonsmoothœ Franck»Condon vibrational quasicontinuum, interference eÜects are expected to be much less pronounced than for the case of a ìsmoothœ channel.This is experimentally manifested in the related context of the lack of interference eÜects, i.e., Fano antiresonances in the absorption spectra of Rydberg states which overlap pp* intravalence excitations in large aromatic molecules (Fig. 6). Model calculations of correlation parameters for a doorway state in the vicinity of the electronic origin are gss{ considerably lower than unity, with their highest values falling in the range o gss{ o\ 0.4»0.2 for a small number of s,s@ pairs diÜering only by a single vibrational quantum number, while for multimode s,s@ changes very low values of are o gss{ o\0.1 exhibited.68,69,73 These propensity rules imply the existence of weak correlations within the Franck»Condon vibrational quasicontinuum, resulting in a partial erosion of resonance interference eÜects, in some analogy with random coupling models for intramolecular coupling and dynamics,76h78 where interference eÜects are completely eroded.Ultrafast intramolecular radiationless transition rates in a bound level structure of overlapping resonances into the Franck»Condon quasicontinuum are expected not to be strictly limited by the level spacing, but rather the temporal upper limit kPV 2Pu/h can be realized.Indeed, some of the ultrafast (ca. 10 fs) relaxation times of intravalence excitations of isolated aromatic molecules (Table 1) exceed most of the intramolecular frequencies. Such temporal records may be achieved for ìnonreactiveœ radiationless transition in large molecules and for nonadiabatic processes in liquids, solids and proteins, providing a uni–cation of intramolecular and condensed phase ultrafast dynamics.Perspectives for future studies of ultrafast dynamics in large isolated molecules pertain to the following. (1) High-energy intravalence and Rydberg excitations of large molecules will constitute a hunting ground for fs intramolecular time-resolved dynamics in electronic origins of jet-cooled isolated molecules (Table 1).These data, which approach or exceed the timescale for intramolecular frequencies, are important in the context of intramolecular dynamics in the Franck»Condon quasicontinuum. Temporal records on the timescale for ultrafast interstate dynamics will prevail.(2) Time-resolved chemistry in isolated supermolecules and linomolecules, mode selectivity and coherent single molecule chemistry. Some of the interesting problems involve electrons in a single supermolecule resulting in the formation of a giant dipole, hole transfer in an isolated polypeptide, with the possible distinction between transfer and transport, vibrational coherence in intramolecular chemistry, vibrational mode selectivity in ET and in EET, and coherent vs.incoherent electronic energy transfer. (3) Quantum beats. The time evolution of a coherently excited wavepacket of molecular eigenstates will exhibit interference eÜects. For large molecules such wavepackets can manifest (i) molecular eigenstates originating from interstate or intrastate coupling; (ii) Jahn»Teller coupled vibronic manifold in doubly degenerate states of a large molecule, e.g., the E state of triptycene, which bears analogy to the adiabatic»diabatic coupling in IBr studied by Stollow;79 (iii) electron»vibrational coherence in mediated coupling; (iv) electron»vibrational coherence in intramolecular chemistry.(4) Dymanics of ultrahigh n (\50»250) molecular Rydbergs. Timescales for the longevity of molecular Rydberg states in were explored by Stollow79 by nuclear I2J.Jortner 13 Fig. 11 Coulomb explosion dynamics of clusters. The ion charge is q\1»10 (ref. 84). (Xeq`)n The Coulomb explosion times from the classical equation84 is in accord with the results of molecular dynamics simulations.Note the dependence, in accord with the classical qc~1Pq picture. wavepacket dynamics. Of considerable interest is the coherent excitation and interrogation of an electronic wavepacket of high n molecular Rydbergs. An interesting related problem involves the dynamics of a wavepacket of one-dimensional Rydberg states of an excess electron bound to a metal or dielectric surface by image forces.80 Dissociative dynamics and Coulomb explosion in molecules and clusters For direct dissociation in molecular systems the dynamics involves the sliding on a repulsive potential surface.8 The characteristic time for dissociation is described in terms of the classical mechanical model of Zewail and co-workers81,82 qc\/R0 R dR@/v(R@), where v(R@) is the velocity at R@.This simple description captures the essential features of the dynamics. The typical timescale for direct dissociation is fs.qcB100 An ultrafast excitation leading to the localization of energy in polyatomic molecules or clusters can be achieved by a Coulomb explosion.83,84 This ultrafast process is characterized by site selective energy acquisition in conjunction with bond-speci–c energy disposal.The mechanical model for the separation of two positive ions of charges and q1 with an eÜective mass (k/AM where AM\atomic mass) initially separated at dis- q2 tance to the distance gives84 where m\ (R0/”) (R/”), (qc/fs)\1.9R0(kR0/q1 q2)1@2Z(m), and the numerical function Z(m)B1 for m\1/2. The timescales for Coulomb R0/R\1 explosion re—ect fs dynamics being shorter by about 1»2 orders of magnitude than the corresponding timescales for molecular dissociation.The timescales obtained from the classical model for the explosion of an cluster reveal that being borne (Xe`q)n qc~1Pq, out by molecular dynamics simulations (Fig. 11). The utilization of the ultrafast fs ìchemical clockœ of Coulomb explosion of molecules,83 surface states,83 and clusters84,85 precludes IVR and shows potential applications for selective chemistry.14 Spiers Memorial L ecture Cluster dynamics Clusters, i.e., –nite aggregates containing 2»109 constituents, provide novel insight into the dynamics of systems with –nite density of states, where separation of timescales can be realized. A key concept for the quanti–cation of the unique characteristics of clusters pertains to cluster size eÜects.40,41,43,86,87 These involve the evolution of structural, thermodynamic, electronic, energetic, electrodynamic and dynamic features of –nite systems with increasing cluster size.Several interesting dynamic cluster size eÜects were explored theoretically by modeling and by simulations. (1) The ì transition œ from molecular-type dissociative dynamics in small clusters to condensed-matter type nonreactive vibrational relaxation in large clusters manifests the bridging between molecular and condensed phase nulcear dynamics.43,86,87 (2) Collective vibrational modes.87,88 Interior, collective, compression nuclear modes of molecular clusters can be treated in terms of the excitation of a liquid drop (Hen, Arn) and were experimentally documented. Complementary to the energetics of these collective modes, their dynamics is interesting.The damping of the collective motion via the coupling of a ìgiant resonanceœ to non-coherent vibrational modes, constitutes a theoretical and experimental challenge. (3) Bubble dynamics. The dynamics of large local con–gurational charge are induced by an extravalence excitation of a probe atom (e.g., excitation of Xe) or mol- 1S0 ]3P1 ecule (e.g., Rydberg excitation of NO) in a rare-gas cluster.89 Molecular dynamics simulations of the dynamics of con–gurational nuclear relaxation around the excitation 3P1 of Xe in clusters (Fig. 12) reveal : (i) large con–gurational dilation, i.e., ìbubbleœ XeArn formation on the timescale of fs ; (ii) marking the timescale for ultrafast tBB100»300 tB energy transfer ; (iii) multimodal time evolution, with slower timescales of 1»5 ps ; (iv) marked impact vibrational coherence excitation (this vibrational coherence characterizes the collective vibrations around the excited probe atom with a long timescale for dephasing of 1»5 ps, considerably exceeding the timescale for initial con–gurational relaxation).(4) Ultrafast energy acquisition via high-energy cluster»wall collisions.90 Highenergy impact of atomic or molecular cluster ions (of sizes 10»1000 constituents, with Fig. 12 The time evolution of the average Xe»Ar distance of at the central site in Rnn Xe(3P1) T \10, 30 K mark the equilibrium cluster temperature prior to excitation. Con–gu- XeAr146 . rational dilation is manifested by the increase of on the timescale of ca. 200 fs. Note the Rnn impact vibrational coherence by oscillations in Rnn .J. Jortner 15 velocities up to vB20 km s~1 and kinetic energies up to ca. 100 eV per particle) on insulator, semiconductor or metal surfaces, produces a new medium of extremely high density (up to ca. 2»4 times the standard density), high temperature (up to ca. 105 K) and high energy density (up to 102 eV per particle), which is temporarily generated during the propagation of a microshock wave within the cluster on the 102»103 fs timescale. Chemical applications, e.g., cluster impact dissociation of a probe diatomic molecule (Fig. 13), were attempted. The dissociation process is limited by the vibrational period of the molecule.Perspectives of future explorations of cluster dynamic size eÜects pertain to the following. (1) Real-time probing of adiabatic nuclear motion on multidimensional potential surfaces. These will involve preparation, e.g., (passive) vibrational mode selectivity and Fig. 13 Snapshots of molecular dynamics simulations of the collision of an cluster with I2Ar53 a Pt surface. The guest molecule (black balls) is located in an interior state within the Ar I2 cluster (white balls).The Pt surface (grey spheres) consists of six layers of 120 atoms each. The cluster temperature is 10 K and the surface temperature is 300 K. The times are marked on the four snapshots. At t\0, the cluster with the initial center of mass velocity of v\10 km s~1 eV) is located at a center of mass distance of 20 from the wall.At (Ek0\1.23]103 ” t\175 fs, the cluster»wall impact achieves a peak of the cluster potential energy. Subsequently, cluster fragmentation occurs at t\247 fs, while at t\578 fs, the dissociation of is I2 clearly exhibited (ref. 90). For eV the average dissociation time for falls in the Ek0/N\10»30 I2 range fs, which is comparable to, or shorter than, the vibrational time SqDT\200»150 qv\ fs of the guest molecule. This process manifests thermal fs dynamics on the timescale of 156 I2 nuclear motion.16 Spiers Memorial L ecture energy storage, e.g., intracluster vibrational energy redistribution.This problem is also central in biophysics, pertaining to protein folding.90,91 (2) Real-time dynamics of nuclear con–gurational changes.The real-time interrogation of cluster isomerization and of rigid»nonrigid transformation (i.e., ìmelting œ) will be of considerable interest. (3) Impact-induced vibrational coherence. These are induced by short-range repulsive interactions with intracluster dissociation fragments in (ref. 92) or (ref. I2Arn I2~Arn 94) or by Rydberg excitation, e.g., and manifest the excitation of a vibrational Xe*Arn ,89 wavepacket.(4) Interstate fs dynamics in clusters. Radiationless electronic»vibrational relaxation in clusters will elucidate the interrelations between electronic level structure and metaln dynamics. (5) Temporal records for nuclear dynamics. These include the Coulomb explosion of highly charged clusters.84,85 (6) Real-time dynamics of elementary excitations in –nite systems.These will involve collective compression nuclear modes and phonons. More esoteric elementary excitations constitute rotons (vortex rings) in quantum boson systems, e.g., with (4He)n n[100 or possibly which can be studied by two-particle excitations in the elec- (H2)n , tronic origin of a probe molecule in the cluster.95 (7) Thermal fs chemistry.Cluster impact dynamics via high-energy cluster»wall collisions or cluster»cluster collisions open up a new research area of thermal femtosecond chemistry. Condensed phase dynamics The pioneering studies of Kubo6,8 on electron»hole recombination in semiconductors, of Marcus on ET in solution9 and of Foé rster on EET in the condensed phase,10 laid the foundations for the theory of nonadiabatic dynamics in the condensed phase and in protein medium.The isomorphism between condensed phase nonadiabatic dynamics and intramolecular radiationless transitions was addressed96 in the context of the incorporation of quantum eÜects in ET theory. Both condensed phase and intramolecular radiationless transitions are induced by the coupling of doorway state(s) to a vibronic quasicontinuum.A uni–ed conceptual framework for all these condensed phase radiationless transitions considers population relaxation between two potential surfaces of the entire system corresponding to distinct zero-order electronic con–gurations with energy conservation being insured by absorption and emission of medium phonons and intramolecular vibrations. For a nonradiative process from a reactant doorway vibronic state o sT to the vibronic manifold Mo aTN of product states quasidegenerate with it, which is induced by the electronic couplings V , the microscopic rate is given by the golden rule expression ks\(2p/Å)o V o2Fs (6) where the Franck»Condon densities are Fs\; a oSs o aTo2 d(Es[Ea) (7) We proceed to consider the broad –eld of ET.A basic assumption underlying the microscopic description of the rate k of such nonadiabatic processes in terms of the microscopic rates (6) is the insensitivity of the ET dynamics to the medium dynamics, which can be realized under one of the following conditions.(i) The common situation of fast medium vibrational dynamics, which allows the separation of timescales betweenJ.Jortner 17 the fast medium relaxation and slow ET, with the microscopic ET rate constants constituting the rate determining step. Under these circumstances the –nite temperature rate k is expressed96,97 in terms of a thermal average where is the thermal k\;s Psks , Ps population of level o sT. (ii) The microscopic rates depend weakly on the initial vibronic manifold. Under these circumstances (for the relevant doorway states).Such a kBks state of aÜairs prevails for activationless ET, where the potential surfaces cross in the vicinity of the minimum of the initial state, which pertains to the optimization of the ET rate. Weak state speci–c also prevails for inverted region ET where high frequency ks vibrations of the D and A centers result in intramolecular vibrational excitation induced by ET.97 Ultrafast femtosecond ET reactions in condensed phase are expected to correspond to activationless ET.Such reactions are not limited by solvent dynamics,98,99 which was traditionally speci–ed by the solvent relaxation time SqT induced by a constant charge, with the solvent adiabaticity parameters For an activationless i\4p o V o2SqT/Åj.iA1 ET would apparently be characterized by kBSqT~1, setting an upper limit on the rate. This expectation was violated98,99 by several ET experiments with ET rates in the range (80»1000)~1 fs~1, which resulted in kSqT\50»100. The origin of the failure of the theory of solvent controlled ET was traced to the weak excess energy dependence of the microscopic rates98,99 for the activationless (and the inverted region) process, which implies that ET cannot be described by diÜusion towards the intersection of the potential energy surfaces at the minimum of the initial DA surface.Rather, the depletion dynamics of the DA manifold occurs from an entire manifold of doorway states. ET fs dynamics is limited by the electronic coupling and the nuclear Franck»Condon factors, in analogy to intramolecular dynamics.Perspectives of future studies of condensed phase dynamics pertain to the following. (1) Real-time dynamics of elementary excitations, e.g., excitons, phonons, vibrons or rotons, in the context of one-particle and two-particle excitations. (2) Real-time dynamics of con–gurational relaxation induced by electron solvation in —uids.The interesting adiabatic electron bubble formation equilibrium radius 17 at ” zero pressure in liquid He, Ne or was studied theoretically,100,101 considering a H2 combination of quantum mechanical and hydrodynamic eÜects, and should be subjected to experimental scrutiny. (3) Dynamics of medium structure. The exploration of the time dependent correlation function g(r, t), following the excitation of a probe ion or molecule in a —uid conducted by Hochstrasser,102 is novel and interesting. (4) Interstate energy and phase relaxation in the Franck»Condon vibronic quasicontinuum.Nonadiabatic fs dynamics is governed by electronic coupling (V ) and nuclear Franck»Condon factors. The coupling to the vibronic quasicontinuum is weakly correlated (i.e., small for multimode model systems) resulting in high rates gss{\0.3 (PV 2) and in phase erosion.71h73 Further exploration of ultrafast fs EET and ET processes102h106 will be of interest.(5) Temporal records on rates for nonadiabatic dynamics. Recent experimental studies on ET dynamics105 established timescales of 80»100 fs, while studies of EET between prosthetic groups in the photosynthetic reaction center and EET in photosynthetic antennas103,104,106 established timescales of 50»100 fs.These ultrafast timescales for ET and EET (q\50»100 fs) correspond to vibrational frequencies of (cq)~1B300»600 cm~1, i.e., being on the timescale of the intramolecular frequencies and considerably exceeding the frequencies of medium (or protein) modes. The theory of radiationless transitions in the (weakly correlated) Franck»Condon quasicontinuum indeed predicts that the characteristic times can exceed the vibrational period.71h73 (6) The ubiquity of vibrational coherence eÜects ranging from small to huge systems102h104,107 raises the conceptual question of the distinction between the experimental condition of the preparation and interrogation on one hand, and the intrinsic18 Spiers Memorial L ecture Fig. 14 Temporal vibrational coherence in nonadiabatic dynamics, showing the nonradiative decay probability P(t) of the reactants manifold to a vibronic quasicontinuum. Data for a four-mode Franck»Condon system with frequencies u/cm~1\(117, 75, 35, 27), coupling parameters S\(1.0, 1.1, 1.2, 3.0), energy gap *E\500 cm~1 and electronic coupling V \20 cm~1.The initial wavepacket consists of the seven lowest states in the doorway manifold with the amplitudes given by the appropriate vibrational overlap integrals from the ground electronic»vibrational state. The inset shows the time dependence of *P(t)\P(t)[Av[P(t)], re—ecting low amplitudes of the quantum beats. aspects of relaxation and dephasing dynamics on the other hand.The manifestation of quantum beats in nonadiabatic dynamics (Fig. 14) is determined by:71 (i) spectroscopic information, i.e., transition moments and periods, and (ii) dynamic information, i.e., modulation amplitudes and (low) correlation parameters For the excited state gss{ . population probability, weak modulation re—ects dynamics information, while the quantum beats in the photon counting rates from the bacteriochlorophyll dimer in the photosynthetic bacterial reaction center just provide spectroscopic information. (7) Homogeneous vs.heterogeneous broadening. These pertain to spatial eÜects, e.g., diagonal Anderson-type and oÜ-diagonal disorder which result in localization,108 and to temporal eÜects, which are re—ected in the spectral density.106 Some facets of biophysical dynamics Remarkable progress has been made in biophysical ultrafast dynamics, with the experimental and the theoretical microscopic exploration of the primary processes of EET in photosynthetic antennae104 and ET in photosynthetic reaction centers.109 The ultrafast EET processes (timescales from ca. 100 fs to ps) in diÜerent (nonuniversal) antenna structures eÜectively preclude energy waste.The basic issues which pertain to the mechanism and unidirectionality of the primary charge separation in the (universal) reaction center (RC) structure of photosynthetic bacteria and photosystem II are not yet fully elucidated. These involve the following. (1) Optimization principles for the primary ET processs. (2) Kinetic redundancy for the primary ET process.This will ensure the stability of the photosynthetic apparatus with respect to mutagenesis, chemical modi–cations and environmental perturbation. (3) Structural redundancy. This is manifested in the unique symmetry breaking, i.e., the unidirectionality of the primary charge separation across the ì active œ A branch of theJ. Jortner 19 RC.110 ET transfer theory implies that unidirectionality is dominated by cumulative eÜects, i.e., electronic coupling and energetic modi–cation of the energy gap across the ì inactive œ B branch.Breaking of the symmetry breaking, i.e., inducing charge separation across the inactive branch, was accomplished by chemical modi–cation of the energetics, which retards the ET process across the active branch of the RC.111 The determination of the structure of the photosynthetic bacterial RC112 constituted a seminal accomplishment.Nevertheless, we should challenge the notion of the structure»function relationship, providing a complete description of the central energy conversion process in photobiology. Structural information alone is not sufficient to understand the function of the RC, which rests on the ingredients of ultrafast dynamics.Dynamic information transcends and complements structural data. We should strive toward the broad uni–cation of structure»dynamics»function relations in ultrafast biophysical and chemical dynamics. Concluding remarks We explored the rich and fascinating world of the dynamics of electronically» vibrationally excited states of isolated molecules, clusters, condensed phase and biological systems on the timescale of nuclear motion. Have we reached the temporal borders of the fundamental processes in chemistry and biology ? The timescales of intermolecular and intramolecular nuclear motion de–nitely provide the relevant temporal limit for biological transformations. For chemical transformations even shorter timescales of femtoseconds to attoseconds (i.e., 10»0.1 fs) for electron dynamics will be unveiled.Examples which come to mind in the realm of intramolecular and cluster dynamics involve hole migration in clusters on the 10~14»10~12 s timescale prior Hen ` to its trapping, as well as early charge delocalization in isolated large molecules, model biomolecules and clusters.113 In the areas of clusters and condensed phase electron dynamics fascinating processes involve bulk and surface electron»electron collisions and plasmon dynamics, incipient excess electron localization in liquids, electron»hole coherence of Wannier excitons and exciton wavepacket dynamics in semiconductor clusters and quantum dots, dynamics of excess electron external image states on metals and adsorbants on metal surfaces,80,114,115 and electron tunneling microscopy in realtime. 116 Such chemical transformations involve changes in electronic state(s) without the involvement of nuclear motion, bypassing the constraints imposed by the Franck» Condon principle. Theory played a central role in establishing the conceptual framework of dynamics in chemistry and biology. From the historical perspective theoretical chemistry, until the 1960s, focused on the nature of the chemical bond.This was beautifully re—ected in the address of Charles Coulson at the Boulder Conference on Molecular Structure Calculations in 1959,117 where the goals of theoretical chemistry at that time were de–ned: ìWe may hope that eventually all problems (of molecular structure) in the range of 1»20 electrons will be solved accurately by computational techniques .. . But surely there is much more in chemistry that covered by this rangeœ.117 Contemporary quantum chemistry has undergone major developments and currently predictions of static molecular structure, molecular properties and intramolecular interactions at the level of chemical accuracy are becoming available.But there is much more in chemistry ! 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ISSN:1359-6640    

DOI:10.1039/a801832d

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss., 1997, 108, 23»34 Excited state dynamics of chromophores in glasses and in photosynthetic proteins Yutaka Nagasawa,§ Jae-Young Yu, Minhaeng Choî and Graham R. Fleming*° Department of Chemistry and James Franck Institute, University of Chicago, 5735 S. Ellis Avenue, Chicago, IL 60637, USA The optical properties of molecules dissolved in glasses and ligated to proteins are very similar.The technique of three pulse stimulated photon echo peak shift is used to explore these properties. For dilute chromophores in a glass, a model of linear coupling to a harmonic bath combined with temperature-independent inhomogeneous broadening works well from 30 to 300 K. For concentrated chromophores, such as exist in photosynthetic light harvesting complexes, energy transfer changes the appearance of the peak shift data.The timescale of energy transfer can be extracted from the peak shift data, along with the coupling to the protein and the width of the inhomogeneous distribution. Introduction The essential distinction between excited states isolated and condensed phase molecular systems is the number of nuclear degrees of freedom coupled to the electronic excitation.Such coupling produces spectral broadening that is generally sufficient to render solution-phase electronic absorption and emission spectra of large molecules almost totally featureless, and apparently worthless for detailed investigation. The coupled nuclear motions also provide energy in—ow from the medium to the molecule to promote reaction and energy relaxation to stabilize products.It had generally been assumed until recently that nuclear momentum was randomized (by ì collisions œ) on a timescale much less than could be relevant chemically and that in condensed phases phase coherence of electronic or vibrational wave functions was similarly destroyed prior to such processes as energy or electron transfer. Thus solution phase dynamics was viewed from a very diÜerent perspective than gas phase dynamics where reactive motion was clearly ì ballistic œ and product internal and kinetic energies dispersed excess energy.A wide variety of experiments in liquids, glasses and proteins with femtosecond resolution coupled with extensive theoretical and simulation work has begun to change this perspective and reveal stronger similarities between gas phase and solution dynamics than had been anticipated.1h3 For example the motion of separating iodine atoms in hexane solution is ballistic through the curve-crossing region and out to separations of at least 4 This behavior is by no means con–ned to small molecules.”.1h3 In the light harvesting complex LH1, which contains 32 bacteriochlorophyll molecules, vibrational coherence apparently survives several energy transfer steps,4 while the isomerization of retinal in rhodopsin proceeds ballistically.5 Indeed it is often likely to be the § Permanent address : Osaka University, Osaka, Japan.î Permanent address : Department of Chemistry, Korea University, Seoul 136-701, Korea. ° Present address : Department of Chemistry, University of California, Berkeley, Berkeley, CA 94720-1460, USA. 2324 Excited state dynamics of chromophores Fig. 1 Ultrashort pulses can be used to probe systems with featureless diÜuse spectra. Impulsive excitation leads to wavepacket motion which can be following in absorption or emission. More sophisticated arrangements, such as various types of echo spectroscopy, allow the origins of the spectral broadening to be studied. Information from both classes of experiment can be used to calculate and understand condensed phase dynamics.case that energy and phase relaxation are signi–cantly decoupled on the timescales of elementary chemical events. Understanding of such phenomena has been hindered by the use of the two-level optical Bloch model to interpret experiments, but can be achieved, for example, from multilevel Red–eld theory,6h8 which explicitly allows for coherence transfer as well as population relaxation and pure dephasing.Increasingly sophisticated experimental techniques have been developed to study the interaction of electronically excited states with their surroundings. Fig. 1 illustrates how femtosecond-duration light pulses can be used to defeat and/or study spectral broadening. In particular, various types of echo spectroscopy, generally at third order in the nonlinear response,9h11 but also at –fth order12 or involving phase control13 or time gating of the echo signal,9,14 have been used.A particular form of the three-pulse stimulated photon echo, the three-pulse echo peak shift (3PEPS), method15h17 has been found to be very useful for characterizing a wide variety of systems.Extensive surveys of the theoretical basis for this work and its application to solvation dynamics have appeared over the past few years.18h21 Rather than cover this ground again in this article we will describe data on solvent»solute interactions for dilute chromophores in glasses17,22 and then go on to discuss the –rst applications of the 3PEPS method to systems of strongly interacting chromophores, the light harvesting complexes of purple bacteria.The results show that the energy transfer process within the antenna systems qualitatively in—uences the form of the echo signal and that the essential parameters controlling the evolution of the system (the timescale and strength of coupling to the protein, the energy transfer timescale, and the inhomogeneous width) can be extracted from measurements of the peak shift. To set these results in context we –rst describe the peak shift method itself and show results for dilute chromophores in polymer glasses.Three-pulse echo peak shift method The experimental layout for a 3PEPS experiment is shown in Fig. 2 and involves simultaneous measurement of the two integrated photon echo signals propagating along k1Y . Nagasawa et al. 25 Fig. 2 Experimental arrangement for three-pulse echo spectroscopy. The two time intervals, q, and T , the population period (see text), are marked. Indicated as A and B are the positions of the two three-pulse echo signals at and respectively.In a 3PEPS measure- k3[k2]k1 k3]k2[k1, ment the integrated intensity of the signals at A and B is simultaneously measured while q is scanned for –xed values of T . and The –gure de–nes the two time variables under experi- [k2]k3 [k1]k2]k3 . mental control ; the –rst interval q is scanned to record the echo signal for various –xed values of T , the second time period. Fig. 3 shows such scans for diÜerent values of T .Note that as T is increased the maxima of the two echo signals both approach q\0. We refer to T as the population period since inspection of the double sided Feynman diagrams for this experiment15,18 show that during the second time period the system propagates in a diagonal density matrix, i.e., either the ground or excited state. This is the key feature of the experiment and gives it its large dynamic range, compared with experiments that measure the decay of the echo itself.In this latter case the observation time window is set by the time for which a coherence (superposition state) exists. In the 3PEPS experiment the observable of interest is (half) the separation of the maxima of the two phase-matched (time-reversed) echo signals as a function of T , which we de–ne as q*(T ), the peak shift from zero q value.To appreciate the information content of the peak shift consider the optical transition frequency of an individual (dilute) chromophore in a host with both rapid ueg i (t) and very slow timescales. ueg i (t)\SuegT]dueg(t)]Di (1) where is the average value of the transition frequency and is a static oÜset from SuegT Di the mean for the particular chromophore.gives the dynamical contributions to dueg(t) the energy gap and is described by the correlation function M(t)\ Sdueg(0)dueg(t)T Sdueg 2 T (2) In order for 3PEPS to be a useful technique it is necessary for the formal connection of q*(T ) with M(T ) and the width of the distribution of values, to be established.Din , Di This has been done in detail elsewhere.15 Although perfectly general expressions can be obtained they are quite complex and, especially when –nite-duration laser pulses are included in the model, require numerical solution. However, much of the physical content of the 3PEPS experiment can be appreciated from simpli–ed expressions that are valid for dilute chromophores, for times longer than the decay time of the bath26 Excited state dynamics of chromophores Fig. 3 Echo signals observed at A and B in Fig. 2 for IR144 in methanol. Panels (a), (b) and (c) were recorded for population periods of T \0.01, 1 and 20 ps, respectively. correlation time and in the intermediate inhomogeneous broadening limit.15 We emphasize that these expressions are to give insight into the nature of the experiment, the full expressions15 are solved numerically actually to –t the experimental data. With these several caveats we can write q*(T )\ [SD2TM(T )]Din 2 ]J[SD2T]Din2 ]f (T )] JpMSD2T[SD2T]2Din2 ]f (T )]]Din 2 f(T )N (3) q*(T ]O)\ Din 2J(SD2T]Din2 ]j2) JpMSD2T[SD2T]2Din2 ]j2]]Din 2 j2N (4) where SD2T is the total coupling strength, j the reorganization energy (2j is the Stokes shift), and f (T )\j2[1[M(T )]2.Thus for a dilute chromophore system the only dynamical quantity appearing in the peak shift is M(T ), which at high temperature is equivalent to the —uorescence Stokes shift function, S(t).15 Eqn. 4 clearly shows that the peak shift will become a non-zero constant at long times only if and the magni- DinD0 tude of this ìasymptoticœ value will depend on the ratio of fast (j) to slow broaden- (Din) ing.For a –xed value of j, the larger is the larger q*(O) will be. Eqn. 3 is not Din accurate at short times, but the full expressions show that q*(0) also depends on the ratio of the dynamic to static broadening and again the value of q*(0) increases as the fraction of the line width arising from dynamical eÜects decreases.Now we consider a non-dilute system of chromophores, such that energy transfer between chromophores is possible, in addition to the dynamical and static broadeningY . Nagasawa et al. 27 processes present for each individual molecule. Since our object is to gain an intuitive understanding we will couch our discussion in terms of the site representation rather than the eigenstate representation for the chromophores.We want to calculate the in—uence of the energy transfer on the lineshape function g(t) from which all linear and nonlinear optical signals can be calculated.23 The lineshape function is directly calculated from M(t) (eqn. 2). To consider the in—uence of energy transfer we write g(t) as the sum of two terms: g(t)\gSB(t)]gET(t) (5) where is the system»bath lineshape function and is given by gSB(t) gSB(t)\;j CSDj2T P0 t dt1 P0 t1 dt2Mj(t2)]ijj P0 t dt1Mj(t1)D]12 (Din t)2 (6) in terms of the quantities de–ned above.Here j is an index for various intra- and intermolecular contributions to M(t). The –rst term in eqn. (6) accounts for the in—uence of —uctuations and is temperature dependent (via D), the second term corresponds to the Stokes shift and the third to the contribution of inhomogeneous broadening to the lineshape.As we will discuss later the balance between the –rst two terms changes with temperature and produces strikingly temperature-independent timescales of dynamics in some cases.17 If we consider the energy transfer term then we can write for gET(t) gET(t)\P0 t dt1 P0 t1 dt2Sdt2Sdueg(t2)dueg(0)T (7) In eqn.(7) represents the transition frequency of the species (call this j) on which ueg(t) the excitation resides at time t and as before Thus if the excita- dueg(t)\SuegT[ueg(t). tion is transferred to species k at time t@, is the transition frequency of species k. ueg(t@) The simplest phenomenological model to account for the in—uence of energy transfer on g(t) (and hence on the 3PEPS signal) is as follows.If the initial site is species j then At time t the probability that is still equal to is simply dueg(0)\dueg i . dueg(t) dueg i proportional to the population remaining on the jth site, i.e., dueg j (t)PdPj(t)4Pj(t)[SPjT (8) Here is the time-averaged population on site j. Now average over the sites of the SPjT system Sdueg(t2)dueg(0)TP 1 N ;j pj dPj(t2)dPj(0) (9) It should be emphasized that the average in eqn.(7) is over the sites. In eqn. (9) is the pj probability of –nding the jth site transition energy. In general, we expect this probability to have a Gaussian distribution. Now if we assume that the populations decay as simple exponentials with rate constant i.e., eqn.(9) can be kET , dPj(t)\dPj(0) exp([kET t), rewritten as : Sdueg(t2)dueg(0)TP 1 N ;j pj(dPj)2 exp([kET t2)\C1 N ;j pj(dPj)2Dexp([kET t2) (10) A purely real exponentially decaying correlation function corresponds to the Kubo model of line broadening.23 If we let the proportionality constant be the inhomogeneous width we can then write Din , gET(t)\Din 2 kET 2 MkET t[1]exp([kET t)N (11)28 Excited state dynamics of chromophores If is very small eqn.(11) simpli–es to kET gET(t)\12 (Din t)2 (12) i.e., it is identical to the –nal term in eqn. (6) for dilute chromophores. Finally an approximate expression for the peak shift itself can be written incorporating the in—uence of energy transfer q*(T )\ SD2TM(T )]Din 2 exp([kET T ) Jp(SD2T]Din 2 ))[SD2T]Din2 ]f (T )] (13) If is zero this expression reduces to eqn.(3), but in the presence of energy transfer kET and an inhomogeneous distribution of site energies an additional exponential component enters into the peak shift that directly re—ects the rate of energy transfer. At the risk of excessive repetition we remind the reader that full numerical expressions are used to –t the experimental data and that eqn.(3), (4) and (13) are given to bring out the physical content of these complex expressions. The approach outlined above is extremely crude but can be systematically improved. For example, the existence of inhomogeneous broadening implies a distribution in energy transfer rates. In general a rate constant may be inadequate to describe the time dependence of energy transfer on ultrashort timescales.Work is in progress to develop a more sophisticated model. Dilute chromophores in polymer glasses Fig. 4 shows the peak shift result for IR144 in PMMA [poly(methyl methacrylate)] at 294 K and 32 K. The lines are calculated curves ; that at 294 K is a –t using j\378 cm~1 and cm~1 and the –t gives a spectral density o(u) that is then used to Din\500 calculate the low temperature peak shift without adjustable parameters.The –t is clearly excellent, not merely is the general shape of the peak shift reproduced but also the increase in the initial and long-time values of q*(T ) are also quantitatively reproduced. In this calculation the full, complex form of eqn. (6) is used. The lower panel of Fig. 4 shows the eÜect of ignoring the imaginary contribution at low temperature.Relaxation on the intermediate timescale (B20»170 fs) is clearly missing in the purely real response. At high temperature the response is dominated by the —uctuations, i.e., the real part of g(t). The —uctuation»dissipation theorem connects the —uctuation amplitude (SDu2T) and the Stokes shift of (2j). At high temperature the two are related by SDu2T\ with T the absolute temperature, thus for high enough temperature the —uc- 2jkBT /+, tuations will dominate over the spectral diÜusion re—ected by the imaginary part of g(t).However at low temperature, since the imaginary component of g(t) is temperature independent, when the —uctuation amplitude drops, the spectral diÜusion takes over as the dominant line-broadening mechanism.Fig. 4(b) also shows that the ultrafast component of the peak shift is unaÜected by temperature since it arises from high frequency vibrational modes that are in the low temperature limit over our whole range. The remarkable lack of change in dynamical timescale with temperature is made clear in Fig. 5 where the long-time [q*(T ]O)] has been subtracted and the curves normalized to their initial values for six diÜerent temperatures in the range 294»32 K.In the IR144/PMMA system we were not very successful in describing the temperature dependence of the long-time value of q*(T ) on temperature.17 We have recently completed studies with IR144 in poly(vinylformal) (PVF) glass and with a second dye, 3,3@-diethylthiatricarbocyanine iodide (DTTCI), in PMMA.22 In both cases the temperature dependence of both the dynamical timescales and the long-time value of the peak shift are quantitatively described by a model using a temperature independentY .Nagasawa et al. 29 Fig. 4 3PEPS data for IR144 in PMMA. (a) Comparison of the calculated (solid line for 294 K and dashed line for 32 K) with the experimental results (–lled squares for 294 K and –lled circles for 32 K).The calculations used cm~1 and j\378 cm~1. (b) Comparison of the Din\500 calculated 3PEPS at 32K with (solid line) and without (dashed line) the imaginary contribution to g(t). inhomogeneous width Fig. 6 shows the temperature dependence of q*(T ]O) for Din . DTTCI in PMMA predicted without adjustable parameters from o(u), (300 cm~1) Din along with the experimental data.The implication of the results in Fig. 4»6 is that the coupling of electronic transitions of large molecules to polymer glass hosts can be well understood by means of a temperature-independent spectrum of harmonic oscillators linearly coupled to the transition and by a temperature independent inhomogeneous width. The two contributions can be treated separately and the entire temperature dependence arises simply from the change in population of the various quantum levels of the oscillators with temperature.Based on the three systems studied so far17,22 extrapolation of data obtained at low temperature, for example from hole-burning spectroscopy, to physiological temperatures may be a more reliable procedure than might be suspected on intuitive grounds.Once the system becomes —uid, however, the situation changes and recent results using the peak shift method16 and non-resonant two-dimensional Raman spectroscopy24,2530 Excited state dynamics of chromophores Fig. 5 Peak shifts vs. population period for six temperatures for IR144 in PMMA. For each curve the value of [q*(T ]O)] was subtracted and the initial peak shifts normalized.Fig. 6 DTTCI in PMMA. Temperature dependence of the asymptotic [q*(T ]O)] peak shift, points and calculated curve (line) based on a constant spectral density and temperature independent spectral density.Y . Nagasawa et al. 31 strongly suggest that motions on diÜerent timescales in liquids cannot be regarded as separable. Concentrated chromophores in a protein host : light harvesting complexes The reasonably complete understanding of the dilute chromophore»glass systems described above suggests that information on systems in which the chromophores interact should be obtainable from peak shift measurements.The light harvesting complexes of purple bacteria, LH1 and LH2, represent important examples of such systems particularly since the high-resolution structure of LH2 is known.26 An important issue in these systems is the degree to which the electronic states can be regarded as delocalized and on which timescale any particular degree of delocalization persists.Localization can be brought about dynamically or through disorder. Thus the strength and timescale of the electron»phonon coupling [i.e., the spectral density o(u)] and the extent of inhomogeneous broadening are important quantities.In the dilute chromophore case the (Din) Stokes shift, j, can be obtained directly from the absorption and —uorescence spectra. In the concentrated case even this is not possible since rapid energy migration means that emission comes from a diÜerent chromophore than was initially excited.There is strong evidence that both LH1, which contains 32 bacteriochlorophyll (BChl) molecules (B875), and LH2 [27 BChl in one ring of 9 (B800) and one ring of 18 (B850)] are inhomogeneously broadened. Yet when the peak shift data from LH1 are compared with IR144/PMMA at room temperature, there is a striking diÜerence. As Fig. 7 shows the pigment protein complex has a peak shift that decays to zero implying the absence of inhomogeneous broadening.27 However, as the analysis sketched in the three-pulse echo peak shift method section shows, the presence of energy transfer now allows the system to average over the inhomogeneous distribution.In other words the ability of the system to rephase (generate an echo) is disabled by the energy transfer.Furthermore, eqn. (13) shows that the amplitude of the term re—ecting energy transfer is given by the (square of the) inhomogeneous width Jimenez et al.27 Din . analyzed the data in Fig. 7 using a model M(t) function containing the term exp Din 2 and obtained a value of 90 fs for The remainder of the spectral density was ([t/qET) qET . attributed to the spectral density arising from intra- and inter-molecular modes coupled to the electronic transition.Thus the inhomogeneous width could be estimated along with the reorganization energy and Stokes shift timescale. The reorganization energy ascribed to the protein is exceedingly small, ca. 100 cm~1. By estimating the electronic coupling and using a simpli–ed treatment due to Leegwater,28 Jimenez et al.estimated that the electronic states were localized onto 3»4 BChl. Similar results were obtained for LH2.27 We have previously used the B820 subunit29,30 of LH1 to address these issues in greater detail.31 The B820 subunit consists of one a and one b transmembrane polypeptide and two BChl molecules.30 It can be reversibly re-associated to the B875 (LH1) complex32,33 and thus can be viewed as the basic dimeric subunit of LH1.LH1 therefore consists of 16 such subunits.34 Clearly energy transfer cannot occur outside the dimer pair in B820 and if the electronic states of LH1 involve many more than two molecules, the optical properties of LH1 and B820 might be expected to diÜer signi–cantly. Fig. 8 shows peak shift data for B820 compared with that of LH1.The two curves are clearly very diÜerent. After ca. 200 fs the B820 peak shift remains almost constant up to 100 ps, whereas the LH1 data decay on two very diÜerent timescales and have almost decayed to zero by 10 ps. Thus B820 shows de–nitive evidence for inhomogeneous broadening. In addition, the initial value of the peak shift is signi–cantly larger in the B820 data. The analysis developed in the previous section suggests a very simple approach to the understanding of Fig. 8. If LH1 and B820 are identical except for the presence of32 Excited state dynamics of chromophores Fig. 7 Comparison of peak shift data for IR144 in PMMA (squares) and light harvesting complex 1 (LH1) (circles) at room temperature. The inset shows the data normalized to the same initial value and clearly reveals the presence of the additional (B100 fs) decay process in LH1 ascribed to energy transfer.energy transfer then we should be able to predict the B820 peak shift data from our previous –t of LH127 by simply setting and changing no other parameter. The qET\O solid line in Fig. 8 shows just such a calculation made by including all possible electronic pathways in a two level system.Both the large long-time value of the peak shift [q*(T ]O)] and the increased initial value [q*(0)] over that in LH1 is reproduced quantitatively. The increase in q*(0) re—ects the absence of the energy transfer process in the loss of the optical transition frequency memory. q*(0) depends on the magnitude of the dynamical broadening processes and on the ratio of dynamic to static processes, the same eÜect is apparent in Fig. 4(a) where the decreased —uctuation amplitude at low temperature results in an increase in the initial value of q*. In a similar way, in B820 the total coupling strength of dynamical contributions to the line shape is reduced by the absence of the energy transfer process. The inhomogeneous contributions also naturally reappear and correspond to a FWHM of )(8 ln 2)\377 cm~1.The excellent agreement between prediction and Din experiment con–rms that the 90 fs timescale in the LH1 peak shift corresponds to energyY . Nagasawa et al. 33 Fig. 8 Comparison of peak shift data for LH1 (circles) and the B820 subunit of LH1 (squares). The solid line is a calculation of the B820 data based on the –t of ref. 27 to LH1 (dashed line), with the energy transfer rate set to zero. Note that the increase in initial value and the –nite asymptotic value of the peak shift are reproduced. transfer, and strongly suggests that the exciton»phonon coupling is the same for LH1 and B820 and that the excitonic states of LH1 and B820 have similar size. Indeed the simplest explanation of Fig. 8 is that the exciton length of LH1 is roughly two BChl molecules. The blue shift that occurs when LH1 (B875) dissociates into B820 subunits must, in large measure, be caused by changes in the local environment of the chromophores rather than by strong changes in the exciton interactions among dimers. Our suggestion that the basic electronic unit of LH1 (and LH2) corresponds to a dimer agrees with earlier Forster-theory calculations of —uorescence depolarization4,35 and spectral equilibration,36 and is in line with the analysis of super-radiance by Monshouwer et al.37 In this context it is important to note that the de–nition of delocalization length depends on the quantity being measured38 and care must be exercised when comparing diÜerent types of experiments.At room temperature a consistent picture of energy transfer between dimeric subunits on a 90»100 fs timescale over a modestly disordered set of energy levels has emerged for the antenna complexes LH1 and LH2.At low temperature the degree of delocalization remains an open question. We have recently extended our peak shift studies to low temperature in LH2 and the analysis of these results will be presented elsewhere.39 Concluding remarks There are strong parallels between the behavior of BChl molecules in protein complexes and dilute dye molecules in protein complexes and dilute dye molecules in polymer glasses.In the absence of energy transfer both systems exhibit inhomogeneous broadening and can be well described by linear coupling to a harmonic bath.The peak shift method is well suited to obtain both quantities. In more complex situations, such as the full LH complex, the potential of the peak shift method to characterize dynamical34 Excited state dynamics of chromophores systems becomes apparent. We expect the technique and multicolor variants of it to be useful for studies of a wide variety of reactive events. This work was supported by a grant from NSF and, in part, by donors to the ACS Petroleum Research Fund.J-Y. Y. was a GAANN fellow and Y. N. a JSPS fellow during a portion of this work. References 1 N. F. Scherer, D. M. Jonas and G. R. Fleming, J. Chem. Phys., 1993, 99, 153. 2 M. Ben-Nun, R. D. Levine, D. M. Jonas and G. R. Fleming, Chem. Phys. L ett., 1995, 245, 629. 3 M. Ben-Nun, R. D.Levine and G. R. Fleming, J. Chem. Phys., 1996, 105, 3035. 4 S. E. Bradforth, R. Jimenez, F. van Mourik, R. van Grondelle and G. R. Fleming, J. Phys. Chem., 1995, 99, 16179. 5 L. A. Peteanu, R. W. Schoenlein, Q. Wang, R. A. Mathies and C. V. Shank, Proc. Natl. Acad. Sci. USA, 1993, 90, 11762. 6 J. M. Jean, R. A. Friesner and G. R. Fleming, J. Chem. Phys., 1992, 96, 5827. 7 J. M.Jean and G. R. Fleming, J. Chem. Phys., 1995, 103, 2092. 8 J. Jean, J. Phys. Chem., 1997, in press. 9 P.Voé hringer, D. C. Arnett, T.-S. Yang and N. F. Scherer, Chem. Phys. L ett., 1995, 237, 387. 10 T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang and G. R. Fleming, J. Chem. Phys., 1996, 104, 6089. 11 W. P. de Boeij, M. S. Pshenichnikov and D. A. Weirsma, J. Phys. Chem., 1996, 100, 11806. 12 T.Joo, Y. Jia and G. R. Fleming, J. Chem. Phys., 1995, 102, 4063. 13 W. P. de Boeij, M. S. Pshenichnikov and D. A. Wiersma, Chem. Phys. L ett., 1995, 238, 1. 14 M. S. Pshenichnikov, K. Duppen and D. A. Wiersma, Phys. Rev. L ett., 1995, 74, 674. 15 M. Cho, J.-Y. Yu, Y. Nagasawa, S. A. Passino and G. R. Fleming, J. Phys. Chem., 1996, 100, 11944. 16 S. A. Passino, Y. Nagasawa and G.R. Fleming, J. Chem. Phys., 1997, 107, 6094. 17 Y. Nagasawa, S. A. Passino, T. Joo and G. R. Fleming, J. Chem. Phys., 1997, 106, 4640. 18 G. R. Fleming and M. Cho, Annu. Rev. Phys. Chem., 1996, 47, 109. 19 G. R. Fleming, S. A. Passino and Y. Nagasawa, Philos. T rans. R. Soc., in press. 20 G. R. Fleming, T. Joo and M. Cho, Adv. Chem. Phys., 1997, 101, 141. 21 M. Cho and G. R. Fleming, Adv.Chem. Phys., 1997, in press. 22 Y. Nagasawa, J.-Y. Yu and G. R. Fleming, J. Chem. Phys., 1997, submitted. 23 S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford University Press, Oxford, 1995. 24 A. TokmakoÜ and G. R. Fleming, J. Chem. Phys., 1997, 106, 2569. 25 A. TokmakoÜ, M. J. Lang, X. S. Jordanides and G. R. Fleming, Chem. Phys., 1997, in press. 26 G. McDermott, S. M. Prince, A. A. Freer, A. M. Hawthornthwaite-Lawless, M. Papiz, R. J. Codgell and N. W. Issacs, Nature (L ondon), 1995, 374, 517. 27 R. Jimenez, F. van Mourik, J.-Y. Yu and G. R. Fleming, J. Phys. Chem. B, 1997, 101, 7350. 28 J. A. Leegwater, J. Phys. Chem., 1996, 100, 14403. 29 M. C. Chang, L. Meyer and P. A. Loach, Photochem. Photobiol., 1990, 54, 873. 30 J. F. Miller, S. B. Hinchigeri, P. S. Parkes-Loach, P. M. Callahan, J. R. Sprinkle, J. R. Riccobono and P. A. Loach, Biochemistry, 1987, 26, 5055. 31 J.-Y. Yu, Y. Nagasawa, R. van Grondelle and G. R. Fleming, Chem. Phys. L ett., 1997, 280, 404. 32 P. S. Parkes-Loach, J. R. Sprinkle and P. A. Loach, Biochemistry, 1987, 27, 2718. 33 R. Ghosh, H. Hauser and R. Bachofen, Biochemistry, 1988, 27, 1004. 34 S. Karrasch, P. A. Bullough and R. Ghosh, EMBO J., 1995, 14, 631. 35 R. Jimenez, S. N. Dikshit, S. E. Bradforth and G. R. Fleming, J. Phys. Chem., 1996, 100, 6825. 36 H. M. Visser, O. J. G. Somsen, F. van Mourik and R. van Grondelle, J. Phys. Chem., 1996, 100, 18859. 37 R. Monshouwer, M. Abrahamsson, F. van Mourik and R. van Grondelle, J. Phys. Chem. B, 1997, 101, 7241. 38 T. Meier, Y. Zhao, V. Chernyak and S. Mukamel, J. Chem. Phys., 1997, 107, 3876. 39 J.-Y. Yu, M. Groot, R. Agarwal and G. R. Fleming, 1997, in preparation. Paper 7/07668A; Received 23rd October, 1997

ISSN:1359-6640    

DOI:10.1039/a707668a

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss., 1997, 108, 35»50 Femtosecond polarisability anisotropy relaxation and solvation dynamics The cases of aniline and methanol Neil A. Smith and Stephen R. Meech* School of Chemical Sciences, University of East Anglia, Norwich, UK, NR4 7T J The polarisability anisotropy relaxation dynamics of liquid methanol and aniline are measured by means of the femtosecond optically heterodyne detected optical Kerr eÜect.The data are converted to a frequency domain spectral density and analysed in terms of contributions from diÜusional reorientation and vibrational dynamics. For aniline a high frequency librational component of Gaussian form makes a large contribution. This is assigned to strong intermolecular interactions in the liquid. In methanol the dynamics are dominated by ultrafast relaxation, in good agreement with simulation.Using these data the solvation dynamics are calculated and compared with experimental measurement. Similarities and diÜerences are discussed. Calculation reproduces the general form of the observations, but predicts a number of features which are not observed. It is suggested that the coupling strength between solvent modes and solute dipole needs to be taken into account.Introduction Solvation dynamics is an important topic of research in condensed phase chemistry. Clearly an understanding of solvation is a prerequisite for an understanding of chemical reactivity in liquids, and an understanding of the dynamics of solvation will be essential in developing microscopic interpretations of reaction rate constants.The connection is clearest in the case of electron transfer reactions, where the transfer of charge immediately suggests a role for solvation. However, solvation dynamics are likely to be important in any reaction that involves a signi–cant degree of charge redistribution. Theoretical and experimental approaches to solvation dynamics are well described in a number of reviews, as is the increasingly important role of molecular dynamics (MD) simulation as the bridge between theory and experiment.1h5 A common theme in many of these reports is the idea that the dynamics of pure liquids can be used to predict the dynamics of solvation, and indeed the rate of electron transfer reactions.6h8 For example, early studies of excited state solvation revealed a close link between the measured solvation dynamics and the solventœs longitudinal relaxation time, qL\(e0/e=)qD , where is the liquidœs Debye relaxation time.1 More detailed measurements revealed qD that the relationship was only qualitative. For example, non-exponential solvation dynamics were sometimes observed even in solvents that were well characterised by a single Debye relaxation time.1,2 More molecularly based theories, such as the dynamical mean spherical approximation (DMSA), which at least accounted for the relative size of solvent and solute, were introduced to account for the failures of theories based on dielectric continuum data.9,10 The DMSA model has been quite successful in reproducing picosecond time resolved measurements of solvation dynamics.5 Perhaps more worrying than the precise form of the measured solvation dynamics was the fact that a substantial fraction of the solvation (i.e.the time resolved Stokes 3536 Polarisability anisotropy relaxation and solvation dynamics shift ; see below) was not resolved at all in picosecond time domain experiments. Evidently an important part of the solvation dynamics occurred on a sub-picosecond timescale.Such an ultrafast component was also predicted in some of the early MD simulations of solvation dynamics.11h13 The –rst experimental observation of this ultrafast component was made following improvements in the time resolution of the —uorescence up-conversion experiment. Rosenthal et al. observed that in excess of 50% of the solvation dynamics in acetonitrile occurred in about 100 fs.14 More recently Horng et al.15 have observed sub-100 fs components in the solvation dynamics of numerous solvents.Such ultrafast components are now routinely observed in increasingly realistic MD simulations of solvation dynamics.3,4 In the spirit of earlier appeals to pure liquid properties as a model for the dynamics of solvation it was proposed that the ultrafast dynamics of the pure liquid could account for the observed sub-picosecond component in solvation dynamics.It had long been appreciated from far-IR and light scattering measurements that liquids exhibited subpicosecond dynamics that were not usually resolved in dielectric relaxation experiments. 16 Cho et al. proposed that the ultrafast liquid dynamics observed in the femtosecond optically heterodyne detected optical Kerr eÜect (OHD-OKE) experiment could be used to model the solvation dynamics.17 This approach proved to be successful in reproducing the ultrafast solvation dynamics observation of Rosenthal et al.in acetonitrile solvents.14 In a similar spirit Maroncelli et al.18 suggested that, to a –rst approximation, the measured solvation dynamics, S(t), could be modelled from the pure liquidœs dipole correlation function, raised to some power related to the solvent C1(t), dipole density, as , Cv(t)\[C1(t)]as (1) and in the limit of a linear response.This model was supported by a number Cv(t)\S(t) of MD simulations.3,18 Raineri and Friedman subsequently derived eqn. (1) on a more rigorous basis.19 Despite the extensive theoretical activity in this area there have, since the original work on acetonitrile,17 been no direct comparisons of sub-100 fs time resolution solvation dynamics experiments with measurements of pure liquid dynamics.The objective of this paper is to make such a comparison, and so provide a test of the range of applicability of the idea that solvation dynamics can be simulated from a knowledge of the dynamics of the pure liquid. To this end we present femtosecond OHD-OKE measurements of the dynamics of two liquids, aniline and methanol.These will be compared with measurements of the solvation dynamics in the same solvents measured by the —uorescence up-conversion method. The two liquids chosen should provide a rather more severe test than did acetonitrile of the idea that OHD-OKE measurements can be used to simulate solvation dynamics.Methanol has very similar static dielectric properties to acetonitrile but exhibits very diÜerent ultrafast dynamics, in which intermolecular H-bond librational relaxation dynamics dominate at early times.20 Aniline will present an even more stringent test, since it is only slightly polar, has an appreciable quadrupole moment, and exhibits H bonding.In this sense aniline is perhaps an eccentric choice. However, aniline is of great importance in studies of ultrafast electron transfer reactions, where it –lls the role of both solvent and electron acceptor.21h25 Thus results derived here can be used as input to models of œfaster than solvationœ electron transfer reactions.Experimental and data analysis Optically heterodyne detected optical Kerr eÜect measurements The details of this well established technique have been presented elsewhere.26h34 Only the main features of the experiments will be described here. The laser source was a modeN. A. Smith and S. R. Meech 37 locked titanium sapphire laser operating at 813 nm with a repetition rate of 100 MHz (Clark MXR).The second order laser pulse autocorrelation function, was mea- G2(t), sured at the sample position to have a width of 75 fs. The observed laser bandwidth was 17 nm, below the transform limit for 50 fs Gaussian shaped pulses and 1.25 times the limit for a sech2 pro–le, suggesting a 50 fs laser pulse operating close to the transform limit.The experimental arrangement for the OHD-OKE measurement was based on published designs.26h34 Important parameters were: pump and probe energy 330 mW and 2 mW respectively, focused onto the sample by a 150 mm lens ; pump and probe linearly polarised, probe at 45° with respect to pump. The probe beam passed a polariser, quarter wave plate, the sample and a second polariser ; attenuation between the polarisers, with the sample cell in place, was 106 times.To obtain a heterodyne signal the –rst polariser is rotated by 1° yielding an out of phase local oscillator, so that the real (birefringence) part of the non-linear response is recorded. Detection was by a photodiode and lock-in ampli–er. For the highest time resolution scans, data points were recorded at 1.3 fs intervals.For long time data, measurements were made out to 60 ps (with a larger step size). The AN sample was distilled under vacuum. Spectroscopic grade methanol was used as received. Samples were injected into the 3 mm pathlength cuvette via a 0.2 lm –lter. All measurements were made at 294 K. The spectral density The analysis of the measured optically induced Kerr eÜect signal has been described previously by McMorrow and co-workers, and others.26h34 The Kerr response contains both an instantaneous electronic hyperpolarisability contribution, p(t), and a sum of nuclear contributions, ri(t) R(t)\p(t)];i ri(t) (2) However, as the femtosecond pulses themselves are not instantaneous, the measured signal, T (q), is a convolution of the true response with the second order intensity cross correlation function, G2(t) T (q)\/~= = G2(t)R(q[t)dt (3) Both the convolution and the electronic response can be separated out from the data by taking the imaginary part of the ratio of the Fourier transforms of T (q) and to G2(t) yield the nuclear dynamics in the frequency domain.26h34 Im[D(u)]\ImGF`[T (q)] F`[G2(q)]H (4) The resulting frequency domain spectrum, the spectral density, is the principal result of the OHD-OKE experiment.It is equivalent to the low frequency depolarised Raman spectrum multiplied by a Bose»Einstein thermal occupation factor.26h35 To obtain a sufficient number of data points to yield a reasonable spectrum it is necessary to extend the high time resolution data of Fig. 1 over a longer time range than it is practical to record. This is important, as an insufficient density of data over too small a time range leads to an underestimation of the low frequency part of the spectral density.36 To achieve good frequency resolution the low time resolution data (Fig. 1 inset) are –t to the following function26h28 r1(t)\I(t)[1[exp([2u0 t)] (5) and the data set is extended to 32 768 points with a time step of 1.33 fs, yielding approximately 0.76 cmv1 per data point in the spectrum.Eqn. (5) was initially introduced by38 Polarisability anisotropy relaxation and solvation dynamics Fig. 1 (a) Experimentally measured OHD-OKE data for pure liquid aniline. Inset are the data recorded with a larger step size out to 20 ps. (b) The spectral density of liquid aniline.Note the low frequency peak associated with the slow relaxation dynamics [inset to (a)] and the complex lineshape above 20 cm~1. The peak at 230 cm~1 is of intramolecular origin, and not included in subsequent calculations. McMorrow and co-workers to describe the long time response of the OHD-OKE signal, which was typically assigned to orientational diÜusional relaxation.The function I(t) describes the relaxation dynamics, and is typically a sum or distribution of exponential relaxation times. The term re—ects an inertial rise-time, and is chosen to be equal to u0 the mean frequency of the high frequency part of the spectral density ; however, the choice of is not critical. To focus on the ultrafast dynamics it is possible to subtract u0 the data in either the frequency or the time domain.r1(t) In Fig. 1 the experimental optical Kerr eÜect data and the resultant spectral density of neat aniline are shown. Further analysis, in the frequency domain, is discussed below. The nuclear dynamics in the time domain, r(t), can be obtained from an inverse transform of the spectral density, or some function to which it has been –t.This is carried out for aniline and methanol below.N. A. Smith and S. R. Meech 39 Solvation dynamics To test the relationship between pure liquid dynamics and solvation dynamics the solvation dynamics of the dye LDS-750 M2-[4-(dimethylaminophenyl)buta-1,3-dienyl]-3-ethylbenzothiazolium perchlorateN were measured in aniline. The concentration was 10~3 M, and aniline was puri–ed by vacuum distillation. Equivalent data for methanol already exist in the literature.15,37 There are several routes to the measurement of ultrafast solvation dynamics, including time resolved —uorescence,1,2 transient absorption/stimulated emission,38 and threepulse photon-echo peak shift measurements.5,39,40 The method chosen here, time resolved —uorescence, is perhaps the best established.Essentially the time dependence of the wavelength resolved —uorescence is recorded at a number of wavelengths throughout the emission band. After deconvolution the resulting intensity time pro–les are normalised to the intensity of the total (time integrated) —uorescence spectrum. Intensity time slices of the resulting three-dimensional surface then reveal the instantaneous —uorescence spectrum.Fluorescence decay data were recorded using a 90 femtosecond time resolution —uorescence up-conversion spectrometer, based around a self mode-locked cavity-dumped Cr:forsterite laser, described in detail elsewhere.41 The 40 fs output pulses (1260 nm, 8 kHz) are –rst routed to a BBO (b-barium borate) crystal. The resultant second harmonic (630 nm) and fundamental beams are separated at a dichroic mirror.The second harmonic was focused into the sample. The LDS-750 —uorescence was collected and focused into the up-conversion crystal. The residual fundamental beam was routed via an optical delay line (accuracy 1 lm) to the same crystal to act as the up-converting gate pulse. The up-converted —uorescence signal was wavelength resolved by a monochromator and detected by a photon counting detection system.The —uorescence decay pro–le was recorded by scanning the optical delay line. Data were recorded between 0 and 80 ps, with a higher density of data in the –rst picosecond, and decreasing density at longer times where the rate of change of the intensity is smaller. The measured —uorescence decay data are distorted by convolution with the –nite width of the laser pulses. This can be removed provided an accurate representation of the relevant response function is obtained.The cross correlation between the fundamental gate pulse and the scattered excitation pulse is a logical choice. This was measured as being of Gaussian shape and width 90 fs, after dispersion compensation.41 However, when this measured function was used in the deconvolution analysis a poor –t was obtained on the –rst part of the rising edge of the —uorescence. This problem can be overcome by making modi–cations to the response function to allow for the additional (and wavelength dependent) dispersion in the optical path of the —uorescence upconversion, compared to cross correlation, experiment. This problem is treated in greater depth by Horng et al.15 A good –t was obtained to our data with a response function of Gaussian shape, width 115 fs with a linear time shift to correct for the wavelength dependence.Once the deconvoluted response is measured it is straightforward to generate the time resolved —uorescence spectra in the manner described above.A typical example is shown in Fig. 2, with the data –t to a log-normal distribution. From such spectra the solvation time correlation function, S(t), can be derived from S(t)\ l(t)[l(O) l(0)[l(O) (6) where l(x) is the mean or peak frequency of the —uorescence spectrum at time x. There is some difficulty associated with the choice of the time zero frequency, as pointed out by Maroncelli and co-workers.15 Here we determine l(0) from an extrapolation of our data back to time zero, and note that the resultant Stokes shift is in reasonable agreement with a back extrapolation of a plot of Stokes shift against diÜerent solvent polarity40 Polarisability anisotropy relaxation and solvation dynamics Fig. 2 Three examples of the time resolved emission spectra for LDS-750 in aniline.The data points have been –t to a log-normal distribution (» » »). parameters. It would appear that in the weakly polar aniline solvent most of the —uorescence is captured in the 115 fs time resolution measurements. The resulting solvation correlation function, eqn. (6), will be discussed below. Results and Discussion Polarisability anisotropy relaxation Aniline.The basic result of the OHD-OKE measurement, the spectral density, is shown for neat liquid aniline in Fig. 1(b). The –gure reveals two distinct peaks, one narrow and peaked near zero frequency, and a complex bandshape between 20 and 200 cm~1. The narrow peak can be associated with the slow bi-exponential relaxation seen in Fig. 1(a), and is well represented by the Fourier transform of eqn.(5) when I(t) is represented by a bi-exponential function. The parameters used in the –t are shown in Table 1. This low frequency relaxation is often assigned to diÜusional orientational relaxation in aniline. The bi-exponential form of the orientational relaxation observed for aniline (and other mono-substituted benzenes) could be ascribed to reorientational dynamics about diÜerent molecular axes.The longest relaxation time would correspond to end over end tumbling, while the short component could comprise contributions from rotations about the long axis and an axis perpendicular to the benzene ring. The fact that the reorientation times are very diÜerent suggests that reorientation about one axis is more hindered than about the others.This can be interpreted as evidence for strong intermolecular interaction. Possibly intermolecular H-bonding or dipole»dipole interactions contribute to local ordering in the liquid.42 A consequence of such strong interactions is that it is difficult to interpret the orientational relaxation times in terms of a simple Stokes»Einstein»Debye (SED) model. A detailed analysis must include the in—uence of shape anisotropy and orientational pair correlation on the dynamics.34,42 Indeed, our comparison of the slow relaxation times in a series of substituted anilines shows that the trend is opposite to that expected from the simplest SED model.34 An additional point to be noted is that the OHD-OKE measurement is sensitive not only to orientational relaxation but also to collision (or interaction) induced dynamics.Typically (see below) this contribution is assumed to be a rapidly relaxing one, contributing only at early times. However, it has recently been shown in some MD simulations that collision induced eÜects can contribute to the polarisability anisotropy relaxationN. A. Smith and S. R. Meech 41 Table 1 Fit parameters to the OHD-OKE spectral density (q in picoseconds, u in wavenumbers) aniline Methanol eqn. (5)a eqn.(7) eqn. (8) eqn. (5)b eqn. (7) q1\1.45 a\1.05 u1\84 q\0.31 a\0.71 q2\16.9 uBL\23.5 *u\76 b\0.5 uBL\60 A1\0.05 A2\0.02 i\1, 2. b I(t)\exp([t/q)b. a I(t)\;i Ai exp([t/qi) ; on all timescales. Thus the observed non-exponential form of the picosecond OHD-OKE dynamics may contain a contribution from collision induced dynamics.Once again these would not be wholly accounted for in a simple SED analysis. It would seem then that the slow relaxation dynamics of liquid aniline cannot be said to be fully understood. Further progress will require a study of the relaxation dynamics as a function of dilution. Such measurements are in progress. Subtraction of the frequency domain analogue of eqn. (5) from the spectral density isolates the ultrafast dynamics of the liquid. The subtraction reveals a complex lineshape, which cannot be –t by a single function. Following the analysis introduced by Chang and Castner this part of Im[D(u)] is –t to two functions29h32 IBL(u)\bua expA[ u uBLB (7) and IG(u)\g1 expC[ 2(u[u1)2 *u2[2 ln(2)]~1D [g1 expC[ 2(u]u1)2 *u2[2 ln(2)]~1D (8) Eqn.(7) and (8) have been very successful in describing the spectral densities of a wide range of molecular liquids, and aniline is no exception. The quality of the –t is displayed in Fig. 3, and the –t parameters are shown in Table 1. The antisymmetrised Gaussian eqn. (8) can be taken as representing an inhomogeneously broadened intermolecular librational mode.29h32 Such librational (or frustrated rotation) dynamics are often observed in studies of the liquid phase, and are a feature of several models of liquid state dynamics.43 In the substituted benzenes a peak response of 60^5 cmv1 is ubiquitous, 32,42,44,45 making the observation of an 85 cm~1 frequency in aniline interesting.This unusually high frequency is believed to be a result of particularly strong intermolecular interactions in this liquid.The only similar case of which we are aware is the 103 cm~1 mode observed in liquid pyrrole, where a T-shaped dimer is thought to be a particularly stable structure in the liquid.46 One possible explanation for the high frequency of librational response in aniline is the formation of a stable co-facial H-bonded dimer. Such structures have been observed in supersonic jet spectroscopy of the aniline dimer.47 The assignment of the contribution of eqn.(7) is less clear. As the ohmic lineshape (a\1) this function has been applied to many relaxation phenomena,48 while eqn. (7) with a\12/7 was derived explicitly for a collision induced lineshape in simple molecular liquids by Bucaro and Litovitz.49 Unfortunately the best –t value of a is rarely equal to these values, as is the case here (Table 1).One disadvantage of the above analysis is42 Polarisability anisotropy relaxation and solvation dynamics Fig. 3 The spectral density of aniline with the low frequency response subtracted [i.e. eqn. (5) with I(t) given by a bi-exponential function] and –t to eqn. (7) and (8). that it suggests that two distinct relaxation mechanisms, represented by eqn.(7) and (8), are operating on the same timescale. This is unlikely to be realistic, and, as mentioned above, MD simulations suggest that collisional dynamics, supposed to be represented by eqn. (7), actually occur over a wide range of timescales, and not only on a subpicosecond timescale as eqn. (7) suggests.Thus analysis in terms of eqn. (7) and (8) is certainly oversimpli–ed, but it does have the considerable merit of actually describing the measured spectral density, required for the simulation of solvation dynamics. We are currently investigating the application of other lineshape functions in our analysis, but thus far these do not provide an adequate description of the data (without proposing an unreasonable number of contributions).Methanol. The OHD-OKE data and resultant spectral density of liquid methanol are shown in Fig. 4. The –rst thing to note is that the response is dominated by ultrafast dynamics. To obtain sufficient accuracy in the Fourier transform analysis it was necessary to record data out to 20 ps, where the response had decayed to \10~5 times its peak intensity.It was found that the slow response was well –tted by eqn. (5) with I(t) given by the Kohlrausch»William»Watts function. The origin of this non-exponential relaxation function has been discussed elsewhere in terms of the non-symmetrical shape of methanol and the diÜering relaxation rates of diÜerent contributions to the polarisability. 50 The Fourier transform of eqn.(5) is also shown in Fig. 4(b). The remainder of the spectral density is described eqn. (7), which is also shown in Fig. 4. This again serves to illustrate the dominance of the ultrafast relaxation in methanol. The –t parameters are shown in Table 1. The dynamics of liquid methanol can be described in more detail than those of aniline because a number of high quality MD simulations have been performed.20,51 In particular Ladanyi and Liang presented simulations of the OHD-OKE data, and found that in excess of 90% of the relaxation occurred in less than 200 fs.20 This is in good agreement with the experimental data, Fig. 4(a), and the time domain response, obtained from an inverse Fourier transform of the (–tted) Im[D(u)], shown in Fig. 5. The MD simulations show that reorientational dynamics, librational and inertial, dominate in theN. A.Smith and S. R. Meech 43 Fig. 4 (a) The experimentally recorded OHD-OKE data for methanol. (b) The spectral density for liquid methanol –t to eqn. (5) and (7), where I(t) in % was given by the Kohlrausch»William» Watts function. –rst 200 fs. The simulation also showed that the time domain response is highly oscillatory, which is not reproduced in the experiment.The reason for this diÜerence is the limited frequency resolution of the OHD-OKE experiment. With a 50 fs laser pulse it is only possible to excite Raman active modes out to ca. 300 cm~1. Simulations show that the oscillatory behaviour arises from intermolecular H-bond librational dynamics, with a peak frequency at around 600 cm~1.51 Thus this mode will not be observed in the experiment.It is debatable if higher time resolution would reveal this response, since there may be intramolecular modes in this frequency region, which are not included in MD simulations ; these would tend to obscure the intermolecular response. The simulations reveal that the major part of the ultrafast response is due to orientational dynamics.However, this is not the sole contribution. Collision induced relaxation, which arises partly in translational motions in the liquid, is also found to contribute at all times to the OHD-OKE response. [This result implies that there is no separation of timescales between these two types of relaxation, which might seem to be implied by the44 Polarisability anisotropy relaxation and solvation dynamics Fig. 5 The pure nuclear dynamics of methanol obtained from an inverse complex transform of the data in Fig. 4(b). The contributions of the individual components are also shown. Note the dominance of ultrafast relaxation. analysis in terms of eqn. (7) ; this highlights the fact that this analysis contains a good deal of ìcurve –ttingœ.] The more important conclusion from the MD simulation is that the OHD-OKE experiment is sensitive to non-reorientational dynamics, while the model of Maroncelli et al.18 [see eqn. (1)], and numerous simulations, suggest that it is reorientational dynamics which dominate in the solvation time correlation function.This might then be one area in which a discrepancy between measured solvation dynamics and those calculated from the OHD-OKE data might be expected.We return to this point below. In summary, the ultrafast OHD-OKE data for methanol are dominated by fast dynamics, with picosecond orientational relaxation making a relatively minor contribution. From MD simulations the fast dynamics are assigned mainly to orientational relaxation, with additional contributions from collision induced dynamics. The complex form of the slow dynamics are described elsewhere.50 Solvation dynamics A method for the calculation of the solvation time correlation function from the spectral density has been described by Chang and Castner.29h32 The nuclear dynamics in the time domain, r(t), are obtained by means of an inverse complex Fourier transform r(t)\2F~MIm[D(u)]NH(t[t0) (9) where H is the Heaviside function.An example is shown for methanol in Fig. 5. The r(t) are obtained from the –tted functions which accurately described the measured spectral density, rather than the density itself. This allows the elimination of contributions from intramolecular modes which are assumed not to contribute to solvation dynamics.Note that r(t) is representative of true nuclear dynamics; it is not convoluted with the laser pulse or distorted by the instantaneous electronic hyperpolarisability of the liquid. The nuclear dynamics are converted to the polarisability correlation function, where C2(t),N. A. Smith and S. R. Meech 45 the subscript indicates a second rank rotational correlation function, by C2(t)\g1[ P0 t r(t)dt P~= = r(t)dth (10) However, the model put forward by Maroncelli et al,18 and derived by Rainieri and Friedman,19 requires the –rst rank correlation function, The connection has been C1(t).made in several theoretical studies, and in measurements of the reorientational relaxation rate that19,29h32,43 C1(t)\[C2(t)]1@3 (11) However, it should be borne in mind that this is an approximation, and that most of the studies mentioned have assumed the dominant relaxation mechanism to be reorientational.It is not clear how valid eqn. (11) will be in cases where a substantial fraction of the polarisability anisotropy relaxation arises from collision induced relaxation. This is one area in which the derivation of solvation dynamics from OHD-OKE data may turn out to be less than quantitative.The –nal step is indicated in eqn. (1), where the function related to the dipole density is given, in the continuum approximation, by as\A4pok2 3kB T BCA 9e= (e0]2)BA1[ e= e0BD~1 (12) and the symbols have their usual meanings. The factor serves to translate between the as single particle reorientational motion characterised by and its eÜect on the extent C1(t) of solvation.3,18 For example, for a given angular displacement of a solvent molecule the eÜect on the solvation energy will be largest for a polar solvent compared to a (as[10) non-polar one (small We reiterate that the model shown in eqn.(1) has so far mainly as). been justi–ed on the basis of MD simulations. The main approximations of the model are that the mechanism of solvation is mainly due to rotational motion of the solvent molecules, and that the precise nature of the solute is not a signi–cant factor.18,19 Comparison of measured and calculated solvation dynamics The solvation dynamics of LDS-750 in aniline were obtained from the mean frequency of the time resolve emission spectra (Fig. 2) and eqn. (6). In Fig. 6 this result is compared with calculated from the OHD-OKE spectral density and eqn.(1), (10) and (11). Cv(t) Immediately one notices that the agreement is, at least qualitatively, very good, bearing in mind the approximations in the treatment [notably eqn. (10)]. This result suggests that solvation dynamics can indeed be calculated from a knowledge of the dynamics of the pure liquid, even in cases, like aniline, where there are signi–cant intermolecular interactions and the polarity is low (as\5). On closer inspection of Fig. 6 there are some noticeable diÜerences between the measured and calculated solvation dynamics. The initial Gaussian form of is absent Cv(t) in the measured S(t). A Gaussian feature in S(t) at very early times has been predicted in numerous models of solvation dynamics.1h5 This arises from the inertial response of the solvent molecules to the changed dipole moment of the solute.However, to our knowledge no Gaussian component has ever been clearly resolved in —uorescence upconversion experiments, although the fast exponential responses which are observed relax on the timescale expected for the inertial motion.15 This failure to observe a component of Gaussian form has often been ascribed to the poor time resolution of the46 Polarisability anisotropy relaxation and solvation dynamics Fig. 6 The calculated and measured solvation dynamics for liquid aniline. Note the overall similarity of the response, but also the absence from the measured response of the Gaussian component seen in the calculation (see inset).—uorescence experiment. Indeed, the importance of sub-100 fs time resolution in —uorescence up-conversion studies of solvation is demonstrated by comparing the present data with earlier measurements with lower time resolution,34 where the fastest component (200 fs) was not clearly resolved. However, inspection of Fig. 6 reveals that the Gaussian component is predicted to exist for at least 200 fs, so its absence from the current measurements suggests a signi–cant diÜerence between the calculated and measured solvation dynamics.The Gaussian part of the calculated arises almost exclusively from Cv(t) the librational response, modelled in the frequency domain by eqn. (8). This component was discussed above in terms of an intermolecular mode of aniline.One possible reason for the failure to observe a clear Gaussian response in the solvation dynamics is that the local order of the solvent is strongly perturbed by the presence of the solute, at least in the –rst solvation shell. Since solvent orientational dynamics in the –rst solvation shell are the main contributor to solvation dynamics then such a perturbation would be consistent with the absence of an observable ultrafast Gaussian component.Essentially the pure liquid dynamics are perturbed by the presence of the solute, an eÜect which is not accounted for in eqn. (1) There are other diÜerences between the measured and calculated dynamics. The weak oscillation seen in at around 400 fs is not detected in S(t). This feature is Cv(t) again associated with the librational response of aniline, so it is also subject to the possibility of a perturbation by the solute.In addition the calculation overestimates the signi–cance of the fast component in solvation dynamics (or vice-versa, underestimates the contribution of the slow dynamics). Thus Fig. 6 shows that eqn. (1), with input from the OHD-OKE spectral density, does, at least qualitatively, a good job of simulating the solvation dynamics in liquid aniline, but fails to reproduce the smooth exponential form found in the experiments. Next the calculated and measured15,37 solvation dynamics in methanol will be discussed.The initial expectation was that eqn. (1) would be more successful for methanol than for aniline, since MD simulations suggest that the polarisability anisotropy relaxation is dominated by reorientational dynamics.18 This is in line with the model leading to eqn.(1). This expectation is not borne out by the results, as can be seen in Fig. 7. Both of the measurements of solvation dynamics displayed reveal an ultrafast com-N. A. Smith and S. R. Meech 47 Fig. 7 The calculated and measured (ref. 15 and 37) solvation dynamics for liquid methanol.Note the dominance of ultrafast relaxation in the calculation, compared to experiment. ponent below 300 fs, with an amplitude between 30 and 70% of the total relaxation. This is followed by a slower bi-exponential relaxation on the picosecond timescale. Qualitatively the calculated reproduces this trend, but it is clear that the calcu- Cv(t) lation signi–cantly overestimates the relative amplitude of the fast component.Such a result could have been predicted from the dominance of the ultrafast relaxation seen in Fig. 5 and the high value of for methanol. as Also noticeable in Fig. 7 is the signi–cant diÜerence between the two measurements of solvation dynamics, which were obtained in diÜerent ways. Horng et al. measured S(t) directly in the manner described above.15 Although their measurements had the highest available time resolution the fastest component of the solvation dynamics in methanol was at the limit of their time resolution.The results of Horng et al. are in good agreement with those of Ernsting and co-workers, obtained by transient absorption.38 Two groups have obtained the solvation dynamics from the three-pulse echo peak shift (3PEPS) experiment.39,40 This experiment has extremely high time resolution (probably better than 20 fs) but does not probe directly solvation dynamics.Rather the solvation dynamics have to be reconstructed from the measured time correlation function.39 It has been suggested that part of the diÜerence between the two measurements might lie in the diÜerent natures of the two experiments.52 However, the question arises : is the greater similarity of the results of Joo and co-workers (Fig. 7) with the calculated due Cv(t) simply to superior time resolution ? To answer this we need to discuss the ìtime resolutionœ of the OHD-OKE experiment. It is true that distortions of the data due to convolution of the laser pulse are removed in the Fourier transform analysis described.However, the limited spectral width of the laser eÜectively limits the observability of ultrafast dynamics. Essentially ultrafast dynamics, e.g. the H-bonded librational dynamics of methanol at 600 cm~1 would not be observed in the OHD-OKE measurement. No such embargo applies to measurements of solvation dynamics. Thus, while some of the diÜerences between the two methods of measuring solvation dynamics may arise from diÜerences in time resolution, the eÜect of higher time resolution in the OHD-OKE experiment on the calculated dynamics would be to increase the disparity between calculated and measured results.There are a number of reasons why one might expect diÜerences between calculated and measured dynamics.The possible role of solute perturbations in the solvent48 Polarisability anisotropy relaxation and solvation dynamics dynamics was discussed above. Once again it is noted that the solvation dynamics in methanol do not exhibit the Gaussian form at early times discernible in the calculations (Fig. 7, inset). In addition, in the case of methanol, the dominant contributions to the polarisability and the dipole moment lie on diÜerent parts of the molecule.Since solvation mainly re—ects dipolar relaxation and OHD-OKE polarisability relaxation one might expect this diÜerence to lead to a disagreement between the measured and calculated data. However, in neither case is it obvious that these eÜects would lead to the observed dominance of the ultrafast component in the calculation.All that can properly be concluded from Fig. 7 is that ultrafast relaxation dynamics in—uence the polarisability anisotropy relaxation to a greater extent than they do solvation dynamics. A similar but smaller eÜect was seen in Fig. 6. Similar conclusions have been reached elsewhere. de Boeij et al. compared the spectral density for solvation dynamics (obtained from the 3PEPS experiment) with the OHD-OKE spectral density.39 They observed that the low frequency part of Im[D(u)] was well reproduced by the solvation dynamics, but the high frequency response revealed excess intensity.Similarly Joo et al.53 were able to reproduce their measurements of solvation dynamics by adding a rapidly decaying term to the spectral density, which has the eÜect of suppressing the contribution of high frequency components. It should be reiterated that the calculation of even in the case of methanol, Cv(t), does a good job of reproducing the form of the solvation dynamics; both the ultrafast (50 fs timescale) relaxation and the slower component seen in the measurements are present in the calculated results.These fast and slow contributions to have their Cv(t) origin, in terms of the pure liquid spectral density, in the separation into low frequency (diÜusive) and high frequency (librational) modes of relaxation.Nowhere in the calculation of described above is any allowance made for the possibility of diÜerent Cv(t) coupling strengths between these solvent modes and the solute dipole moment.We suggest that with the addition of a coupling strength term a good agreement between measured and calculated solvation dynamics could be obtained. Recent discussions of the instantaneous normal mode approach to solvation dynamics seem to contain the main features of this proposal.3 Conclusions The pure liquid dynamics of aniline and methanol have been studied using the femtosecond OHD-OKE technique. For aniline the resultant spectral density revealed a complex lineshape which was, as a –rst approximation, analysed in terms of a diÜusional orientational relaxation at low frequency and a combination of librational and collision induced relaxation at higher frequency.The limitations of this approach were mentioned. The frequency of the librational response suggests an unusually strong intermolecular interaction in aniline.For methanol the polarisability anisotropy relaxation was found to be dominated by an ultrafast component, accounting for 90% of the sub picosecond relaxation. This is in good agreement with MD simulations. Measurements of the solvation dynamics of LDS-750 in aniline with 100 fs time resolution were reported. The solvation time correlation function revealed a 200 fs component and a bi-exponential relaxation on the picosecond timescale.The importance of a high time resolution in the —uorescence is con–rmed by a comparison with earlier measurements. The solvation dynamics for aniline and methanol (which are available from the literature) were compared with those calculated from the pure liquid dynamics using the model of Maroncelli and Castner and their co-workers.3,18,29h32 For aniline the overall agreement was quite good, but the detailed results of the calculation (a Gaussian pro–le at early times and an oscillatory response) were not found in the measurements. These diÜerences may arise from a solute perturbation of the pure liquidN. A.Smith and S. R. Meech 49 structure.For methanol the Gaussian behaviour at early times is again predicted but not observed. More seriously the calculation greatly overestimates the relative importance of the ultrafast component in the solvation dynamics. This cannot be ascribed to an eÜect of time resolution. It is suggested that this observation indicates a need to include a term for the coupling strength between diÜerent modes of the liquid dynamics and the solute dipole moment.Further progress requires measurements in a greater range of solvents than employed here ; such work is in progress.54 The authors are grateful to Prof. K. Yoshihara and Dr. Igor Rubutsov (Institute for Molecular Science) for their help in the solvation dynamics measurements and to Profs. M. Maroncelli and G.Fleming for permission to use the data in Fig. 7. S.R.M. is grateful to EPSRC for a generous equipment grant. N.A.S. thanks EPSRC for a research studentship. References 1 M. Maroncelli, J. Mol. L iq., 1993, 57, 1 2 P. F. Barbara and W. Jarzeba, Adv. Photochem., 1990, 15, 1. 3 R. M. Stratt and M. Maroncelli, J. Phys. Chem., 1996, 100, 12981. 4 B. M. Ladanyi and M. S.Skaf, Annu. Rev. Phys. Chem., 1993, 44, 335. 5 G. R. Fleming and M. Cho., Annu. Rev. Phys. Chem., 1996, 47, 109. 6 I. Rips and J. Jortner, Chem. Phys. L ett., 1987, 133, 411. 7 I. Rips and J. Jortner, J. Chem. Phys., 1987, 87, 2090. 8 D. F. Calef and P. G. Wolynes, J. Phys. Chem., 1987, 87, 3387. 9 P. G. Wolynes, J. Chem. Phys., 1987, 86, 5133. 10 A. L. Nichols, III and D. F. Calef, J.Chem. Phys., 1988, 89, 3783. 11 M. Maroncelli and G. R. Fleming, J. Chem. Phys., 1988, 89, 8044. 12 M. Maroncelli, J. Chem. Phys., 1991, 94, 2084. 13 T. Fonseca and B. M. Ladanyi, J. Phys. Chem., 1991, 95, 2116. 14 S. J. Rosenthal, X. Xie, M. Du and G. R. Fleming, J. Chem. Phys., 1991, 95, 4715. 15 M. L. Horng, J. A. Gardecki, A. Papazyan and M. Maroncelli, J. Phys. Chem., 1995, 99, 17311. 16 See, for example, J. Yarwood, Annu. Rep. Prog. Chem., Sect. C, 1990, 87, 75. 17 M. Cho, S. J. Rosenthal, N. F. Scherer, L. D. Ziegler and G. R. Fleming, J. Chem. Phys., 1992, 96, 5033. 18 M. Maroncelli, V. P. Kumar and A. Papazyan, J. Phys. Chem., 1993, 97, 1. 19 F. O. Rainieri and H. L. Friedman, J. Chem. Phys., 1994, 101, 6111. 20 B. M. Ladanyi and Y. Q. Liang, J. Chem. Phys., 1995, 103, 6325. 21 Y. Nagasawa, A. P. Yartsev, K. Tominaga, P. B. Bisht, A. E. Johnstone and K. Yoshihara, J. Chem. Phys., 1994, 101, 5717. 22 K. Yoshihara, K. Tominaga and Y. Nagasawa, Bull. Chem. Soc. Jpn., 1995, 68, 696. 23 C. F. Wang, B. Akhremitchev and G. C. Walker, J. Phys. Chem., 1997, 101, 2735. 24 W. Zinth, Proceedings of ìFemtochemistry IIIœ, L und, 1997, to be published. 25.E. W Castner, Jr., in preparation. 26 D. McMorrow, W. T. Lotshaw and G. Kenney-Wallace, IEEE J. Quantum Electron., 1988, 24, 443. 27 D. McMorrow and W. T. Lotshaw, J. Phys. Chem., 1991, 95, 10395. 28 D. McMorrow and W. T. Lotshaw, Chem. Phys. L ett., 1993, 201, 369. 29 Y. J. Chang and E. W. Castner, Jr., J. Chem. Phys., 1993, 99, 113. 30 Y. J. Chang and E. W. Castner, Jr., J. Chem. Phys., 1993, 99, 7289. 31 Y. J. Chang and E. W. Castner, Jr., J. Phys. Chem., 1994, 98, 9712. 32 Y. J. Chang and E. W. Castner, Jr., J. Phys. Chem., 1997, 100, 3330. 33 N. A. Smith, S. Lin, S. R. Meech and K. Yoshihara, J. Phys. Chem. A, 1997, 101, 3641. 34 N. A. Smith, S. Lin, S. R. Meech, H. Shirota and K. Yoshihara, J. Phys. Chem. A, 1997, 101, 9578. 35 S. Kinoshita, Y. Kai, M. Yamaguchi and T. Yagi, Phys. Rev. L ett., 1995, 75, 148. 36 M. J. Feldstein, P. Voé hringer and N. F. Scherer, J. Opt. Soc. Am. B, 1995, 12, 1500. 37 T. Joo, Y. Jia, J.-Y. Yu, M. J. Lang and G. R. Fleming, J. Chem. Phys., 1996, 104, 6089. 38 S. A. Kovalenko, N. P. Ernsting and J. Ruthmann, J. Chem. Phys., 1997, 106, 3504; D. Bingemann and N. P. Ernsting, J. Chem. Phys., 1995, 102, 2691. 39 W. P. de Boeij, M. S. Pshenichnikov and D. A. Wiersma, J. Phys. Chem., 1996, 100, 11 806. 40 S. A. Passino, Y. Nagasawa, T. Joo and G. R. Fleming, J. Phys. Chem. A, 1997, 101, 725. 41 I. V. Rubtsov, H. Shirota and K. Yoshihara, to be published. 42 P. Cong, H. P. Deuel and J. D. Simon, Chem. Phys. L ett., 1995, 240, 72. 43 R. M. Lynden-Bell and W. A. Steele, J. Phys. Chem., 1984, 88, 6514. 44 J. L. Friedman, M. C. Lee and C. Y. She, Chem. Phys. L ett., 1991, 186, 161.50 Polarisability anisotropy relaxation and solvation dynamics 45 J. L. Friedman and C. Y. She, J. Chem. Phys., 1993, 99, 4960. 46 K. Wynne, C. Galli and R. M. Hochstrasser, Chem. Phys. L ett., 1992, 193, 17. 47 K. Sugawara, J. Miyawaki, T. Nakanaga, H. Takeo, G. Lembach, J. Djafari, H. Barth and B. Brutschy, J. Phys. Chem., 1996, 100, 17145. 48 A. J. Leggett, S. Chakravarty, A. Dorsey, M. P. A Fisher, A. Garg and W. Zwerger, Rev. Mod. Phys., 1987, 59, 1. 49 J. A. Bucaro and T. A. Litowitz, J. Chem. Phys., 1971, 54, 3846. 50 H. Shirota, K. Yoshihara, N. A. Smith, S. Lin and S. R. Meech, Chem. Phys. L ett., 1997, 281, 27. 51 M. S. Skaf, T. Fonseca and B. M. Ladanyi, J. Chem. Phys., 1993, 98, 8929. 52 R. Biswas, N. Nandi and B. Bagchi, J. Phys. Chem. B, 1997, 101, 2968. 53 T. Joo, Y. Jia and G. R. Fleming, J. Chem. Phys., 1995, 102, 4063. 54 M. Maroncelli and E. W. Castner, Jr., J. Mol. L iq., in press. Paper 7/06940E; Received 25th September, 1997

ISSN:1359-6640    

DOI:10.1039/a706940e

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss., 1997, 108, 51»62 Optical properties of solvated molecules calculated by a QMMM method Chlorophyll a and bacteriochlorophyll a Ian P. Mercer, Ian R. Gould and David R. Klug Department of Chemistry, Imperial College, South Kensington, L ondon, UK SW 7 2AY We have applied a hybrid quantum mechanical»molecular mechanical (QMMM) approach to the calculation of electronic»vibrational coupling.To test the validity of this approach, we compare results to the steady state absorption and emission spectra of chlorophyll a (Chl-a) and bacteriochlorophyll a (BChl-a). We –nd that the Stokes shift and the widths of the spectra are reasonably well represented while the amplitudes of the vibrational side band in both molecules are greatly underestimated. Introduction The extent of a chemical reaction is determined by the Gibbs free energy diÜerence between reactants and products, and it would be useful to be able to predict this in condensed phase chemical reactions.One would also like to know the time-scale over which these Gibbs free energy gaps develop, and details of the relevant dynamics. A liquid or protein will respond to a rapid change in charge distribution by structural rearrangements which minimise the energy of the new electronic con–guration.The energy associated with these rearrangements is usually called the reorganisation energy, and has a well established role in, for example, non-adiabatic electron transfer theory. The reorganisation energy also appears in the response of a condensed phase chemical system to optical excitation.The creation of an excited electronic state causes a rearrangement of electron density in the excited molecule, and a consequent rearrangement of the surrounding medium in response to this. The lowering of the excited state energy is revealed by the —uorescence Stokes shift which is directly related to the reorganisation energy of the system. In one sense, creation of an excitated state and the subsequent —uorescence Stokes shift can be regarded as an extremely simple type of chemical reaction.The reactant in this case is the excited state of the molecule initially created by the applied optical –eld, and the product is the state created by relaxation of the system. The Gibbs free energy gap between reactants and products is indicated by the shift in the peak of the steady state absorption band from that of the steady state emission band.The steady state emission spectrum is a good representation of the product state, as most of the relaxation occurs on the femtosecond and picosecond time-scale, while in the singlet state many systems last for nanoseconds. Attempts to calculate the Gibbs free energy diÜerence between the initial excited and relaxed states is a natural –rst step, prior to calculating Gibbs free energy gaps in more 5152 Optical properties of solvated molecules complex chemical processes.In order to make some progress towards this goal, we have attempted to calculate the —uorescence Stokes shift in two solvated molecules, chlorophyll a and bacteriochlorophyll a.This paper represents our –rst attempts at such calculations. Chlorophyll a and bacteriochlorophyll a have also been chosen for this study because of their central role in the photosynthetic processes of higher plants and bacteria. Obtaining absorption and emission spectra from a QMMM simulation The incident light –eld is taken to interact with two electronic levels ; the ground and lowest excited singlet state of the molecule. The energy of these levels —uctuates due to interactions with the surrounding bath which results in a time-varying Bohr frequency.The time evolution of this system is describes by the Liouville»von Neumann equation: do(t) dt \[i + [H(t), o(t)] (1) where o(t) is the density operator for a two-level system and H(t) is the Hamiltonian operator.Following an optical interaction at t\0, and assuming no population loss, the solution to eqn. (1) is given by: oab(t)\oab(0)exp([iuab t)TexpG[i P0 t *u(q) dtHU (2) where is an oÜ-diagonal element of the density matrix, is the mean angular oa(t) uab frequency associated with the electronic energy gap and t is the time of the second interaction with the light –eld.Finding the polarisation of the ensemble requires taking the trace of the product of the transition dipole operator with the density matrix. Within the rotating wave approximation, and assuming that the transition dipole moment is constant in time (Condon approximation), this yields the linear optical response function, R(t) : R(t)\Tk2 expAi P0 t *u(t) dtBU (3) If the —uctuations of the energy are Gaussian and where sufficient phase space has been sampled, the cumulant expansion can be applied to eqn.(3).1 The response function then becomes: R(t)\exp[[g(t)] (4) where g(t), the line broadening function, is given by: g(t)\D2 P0 t dq1 P0 t M(q2) dq2 (5) and M(t) is the auto-correlation function of the energy gap —uctuations scaled to unity, given by: M(t)\P= =*u(t]q)*u(q) dq/D2 (6) where D is the root mean square deviation of the energy gap —uctuations.I.P. Mercer et al. 53 Note that ensemble average [eqn. (3)] is now represented by the correlation of a single variable ; the deviation from the mean of the energy gap Bohr frequency [eqn. (4)»(6)]. It is this which is delivered by the QMMM simulations. In linear response theory, the spectral response of a system is related to the impulse response.The steady state absorption and emission spectra are given by:2,3 pab\ReGP0 t dtR(t)exp[iu[ueg)t]H (7a) pem\ReGP0 t dtR*(t)exp[i(u[ueg)r]H (7b) To –nd the emission spectrum, it is assumed that the excited state potential energy surface has the same shape as that of the ground state, but with a shifted minimum.Note that up to these point, the response function R(t) is real, and as such eqn. (7a) and (7b) are identical ; there is no spectral shift between the emission and absorption spectra. In order to introduce a Stokes shift, M(t) can be modi–ed to satisfy detailed balance, imparting a complex component. By asserting detailed balance, the response of the system is made to conform to the —uctuation»dissipation theorem.4 The —uctuation dissipation theorem is the cornerstone of linear response theory.In this case the theorem connects —uctuations of the electronic energy levels to the rate of relaxation of these levels after the system has been displaced from equilibrium by an interaction with the light –eld. Detailed balance is included by operating on the spectrum of oscillators J(u), which is given by the Fourier transform of M(t).With M(t) being real and symmetric, J(u) is necessarily also real and symmetric. However, to satisfy detailed balance, it is required that positive frequencies should be related to their negative counterparts by a Boltzman coefficient, such that J([u)\exp([+u/kT )J(u) (8) To satisfy this relationship, a modi–ed semi-classical form of the spectral density can be given by:6 JSC(u)\ 2J(u) [1]exp([+u/kT )] 4[1]tanh([+u/2kT )]J(u) (9) Real components of a function are determined by the even component in the Fourier domain, and odd components are related to complex components in the Fourier domain.With the transformation given by eqn. (9), the even part of the spectrum of oscillators [and hence the real part of M(t)] is left unchanged and only an odd component is added, which delivers a complex part for M(t).This in turn delivers a complex component for the linear response function, resulting in a Stokes shift between the calculated absorption and emission spectra [see eqn. (7a), (7b)]. Note that in the high temperature limit, the above method yields the same result as the multi-mode Brownian oscillator (MBO) picture,3 where: g(t)\ij P0 t M(t) dq]D2 P0 t dq1 P0 t1M(q2) dq2 (10) and in the high temperature limit : j\ +D2 2kT where j is the reorganisation energy, k is Boltzmannœs constant, and T is temperature.54 Optical properties of solvated molecules Quantum mechanicalñmolecular mechanical (QMMM) methodology The initial starting geometry for BChl-a was obtained from the crystal structure of Ermler et al.7 from Rhodobacter sphaeroides, with the phytyl chain replaced by a terminal methyl group.This resulted in a structure containing 82 atoms with the addition of hydrogen atoms to ful–l the valence requirements. This procedure was repeated for the Chl-a chromophore; the initial starting geometry was obtained from the crystal structure of Chow et al.8 For both BChl-a and Chl-a, the hydrogen atoms (which are not seen in the crystal structure) are added to the structures at somewhat idealised bond lengths and angles.In order to deal with this, the bond lengths and angles formed by these hydrogen atoms with respect to the chromophore atoms were geometry optimised to yield a low energy starting conformation, whilst retaining the same geometry for the non-hydrogen atoms.This was achieved using the semi-empirical quantum mechanical method of Stewart,9 employing a Hamiltonian known as PM3, which was performed using MOPAC-93.10 PM3 is a derivative of the MNDO11 (modi–ed neglect of diatomic overlap) method, which is an approximation to the ab initio molecular orbital (MO) method.The core procedure of such calculations are to solve the Roothaan»Hall equations12 to yield the wavefunction, energy, electron density and molecular orbitals of the system, which for a closed-shell system are : FC\SCE (11) F is the Fock matrix, C is the matrix of coefficients which describe the components of the underlying basis functions representing the atomic orbitals in the resulting molecular orbitals, S is the overlap matrix and E is the energies of the molecular orbitals.Fk“\Hk“ core] ; j/1 K ; p/1 K Pjp[(kt o jp)[12 (kj o tp)] (12) Pjp\2 ; i/1 N@2CjiCpi (13) Hk“ core\Pdt1/k(1)C[12 Z2[ ; A/1 M ZA o r1[RA o D/“(1) (14) In the above equations, P is the electron density matrix, and are the basis /k , /“ , /j /p functions, and are the coefficients of the basis functions, is the one-electron Cji Cpi Hk“ core Hamiltonian, N is the number of electrons and M is the number of atoms.In ab initio calculations, all elements of the Fock matrix are calculated explicitly, which requires the evaluation and manipulation of a considerable number of integrals. The clearest way to reduce the computational eÜort is to neglect or approximate some of these integrals.Semi-empirical methods, such as MNDO and PM3, achieve this in part by explicitly considering only the valence electrons of the system, where the basis set comprises Slater-type s and p orbitals. Furthermore, the overlap matrix S is set equal to the identity matrix. The PM3 Hamiltonian contains essentially the same parameters as AM1,13 another derivative of MNDO, the fundamental diÜerence being in the derivation of the parameters; those for PM3 having been derived by an automated procedure whilst those for AM1 are derived from a heuristic mix of experimental data.In order to apply the AMBER force –eld14 to BChl-a and Chl-a it is necessary to derive the atom centred point charges for the ground and excited state representations of the molecules.The AMBER force –eld comprises terms for bond stretching, bond angle deformation, torsional barriers to rotation, van der Waals and Coulombic inter-I. P. Mercer et al. 55 actions : Etotal\ ; bonds Kr(r[req)2] ; 1,3 Kh(h[heq)2 ] ; 1,4 Vn@2[1]cos(n/[c)] ] ; 1, nonvbonds CApij rijB12[Apij rijB6D] ; i:j qi qj erij (15) A series of ab initio MO studies to investigate the ground and excited state properties of BChl-a were performed in order to determine the atom centred point charges.Single point con–guration interaction singles (CIS) calculations (with only the core MOs frozen), were performed on a variety of SGI workstations and a Power Challenge using Gaussian94.15 A hierarchical series of basis sets were used, starting with STO-3G,16 SV-3-21G17 and ultimately SV-6-31G*.18 We also investigated the use of the semiempirical PM3 Hamiltonian, again using CIS, to investigate the excited states of the BChl-a.Atom centred point charges were derived for the ground and –rst excited states of BChl-a using the density matrices obtained with the SV 6-31G* basis set in accordance with the RESP19 method for the AMBER force –eld.14 Having developed a set of point charges for the chromophore ground and –rst excited state, we then performed molecular dynamics (MD) on the ground system in a bath of methanol molecules using the AMBER20 suite of programs using the force –eld described by eqn.(15). The protocol used for our MD simulations is as follows. The chromophore was placed in a cubic box of side 50 containing approximately 1500 methanol molecules. ”, The system was then subjected to a few hundred steps of conjugate gradient minimisation21 to alleviate any bad van der Waals contacts.A residue-based nonbonded cut-oÜ of 12 was used for this and all subsequent simulations, where energies ” and forces due to the van der Waals and Coulombic interactions are neglected if the distance between all the atoms in two residues is greater than the cut-oÜ distance.The system was then subjected to MD at constant temperature (298 K), constant pressure (1 atm) and with periodic boundary conditions. The integration time step was set to 1 fs and Shake22 was applied to all bonds involving hydrogen atoms. This constrains the bond length to be the same throughout the length of the simulation and as a consequence the forces due to bond interactions involving hydrogens are omitted in the evaluation of the potential function.The temperature control was performed by independent scaling of the velocities of the solute and solvent following the method of Berendsen et al.23 An initial equilibration phase of some 80 ps was performed and equilibration was deemed to be obtained by inspection of the trace of the overall energy of the system.A data production run was then performed for 30 ps with the coordinates of the system being taken every 5 fs, resulting in a trajectory consisting of up to 6000 coordinate sets. This trajectory was then used to calculate the energy of the system for the chromophore in the excited state by replacing the charges of the chromophore ground state with those of the excited state. We now discuss the implementation and application of the combined quantum mechanical (QM)»molecular mechanical (MM) method to both BChl-a and Chl-a in methanol.The QMMM method used in this study is implemented within the semiempirical package MOPAC93.10 The method consists of incorporating the point charges of the methanols in the one-electron Hamiltonian.We could include the van der Waals interactions also, but since these do not change in going from the ground to the excited state, they have been neglected. We have used the trajectories from the classical MMMD simulations and performed single point calculations using the PM3 Hamiltonian and the CIS method, where we have restricted the active space to the three, –ve and ten highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO).56 Optical properties of solvated molecules Results and Discussion Before discussing the results of our MD simulations, it is pertinent to review brie—y the –ndings of the ab initio and semi-empirical investigations of the energy gap between the ground and –rst excited states for BChl-a, especially as the ground and excited state atom centred point charges for the classical MD simulations were derived from the SV-6-31G* calculations. The values given in Table 1 relate the calculated energy gap between ground and –rst excited state to the computational method and relative computational cost.It is clear from this table that even for the highest level of ab initio MO theory applied to this system (CIS/6-31G*), there is a resulting error of approximately 20% of the true energy gap, and a cost of the order of 11 days of computational eÜort.This should be compared with the results for the semi-empirical PM3 investigation which yields an energy gap within 10% of the true experimental value whilst taking one minute of computational eÜort.Our initial attempts to use a classical MMMD approach for the investigation of the energy gap —uctuation of BChl-a met with a spectacular lack of success. The energy gap between the ground and excited state for BChl-a was obtained by evaluating the energy of the system using the trajectory with the ground and excited state charges for the solute.The total energy for the excited state was approximately 10 kcal mol~1 lower in energy than the ground state using this method of calculation. The failure of MMMD to represent correctly even the ordering of the energy levels meant that we had to rule out a purely classical approach to these calculations. This inability of classical MD to reproduce the energy diÜerence between the ground and excited state was the catalyst for investigating the system using the QMMM approach.Using the ground state trajectory we calculated the energy gap for the chromophore between the ground and excited state every 5 fs for the duration of a production run of 30 ps using the PM3 Hamiltonian with CIS restricted to a 3-in-3 representation. This de–nes which electrons may be promoted from occupied orbitals into vacant or virtual ones. In this manner the number of possible excitations is signi–- cantly reduced, and in the 3-in-3 case, only the top three occupied and bottom three unoccupied orbitals are considered ; some nine unique con–gurations of orbital occupation. The results of these investigations were reasonable with the Stokesœ shift being tolerably well reproduced (see Table 2).The same protocol was then applied to Chl-a. The results from this investigation were, however, not as successful. Critically, the energy gap between the ground and excited state was smaller than that for BChl-a, whereas experimentally the gap for Chl-a is greater than BChl-a. Visual inspection of the Table 1 The electronic energy gap obtained from diÜerent methods, related to computational eÜort method energy gap/eV frequency/nm time/h CIS/STO-3G 2.47 501 4 CIS/6-31G* 1.80 688 273 PM3 1.74 711 0.0013 experiment 1.61 770 Table 2 Optical parameters for increasing active orbital space method 3»3 5»5 10»10 experiment mean wavelength for absorption/nm 739 775 819 776 absorption width/nm 32.4 31.8 32.8 57.5 Stokesœ shift/nm 14.3 13.6 14.7 21.8I.P. Mercer et al. 57 Fig. 1 Optical absorption and emission spectra for (a) BChl-a and (b) Chl-a, showing experimental (dotted) and calculated 3-HOMO 3-LUMO, 3000 points (solid). Inset are shown the side bands of the calculated spectra enlarged. classical MD trajectory for Chl-a revealed that the Mg, at the centre of the haem unit, had equilibrated to a position far from the initial crystal structure ; an eÜect not observed for BChl-a.The inability of the Chl-a to reproduce the average energy gap between the ground and –rst excited state can be traced to the classical MD simulation. Investigation of both Chl-a and BChl-a with a molecular mechanical force –eld description of the system results in a compromise: one has to choose between not having the magnesium atom bonded to any of the four nitrogen atoms, having it bonded to all four or to try to bond it to just two of the nitrogen atoms in the haem unit.In our simulations we chose the former option and represented bonding to the Mg with just Coulombic and van der Waals terms. This compromise is not pertinent to a QM description of either Chl-a of BChl-a since the bonding situation is described through the electron density distribution.In order to attempt to circumvent this problem with Chl-a, we chose to repeat the protocol for the classical MD simulation with one important constraint : the distance58 Optical properties of solvated molecules between the Mg and the four nitrogen atoms was kept at the crystal structure separations during the course of the simulation.This re–ned protocol had a signi–cant eÜect upon the resulting investigation. An immediate quanti–able diÜerence between the modi–ed and original Chl-a simulations was manifest in the correct description of the magnitude of the energy gap between the ground and excited state, with the former correctly describing the gap as being greater than the corresponding gap for BChl-a. In order to maintain a high degree of comparability we again performed the classical MD and QMMM simulations on BChl-a using the same constraint on the Mg atom with respect to the nitrogen atoms as for Chl-a.Comparison of the results for BChl-a between the Mg being unrestrained and restrained shows little diÜerence in terms of the calculated average energy gap and Stokesœ shift, qualifying this approach to the simulation of Chl-a.The optical absorption and emission spectra derived for BChl-a and Chl-a in methanol are shown in Fig. 1. The Stokes shifts are well represented for both BChl-a and Chl-a, being within 10% of the experimental value for Chl-a, and 25% for BChl-a. The spectral width of BChl-a is 65% of the experimental value, and the width of Chl-a lies within 2% of experiment.The spectral side bands, although present, are smaller than those in the experimental spectra and are a factor of 6% and 15% of experiment for BChl-a and Chl-a, respectively. The optical absorption and emission spectra are given by the real part of the Fourier transform of the linear optical response function, which is shown in Fig. 2 for BChl-a. The gradient of the response function phase at t\0 yields the –rst moment of the absorption and emission spectra from the mean electronic gap energy. The half width of the amplitude of the response function gives a time-scale of importance. Fluctuations which occur on a much faster time-scale than the response function halfwidth can be said to give a homogeneous contribution to the optical absorption and emission. Likewise, coupled —uctuations that occur over much longer time-scales can be said to give an inhomogeneous contribution to the optical absorption and emission.Fig. 3 shows the Stokes shift and absorption width as a function of run length. The Stokes shift closely follows the spectral width, with the values having largely stabilised after about 2 ps.Beyond this duration, neither optical observable changes signi–cantly. This behaviour can be understood by investigating the energy gap auto-correlation function M(t), as shown in Fig. 4 and 5. The correlation function is naturally separated into a fast component of less than 5 fs duration, and slower components that occur on time-scales longer than 100 fs.The Fig. 2 Optical response function for BChl-a 3»3, for a 3000 point QMMM run, with 5 fs step sizeI. P. Mercer et al. 59 Fig. 3 Stokes shift and absorption bandwidth vs. run length, for BChl-a, 3 HOMO»3 LUMO for increasing QMMM run lengths of up to 30 ps duration of the linear optical response function (of ca. 40 fs) lies between the two timescales, thus forming a natural delineation between the two.As discussed above, components of M(t) that occur much faster than the duration of the linear response function can be said to be largely homogeneous, and components that are much slower can be said to be largely inhomogeneous as far as the processes of absorption and emission are concerned. The Stokes shift and optical widths are largely determined by the oÜset of the correlation function on the time-scale of the response function width.Indeed, when this eÜective oÜset is removed such that M(t) is non-zero only for the –rst point of the trajectory (whilst leaving unchanged the mean square deviation of the energy gap —uctuations, D2) the Stokes shift is reduced to 8% and the optical width is reduced to 30% of their previous values. As the run length increases, so the contribution of low frequencies also increases. It is necessary to sample one cycle of a coupled oscillation in order to ascertain its frequency and coupling amplitude.In our simulations, the rate of convergence of the optical absorption and emission widths and Stokes shift for BChl-a, is largely determined by the requirement to sample a 15 cm~1 mode. This mode is clearly seen in Fig. 5, which shows Fig. 4 The —uctuation auto-correlation function of the electronic energy gap M(t), plotted for QMMM run lengths of 0.38 ps (dashed), 0.5 ps (dotted) and 30 ps (solid)60 Optical properties of solvated molecules Fig. 5 The —uctuation auto-correlation function of the electronic energy gap M(t), plotted for a 30 ps QMMM run length, showing features in the correlation function present on a picosecond time-scale Fig. 6 Spectra of oscillations coupled to the electronic energy gap for (a) frequencies less than 800 cm~1 and (b) frequencies greater than 1500 cm~1I. P. Mercer et al. 61 the correlation function for BChl-a over 5 ps. The requirement to sample this mode is the dominant restriction to determining the linear optical parameters, with apparently no need to sample further the phase space of the solvated chromophore.We have also investigated the sensitivity of the optical Stokes shift and widths calculated from CIS QMMM simulations for BChl-a, to an extension of the orbital space available for excitation. The three, –ve and ten highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO) were considered, corresponding to the consideration of 9, 25 and 100 con–gurations, respectively.A comparison of the results is shown in Table 2. All three cases deliver a Stokes shift and optical widths within 10% of each other. We can conclude that the derived absorption and emission spectral parameters are not sensitive to an extension of the active orbital space for the CIS calculation.As discussed earlier, 70% of the optical widths and 90% of the Stokes shift are determined by modes coupled to the electronic transition which are of a period greater than the duration of the linear response function. This corresponds to coupled modes of frequency much less than 800 cm~1. The spectra of coupled oscillators given by considering three, –ve and ten HOMO and LUMO for BChl-a in MeOH are shown in Fig. 6(a) and (b). The three cases yield similar spectra for modes with frequencies less than 8900 cm~1 [see Fig. 6(a)] ; however, for modes above 1500 cm~1 [see Fig. 6(b)], there are signi–cant diÜerences. For example, taking –ve HOMO and –ve LUMO gives a strong feature at 1805 cm~1, which is not visible when taking three or ten of each orbital.There are three possible reasons for the discrepancies associated with the high frequency modes. First, it may be expected that the molecular mechanics should represent well only the low frequency motions in the system, which are in high-temperature limit (highly populated oscillators), and fail to represent adequately the high frequency motions of the system.Secondly, we can see in Fig. 6(a) and (b) that the chosen orbital space available for excitation also mostly aÜects the high frequency coupled modes. It is therefore possible that the coupling factors which are eÜectively determined from the semi-empirical quantum mechanics are at fault. Finally, there is the possibility that the molecular mechanical component of the calculations is failing to represent the nuclear motions due to the charge –tting procedure used to establish the driving forces for the simulation, or indeed that the terms in the AMBER force –eld [eqn.(15)] are not adequate. Conclusion Our QMMM method provides information that can be applied to the determination of optical absorption and emission spectra in methanol solvated Chl-a and BChl-a.The auto-correlation functions of the energy gap are dominated by fast (\5 fs) and slow ([2 ps) components. The Stokes shifts and therefore the reorganisation energies are well reproduced using our method; however, the contributions of underdamped high frequency modes are poorly represented as can be seen by underestimation of the side band. The fact that the widths of the spectra are not well represented for BChl-a allows for the possibility of some inhomogeneity on a time-scale much longer than our simulation. Furthermore, in order to obtain a more accurate representation of the spectral widths and Stokes shifts, it may also be necessary to take into account factors such as the time dependence of the transition dipole moment.References 1 R.Kubo, J. Phys. Soc. Jpn., 1962, 17, 1100. 2 R. Kubo, Adv. Chem. Phys., 1969, 15, 101. 3 S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford University Press, 1995. 4 D. Chandler, Introduction of Modern Statistical Mechanics, Oxford University Press, 1987.62 Optical properties of solvated molecules 5 R. Kubo, Rep. Prog. Phys., 1996, 29, 255. 6 S. Mukamel, J.Phys. Chem., 1985, 89, 1077. 7 U. Ermler, G. Fritzsch, S. K. Buchanan and H. Michel, Structure, 1994, 10, 925. 8 H. C. Chow, R. Serlin and C. E. Strouse, J. Am. Chem. Soc., 1975, 97, 7230. 9 J. J. P. Stewart, J. Comput. Chem., 1989, 10, 209; 221. 10 J. J. P. Stewart, MOPAC-93, Release 2, Fujitsu Ltd., Tokyo, 1994. 11 M. J. S. Dewar and W. Thiel, J. Am. Chem. Soc., 1997, 99, 4899. 12 C. C. J. Roothaan, Mod. Phys., 1951, 23, 69; G. G. Hall, Proc. R. Soc. L ondon, Ser. A, 1951, 39, 343. 13 M. J. S. Dewar, E. G. Zoebisch, E. F. Healy and J. J. P. Stewart, J. Am. Chem. Soc., 1985, 107, 3902. 14 W. D. Cornell, P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz, D. M. Ferguson, D. C. Spellmeyer, T. Fox, J. W. Caldwell and P. A. Kollman, J. Am. Chem. Soc., 1995, 117, 5179. 15 GAUSSIAN94, Revision D.3, M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A. Pople, Gaussian Inc., Pittsburgh, PA, 1995. 16 W. J. Herhe, R. F. Stewart and J. A. Pople, J. Chem. Phys., 1969, 51, 2657. 17 J. S. Binkley, J. A. Pople and W. J. Herhe, J. Am. Chem. Soc., 1980, 102, 939. 18 R. Ditch–eld, W. J. Herhe and J. A. Pople, J. Chem. Phys., 1971, 54, 724. 19 C. I. Bayly, P. Cieplak, W. D. Cornell and P. A. Kollman, J. Phys. Chem., 1993, 97, 10269. 20 D. A. Perlman, D. A. Case, J. W. Caldwell, W. S. Ross, T. E. Cheatham III, D. M. Ferguson, G. L. Seibel, U. C. Singh, P. K. Weiner and P. A. Kollman, AMBER 4.1, University of California, San Francisco, CA, 1995. 21 W. F. Van Gunsteren and M. Karplus, Macromolecules, 1982, 15, 1528. 22 W. F. Van Gunsteren and H. J. C. Berendsen, Mol. Phys., 1977, 34, 1311. 23 H. J. C. Berendsen, J. P. M. Postma, W. F. Van Gunsteren, A. DiNola and J. R. Haak, J. Chem. Phys., 1984, 81, 3684. Paper 7/05648F; Received 4th August, 1997

ISSN:1359-6640    

DOI:10.1039/a705648f

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss., 1997, 108, 63»80 Concerted elimination dynamics from highly excited states Qingguo Zhang,§ Una Marvet and Marcos Dantus Department of Chemistry, Michigan State University, East L ansing, Michigan 48824, USA Photoinduced molecular detachment has been investigated for methylene iodide and several related compounds and (CH2I2) (CH2Br2, CH2 Cl2 Multiphoton excitation of these molecules at 310 nm gives rise to CF2Br2).halogens in the D@ state. Femtosecond pump-probe experiments on the dissociation of these compounds indicate that the process is extremely fast (\60 fs) and proceeds without an intermediate. In addition to the characteristic D@]A@ —uorescence at 342 nm, photodissociation of also pro- CH2I2 duces several —uorescence bands in the 260»290 nm region. The CH2I2 transients show characteristic vibrational coherence.Time resolved data I2 collected by detection at 272 nm also demonstrate clear, fast decaying rotational anisotropy, analysis of which reveals a distribution of rather high rotational levels of Based on analysis of the dissociation time, rotational I2 . anisotropy and vibrational coherence, and on the estimated partitioning of energy in the fragments, an concerted molecular detachment mechanism I2 has been proposed. 1 Introduction Understanding of molecular detachment processes represents an interesting and challenging area of research in the photodissociation research community. Processes of this type include, for example, the production of from photolysis of and H2 NH3, H2O molecules,1 from IBr from and from H2CO Cl2 COCl2 ,2 CH2IBr3 I2 CH2I2 .4h10 Unlike most well known photodissociation processes, where dissociation involves only one bond, molecular detachment requires the breaking of more than one existing bond in addition to the formation of one or more new ones.Understanding of these processes thus presents a great challenge to both experimentalists and theoreticians, particularly following high energy excitation.In this paper, the femtosecond time resolved dynamics resulting from the photoinduced molecular detachment of from molecules Y2 CX2Y2 (where X\H or F and Y\Cl, Br or I), are analysed with particular emphasis on the photodissociation of CH2I2 . Elimination of halogen molecules from dihaloalkanes has been investigated in several systems.1h10 In general, this pathway is observed only at high excitation energies ([9 eV) and is usually a minor channel.Style and coworkers4,5 were perhaps among the –rst to observe the 342 nm (D@]A@) emission of resulting from photolysis of I2 CH2I2 in the 125»200 nm vacuum ultraviolet region. Subsequent detailed analysis of the emission by Black6 and Okabe et al.7 revealed that the quantum yield for this channel is less than 1% at 123.6 nm.Weak emission bands in the 250»290 and 450»490 nm regions I2 were also observed. The dissociation process was CH2I2 ]CH2 X3 (3B1)]I2 D@(3%2g) found to involve an energy barrier of almost 1 eV. Fotakis et al.8 observed —uores- I2 cence in the 260»290 and 300»340 nm regions by photodissociation of upon CH2I2 excitation with two 248 nm photons.Butler et al.3 observed concerted elimination of the § Present address : George R. Harrison Spectroscopy Laboratory, Massachusetts Institute of Technology, Cambridge MA, USA. 6364 Concerted elimination dynamics from excited states mixed halogen molecule IBr from excitation of at both 210 nm and 193 nm. CH2BrI Their interpretation of the experimental data was that Rydberg and n]r* transitions were responsible for the IBr detachment at 193 and 210 nm, respectively.Recently, Marvet and Dantus10 conducted femtosecond pump»probe experiments on the photodissociation of to produce Coherent vibrational motion11 of the CH2I2 I2 . nascent fragment was observed by monitoring depletion of the I2 I2 D@(3%2g)]A@(3%2u) emission. It was determined in this experiment that the process resulting in the formation of is concerted ; two possible mechanisms were proposed. I2 This study represents a continuation of our eÜort to elucidate the photoinduced molecular detachment mechanism of and related compounds.Dispersed —uores- CH2I2 cence spectra following multiphoton excitation of and CH2I2, CH2Br2, CF2Br2 CH2Cl2 revealed the D@]A@ —uorescence of the relevant halogen product in every case.In addition to the D@]A@ —uorescence at 342 nm following dissociation of several CH2I2, I2 —uorescence bands in the 260»290 nm region were also observed. By monitoring the emission at 272 nm from the photodissociation product, both coherent vibrational I2 motion and rotational anisotropy were observed in the nascent fragment.Analysis of I2 the observed vibrational coherence indicates which electronic state of produces the I2 —uorescence at 272 nm. From the dissociation time of the molecule, the amount of kinetic energy in the fragments can be estimated. The detachment mechanism can I2 then be inferred by consideration of the partitioning of energy in the fragments. The paper will be organised as follows.In the following section a brief description of the experimental apparatus and techniques will be given. Presented in Section 3 are the dispersed —uorescence spectra and the time resolved transients resulting from the photodissociation of and along with analyses of these CH2I2, CH2 Br2, CF2 Br2 CH2Cl2 , data. In Section 4, implications of the observed fast photodissociation, rotational anisotropy and vibrational coherence are discussed. Based on these discussions, a mechanism for the halogen detachment is proposed. Since the pump excitation involves a multiphoton transition, an extension of Baskin and Zewailœs classical treatment of time dependent rotational anisotropy12 to the case of multiphoton transitions has been implemented.A derivation of this is included in the Appendix. 2 Experimental The experiments were performed using a femtosecond laser system capable of producing 60 fs pulses centered at 620 nm, with a pulse energy of 500 lJ, as described in refs. 10 and 13. Pump and probe pulses were prepared using a Mach Zhender interferometer. The beam in one arm of the interferometer was converted to 310 nm by second harmonic generation in a 0.1 mm potassium dihydrogen phosphate (KDP) crystal.Pump and probe beams were collinearly overlapped and focused in a quartz sample cell using a 200 mm focal length lens. Fluorescence from the product molecules was focused into a spectrometer. All experiments were performed on neat vapour (1»10 Torr) of the relevant alkyl halide in a quartz cell (ice baths were used when necessary).Dehydrated sodium thiosulfate was used as a scavenger to prevent the accumulation of molecular halogens. The 310 nm (pump) pulse initiates the reaction by multiphoton excitation of the sample vapour. The dissociation products are detected by —uorescence. Spectra were taken using the 310 nm laser only and the wavelength scale was calibrated with Hg lamp emission.To obtain time resolved data, the probe pulse at 620 nm was used to deplete the population of halogen molecules in the —uorescent state and transients were recorded as a function of —uorescence signal versus time delay between pump and probe pulses. At each pump» probe time delay, the signal was collected for 10 laser shots ; laser pulses with intensity more than one standard deviation from the mean were discarded.Typical transients contain data from 200 diÜerent time delays and are averages of 100 scans.Q. Zhang et al. 65 3 Results 3.A Dispersed —uorescence spectra The dispersed —uorescence spectra resulting from multiphoton excitation of CH2I2 , and at 310 nm are presented in Fig. 1 Fluorescence intensity CH2Br2, CF2Br2 CH2Cl2 has not been corrected for detection efficiency of the spectrometer.Most of the spectral features can be assigned to —uorescence from nascent halogen molecules resulting from the photodissociation. One of the most striking observations is that in all cases the principal —uorescent product is a halogen molecule in the D@ state.14h17 It can be seen Fig. 1 Fluorescence spectra of diatomic halogens from multiphoton dissociation of haloalkanes at 310 nm.All spectra were obtained by gas-phase excitation at 310 nm in a static cell. (a) From The dominant —uorescence is from the D@]A@ transition peaked at 342 nm. The region CH2I2. I2 marked (i) corresponds to the f]A, F]X and f @]B transitions. A small amount of laser scatter was observed at 310 nm. (b) From showing the D@]A@ —uorescence of (c) From CH2Br2, Br2 .The D@]A@ spectrum of is again observed. The product was found to be vibra- CF2Br2. Br2 tionally colder than in (d) From Again, a characteristic D@]A@ —uorescence CH2Br2. CH2 Cl2 . was observed, this time due to In this case the signal is weak. The increased signal from 280 Cl2 . towards 310 nm is due to laser scatter.66 Concerted elimination dynamics from excited states from the spectrum that there are also bands in the 260»290 nm region ; the CH2I2 and transitions of f (3%0g`)]A(3%1u), F(1&0u])]X(1&0g`) f@(1&0g`)]B(3%0u`) I2 —uoresce in this region.18,19 Comparison of the spectra produced from and CH2Br2 shows that although in both cases in the D@ state is a reaction product, CF2Br2 Br2 there is a diÜerence in the vibrational population.As expected, formed from the Br2 dissociation of is vibrationally colder. This is to be expected, since the di—uoro- CF2Br2 methyl fragment, having a lower frequency bending mode, will absorb more of the available energy than the methyl radical upon detachment. 3.B Time-resolved data Fig. 2 shows time resolved data obtained from the dissociation of CH2I2, CH2 Br2 , and Each transient was obtained by multiphoton excitation at 310 CF2Br2 CH2Cl2 .nm, followed by depletion probing at 620 nm from the D@ state of the relevant diatomic Fig. 2 Time resolved data from the multiphoton dissociation of alkyl halides at 310 nm followed by probing at 620 nm and detection of the D@]A@ transition. (a) Dissociation of produces CH2I2 Dynamics of the nascent molecule are probed by depletion at 620 nm and detected by D@ I2.I2 state —uorescence at 340 nm. The large signal at time zero is a multiphoton eÜect (see text). The region to the left of time zero (negative time) is when the probe pulses arrive at the sample –rst. Vibrational oscillations are visible at positive time delays. This indicates that formation is I2 concerted.(b) As with the data, the transient shows depletion at positive times, CH2I2 CH2Br2 and a strong time zero feature. Detection was at 287 nm. (c) The transient of also shows CF2Br2 depletion at positive times and a strong time zero feature. Again, detection was at 287 nm. (d) The signal is of low intensity and therefore noisy, but depletion by the 620 nm pulse at CH2Cl2 positive times is clear.Q.Zhang et al. 67 pump-probe data recorded at 272 nm, corresponding to the f]A transition (see Fig. 3 CH2I2 text). The data are plotted as a function of time delay between the pump (310 nm) and probe (620 nm) pulses and clearly show vibrational coherence. The transients were obtained for parallel and perpendicular polarization between pump and probe lasers. DiÜerences between the two transients clearly indicate rotational anisotropy in the product.I2 halogen product. The polarisation of pump and probe pulses were aligned parallel to each other. Fluorescence was detected at the wavelength corresponding to the maximum intensity of the appropriate D@]A@ transition. Fig. 2 shows that in each case, the —uorescence is depleted at positive times (probe pulse following pump, to the right of time zero).The intense features at time zero (pump and probe pulses overlapped in time) are due to a cooperative multiphoton eÜect which enhances the —uorescence signal. In this region, the molecule absorbs 310 nm photons and 620 nm photons simultaneously, which will enhance the —uorescence signal if it opens up another reaction pathway for the production of Because this process is only possible while the transition state Y2(D@).exists, it is possible to determine a maximum dissociation time from the temporal width of this feature. The dissociation time of was found to be fs,13 indicating CH2I2 qMeI2O47 that elimination is prompt and that no intramolecular vibrational redistribution (IVR) takes place during dissociation. This was further con–rmed by the dissociation time of gem-diiodobutane which was found to be fs ;13 the increase can C3H7CHI2 , qBuI2O87 be completely accounted for by considering the diÜerence in mass of the alkyl fragment.Fig. 2 also clearly shows vibrational coherence in the fragment. This is an indication I2 that the process responsible for formation of the halogen molecules is concerted, since in-phase vibrations could not result unless the molecules formed within a short time of each other and on the same region of the product potential energy surface (PES).The observed oscillations were –tted to vB10 of the D@ state.13 While vibrational coher- I2 ence in the fragment has not to date been resolved, further eÜorts to do so are Br2 underway.The low signal to noise ratio in both the spectral and dynamic data from the sample is due to rather weak —uorescence from the nascent fragment. CH2Cl2 Cl2 In order to investigate the processes producing —uorescence in the 260»290 nm I2 region, data were obtained from the sample by detection at 272 nm and at 285 CH2I2 nm. The dynamics observed for 285 nm detection are very similar to those found when68 Concerted elimination dynamics from excited states detecting the D@]A@ transition (shown in Fig. 2). However, time resolved data collected at 272 nm was noticeably diÜerent, as can be seen in Fig. 3. At this wavelength there was no intense time zero feature, which indicates that there is no cooperative process available to produce in the state which —uoresces at 272 nm.The data shown in Fig. 3 I2 were collected by setting the polarisation of the pump (310 nm) pulses to be normal to the optical table ; the polarisation of the probe (620 nm) pulses was then aligned either parallel or perpendicular to the pump. Examination of the data reveals that depletion immediately after time zero is more efficient when pump and probe pulses are polarised perpendicular to each other than when they are parallel.This indicates that the dipole of the probe transition is perpendicular to the dipole of the pump transition at time zero. It is apparent from Fig. 3 that there is a considerable degree of anisotropy in the data, most of which decays during the –rst 500 fs after formation of the photodissociation I2 product.The fast decay indicates a high degree of rotational excitation in the frag- I2 ment. Although anisotropy was observed in the data collected at 340 nm, it was not sufficiently clear for rotational analysis because the large time zero feature overwhelms any fast dynamics nearby. The time dependent rotational anisotropy is extracted from the data using the formula r(t)\ IA[IM IA]2IM (1) where is the —uorescence intensity when pump and probe lasers are polarised parallel IA to each other and the intensity when they are perpendicularly polarised.This allows IM us to study the pure rotational dynamics, with no interference from vibrational oscillations. The experimental r(t) curve is presented in Fig. 4. The average —uorescence intensity at negative time delay (probe earlier than pump) was subtracted from the parallel and perpendicular transients and proper normalisation of these transients at long time delay to their respective asymptotic limits was performed (see Appendix for Fig. 4 Time resolved anisotropy, r(t), obtained from the transients in Fig. 3. The experimental data were –tted by a least-squares algorithm taking into account the three photon excitation and the perpendicular orientation between pump and probe transition dipoles.Notice the anisotropy is close to [1/3 at time zero and reaches the asymptotic value of [1/12.Q. Zhang et al. 69 Fig. 5 Isotropic component of pump»probe data, showing the vibrational coherence at (IA]2IM) 272 nm in the product of photodissociation. The data were –tted using a least-squares I2 CH2I2 procedure to obtain a Gaussian distribution of vibrational populations centered at vB11 of the f state.This corresponds to an average period of 335 fs. details). The observed data were not manipulated in any other way before evaluating r(t). The observed r(t) is modelled using the equation r(t)\ ;i P( j )r( j, t) ;j P( j ) (2) where the expression for r( j, t) is given in Section 4C and P( j) describes the rotational population of the fragment, in this case a Gaussian function given by I2 P( j )\ 1 )n* j expC( j[jmax)2 (*j)2 D (3) Assuming a three photon excitation, a least-squares –t of the observed r(t) data yields a rotational distribution having central value and a 1/e width jmax\354^38 *j\509^52.In order to analyse the vibrational dynamics in the absence of rotational anisotropy the two transients were combined according to the formula20 Iisotropic\IA]2IM (4) The isotropic transient is shown in Fig. 5. The vibrational modulation in the data indicates that a signi–cant portion of the iodine molecules resulting from this elimination channel are vibrating in phase. A least squares –t of the pure vibrational coherence was obtained using the spectroscopic parameters of the f state.19 The observed dynamics were –tted to a Gaussian distribution of vibrational level population, centered at vmaxB 11. 3 Discussion 3.A Energetics for the elimination of halogen molecules It is clear that the photodissociation pathways of dihaloalkanes leading to molecular halogen products require energies that are well above the thermodynamic threshold ; for70 Concerted elimination dynamics from excited states the energy diÜerence is approximately 5 eV.6,7,21,22 This indicates that there are CH2I2 certain fundamental reasons why low energy excitation does not lead to molecular product formation.One of the reasons that has been advanced is based on the symmetry of the lower excited states of A dihaloalkane molecule has symmetry CH2I2.CX2 Y2 C2v (Fig. 6 shows the case for where X\H and Y\I). Transition dipole moments CH2I2 , can therefore be parallel to the X, Y or Z directions (see Fig. 6). The UV absorption spectrum of has been deconvoluted into four bands, centered around 312, 286, CH2I2 250 and 211 nm. These have been assigned to transitions to states having and B1, B1, B2 symmetries respectively.21,23,24 States with symmetry are expected to have a A1 B1 nodal plane between the iodine atoms, preventing the formation of molecular iodine products.Mixed alkyl halides, however, have been found to produce dihalogen products at lower excitation energies. Butler et al.3 observed IBr from the photodissociation of at 210 and 193 nm.The product was found to be IBr in the state. No CH2BrI 3%1 ground state product was observed. Because the symmetry of mixed dihaloalkanes is not the symmetry constraints on the formation of molecular photoproducts discussed C2v , above are not applicable, which may account for the lower energy threshold and diÜerent electronic state of the dihalogen product. Although symmetry considerations do not preclude the possibility of forming as a Y2 photodissociation product from or states, little evidence of this pathway has been A1 B2 found upon excitation at 248 and 193 nm.22 Pence et al.did –nd an unusual emission at 1.3 lm upon excitation of at 193 nm.25 They attributed this to the formation of CH2I2 highly vibrationally excited in the state, which would be expected to —uores- I2 B(3%0u`) ce at this wavelength.26 If the 1.3 lm emission is indeed a result of this process, an alternative explanation for the apparent absence of molecular halogen products on photodissociation of is that the lower electronic states are shallow compared to CX2Y2 the excess energy available for the reaction.Therefore, although their formation is possible according to symmetry considerations, these products are not observed because they are formed with energies above their dissociation limit. In our experiments we observed no evidence of iodine products in any of the lower valence states has a (I2 dissociation energy of ca. 1.5 eV in its ground state, ca. 0.5 eV in its B state and ca. 0.3 Fig. 6 3D model of a molecule, showing the principal (X, Y , and Z) and rotational axes (a, CH2I2 b, and c) as well as their transformation in symmetry.Notice that the center of mass is very C2V close to the I»I axis.Q. Zhang et al. 71 eV in its A and A@ states). An ion-pair state, which correlates to X`]X~, would be a good candidate for a dissociation product because these states are strongly bound. For halogens there are eighteen of these, corresponding to the 3P, 1D and 1S terms of the X` ion.The thermodynamic threshold for the formation of iodine in the lowest energy ion-pair state, the D@ state, is 8.43 eV.6,21,22,26 The threshold for observation of iodine in this state following the dissociation of measured by Okabe et al., was found to CH2I2 , be at 9.39 eV, indicating a 0.96 eV barrier.7 Black found the threshold to be at 8.73 eV, indicating a lower barrier.6 In either case, the elimination of from would I2 CH2I2 require an excitation energy of more than 8.5 eV.In an eÜort to elucidate the nature of the parent electronic state that correlates to dihalogen products, Okabe et al.7 compared the absorption spectrum of in the CH2I2 vacuum ultraviolet region with the —uorescence excitation spectrum in the same region (342 nm detection).The absorption and —uorescence excitation spectra both showed broad continua, which were ascribed to C»I r]r* transitions. Although features assignable to Rydberg transitions appeared in the absorption spectrum, their absence from the —uorescence excitation spectrum seems to exclude the involvement of Rydberg excitation in the photoinduced detachment process.I2 3.B Predominance of the Dº ion-pair state In this section we focus on the predominance of the state. First tier ion-pair D@(3%2g) states have equilibrium energies within 0.16 eV of each other but they also have very diÜerent spectroscopic characteristics ; for example the E]B transition occurs in the 400»436 nm region.27 The two other ion-pair families are found approximately 0.9 and 1.5 eV higher.Three photon excitation with 310 nm is equivalent to 12 eV, which translates into an excess energy of 3 eV above the observed barrier to photoinduced molecular detachment at ca. 9 eV, thus bringing all the ion-pair states within energetic reach. The observed data for photodissociation indicates that only a small percentage CH2I2 (10%, not corrected for —uorescence yield or detection efficiency) of —uorescence occurs at wavelengths between 265 and 285 nm.These wavelengths correspond to the second tier of ion-pair states, which correlate with X` The observed predomi- (3P0)]X~(1S).28 nance of the D@ state strongly suggests that electronic excitation directly correlates to this state.The ion-pair states are known to be collisionally coupled to the D@ state,14,29 but the mechanism for collisional coupling is not known. The collisional relaxation of many ion-pair states is extremely efficient, to the extent that it is used as the basis for the I2 laser.14 Perhaps the photodissociation process serves the role of a half-collision, thus forming primarily D@ products. 3.C The photodissociation mechanism In this section, we will present a detailed analysis of the photodissociation CH2I2 process. As mentioned in Section 3.A, excitation of at 310 nm yields —uorescence CH2I2 bands that closely resemble the emission from the D@, F, f and f@ states of Thus the I2 . following discussion will only consider dissociation pathways leading to formation of these states.Since production of molecules in the D@, F, f and f@ states from a thermal I2 sample of requires minimum energies of 8.38, 9.22, 9.20 and 10.2 eV respectively, CH2I2 at least three 310 nm photons are needed in each case to supply the necessary energy.21,22 A four photon excitation would provide 16 eV of energy, which is far above the ionisation threshold of so we believe that a three photon excitation is more CH2I2 , likely. Preliminary power dependence results also seem to support this conclusion. The following analysis is therefore made assuming that the excitation is a three photon process.72 Concerted elimination dynamics from excited states If a 12 eV excitation produces in the D@, F, f and f@ states, only the three lowest I2 electronic states of i.e.eV), eV), and CH2, X3 (3B1) (T0\0.0 a8 (1A1) (T0\0.39 b 8 (1B1) 1.27 eV), can be produced by the photodissociation process. Table 1 lists the (T0\ possible combinations of the and states, each of which represents a distinct I2 CH2 photodissociation channel of For each channel, Table 1 also presents the CH2I2 . minimum energy required for the dissociation process, and the remaining energy available for internal and kinetic energy of the fragments.To understand the photodissociation process properly, we must –rst gain an understanding of how internal energy in the parent molecule becomes distributed in the fragments. Most of the rotational energy about the Z axis, the symmetry axis of CH2I2 , remains as rotational energy in the fragment because the moment of inertia of is I2 I2 signi–cantly larger than that of (see Fig. 6 for de–nition of the axes). Because the CH2 center of mass of is extremely close to the iodine atoms, rotational motion of CH2I2 about the X axis will be manifested as translational motion of the fragment, CH2I2 CH2 while rotational motion about the Y axis will be partitioned upon dissociation into I2 rotation and translation.Thus gains some translational energy from the dis- CH2 CH2 sociation process but the fragment essentially gains no translational motion in the I2 center»of»mass frame. To estimate the amount of available energy that is partitioned into center-of-mass translational motion of the fragments we use a dissociation time of 47 fs for the dissociation of as an upper limit.19 Assuming an exponential form of repulsive poten- CH2I2 tial with a 1/e length parameter L , the estimated dissociation time can be related to q1@2 the amount of translational energy E as follows : q1@2\L SA k 2EBlnA4E c B (5) where c is the half-width of the energy distribution of the probe pulse (0.0125 eV for the 620 nm pulses) and k is the reduced mass of the and products, assuming they CH2 I2 form a pseudodiatomic (essentially the mass of the fragment). Using a length CH2 parameter of L \0.35 which has been found for the translational energy ”, CH3 I,31,32 is estimated to be 1.4 eV.A quantitative evaluation of the partitioning of parent rotational energy can to some extent be determined indirectly, from analysis of the rotational anisotropy of the fragments. Since clear rotational anisotropy was observed only for —uorescence at 272 I2 nm, the following discussion will concentrate on this region.Table 1 Possible combinations of and states I2 CH2 I2 states CH2 states energy required/eV21,22 available energy/eV D@(3%2g)14 X3 3B1 8.38 3.62 a8 1A1 8.77 3.23 b 8 1B1 9.65 2.35 F(1&0u`)15 X3 3B1 9.22 2.78 a8 1A1 9.61 2.39 b 8 1B1 10.49 1.51 f (3%0g`)19 X3 3B1 9.20 2.80 a8 1A1 9.59 2.41 b 8 1B1 10.47 1.53 f @(1&0g`)19 X3 3B1 10.2 1.8 a8 1A1 10.6 1.4 b 8 1B1 11.5 0.5Q.Zhang et al. 73 Fig. 4 shows anisotropy data collected at 272 nm for dissociation of Analysis CH2I2. of these data using a simple one photon pump and probe model for r(t) failed to reproduce the experimentally observed value at time zero ; one can see from Fig. 4 that the r(t) value at time zero is close to [0.3 rather than the expected value of [0.2 for a situation where pump and probe transition dipoles are perpendicular to each other. Although one can simply dismiss this discrepancy based on the level of signal to noise ratio, we suspect that it is caused by the multiphoton nature of our pump transition.A three photon pump transition would be expected to produce a greater degree of alignment than is expected for a single photon transition because it produces a (cos h)6 distribution in the nascent products rather than a (cos h)2 distribution.33 The narrower initial alignment causes the dephasing of rotational anisotropy to appear faster than it really is. In order to model time-dependent rotational anisotropy experiments in which the excitation is a multiphoton process, we extended the classical treatment by Baskin and Zewail12 (detailed derivation given in the Appendix). For an m-photon pump and one photon probe experiment, if all the pump transition dipoles are aligned parallel to each other, we –nd that the rotational anisotropy can be expressed simply as follows : r( j, t)\ 2m 2m]3 SP2[cos gj(t)]T (6) where is the time-dependent angle between the pump transition dipole at time zero gj(t) and the evolving direction of the probe transition dipole of the product.P2(x)\(3x2[ 1)/2 is the second order Legendre polynomial. The average is over the rotational degrees of freedom of the photodissociation product being probed. When the pump transition dipole is parallel to the probe dipole at time zero, one can specialize eqn.(6). Assuming that the product is a linear species and that its electronic and spin angular momenta can be neglected, one –nds rA, A( j, t)\ m 2(2m]3) (1]3 cos 2uj t) (7) where denotes the j-dependent nutational frequency of the fragment being uj\4pBj probed. B is the rotational constant of the fragment.Similarly, for the situation where the pump and probe dipoles are perpendicular to each other at time zero, one obtains rA, M( j, t)\[ m 4(2m]3) (1]3 cos 2uj t) (8) Application of eqn. (8) to our case, i.e. a three-photon pump with perpendicular pump» probe dipole orientation, gives rise to the following expression for the j-averaged rotational anisotropy : rA, M(t)\[ 1 12 [1 4 ;j P( j)cos 2uj t ;j P( j) (9) Here P( j) stands for the relative population of level j.It is obvious from eqn. (9) that which is in close agreement with the observed value (see Fig. 4). We have r(0)\[13 , –tted the observed rotational anisotropy data shown in Fig. 4 to eqn. (9). The best least-squares –t is found for a rotational distribution centered at and jmax\354^38, width *j\509^52.This implies that the average rotational energy of the product I2 molecules is 0.3 eV. To facilitate the discussion, Table 2 lists certain structural and spectroscopic information for and As we can see, the B and C rotational constants of the CH2I2, CH2 I2 . ground state are very similar to the B rotational constant of with a value of CH2I2 I2,74 Concerted elimination dynamics from excited states Table 2 Structural and spectroscopic data for and CH2I2, CH2 I2 RIhI/” uIhI/cm~1 HCH/degrees uHCH/cm~1 A/cm~1 B/cm~1 C/cm~1 CH2I2 X 3.579b 112.7 0.710 0.020 0.019 CH2 X3 c 134.0 963.1 73.81 8.45 7.18 CH2 a8 c 102.4 1352.6 20.14 11.16 7.06 CH2 b 8 c 140 357 7.57 I2 D@15 3.5944 103.960 0.020563 I2 Fd 3.596 96.313 I2 f19 104.1447 I2 f @19 96.980 a Values calculated by the HF/3-21G method.b Z. Kisiel, L. Pszczoç lkowski, W. Caminati and P. G. Favero, J. Chem. Phys., 1966, 105, 1778. c G. Herzberg, Molecular Spectra and Molecular Structure III, Reprint edition, Krieger, Malabar 1991. d T. Ishiwata, T. Kusayanagi, T. Hara and I. Tanaka, J. Mol. Spectrosc. 1986, 119, 337. approximately 0.02 cm~1. This gives a Boltzmann distribution at room temperature centered at jB90.Thus for a room temperature sample of the average rotation- CH2I2 , al quantum number is expected to be of the order of 100. This is much smaller than the measured rotational distribution of the products. Conservation of angular momentum I2 demands that the diÜerence, about 250 +, be taken up by the fragment. CH2 The rotational excitation of the fragment can be accounted for if one of the two I2 CwI bond breaking processes happens faster than the other.This would exert a large torque on the fragments, causing them to exhibit counter rotation and a high degree of rotational excitation. The strong torque and available excess energy would break the second CwI bond within 50 fs of the –rst. This corresponds to the concerted sequential mechanism shown in Fig. 7. By contrast, if the photodissociation process proceeded by the concerted simultaneous mechanism, one would not expect to observe rotational excitation in either fragment. If all of the 250 + of angular momentum were to go into the rotation of the CH2 fragment, a simple BJ2 argument predits that the amount of rotational energy would be of the order of 60 eV! This is clearly impossible ; in fact, much of the torque exerted on will cause translational excitation.The 250 + de–cit in angular momentum must CH2 then be accounted for by a non-zero impact parameter b using L\kvb, where v is the relative velocity of the fragments. Assuming an impact parameter of 2 the trans- ”, lational energy of the fragment can be estimated to be 2.3 eV.On the other hand, if CH2 we assume an impact parameter of 3 the estimated translational energy would ”, CH2be 1.0 eV. Thus the estimated translational energy is very sensitive to the impact parameter, a quantity that depends critically upon the details of the dissociation mechanism, such as at what point the second CwI bond breaks and in which direction the two fragments —y apart.If comparison is made with the previous 1.4 eV estimation of the translational energy, we –nd that the impact parameter is approximately 2.6 CH2 ”. Since the IwI interatomic distance in ground state is rather close to the bond CH2I2 lengths in the D@, F, f and f@ states of the molecule, signi–cant vibrational excitation in I2 the fragment is not expected.However, because the HCH angle in ground state I2 diÜers signi–cantly from the bond angle of particularly in the and CH2I2 CH2, X3 b 8 states, vibrational excitation should be expected in the photofragment. This could CH2 represent a signi–cant amount of energy, especially when one considers the high vibrational frequencies in electronic states. CH2 For most of the pump»probe data we collected, only a few vibrational oscillations were observed (see Fig. 5). It is not certain whether one could observe more if the signal-to-noise ratio was improved, or whether the dephasing is due to the nature of theQ. Zhang et al. 75 Fig. 7 Schematic diagram of possible reaction mechanisms for the photoinduced molecular detachment of from Two concerted processes are depicted.In the concerted sequential I2 CH2I2 . mechanism the –rst carbon»iodine bond breaks and an iodine»iodine bond is formed while the second iodine is still attached to the carbon. This –rst step imparts a large torque on the CH2 fragment. Subsequent breaking of the second carbon»iodine bond completes the reaction. This mechanism produces iodine molecules with a high degree of rotational angular momentum (see text).The time scales given for this process are based on our experimental results. The concerted simultaneous mechanism involves the breaking of the two carbon»iodine bonds simultaneously with formation of an iodine»iodine bond. This would be expected to produce molecular iodine products with very little rotational angular momentum in direct contrast to our experimental –ndings.nascent vibrational population. For the present, we will simply model the vibrational motion of the fragment as a classical anharmonic oscillator with the observed depha- I2 sing accounted for by anharmonicity. Assuming a Gaussian distribution of vibrational level populations, a least squares –t to the pure vibrational coherence data yields the –t shown in Figure 5.The –t was obtained using a vibrational level distribution that is centered around v\11 of the f state. Fits were also attempted using the parameters I2 of the F and f @ states, but did not match the data as well. This suggests that the —uorescence detected at 272 nm originates from the f]A transition. If the above arguments are correct, the fragments contain at least 1.7 eV of translational and rotational energies.Therefore, if we assume that excitation is a threephoton process and that is formed in the f state, the formation of can be I2 CH2 (b8 ) ruled out because there is not enough energy available (see Table 1). If this is the case, we are left with two choices, i.e. (f ) and (f ). Which of the two CH2 (X3 )]I2 CH2 (a8 )]I2 channels is responsible for photodissociation of to yield —uorescence at 272 nm CH2I2 I2 remains to be investigated.Thus, much of the following discussion is meant to be taken more as speculation than as matter of fact. Fig. 3 clearly shows that there is a high degree of anisotropy as a result of the CH2I2 photodissociation process. If each of the transition dipoles corresponding to the three photon pump transition had diÜerent orientations, one would not expect the anisotropy to be so clear.33 Thus, the three transition dipoles are likely to be parallel to each other, particularly when excitation is by a femtosecond pulse because this is the most favourable situation for absorption.Since absorbs at 310 nm and leads to a state,21 CH2I2 B1 one expects resonance enhancement if the three photon process involves the state as B176 Concerted elimination dynamics from excited states the –rst transition.If this is the case, the dissociative state reached is expected to be a B1 electronic state at about 12 eV above the ground state. A transition in this molecule B1 is aligned along the I»I direction (see Fig. 6) ; in this case the probe transition would be perpendicular to the bond.However, as we have already discussed, formation of I2 I2 from a state of is symmetry forbidden. It is also possible that there is a B1 CH2I2 two[photon resonance enhancement transition from the ground state, in which case (parallel to the Z axis) and (perpendicular to the plane) symmetries would be A1 B2 CH2 allowed as well. It is possible that the molecular detachment proceeds by a charge transfer type mechanism such that one of the iodine atoms gains electron density while the other loses it.The electron density redistribution would have the eÜect of generating a Coulombic attraction between the two iodine atoms while at the same time weakening the two CwI bonds. This is also supported both by the fact that the halogen states that have been observed are all ion-pair, i.e.charge transfer, states and that molecular dissociation products are not observed until the excitation energy approaches the ionisation threshold of the molecule. To summarise the above discussion, we can construct the following picture about how we think of the photodissociation process of at an excitation energy of 12 CH2I2 eV.A three (310 nm) photon transition excites molecules from the thermally CH2I2 populated ground electronic state to a dissociative state ; the transition may be of a charge transfer type. One of the CwI bonds breaks and a bond forms between the two iodine atoms (see concerted sequential mechanism in Fig. 7) ; this generates an enormous amount of torque on the and moieties to tear the second CwI bond apart.CH2 I2 Dissociation occurs within 50 fs of the initial excitation. The remaining energy from the 12 eV initially deposited in the molecule is distributed between the photofrag- CH2I2 ments in the following fashion. The fragment gains a tremendous amount of trans- CH2 lational energy and a sizeable degree of vibrational excitation but little rotational or electronic excitation.On the other hand, the fragment is left in a highly excited elec- I2 tronic state with a large amount of rotational excitation but only moderate vibrational excitation and very little translational energy. This mechanism is quite in keeping with the mechanism proposed by HoÜmann and coworkers,9 although the latter was proposed for dissociation from low-energy potential surfaces.The concerted simul- CX2Y2 taneous mechanism shown in Fig. 7 would not yield the high rotational energies observed experimentally. 4 Conclusions Molecular halogen detachment processes have been investigated for methylene iodide and some related haloalkanes. It was found that multiphoton excitation of these molecules at 310 nm gives rise in every case to halogen molecules in the D@ state.Femtosecond time-resolved experiments performed on these dihaloalkanes show that the photoinduced molecular detachment processes are extremely fast (\60 fs). Selective detection of —uorescence from photodissociation products at 340 nm, 286 nm CH2I2 and 272 nm reveals characteristic vibrational coherence, indicating that the reaction I2 mechanism is concerted.The 272 nm transients also clearly demonstrate fast decaying rotational anisotropy. Least squares –t of the anisotropy to a Gaussian distribution of rotational level occupations reveals a distribution of rather high rotational levels, with the distribu- I2 tion center at around j\350 and a width of *j\500. This high degree of rotational excitation has been explained by invoking the following so-called concerted sequential I2 detachment mechanism (see Fig. 7). When is excited to a highly electronically CH2I2 excited dissociative state, one of the two CwI bonds breaks and an IwI bond forms. Then the second CwI bond ruptures, leaving rotationally excited and translationally I2Q. Zhang et al. 77 hot fragments. This occurs within 50 fs of the initial excitation. The high degree of CH2 rotational excitation in the product rules out the concerted simultaneous mechanism I2 shown in Fig. 7 as a possible reaction pathway; if this were the process that occurs, C2V symmetry would be maintained throughout the dissociation and there would be no rotational excitation in either fragment. Although the 272 nm —uorescence resulting from excitation of can in principle CH2I2 be attributed to emission from any of three ion-pair states of (F, f, or f @), analysis of I2 the vibrational coherence at this wavelength suggests that the f]A transition is the source of this —uorescence.The electronic state of the fragment has been deter- CH2 mined to some extent for this particular dissociation channel by energetic considerations.Assuming three-photon excitation of and taking into consideration the CH2I2 high translational energy imparted into the fragment and the relatively high rota- CH2 tional energy in the fragment, we have argued that the fragment is likely to be in I2 CH2 its ground or –rst excited (a8 ) electronic state. Time-of-—ight mass spectrometry fol- (X3 ) lowing photodissociation of in the molecular beam will allow us to analyse the CH2I2 –nal electronic state of the fragments.Future experiments on will also allow CH2 CF2I2 us to obtain electronic and vibrational information by detection of the UV —uorescence of the CF2 fragment. We would like to thank Professor S. Stolte and Dr S. Baskin for helpful discussions. This work was partially supported by a Camille and Henry Dreyfus New Faculty Award. M.D.is a Beckman Young Investigator and a Packard Science and Engineering Fellow. Appendix In this appendix, a brief formulation of the rotational anisotropy r(t)\ ;j P( j)r( j, t) ;j P( j) (A1) will be presented for experiments with an m-photon pump transition and one-photon probe. In eqn. (A1), r( j, t) is the anisotropy speci–c to a particular j level with population P( j) of the fragment being probed.The following derivation assumes that all dipoles of the pump transition are parallel to each other. Extension of eqn. (8) from Baskin and Zewail12 to such cases, gives Id( j, t)PS[1]2P2(cos a)]m[1]2P2(cos d)P2[cos gj(t)]P2(cos a)]T (A2) where a denotes the angle between the polarization of the pump pulse and the pump transition dipole, d the angle between the pump and probe polarizations and the gj(t) angle between the pump and the probe transition dipoles.Since the probe dipole rotates with the fragment being probed, is dependent on the rotational quantum number j gj(t) and is a function of time. The average is over certain rotational degrees of freedom, such as the angle a. The second order Legendre polyomial P2(x)\(3x2[1)/2.Note that Thus, raising the –rst term in eqn. (A2) to the 1]2P2(cos a)\3 cos2a. power of m accounts for the transition probability of the m-photon pump excitation. Substituting which is independent of a, eqn. (A2) can be recast m\P2(cos d)P2[cos( j(t)], as Id( j, t)P 1 2 P0 n da sin a[1]2P2(cos a)]m[1]2mP2(cos a)] \a]bm (A3)78 Concerted elimination dynamics from excited states where the average over a in eqn.(A2) is now explicit. The integral yields two terms, one of which is linear with m and the other independent of it. The coefficients a and b can be evaluated in terms of m: a\2 3m 2m]1 b\8m 3m (2m]1)(2m]3) (A4) When the polarisations of pump and probe are parallel to each other d\0, which gives d)\1. When the pump and probe are polarised perpendicular to each other, on P2(cos the other hand, we have d\n/2 and d)\[1/2.Recalling that and P2(cos Id\a]bm g), the result is m\P2(cos d)P2(cos IA( j, t)Pa]bP2[cos gj(t)] IM( j, t)Pa[ b 2 P2[cos gj(t)] (A5) The time-dependent anisotropy is then obtained by substitution of eqn. (A5) into eqn. (A1) to give r( j, t)\ b 2a SP2[cos gj(t)]T\ 2m 2m]3 SP2[cos gj(t)]T (A6) For the case of m\1, i.e.one-photon pump and one-photon probe, (A6) reduces to the well known expression for r(t).12 It is interesting to note that the anisotropy increases with the number of photons involved in the transition. This can be attributed to the sharpening of the initial alignment when all transition dipoles in a multiphoton transition are parallel to each other.In order to express the time dependent angle between the pump dipole (at t\0) and the evolving probe dipole g(t), knowledge of the initial relative orientation between these two dipoles is necessary. The following treatment will concentrate on two particular cases, g(0)\0 and g(0)\p/2. The former has a probe dipole parallel to the pump dipole at time zero ; this is the (p, p) case.When g(0)\p/2, the probe dipole is perpendicular to the pump dipole at time zero ; this is the (p, o) case. We will assume that the fragment being probed is a linear species and that its electronic and spin angular momenta are negligible compared with its rotational angular momentum. With these assumptions in mind, we can write (see Baskin and Zewail12 for details) cos gj A, A(t)\cos uj t cos gj A, M(t)\cos t0 sin uj t (A7) where is the rate of nutation of the fragment with a rotational quantum uj\4pBj number j about its total angular momentum j and B is the rotational constant of the fragment.The quantity in eqn. (A7) denotes the initial angle about the –gure axis. t0 Substituting eqn. (A7) for the parallel case into eqn. (A6), we –nd the rotational anisotropy for the (p, p) case to be rA, A( j, t)\1 2 m 2m]3 (1]3 cos 2uj t) (A8) Substitution of eqn.(A7) for the perpendicular case to eqn. (A6) and noting that averaging cos2 over (from 0 to 2p) yields 1/2, we obtain the rotational anisotropy for the t0 t0Q. Zhang et al. 79 (p, o) case to be rA, M( j, t)\[1 2 m 2m]3 (1]3 cos 2uj t) (A9) This –nal expression is very similar to eqn.(A8) except for a factor of [1/2. The overall reduction in alignment arises from diÜerences in the initial population being described by cos2mh for parallel transitions or sin2mh for perpendicular transitions.33 The overall experimentally measurable rotational anisotropy r(t) can be evaluated as an average of the j-dependent r( j, t) in eqn. (A6), eqn.(A8), or eqn. (A9) using eqn. (A1). If the j-dependent rotational anisotropy r( j, t) in eqn. (A1) is substituted with the expression in eqn. (A8) or (A9), we obtain the following expressions of rotational anisotropy for the (p, p) and the (p, o) cases : rA. A(t)\1 2 m 2m]3 ]3 2 m 2m]3 ;j P( j) cos 2uj t ;j P( j) rA, M(t)\[1 4 m 2m]3 [3 4 m 2m]3 ;j P( j)cos 2uj t ;j P( j) (A10) The asymptotic limits at t\O are m/[2(2m]3)] for the (p, p) case and [m/ [4(2m]3)] for the (p, o) case.References 1 H. Okabe, in Photochemistry of Small Molecules, wiley, New York, 1978, pp. 73»80. 2 H. Okabe, A. H. Laufer and J. J. Ball, J. Chem. Phys., 1971, 55, 373. 3 L. J. Butler, E. J. Hintsa, S. F. Shane and Y. T. Lee, J. Chem. Phys., 1987, 86, 2051. 4 P. J. Dyne and D. W.G. Style, J. Chem. Soc., 1952, 2122. 5 D. W. G. Style and J. C. Ward, J. Chem. Soc., 1952, 2125. 6 G. Black, Research on High Energy Storage for L aser Ampli–ers, Stanford Research Institute Report MP76-107, 1976. 7 H. Okabe, M. Kawasaki and Y. Tanaka, J. Chem. Phys., 1980, 73, 6162. 8 C. Fotakis, M. Martin and R. J. Donovan, J. Chem. Soc., Faraday T rans. 2, 1982, 78, 1363. 9 S. R. Cain, R. HoÜmann and E. R. Grant, J. Phys. Chem., 1981, 85, 4046. 10 U. Marvet and M. Dantus, in Femtochemistry, ed. M. Chergui, World Scienti–c, Singapore, 1996, p. 134; U. Marvet and M. Dantus, Chem. Phys. L ett., 1996, 256, 57. 11 The term coherence is used here to imply that molecules share a common vibrational phase as determined by their vibrational frequency. 12 J. S. Baskin and A. H. Zewail, J. Chem. Phys., submitted; Q. Zhang, U. Marvet and M. Dantus, J. Chem. Phys., submitted. 13 U. Marvet, Q. Zhang, E. J. Brown and M. Dantus, manuscript in preparation. 14 J. B. KoÜend, A. M. Sibai and R. Bacis, J. Phys. (Paris), 1982, 43, 1639 and references therein. 15 J. Tellinghuisen, J. Mol. Spectrosc., 1982, 94, 231; X. Zheng, S. Fei, M. C. Heaven and J. Tellinghuisen, J. Chem. Phys., 1992, 96, 4877. 16 A. Sur and J. Tellinghuisen, J. Mol. Spectrosc., 1981, 88, 323. 17 P. C. Tellinghuisen, B. Guo, D. K. Chakraborty and J. Tellinghuisen, J. Mol. Spectrosc., 1988, 128, 268. 18 U. Heemnan, H. Knockel and E. Tiemann, Chem. Phys. L ett., 1982, 90, 17. 19 P. J. Wilson, T. Ridley, K. P. Lawley and R. J. Donovan, Chem. Phys., 1994, 182, 325. 20 R. G. Gordon, J. Chem. Phys., 1966, 45, 1643. 21 M. Kawasaki, S. J. Lee and R. Bersohn, J. Chem. Phys., 1975, 63, 809. 22 S. L. Baughcum and S. R. Leone, J. Phys. Chem., 1980, 72, 6531. 23 A. Gedanken and M. D. Rowe, Chem. Phys., 1979, 36, 181. 24 J. B. KoÜend and S. R. Leone, Chem. Phys. L ett., 1981, 81, 136. 25 W. H. Pence, S. L. Baughcum and S. R. Leone, J. Phys. Chem., 1981, 85, 3844. 26 J. Tellinghuisen, J. Quant. Spectrosc. Radiat. T ransfer, 1978, 19, 149. 27 K. Wieland, J. B. Tellinghuisen and A. Nobs, J. Mol. Spectrosc., 1972, 41, 69. 28 K. Lawley, P. Jewsbury, T. Ridley, P. Langridge-Smith and R. Donovan, Mol. Phys., 1992, 75, 811.80 Concerted elimination dynamics from excited states 29 A. L. Guy, K. S. Viswanthan, A. Sur and J. Tellinghuisen, Chem. Phys. L ett., 1980, 73, 582. 30 M. Dantus, M. J. Rosker and A. H. Zewail, J. Chem. Phys., 1988, 89, 6128. 31 M. Shapiro and R. Bersohn, J. Chem. Phys., 1986, 90, 3644. 32 M. Shapiro, J. Chem. Phys., 1980, 73, 3810. 33 R. N. Zare, Mol. Photochem., 1972, 4, 1. Paper 7/05759H; Received 6th August, 1997

ISSN:1359-6640    

DOI:10.1039/a705759h

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss. 1997 108 81»100 General Discussion Dr Hunter communicated regarding the Spiers Memorial Lecture You mentioned the timescales over which diÜerent molecular processes take place this being about h/*E where *E is the energy change involved in the process and h is Planckœs constant. For electronic transitions this ranges from ca. 1 to 5 fs whereas nuclear rearrangements take longer about 10 fs for light loosely bound nuclei up to several hundred fs for heavy and more tightly bound nuclei. For relaxation processes involving many vibrational periods (in clusters and in large molecules such as proteins) the timescale of the process may be tens or hundreds of picoseconds. Underlying these molecular timescales is the time for photon absorption to take place.This is believed to be the period of oscillation of the light q\l~1\j/c (ref. 1). For UV photons (j\150 nm) j/c\0.5 fs and for IR photons (j\1500 nm) j/c\5 fs. This photon absorption timescale is a lower limit on the width of the pulses of radiation used in experiments to explore molecular processes. In the study of molecular processes produced by multiphoton absorption one should distinguish between true multiphoton absorption (in which the photons are absorbed simultaneously i.e. within one optical period1\j/c) and cascading in which an excited state populated by an initial single or multiphoton absorption subsequently absorbs more photons to produce the chemical change being studied. Experimentally cascading is not readily distinguished from simultaneous multiphoton absorption.However the latter has an intensity threshold I\4nhc2/j4 e.g. I\1 Mwatt cm~2 for j\523 nm (ref. 2) whereas cascading is dependent upon the existence of intermediate molecular states and their lifetimes. Thus varying the light intensity within the reaction zone provides a parameter for controlling the type of multiphoton absorption produced. 1 G. Mainfray and C. Manus in Multiphoton Ionisation of Atoms ed. S. L. Chin and P. Lambropoulos Academic Press New York 1984. 2 G. Hunter and R. L. P. Wadlinger Phys. Essays 1989 2 158 (on p. 165). Prof. Jortner communicated in reply Dr Hunter has raised some issues concerning the timescales for non-radiative dynamics and for optical excitation. The theory of intramolecular and condensed phase relaxation dynamics relates the lifetime q of a metastable state to the (homogeneous) linewidth C of the resonance and not to the energy change *E involved in the process.The lifetime is q\+/C; for a single resonance C\2p o V o 2o where V is the matrix element causing the transition and o is the density of states in the dissipative continuum or quasicontinuum. What is the temporal limit for dynamic processes ? This is determined by the correlation parameter (s) css{\SV sl Vls{T/[SV sl2TSV s{l2T]1@2 (introduced by Bixon and Jortner1). For a ìsmoothœ decay channel involving slow energy dependence of sl V (vs. w E e sl gss{B1 as is the case for predissociation or autoioniza- expect correlated coupling i.e. l) tion for a ìnon-smoothœ decay channel where V exhibits irregular energy variation i.e.o gss{ o@1 which is the case for non-radiative decay into Franck»Condon quasicontinuum in large molecules and for non-adiabatic processes in the condensed phase. For relaxation into a smooth dissipative channel the relaxation rate k is limited (due to interference between resonances) by the level spacing of vibronic states in the initial electronic manifold (i.e. the vibrational frequency u in energy units) i.e. kOu/h. For a ìnon-smoothœ quasicontinuum interference eÜects between resonances are eroded and temporal limits kPV 2[u/h can be realized. Thus the characteristic times for 81 82 General Discussion dynamics can be faster than the periods of vibrational motion. This is the signi–cance of ìdynamics on the timescale of nuclear motionœ.The argument regarding the timescale for photon absorption is grossly overqF) and not by j/c (see for example ref. 2) ; only q and +/C are diÜerent can one separate optical excitation and simpli–ed. The response of a two-level system (model atom or molecule) to an electromagnetic –eld results in Rabi oscillations and no energy absorption which occurs only in the presence of (radiative or non-radiative) dissipation. The temporal response of an atom or molecule to a (weak) electromagnetic –eld is determined by the autocorrelation function of the –eld (characteristic time when the timescales dynamics. F 1 M. Bixon and J. Jortner J. Chem. Phys. 1997 107 1970. 2 S. Mukamel and J. Jortner J. Chem. Phys. 1975 62 3609.Prof. Beddard opened the discussion of Prof. Flemingœs paper In the X-ray structure of the light harvesting complex you showed that there are many bacteriochlorophyll molecules forming a ring like structure. Examination of this structure revealed that these chlorophyll molecules are not evenly spaced but exist in pairs having only a slightly larger separation to the next pair than is the separation between a pair. This would seem to indicate that electronic coupling should be extensive around the structure. On the other hand you described your experiments which showed that the exciton could satisfactorily be described as covering only a pair of molecules. I am not clear therefore as to how one should view this. Is it the case that because of some particular detail of the geometry the near neighbour oÜ-diagonal coupling terms in the matrix describing the interaction are sufficiently large compared to other terms that pair-wise coupling dominates ; or is it that random static site eÜects vary the values of both the diagonal and oÜ-diagonal coupling; or is it that no such particular eÜects are occurring but dynamic eÜects such as those caused by photons can so eÜectively scatter to exciton states that they appear to be localised after only a few femtoseconds; or are none of these eÜects important or a proportion of each? Prof.Fleming responded The degree of localization depends on several factors the strength of the electronic coupling the degree of disorder (diagonal i.e. site and oÜdiagonal i.e.coupling) the strength of coupling to the phonons the timescale of phonon relaxation the temperature and the timescale on which the question is to be answered. Our results very clearly reveal the presence of signi–cant site energy disorder (ca. 300»400 cm~1). We know little about disorder in the couplings. Our ab initio molecular orbital calculations based on the LH2 structure gave a small alternation in the coupling within and between ab dimer pairs. The calculated coupling at the current level of basis set (3-21 G*) is about 300 cm~1 (intradimer) vs. about 260 cm~1 (interdimer). The protein response (reorganization energy) is very small but also very fast. Our temperature dependent data (300 K vs. 40 K) strongly imply that the homogeneous contribution to the line broadening (exciton localization) is small at room temperature since making it substantially smaller by going to 40 K has negligible eÜect on the photon echo peak shift.[Lowering the temperature does shift some members of the population from the dynamical group»able to transfer energy rapidly into the static group»unable to transfer energy (because it is uphill) but this is quite consistent with a static inhomogeneous distribution.] Further our comparison of LH1 with the B820 dimeric subunit strongly implies that the basis electronic unit is the same in both cases. If the excitation were strongly delocalized on the energy transfer timescale the motional narrowing would mean that the coupling constants to the nuclear degrees of freedom would be underestimated for the dimer subunit.This is not the case. Thus to sum up while the localization/delocalization issue remains controversial my current opinion is that static disorder localizes the excitation on roughly two bacterio-83 General Discussion chlorophyll (Bchl) molecules within a few tens of fs. Finally I note that the superradiance results of Monshower et al.1 also imply a delocalization over roughly two pigments in these systems. 1 R. Monshower M. Abrahamsson F. van Mourik and R. van Grondelle J. Phys. Chem. 1997 101 7241. Prof. Gerber said Prof. Schulten and co-workers1 have proposed that excitonic delocalization as implied by the structure of LH2 explains the evolutionary advantage of the structure. Can you see any advantage to the delocalization across two units that you have found for excitons ? 1 X.Hu D. Xu K. Hamer K. Schulten J. Koé pke and H. Michel Protein Sci. 1995 4 1670. Prof. Fleming answered I think the circular structures arise simply from the selfassembly of the dimeric subunits. The geometry controls the couplings and the typical distribution of side chain conformations etc. in proteins controls the inhomogeneity. The degree of delocalization (referred to above) then follows. I see no particular value in the precise value of delocalization length that appears. Prof. Jortner commented The structure»function relationship between the ring structures of the light harvesting photosynthetic antennas LH1 at LH2 of purple bacteria pertains to the central issue of universality.The structure of antennas is not universal e.g. other bacteria are characterised by diÜerent antenna structures and so is the structure of the plant photosynthetic antenna. This is in contrast to the universal structure of the reaction center of bacteria and plant photosystem II. Accordingly any conclusions concerning the general biological functions of the highly symmetric LH1 and LH2 should be precluded. Of course these are fascinating systems for the exploration of ultrafast excited state dynamics. Dr Fidder asked Given the pulse duration of about 20 fs in your experiments youœre bound to create a coherent superposition of exciton states in both the light harvesting complexes and B820. How does this aÜect your estimate of the delocalisation length from the experiment? Prof.Fleming replied Indeed we probably prepare delocalized states but as I discussed in response to Prof. Beddardœs question disorder rapidly localizes the excitation in the ensemble. The question of what happens at very short times is still open and is very intriguing. Prof. Butler said Let me try to understand what you and Dr Gould are trying to do. Are you taking as your basis con–gurations where the electronic excitation is localized on one dimer subunit on the ring or localized on another or another and then another and then calculating con–guration interaction (CI) matrix elements between these locally excited con–gurations to try to get the ìV1,2œ for reproducing the 90 fs decay time in the experiment? Would you comment on whether orthogonality of orbitals in the basis is imposed or not; often one needs to use a natural orbital basis not an orthonormal basis if you need locally excited con–gurations to do the CI between but perhaps in your case since your locally excited con–gurations are coupled only by 2e~ matrix elements the orthogonality of the MOs in the RHF (restricted Hartree»Fock) basis is already there i.e.the natural orbital description is already an orthogonal one»no 1e~ covalent or exchange contributions. Prof. Fleming responded In essence the basis con–gurations are taken to be molecular orbitals localized on each Bchl-a monomer. Thus this is a non-orthogonal basis (i.e. electron transfer and electron exchange to any number of permutations are admitted to the calculation).In practice this is accomplished by calculating the electronic excited 84 General Discussion states of the dimer unit ; it can be demonstrated that such a CI-singles calculation is isomorphic to the localized molecular orbital based on theory developed by Harcourt et al.1 We are calculating the electronic coupling between excited state donor and ground state acceptor. 1 R. D. Harcourt G. D. Scholes and K. P. Ghiggino J. Chem. Phys. 1994 101 10 521. Dr Gould added The molecular orbital pictures shown by Prof. Fleming are from single point SCF calculations performed by us on part of the peripheral light harvesting complex (LH2) of purple photosynthetic bacteria. The calculations involve a pair of closely interacting Bchl-a molecules (B850) one Bchl-a (B800) and one of the two carotenoid (Car) molecules which make close contact with the B800 and one of the B850 chromophores.The cartoons shown by Prof. Fleming illustrate the HOMO and LUMO orbitals obtained at the SCF level with a 3-21G* basis set these can be used in the rationalisation of the method of energy transfer within the system. We are currently investigating the excited states of these systems using the con–guration interaction singles (CIS) method. Dr van der Zande asked The mysterious aspect regarding photosynthesis and many other biological processes from the point of view of a chemical physicist is the ìconservationœ of potential energy during a spatially delocalized overall process. Has ultrafast spectroscopy brought essential progress with respect to the question above in other words ìhow does nature prevent IVR? œ.Prof. Fleming answered This is a very interesting point. In both light harvesting (i.e. energy transfer) and primary charge separation (i.e. electron transfer) the reorganization energy is extremely small. In B820 (the dimeric subunit of LH1 I discussed) the Stokes shift is only 80 cm~1. The origins of this very weak electron»phonon coupling are not completely clear to me. The chromophores are large electronically delocalized molecules which are very rigid. The protein is non-polar (to quote the late Gerhard Closs ìYou want to run photosynthesis in butter not waterœ). Perhaps the ligation to the magnesium rather than the normal liquid/glass packing around a solute is signi–cant.Also timescale is important here. The reorganization energy is very small on the relevant timescale (i.e. 100 fs»10 ps). This was a point made many years ago by Miller.1 Perhaps this is another reason why the primary processes are so fast. 1 J. R. Miller in Antennas and Reaction Centres of Photosynthetic Bacteria ed. M. E. Michel-Beyerle Springer Berlin 1985 p. 234. Dr Klug added The free energy available to a photosynthetic system has to be conserved and therefore it is correct that extensive IVR or intersystem crossing would cause problems. The lowest singlet excited state of chlorophyll-a in ether has a lifetime of 6 ns a 66% triplet yield and a 33% singlet yield and therefore shows little or no IVR. Moreover it has a very small Stokes shift which means that loss of energy via environmental relaxation is also avoided.For isolated chlorophyll it is therefore triplet formation which is the dominant loss mechanism and the forward reactions of photosynthetic systems have to compete with the singlet state lifetime of 6 ns which is limited by triplet formation. It is straightforward to produce electron transfer reactions that are much faster than this and overall the system functions simply by ensuring that the required forward electron transfer reactions are always faster than competing reactions. The –rst electron transfer in photosynthetic systems has a rate constant of about 1012 s~1 in order to compete with various loss pathways. Subsequent electron transfers have rates of 1010»103 s~1.These slower reactions can be thought of crudely as charge motion through a dielectric medium as the electron tunnelling matrix element between the primary electron donor anion and secondary or tertiary cation then becomes far too small to allow charge recombination in a single step. General Discussion 85 Prof. Simons asked A central aspect of this Discussion is the manner in which the electronically excited chromophore interacts with its environment. The environment may be chemically bound to the chromophore e.g. in a large polyatomic molecule; or bound via weaker interactions e.g. through H-bonding in a biological system; or it may be non-bonded e.g. when the chromophore is located within or adsorbed on a rare gas environment. The interaction between the chromophore and its nearest neighbours could be described as ìthrough bondœ or ìthrough spaceœ is this distinction a fundamental one or simply one of degree? Prof.Fleming answered I think the distinction is simply one of degree. The exponential coupling of electron transfer donor»acceptor complexes probably falls oÜ faster in solvent than along r-bonded networks but the fundamental mechanism is likely to be identical. Prof. Fleming opened the discussion of Dr Meechœs paper What is known about the relative magnitudes of orientational and interaction induced (II) contributions to the optical Kerr eÜect (OKE) signal ? I expect that the II contribution to methanol is small yet the correspondence with the —uorescence Stokes shift is better in the case of aniline.Dr Meech responded It is very difficult to separate in any rigorous fashion the II and orientational contributions to the OKE signal. This is perhaps its main shortcoming with regard to the calculation of solvation dynamics where only the orientational response is thought to be important. MD calculations do allow a separate estimate of II and orientational contributions and these have been made for methanol (ref. 20 and 51 of our paper). The results suggest that orientational dynamics dominate the OKE response. This might be expected since methanol is only weakly polarisable and II eÜects re—ect dipole»induced-dipole interactions. For aniline no similar calculations have been made. Signi–cant II contributions might be expected since aniline is both polarisable and polar.Our aniline spectral density was analysed (somewhat arbitrarily) in terms of a librational [eqn. (8)] and II [eqn. (7)] part where the latter was smaller but signi–cant (Fig. 3 of our paper). It is then correct to say that the model for the calculation of S(t) should be more accurate for methanol than aniline while we –nd the opposite. This suggests that some of the modelœs approximations are not really appropriate in the methanol case. It is possible that the solute does indeed have some in—uence on the liquid such that the pure solvent response would not be an exact model for dynamics in the –rst solvation shell which dominates the solvation response. Prof. Fleming commented In recent 2D Raman work1 we studied whether decompositions of the 1D spectral density of CS using for example three Brownian oscillators could reproduce our 2D data at 298 K and 165 K.By using polarizability 2 coupling we could reproduce the low temperature data with three coupled Brownian oscillators. However we could not reproduce the room temperature data. We conclude that only when a complete separation of timescales between fast and slow motions exists can such a model be used. In the —uid no separability of the motions exists and even coupled collective coordinates such as the Brownian oscillators do not adequately describe the underlying microscopic behavior. Thus decompositions of 1D spectral densities of liquids obtained via optical Kerr or other methods should be regarded skeptically at present.1 G. R. Fleming and A. TokmakoÜ Chem. Phys. in press. Dr Whitehead asked My question relates to Fig. 7 of Dr Meechœs paper. In this –gure you present the results of two diÜerent experimental techniques (OHD-OKE and 86 General Discussion 3PEPS). You mention that 3PEPS has superior time resolution but does not probe solvation dynamics directly. The experimental results are compared to a calculation which over-estimates the very fast component of the dynamics and you suggest some additional contributions to the calculations that might improve the agreement with experiment. There is however some diÜerence between the results from the two experiments. As a guide to those wishing to test future calculations can you suggest which set of experiments should be regarded as the benchmark for the solvation dynamics? As Prof.Fleming is responsible for one of the sets of experimental data he might also wish to comment. Dr Meech answered Essentially OHD-OKE focuses on the pure liquid and is related to solvation dynamics S(t) in the way (and with the approximations) described. The 3PEPS introduced in Prof. Flemingœs paper and time resolved —uorescence (TRF in our paper) experiments focus on the solvation dynamics observed through the solute response. The diÜerence between the two data sets shown in Fig. 7 is worrying. It has been shown by Fleming and co-workers that at least in the high temperature limit (likely to be appropriate for the fast dynamics) the M(t) from 3PEPS and S(t) from TRF are closely related.1 The diÜerence between the two measurements may arise from solute eÜects since diÜerent solutes were used in the two experiments.Equally it may be that the much higher time resolution of 3PEPS is simply observing more of the solvation dynamics. With regard to which experiment should be the target for simulation ones –rst answer would be that the higher time resolution data should be preferred. However as a consequence of its very high time resolution the 3PEPS experiment reveals dynamics which are not easily included in MD simulation. Most notably ultrafast vibrational dephasing and intramolecular vibrational quantum beats. These must be suppressed in the M(t) data before comparison with conventional MD simulations. 1 M. Cho J-Y. Yu T. Jao Y. Nagasawa and G.R. Fleming J. Phys. Chem. 1996 100 11 944. Prof. Fleming added There is no fundamental reason to expect the OKE and solvation responses to be identical. The former relates to —uctuations in the polarizability anisotropy while the latter involves Coulombic interactions usually dominated by molecular dipoles. In solvents with low symmetry and without speci–c interactions with the solute however similar timescales might be reasonably expected since the same motions are involved in both cases. The connection between OKE Stokes shift and dielectric dispersion has been examined in detail by Castner and Maroncelli.1 They conclude that the dielectric dispersion and Stokes shift can be treated as arising from the same underlying motions but that the polarizability monitored by the OKE method is often not simply related to the former two dynamics.This is likely to arise from the substantial contribution of collision induced (interaction induced) eÜects to the polarizability anisotropy relaxation. In comparing time resolved —uorescence and 3PEPS measurements there are several points to consider. First as Dr Meech points out the time resolution of 3PEPS is much higher than for —uorescence. However for times less than approximately the decay time of the solvation correlation function the 3PEPS decay does not correspond directly to the underlying correlation function M(t). The short time part of M(t) has to be extracted by numerical modelling. At longer times the PEPS function and M(t) are identical. But it is very misleading to directly compare 3PEPS data with S(t)s from —uorescence.The extent to which the timescale of the ultrafast component of solvation is solute dependent is somewhat controversial. My own view is that the time dependence is not strongly dependent on for example overall solvent»solute coupling but of course the amplitude of this component is. 87 General Discussion Finally Dr Meech is correct to stress the complicating eÜect of vibrations on the 3PEPS data. In water this is a very severe problem because the medium (100»1000 cm~1) intramolecular frequencies overlap with the water spectral density. 1 E. W. Castner and M. P. Maroncelli J. Mol. L iq. in press. Prof. Jortner said The same correlation function for the polar liquid nuclear dynamics is obtained from the time resolved —uorescence spectra and from photon echo experiments.An interesting question pertains to the relationship between the solvation time correlation function and electron transfer (ET) dynamics. Early studies1 provided such relations for non-adiabatic ET where the dominant contribution to the rate occurs in the vicinity of the crossing of the diabatic potential surfaces as is the case for the normal Marcus region. Under these circumstances the breakdown of the assumption of the separation of timescales between fast medium vibrational dynamics and slow electronic processes results in the dependence of the pre-exponential factor in the ET rate on the solvent longitudinal dielectric relaxation time q ation times.This theory seemed to indicate that for activationless ET the upper limit for L or a combination of such relaxthe rate is kBqL~1. The violation of this prediction was experimentally demonstrated2 kAq revealing that for some activationless and inverted regions ET L~1 with k being independent of q ed that the microscopic rates are sensitive to the distributions of the initial states. For L . Medium controlled activationless ET will be manifested only providactivationless ET the microscopic rates are weakly dependent on the initial vibrational state. Accordingly activationless ET is expected to be invariant with respect to medium relaxation dynamics being adequately described in terms of a radiationless transition of the initial vibronic manifold to a Franck»Condon quasicontinuum.3 This description of activationless and inverted region ET is important for the establishment of optimization principles for the temporal limits of ultrafast ET which is not restricted by solvent dynamics.1 I. Rips and J. Jortner J. Chem. Phys. 1987 87 2090; Chem. Phys. L ett. 1987 133 411 and references therein. 2 T. Kobayashi Y. Tagaki H. Komdori K. Kemmits and K. Yoshihara Chem. Phys. L ett. 1991 180 416; H. Heitele F. Pollingh T. Halale M. E. Michel-Beyale and H. Staab J. Phys. Chem. 1997 98 7402. 3 M. Bixon and J. Jortner Chem. Phys. 1993 176 467. Prof. Beddard responded Prof. Jortner has made very interesting comments concerning activationless electron transfer. We have measured the electron transfer from aniline or N,N-dimethylaniline to the –rst excited singlet state of the dye molecule Methylene Blue at diÜerent temperatures and in the case of aniline from close to the freezing point and up to 60 °C.Using femtosecond pump»probe methods we observed two processes which we attributed to (1) mb` »» hl ’ mb* »»kl ’ mb~]A` (2) mb~]A` »» k2 ’ mb`]A where mb` is Methylene Blue and A is aniline or N,N-dimethylaniline which is the solvent and also electron donor. The log k and k are of the measured rate constants 10 1 shown in Fig. 1 vs. temperature. The top points in each plot are the charge separation 2 rates k1 and the lower points are the charge recombination rates k2 . As is well documented1 the electron transfer rates k1 k2 should vary as (I) 1,2\ f (qL)+2J4jkB T exp[[(*E1,2]j)2/4jkB T ] k 2pV 2 L where f (qL) is a function describing the dynamic contribution of the solvent via the longitudinal relaxation rate q which is calculated from the measured Debye relaxation *E rate is the energy gap and j the reorganisation and V the coupling energy.In its 1,2 88 General Discussion q Fig. 1 Electron transfer rate constant between Methylene Blue dissolved in aniline (left) and N,Ndimethylaniline (right) vs. temperature. The top points in each plot are the charge separation rate constants k and the lower points are for the charge recombination rate constants k2 . The solid 1 lines are the longitudinal relaxation rate L~1 calculated from the measured Debye relaxation rates. simplest form f (qL)\qL but other and more complex relationships have been developed.1 Both processes (1) and (2) are close to being activationless (*E\[j) but the charge separation step is more so in N,N-dimethylaniline than aniline and vice versa for q recombination. We measured from 13C NOE NMR experiments over the temperatures range shown in Fig. 1 and expected that the rates would follow a similar trend L according to eqn. (I). It is clear from the data that this is not the case particularly for k1 but also for k where the change of rate constant with temperature and hence q is far 2 less than predicted via eqn. (I) and even though the reaction is not completely activa- 1 tionless. One possibility could be that the temperature dependence of the exponential term in eqn. (I) compensates for that of q1~1 but this is unlikely as both increase with temperature.We try to explain our results by considering that in a neat solvent where many diÜerent con–gurations of donor molecules around the acceptor exist at the instant of excitation it may be that very little dynamic solvent reorganisation is needed as some molecules with the correct con–guration to cause reaction will always be present. Additionally we performed optical Kerr experiments on neat aniline and observed that in common with other solvents short lived polarisability components are present. In this case of lifetime of ca. 0.5 ps and a minor one of ca. 16 ps (at 294 K) which is approximately the same value as measured by NMR and represents the rotational motion of the whole molecule. The shorter component would indicate that the rotation of the solvent is not essential to equalise the energies of the donor and acceptor states prior to transfer but that other solvent motions such as libration could also help to do this.Our observation is consistent with the suggestion that tunnelling may be important in this type of reaction. 1 (a) D. Calef and P. Wolynes J. Phys. Chem. 1983 87 3387; (b) J. Cowans J. K. M. Sanders R. Harrison B. Pearce and G. S. Beddard Chem. Phys. 1987 116 429; (c) I. Rips and J. Jortner J. Chem. Phys. 1988 88 818. Prof. Jortner concluded the discussion Prof. Beddard described some very interesting observations on excited state electron transfer (ET) between aniline or N,Ndimethylaniline and Methylene Blue. These experimental data reveal that the charge 89 General Discussion separation rates k1AqL~1.This pattern re—ects on the breakdown of the solvent controlled ET theory.1 A central conclusion emerging from these studies was that medium relaxation dynamics can be characterized by the solvent adiabaticity parameter (1) i\4pV 2qL/+j with the ET rate being given by (2) k\kNA/(1]i) APqL~1 ( while for activationless ET EA\0) the ET rate is where kNA is the standard non-adiabatic ET rate. Note that f (qL)\(1]i) in eqn. (I) of Prof. Beddardœs comment. In the solvent controlled limit i.e. iA1 the rate assumes the form k\A exp ([E A\d/q with d\(j/16pk A/kB T ) with the frequency factor B T )1@2. L For typical medium reorganization energies e.g. j\0.5»1.0 eV for polar solvents or j\0.15 eV for aliphatic hydrocarbons dB0.3»1.0.Thus for solvent controlled ET (iA1) one expects that kBqL~1. These theoretical predictions are violated by a variety of photoinduced fast (ps»100 fs timescale) ET processes e.g. betaines (Nile Blue)`DMA porphirine»quinone paracyclophanes Oxazine 1-DMA and mixed valence compounds (for reviews see ref. 2). qETBk~1 q kA(qL)~1. In all these cases the (mean) ET lifetime i.e. is not limited by In all these systems the fast rates exhibit a weak temperature dependence as appropriate L either to activationless or inverted region ET. The Methylene-Blue»DMA or aniline system studied by Prof. Beddard falls in the same category violating the solvent controlled ET theory and concurrently exhibiting a weak temperature dependence.We accounted for the failure of the solvent controlled theory in terms of the radiationless transitions theory of ET.2a For activationless ET we showed that the microscopic non-adiabatic energy (E) dependent rates k exhibit a weak excess (vibrational) EP(E]en)~1@2, E where en is the zero point energy. energy dependence of the form k Accordingly the averaged experimental activationless ET rates exhibit a weak variation between the limits of slow medium-induced relaxation and that of fast medium-induced dynamics. Subsequently the theory of k was extended to include the eÜects of ET- E induced excitations of high-frequency intramolecular vibrational modes providing a uni–ed description of the weak E dependence of k in the activationless and inverted E regions.We predicted that for activationless and inverted-region ET the experimental ET rates are only weakly dependent on the characteristics of medium relaxation dynamics and can be appreciably higher than the solvent controlled values (i.e. the reciprocal values of the medium relaxation time induced by a constant charge distribution). Our analysis provides an adequate explanation for recent experimental observations of ultrafast k\(1 ps)~1»(100 fs)~1 activationless and inverted-region ET which apparently violate the predictions of the solvent controlled ET theory. 1 (a) L. D. Zusman Chem. Phys. 1980 49 295; (b) D. F. Calef and P. G. Wolynes J. Phys. Chem. 1983 87 3387; (c) J. N. Onuchic J. Chem. Phys. 1987 86 3925; (d) I Rips and J. Jortner J.Chem. Phys. 1987 87 2090. 2 (a) M. Bixon and J. Jortner Chem. Phys. 1993 176 467; (b) K. Yoshihara K. Tominaga and Y. Nagasawa Bull. Chem. Soc. Jpn. 1995 68 696. Prof. Gerber opened the discussion of Dr Klugœs paper Given the difficulty of calculating accurate partial charges by semi-empirical or simple ab initio methods and the sensitivity of the energy gap to the interaction between the charges to what do you attribute the quantitative success of your calculations ? Dr Klug responded It is at –rst sight somewhat surprising that our method works as well as it does but there are good reasons for this. We believe that the dominant contribution to the reorganisation energy in these particular chemical systems comes from the 90 General Discussion intramolecular dynamics of the chromophore.This is because the charge distribution in the ground and –rst excited states are similar and consequently there are only small changes in driving forces to cause solvent reorganisation. This is supported by the small value of the experimentally determined Stokes shifts. In chemical systems where the reorganisation energy is greater it is possible that we will have to move beyond point charges. As yet however we do not know at what point the use of partial charges becomes too inaccurate to be useful. It is of course true that the energy gap is sensitive to the partial charges but the spectral shapes and the Stokes shift are a measure of the —uctuations of the energy gap rather than its absolute value. More particularly it is the diÜerences in the —uctuations of ground and excited state that causes the Stokes shift.In short the relatively slow solvent reorganisation does not seem to play a dominant role in the Stokes shifts or spectral shapes of solvated chlorophyll-a and bacteriochlorophyll-a. Dr McKinnon asked To obtain the absorption spectrum and Stokes shift for the system you have calculated the energy gap between the ground and excited states as a function of time. However the Hamiltonian used to calculate the energy gap and the Hamiltonian for the potential surface on which the nuclei are propagated are diÜerent. Nevertheless the agreement between the experimental and theoretical Stokes shift is very good. Would you comment upon this ? Dr Klug answered If the forces due to electron distribution in ground and –rst excited states of chlorophyll-a and bacteriochlorophyll-a are rather similar then one might expect the dynamics of these systems to be rather similar in either state.The small value of the experimental Stokes shift and the fairly high degree of symmetry between the absorption and emission spectra suggested to us that this is indeed the case and this is born out by our calculations. Moreover the very small Stokes shift shown by chlorophyll-a in particular (about 8 nm in methanol) is mechanistically important in photosynthesis as chlorophyll-a has to maintain a particular singlet state energy to enable the efficient function of photosystem two and regulation of the process. By performing the calculations using the ground state driving forces only we are emphasising the point that the similarity of the driving forces in the ground and excited states causes the reorganisation energy to be small.Prof. Schatz asked Is it possible that more than one excited state contributes to your energy gap results in either the ab initio or semiempirical calculations ? Dr Gould replied For the ab initio work the energy gap between the –rst and second excited states remained consistently large in general of the order of ca. 0.5 eV throughout the course of the simulation. In addition the diÜerences in the oscillator strengths of the –rst and second excited states enabled easy identi–cation of the nature of the excited state thus our energy gap which we use in producing our Stokes shift is guaranteed to be for the ground to –rst excited state only with no mixing of diÜerent states.For the semiempirical calculations the issue is somewhat more complex as in general the gap between the –rst second and third excited states can be very small of the order of ca. 0.2 eV in some cases and so it is possible that more than one excited state is contributing to the energy gap. Dr Meuwly asked The general use of point charges in molecular mechanics (MM) calculations is well established. What are the changes one could expect if more sophisticated methods for describing the electrostatic interactions were employed (e.g. DMA)? Are there any MM studies known to date which depart from the use of point charges especially for larger systems? General Discussion 91 Dr Gould and Dr Klug answered It is unclear as to what changes would occur in the energy gap of the ground to –rst excited state in the Bcl-a if one were to adopt another representation for the electrostatic interaction between the MM solvent and the QM solute.In this work the molecular dynamics (MD) has been performed using a classical (AMBER) force –eld. Undoubtedly the MD trajectory would not be identical if one were to use a diÜerent representation of the electrostatics say DMA and therefore the structures used in the evaluation of the QM»MM energy gap would also be diÜerent. Without performing such calculations there is no a priori way of estimating these changes in the gap. Should our method not be capable of general application to other systems to the same level of accuracy as for Bcl-a we will investigate the use of other electrostatic models for the MD simulations initially polarisable charges and possibly DMAs.We are not aware of MM studies using DMAs for large systems but we know of attempts to use polarisable force –elds for liquids and proteins by Kollman and coworkers. 1 1 J. W. Caldwell L. X. Dang and P. A. Kollman J. Am. Chem. Soc. 1990 112 9144. Prof. Jortner said It will be instructive to compare the calculations of the semiclassical spectral density for the absorption and emission lineshapes of chlorophyll-a in a polar solvent with similar calculations for the linear response of aromatic molecules in rare gas clusters.1 In the latter case the spectral density was decomposed into contributions of a set of damped oscillators.Useful information on the cluster nuclear dynamics was inferred from the analysis of each individual contribution which corresponds either to the slow modulation or the fast modulation limit. Such a procedure will be useful for the chlorophyll in solution. L It will also be interesting to perform a model calculation for the lineshape of the necessary bacteriochlorophylls in the bacterial photosynthetic reaction center. Here q processes due to ultrafast energy transfer to the dimer on the timescale of ca. 70 fs as documented by Prof. Fleming will provide a large contribution to the lineshape. 1 A. Heidenreich and J. Jortner J. Chem. Phys. 1994 100 6300; Isr. J. Chem. 1993 33 467.Dr Klug responded One of the objectives of this study was to justify a previous calculation that we made for a photosynthetic reaction centre. We have previously succeeded in accounting both for the major spectral features and the rates of excitation energy transfer in the photosystem two reaction centre.1 This was achieved by partitioning the electron»vibration coupling timescales into Markovian and static limits (relative to the rates of energy transfer of about 100 fs). The conclusions of the paper which we present here are that the autocorrelation functions of the energy gap are dominated by fast (\5 fs) and slow ([2 ps) timescales which supports the assumptions that we made in our earlier work.1 As we believe that the modes which contribute to the \5 fs timescale are intramolecular then we anticipate a similar decay of the autocorrelation function even when the chlorophyll is embedded in a protein.We cannot be sure of this however until we undertake QMMM calculations in the reaction centre itself. 1 J. A. Leegwater J. R. Durrant and D. R. Klug J. Phys. Chem. B 1997 101 7205. Prof. Fleming asked A number of years ago Leslie Root1 did a classical simulation of resoru–n in glycerol. She found an enormous range of site energies in both ground and excited states but there was a quite good linear correlation between the energies of the two states. What do your calculations say about this ? 1 L. Root J. Chem. Phys. 1990 93 4364. 92 General Discussion Dr Klug replied In our calculations we certainly –nd extensive correlation between the energies of the ground and excited states.We have not quanti–ed the extent of the correlation nevertheless the —uctuation of the energy gap is signi–cantly less than the —uctuation of either of the state energies. Prof. Neumark opened the discussion of Prof. Dantusœs paper Your —uorescence and CH all spectra for the other molecules you have studied (CH2Br2 CF2 Br2 2Cl2) show that at least some of the dihalogen product is formed in the D@ state. However vibrational coherences are only observed for the I product from CH2I2 . Is this related to the dissociation mechanism or does it merely re—ect the greater ease in observing 2 coherences in I2 ? Prof. Dantus responded Until now we have only studied the photodissociation in the product.Our laser system has the temporal resolution to observe the vibrational dynamics of CH2I2 with sufficient time resolution to observe the vibrational coherence coherence in the product from the brominated compounds. We are presently pursuing these measurements. The vibrational frequency of the molecular chlorine may be too fast for our observation. However a fast dissociation time (well under 100 fs) was observed for all compounds. This implies that there is no intermediate therefore the photoinduced molecular detachment occurs by a concerted mechanism. 2 Dr Soep asked In your paper you mention the energetics of the ion pair states as being essential in –nding the concerted I elimination mechanism. But is not the radial extension of the potential in ionic states (–nal) an important parameter in favouring the concerted process since at long distances the iodine atoms still feel attraction ? 2I2 CH2 (a8 1A1)]I2 (X) formation is 3.7 eV.1 The Prof.Dantus replied The energetics argument is based on the fact that molecular products are not observed until excitation energies exceed 9 eV in CH despite the fact that the thermodynamic threshold for thermodynamic threshold for the formation of ion pair states and ground state carbene is ca. 8.4 eV. As you say the ion pair states have much stronger bonding than all valence states and extend to much longer internuclear distances. It is conceivable that the state reached at 12 eV has an ionic character and that the Coulomb attraction of the two iodine atoms allows the formation of molecular product.1 S. L. Baughcum and S. R. Leone J. Chem. Phys. 1980 72 6535. Dr Fuê asked (i) You have presented impressive evidence for a concerted two-step process in which one of the CwI bonds stretches –rst and only then is the second I torn away. You also found evidence that the primary excitation is of r]r* type. I would like to suggest more speci–cally that this excitation is an ionic r]r* transition which correlates to ICH2~]I`. The (partially) positive iodine atom would at an early time form an IwI bond possibly with formation of the ionic D@ state of I2 . (ii) Why is it do you think that a positive chirp has such a dramatic eÜect on the yield of I2(D1) ? Prof. Dantus answered (i) In the text we mention the possibility that the photoinduced molecular detachment proceeds through a charge transfer type mechanism.By this we mean that the excited state has ionic character as you suggest but the exact nature of the transition is not clear at present. We are at present exploring the high energy excited states of dihalogen compounds by ab initio methods in search of this type of charge transfer state. (ii) Enhancement in the multiphoton population transfer by the use of positively chirped pulses has been demonstrated in atoms,1 and diatomic molecules.2,3 Our experi-93 General Discussion ments on the photoinduced molecular detachment of CH2I2 demonstrate an order of magnitude enhancement in the yield of I2(D@) for 2500 fs2 positively chirped pulses.4 No such enhancement was observed for negatively chirped pulses.We hope to have three dimensional quantum mechanical simulations in the future in order to explore the precise mechanism for the enhancement. 1 B. Broers H. B. van Linden van Den Heuvell and L. D. Noordam Phys. Rev. L ett. 1992 69 2062; and related theory Y. B. Band Phys. Rev. A 1994 50 5046. 2 J. S. Melinger A. Hariharan S. R. Gandhi and W. S. Warren J. Chem. Phys. 1991 95 2210; Y. B. Band and P. S. Julienne J. Chem. Phys. 1992 96 3339. 3 V. Yakovlev C. J. Bardeen J. Che J. Cao and K. R. Wilson J. Chem. Phys. 1998 108 230; C. J. Bardeen V. Yakovlev K. R. Wilson S. D. Carpenter P. M. Weber and W. S. Warren Chem. Phys. L ett. 1997 280 151. 4 I. Pastirk E. J. Brown Q. Zhang and M. Dantus J.Chem. Phys. 1998 in press. I3~ or Br3~.2 In the case of CF2Br2 it was also possible to 2 Prof. Simons commented In the spirit of this Discussion which addresses ìthe eÜects of the medium on the dynamics of electronically excited states œ I would like to recall the results of an ancient study of the UV photochemistry of polyhalomethanes such as CH dissolved in a hydrocarbon environment.1 When the dilute 2I2 CF2Br2 and CHBr solutions frozen into a glassy state at 77 K were exposed to UV light they each devel- 3 oped intense ìcolour centresœ. They could all be bleached (reversibly) by exposure to visible light and the colours faded on softening the glass. When the solutions also contained an alkene as the visible absorption bands faded they were replaced by new transient absorption bands associated with a molecular halogen»alkene charge transfer trace of a polar solvent such as ethanol the transient bands associated with the molecucomplex o e.g.I2»alkene r Br2»alkene. If in addition the solutions also contained a lar halogen complex were replaced in their turn by new absorption bands associated with the trihalide ions e.g. detect the transient UV absorption of CF as the colour centre faded in the softening glass i.e. CF was formed as a secondary product. 2 These experiments established the importance of ionic intermediates in the condensed medium in sharp contrast to the photochemical behaviour of the same molecules when isolated in the gas phase. The colour centres were tentatively associated with ionic intermediates generated through electron transfer between neighbouring polyhalomethane molecules trapped as clusters within the non-polar hydrocarbon glass.Subsequent studies of alkyl halide photochemistry in liquid solutions have con–rmed the importance of ionic intermediates.3 I believe a re-investigation of the excited state dynamics using the modern ultrafast techniques now available would be a rewarding one. 1 J. P. Simons and P. E. R. Tatham J. Chem. Soc. A 1966 854. 2 G. P. Brown and J. P. Simons T rans. Faraday Soc. 1969 65 3245. 3 P. J. Kropp Acc. Chem. Res. 1984 17 131. Prof. Dantus said We agree that it is of interest to investigate the time resolved dynamics of the low energy ionic intermediates. In the near future we intend to explore these and the caging dynamics by ultrafast time resolved techniques in clusters.The long lived intermediates are as you mentioned observed following excitation in the 4 eV energy range. The excited state reached at 12 eV following multiphoton excitation has a completely diÜerent electronic con–guration and is therefore expected to be quite diÜerent from the long lived species formed in matrices. 2 Prof. Scoles asked Given that at energies as high as 0.75 eV IVR in ethane and propane occurs with timescales on the order of 100 ps and that in your experiment I is photodetached in times shorter than 100 fs with an energy release of 1.4 eV could you 94 General Discussion please comment on why you seem to –nd the lack of IVR in your measurements surprising ? Prof.Dantus answered The energy required to reach the excited state that leads to the observation of photoinduced molecular detachment is 12 eV. For CH2I2 the density of states at this energy is sufficient for very fast IVR. A quantitative assessment of the unexpected IVR can be obtained by comparing the experimentally measured IVR rates of related compounds. IVR rates have been measured recently for a family of alkyliodides. 1 The percentage of the available energy that ends up as internal alkyl energy (a measure of IVR) was found to vary from 17% for methyliodide to 76% for nbutyliodide. 1 One would expect a similar trend to be found in the diiodo compounds studied in our experiments. In this case an increase in the lifetime of the transition state of a factor of at least ten would have been observed for 1,1-diiodobutane.Given that the measured diÜerence was not quite a factor of two which can be explained by the diÜerence in the reduced mass we conclude that there is no apparent IVR. We –nd the diÜerences between the iodo- and the diiodo-alkane compounds surprising in view of the observations on dissociation of the alkyl halides. 1 W. K. Kang K. W. Jung K-H. Jung and H. J. Hwang J. Phys. Chem. 1994 98 1525; W. K. Kang K. W. Jung D. C. Kim K-H. Jung and H. S. Im Chem. Phys. 1995 196 363. Prof. Grice asked Have you attempted to measure the electronic state of the CH2(X3 3B1) CH2(a8 1A1) products? This might help to test the proposition of an ion pair transition state which would involve a signi–cant transfer of spin density to the positively charged I atom in the CH2I`I~ electronic structure.The increased spin»orbit interaction would then allow intersystem crossing from the initial singlet to a product triplet potential energy surface. 2 Prof. Dantus replied We hope to learn about the electronic state of the CH fragments from future molecular beam experiments in our laboratory. We also plan to study 2 2Br2 because of the CF radical has spectroscopic transitions that are accessible with CF our laser system. 3NH2 results in product rotation of the non-C2v RwNH2 geometry of the molecule when it can pass the conical Prof. Butler said My question concerns both the formation of fI and the rotation of the products. Your situation is more complicated than CH IBr but I think I know how 2 to start to think about it.Your CH 2 2I2 excited state in the FC region that you state is r»r* in character must be at C geometries an equally weighted linear combination of two locally excited r»r* (CwI) con–gurations. At non-C2v geometry due to the band 2v (even zero point motion is sometimes OK) the linear combination of the two locally excited con–gurations will favour one of the two locally excited r»r* con–gurations. This suggests to me that the rotational excitation of the products simply results from the molecule dissociating through bent geometries perhaps at a conical intersection along the reaction coordinate (e.g. dissociation of CH NH from the 2 intersection adiabatically). In this study saying the C I wI bond breaks –rst as the bond forms then the other is perhaps more accurately described by saying the dissociation 2 arises from bent geometries where the contribution for the two locally excited r»r* states is not equal (not that one CwI bond breaks –rst completely at the transition state).To –gure this out you need to consider the diabatic correlation from the locally excited con–guration of the excited electronic state reached in the FC region by the 3hl excitation at 310 nm. You donœt need the help of ab initio people to do this just look at how we did this with CH IBr. This is the place to start. 2 95 General Discussion Prof. Dantus responded The nature of the excited state reached at 12 eV almost twice the excitation energy used in your CH IBr experiment is not known.Only 1% of 2 the excited molecules yield I in the D@ state and an even smaller percentage ca. 0.1% yield the f state that we know dissociates with high rotational excitation. This implies 2 that most molecules undergo ionization or photodissociation into two iodine atoms and carbene. Given the electronic complexity of these dihalogenated molecules at high energy it is not straightforward to draw electronic correlation diagrams to the observed products. We hope that our time resolved measurements and a combination of dynamic simulations on semiempirical potentials and ab initio calculations will help us converge to a full description of the reaction mechanism. 2 Dr Whitaker asked I have a very simple question. In your paper you describe attempts to observe concerted elimination of a molecular fragment but the process you observe is a sequential elimination.I would therefore like to ask if there are any examples of truly simultaneous molecular elimination known and if not why not? I would also like to know what is the origin of the vibrational coherence that you observe in the concerned sequential elimination of I from CH2I2 ? Prof. Dantus answered Even though there are a number of reactions thought to occur by simultaneous (synchronous) concerted mechanisms we are not aware of time resolved experiments that have con–rmed this expectation. There are two probable reasons for this lack of observation. First only a few groups have attempted these time resolved studies. Second for a purely synchronous reaction to occur molecular constraints in terms of symmetry and surface crossing would be required to allow only these reaction pathways and not asynchronous ones.It is possible that the photoinduced molecular detachment leading to I in the D@ state proceeds through a synchronous concerted pathway. We have not been able to measure the rotational excitation of 2 these products. We have demonstrated that the process leading to I in the f state proceeds through an asynchronous concerted pathway where the product shows vibra- 2 tional coherence and high rotational excitation. Prof. Ashfold said Examples of molecular fragmentations which have been shown unambiguously to involve the simultaneous cleavage of two or more bonds remain fairly uncommon.Two examples which spring to mind involve elimination of molecular H2 from respectively 1,4-cyclohexadiene following excitation at 193 nm (ref. 1) and H2S following two photon absorption at ca. 290 nm.2 In the former case polarised Doppler spectroscopy studies of the H product lineshapes indicates that these fragments are 2 formed with their recoil velocity vector ø and the rotational angular momentum vector J aligned parallel to each other»an observation rationalised by assuming that the H product molecule lifts oÜ the parent ring with a concerted helicopter-like motion. In the2 latter case the evidence comes in the form of two photon REMPI resonances indicative of formation of H molecules carrying high levels of vibrational excitation»an observation which suggests that at least at wavelengths around 290 nm two photon excitation 2 of H2S results in population of excited states involving sufficiently large amplitude bending motion to encourage HwH bond formation and simultaneous cleavage of the two SwH bonds.1 E. F. Cromwell D-J. Liu M. J. J. Vrakking A. H. Kung and Y. T. Lee J. Chem. Phys. 1991 95 297. 2 J. Steadman and T. Baer J. Chem. Phys. 1989 91 6113. Prof. Gerber added It is usually very hard to provide evidence of two bonds breaking simultaneously but according to accepted theoretical models this actually takes 2O is an example. Desorption of place in a large number of cases. The photolysis of CH H from hydrogen chemisorbed on metals is another. 2 96 General Discussion 2Y2 would be symmetric enough to be expected 3Y C2 might also be suitable as mightXYZ.Many Prof. Beddard and Dr Whitaker communicated Prof. Ashfold and Prof. Dantus hypothesise that in several types of reaction it might be possible to observe concerted photodetachment of a molecular product. However very few reactions appear to actually do so. Let us look at the types of simple molecules in which we wish to break two CX bonds. We can imagine that CX to show concerted behaviour but CX other organic molecules such as 1,4-butadiene are also postulated to undergo concerted conrotatory and disrotatory bond –ssion and formation when excited photochemically according to Woodward»HoÜman rules. We split the photodetachment process into diÜerent categories (a) simultaneous bond breaking and formation through a three or more atom-centred transition state ; (b) double simultaneous bond –ssion followed by product molecule bond formation; (c) as (b) but with no –nal molecule formation; and (d) sequential bond breaking and formation as described by Prof.Dantus. We think that a number of factors are important for determining into which category [(a)»(d)] a concerted photodetachment reaction will fall. These are (I) the excess energy in the parent molecule above the dissociation threshold (II) the symmetry of the normal mode excited ; (III) the shape of the potential energy surface ; (IV) the symmetry of the molecular wavefunction excited that is that nodes should exist between both X atoms and the C atom and not between the X atoms themselves ; (V) the duration and properties of the excitation laser pulse ; and (VI) the mass of the atoms with respect to the bond force constant.The question is which of these factors is crucial in determining the nature of the photodetachment. We maintain that to be concerted in the strict sense of the word then a symmetric stretch of both CX bonds is required and for the reaction to be con–rmed the product in our example X has to be detected before other intermediates involving other atoms are observed. 2 Clearly our de–nition now restricts the concept of concertedness to categories (a) and (b) above. Case (c) we consider to be a pseudo-concerted reaction and note that experimentally it would be difficult to con–rm the simultaneous bond –ssion.Prof. Dantus uses the names ìconcerted simultaneousœ and ìconcerted sequentialœ to distinguish cases (a) and (b) from (d). We feel these names are confusing and could be better replaced by the words ìconcertedœ and ìconsequentialœ the last name being used to indicate as in case (d) that the subsequent reaction is inevitable once the –rst bond is broken. Assuming that the excitation is such that sufficient energy exists to break two CX bonds we want to discuss which factors [(I)»(VI)] are important. The symmetry of the normal mode excited is clearly important. First consider an antisymmetric vibration one CX bond extends while the other compresses. This cannot by our de–nition lead to a concerted reaction. In the case of a symmetric stretch both bonds move in phase and could dissociate together as we excite onto the repulsive part of the potential.The excitation has to be completed in less than approximately half a vibrational period for otherwise the time resolution is not sufficient to observe concertedness. This restriction ensures that all the molecules are excited simultaneously but it is also important that they are excited within a narrow range of internuclear separations near to the repulsive wall so as to remain in phase as the bonds subsequently expand. In the ground state some molecules will be undergoing compression others expansion. So during the excitation pulse and because of the Franck»Condon principle the wavepacket produced on the dissociating surface comprises a range of bond lengths of variance p(x) say with an associated range of momenta p(p).This imposes a natural limit on the timescale for concertedness. We can use the variance p(x) to de–ne this timescale namely the time taken for the wavepacket to move through this distance. If during this characteristic time energy —ows into or out of the breaking bonds via non-Born»Oppenheimer coupling it is possible that the motion leading to X can be frustrated which could lead to an intermediate XCY as observed by Prof. Dantus in his elegant experiments. In these 2 2 X\iodine and Y\hydrogen and the CH group moves relatively quickly with respect 2 97 General Discussion to the iodine leading to consequential reaction. This leads us to consider therefore that the important factors in determining the type of reaction are the time and amplitude —uctuations of the energy in the dissociating bonds with respect to their movement along the reaction path.If the potential is coupled to other states or vibrations then the energy —uctuations can be large and fast. If the atomœs impulse is small such as for heavy atoms on a weakly repulsive potential or close to threshold then the departing atoms may barely move before the energy —uctuates and concertedness is lost. On the other hand if the atoms are light and the excitation is well above threshold then they move apart rapidly and there may be insufficient time to form an X bond and similarly concertedness is frustrated. Possibly there is a region in which to observe concertedness. Here there has to 2 be weak coupling and small impulse with respect to the duration and magnitude of the energy —uctuations.In the limit in which the excited state potential is uncoupled from the rest of the molecule then the dissociation would be concerted but no such case is likely to exist. With weak coupling and if the atoms move slowly for example they are heavy or are on a weakly repulsive potential or close to threshold then X bond formation may occur before the atoms move too far apart particularly if they are large and easily 2 polarisable. But this appears to be exactly the case studied by Prof. Dantus in which concertedness was not observed. We therefore conclude that a concerted reaction may occur only rarely. intermediate having a 500 fs lifetime.3 Prof.Dantus communicated in response A concerted reaction is de–ned as one which proceeds without intermediates.1 Based on this de–nition our observations of photoinduced molecular detachment of I in the D@ state and in the f state are consistent with a concerted reaction mechanism. For both cases no intermediate was observed. For 2 the f state products high rotational excitation of the I fragment indicated that the symmetry i.e. a sequential concerted C2v molecular detachment does not conserve 2 mechanism as de–ned in our manuscript. A similar argument for the product in the D@ state can not be made at this time it may proceed through a simultaneous concerted mechanism. The de–nition of a concerted reaction mechanism predates the use of ultrafast lasers that are capable of detecting the transition states of chemical reactions proceeding on purely repulsive potentials i.e.without intermediates.2 Probing reactions with ultrafast time resolution allows one to better distinguish between concerted reactions and those that proceed through short lived intermediates. Non-concerted stepwise reaction mechanisms involve an intermediate. The lifetime of the intermediate is typically longer than vibrational motion. Progress therefore is usually statistical in nature. The photodissociation of acetone studied in Zewailœs group is an excellent example of this type of reaction mechanism. They observed the CH The existence of an intermediate in stepwise reactions facilitates IVR because of the 3CO increased coupling timescale.The statistical lifetime of the intermediate prevents the observation of coherent vibrational motion in the product because each product is formed at essentially random times. For the photoinduced molecular detachment on I2 in the D@ and f state we measured very fast direct dissociation and coherence in the I2 product. Measurements on 1,1-diiodobutane indicate essentially no IVR in the dissociation process. Therefore we conclude that the reaction mechanism must be concerted. Based on these observations the term concerted reaction should not be reserved for those processes which preserve perfect symmetry. The de–nition as it stands is clear. As you comment it is important to investigate which parameters lead to concerted reaction mechanisms. Certainly the topology of the potential energy surface symmetry of the electronic state energy of excitation and characteristics of the electric –eld are important.For the dihalogen compounds of interest here it is perhaps the charge trans-98 General Discussion fer nature of the excited state reached that leads to the formation of an ion pair molecular product. It is conceivable that formation of the halogen ion pair occurs prior to complete separation from the carbene fragment. If this is indeed the case then the potential energy surface must have a long range Coulomb attraction term along the I»I coordinate. We have begun to investigate the role of vibrational normal mode excitation on the yield of the concerted mechanism. Using ab initio techniques we have found that one quantum of the IwCwI bending mode corresponds to over one angstrom motion along the CH2»I2 distance with concomitant but opposite motion along the I»I coordinate.4 For this reason we consider this the most important vibrational mode in this reaction.1 See for example R. B. Woodward and R. HoÜmann Angew. Chem. Int. Ed. Engl. 1969 8 781; W. T. Borden R. J. Loncharich and K. N. Houk Ann. Rev. Phys. Chem. 1988 39 213; M. J. S. Dewar J. Am. Chem. Soc. 1984 106 209; C. E. M. Strauss and P. L. Houston J. Phys. Chem. 1990 94 8751; C. Maul and K-H. Gericke Int. Rev. Phys. Chem. 1997 16 1. 2 M. Dantus M. J. Rosker and A. H. Zewail J. Chem. Phys. 1987 87 2395; ibid 1988 89 6128. 3 S. K. Kim J. Guo J. S. Baskin and A. H. Zewail J. Phys. Chem. 1996 100 9202. 4 U.Marvet Q. Zhang E. J. Brown and M. Dantus J. Chem. Phys. 1998 submitted; Q. Zhang U. Marvet and M. Dantus J. Chem. Phys. 1998 submitted. Dr Balint-Kurti said Prof. Dantus has presented evidence for a ìconcerted sequential mechanismœ for the breaking of two bonds in CH CH2]I2 . The best way to 2I2 to form view mechanisms of molecular break-up is in terms of motion on a potential energy surface. In the case of SiH2 ` (ref. 1) the system can dissociate to form Si`]H2 nominally breaking two chemical bonds. The topology of the potential energy surface is dominated by the conical intersections and the break-up process is best described by discussing the motion of the system point on the surface. 1 S. P. Mort G. G. Balint-Kurti N. A. Jennings and D. M.Hirst J. Chem. Phys. 1994 101 10576. Dr Fuê added Concerning the question of whether there are more reactions in which two bonds are broken simultaneously there should be a whole group of such reactions namely the pericyclic ring cleavage (cycloreversion) speci–cally the photochemical ones. Dr van der Zande asked Do experiments using chirped pulses in a multiphoton (i) an intermediate resonance allows for storage of the excited state at the beginning process accelerate the processes because of the pulse (ii) the power is sufficiently high that by adiabatic passage one can transfer 100% of the population? The wavepacket focusing seems much more improbable. Prof. Dantus responded Among the reasons why chirped pulses enhance multiphoton transitions in molecular systems the following have been considered (a) resonance following where wavepacket motion in the intermediate state(s) results in a time dependent transition energy and the chirp follows this dependence; (b) intra-pulse time delay where the wavepacket in the –rst excited state must propagate to a new region in the PES for further excitation ; (c) wavepacket focusing where the wavepacket generated by the chirped pulse focuses at a certain position in the PES which is favorable for further excitation ; (d) sequential resonance eÜect or adiabatic passage (independent of wavepacket motion) where a portion of the chirped pulse couples the higher intermediate states and increases the transition probabilities ; (e) intra-pulse pump»dump cancellation where stimulated emission which back-transfers population to the ground state is 99 General Discussion prevented.1 In the absence of potential energy surfaces for the excited states involved it is not possible to determine which of these alternatives predominates.Even though our experiments demonstrate an enhancement of the product signal for positive chirps centered at 310 nm but not for negatively chirped pulses,2 these observations could be consistent with any of the above alternatives. The magni–cation of the observed chirp enhancement with laser intensity is indicative of processes (d) and (e). We hope to have three dimensional quantum mechanical simulations in the future to explore in greater detail the mechanism for the enhancement. 1 J. Cao J.Che and K. R. Wilson J. Phys. Chem. submitted and references therein. 2 I. Pastirk E. J. Brown Q. Zhang and M. Dantus J. Chem. Phys. 1998 in press. Prof. Dagdigian asked In the work presented in your paper a single excitation wavelength was employed. Have you carried out any experiments in which the wavelength was varied ? In this way the possible role of resonances at the one or two photon level could be explored. These could also possibly be important in understanding the results presented at the meeting on the eÜect of chirped pulses. Prof. Dantus replied The use of diÜerent excitation wavelengths has been in our project schedule for some time. We plan some experiments at higher photon energies (208 nm) that will reach the threshold energy for the photoinduced molecular detachment by two rather than three photons.Your observation that this may allow us to further understand the eÜect of chirped pulses is correct. In particular it may allow us to determine if the –rst excited state is involved in the three photon excitation that leads to photoinduced molecular detachment. Prof. Polanyi said Central to this Discussion in common with many antecedent Discussions has been the molecular dynamics of chemical reaction. Four decades ago it was routine to preface oneœs remarks by writing on the board the prototypical exchange reaction A]BC][ABC]î]AB]C. Those in this –eld tried at –rst to infer the dynamics from the motions in the newly formed reaction products. We still do so in papers presented at this Discussion.But the inferences regarding the dynamics obtained in this way are imprecise since A meets BC in such a wide variety of con–gurations forming a wide variety of [ABC]î. ìTransition state spectroscopyœ was introduced as a means to prepare [ABC]î in a more restricted range of con–gurations. The most successful avenue to doing this till now has been to complex A with BC prior to initiating reaction i.e. to start with A… … …BC rather than A]BC. We have examples of this too in work presented at this Discussion. All this is old-hat. My reason for referring to it is that it sets the work of Prof. Dantus and co-workers at this meeting into an interesting context. They start with what is characterised as chemically bound ABC (rather than A]BC or A… … …BC) and excite it to a state [ABC]î which can unfold to give products AB]C by the formation of a new chemical bond concurrently with the dissolution of an old one; precisely what happens in the transition state of a reaction A]BC]AB]C. The modelling of the half-reaction from [ABC]î]AB]C is simpli–ed in one respect the internuclear con- –guration in the transition state [ABC]î is (within the Franck»Condon approximation) given by the well de–ned con–guration in a strongly bound precursor the readily observed ground electronic state molecule ABC. The outcome of the reaction originating in this transition state will be more sharply de–ned than has been the case till now and the transition state will be correspondingly derivable. Prof. Simons concluded the discussion The question of molecular elimination (or rather its absence) has been reviewed recently by Maul and Gericke within the context 100 General Discussion of three body photodissociation in a molecule such as COCl2 .1 They distinguish concerted and sequential mechanisms of photodissociation and further subdivide the concerted pathway into synchronous (symmetric stretch) and asynchronous (anti-symmetric stretch) routes. Their experiments conducted at 230 nm found no evidence for molecular elimination from COCl and the current ì received wisdomœ seems to suggest that molecular elimination is a rarity»but ì received wisdomœ is not always a reliable guide. 2 1 C. Maul and K-H. Gericke Int. Rev. Phys. Chem. 1997 16 1. 2 J. K. Galbraith personal communication.

ISSN:1359-6640    

DOI:10.1039/FD108081

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss., 1997, 108, 101»113 Time-resolved studies of dynamics in molecular and cluster anions B. JeÜerys Greenblatt, Martin T. Zanni and Daniel M. Neumark* Department of Chemistry, University of California, Berkeley, CA 94720, USA and Chemical Sciences Division, L awrence Berkeley National L aboratory, Berkeley, CA, USA Femtosecond photoelectron spectroscopy (FPES) is used to study the timeresolved photodissociation dynamics of clusters excited at I2~(CO2)n/4, 16 780 nm.The FPES experiment on shows that the I~ fragment I2~(CO2)4 formed by excitation to the repulsive state of initially pulls A@ 2%1@2, g I2~ away from the cluster, but by 0.2 ps it is drawn back to complex with more of the solvent molecules. In the n\16 cluster, where caging of the is I2~ known to be complete, FPES probes the recombination dynamics of the I2~ in considerable detail.Speci–cally, vibrational relaxation on the I2~ X2&u ` state and the accompanying evaporation on molecules can be followed CO2 in real time. Vibrational relaxation is essentially complete by 10 ps, whereas solvent evaporation is not entirely complete by 200 ps. The spectra also show evidence for short-lived recombination on the state.The I2~ A2%3@2, g results are compared to previous experimental results for clusters I2~(Ar)n and recent simulations of cluster dynamics. Introduction The eÜect of clustering on the dynamics of elementary chemical processes has been the focus of considerable interest, as it oÜers a route toward understanding the evolution of chemistry from gas phase to condensed phase environments.Much of the original work in this area focused on neutral van der Waals clusters,1h3 in which a chromophore such as was complexed to one or more solvating species, and the resulting eÜects on the I2 chromophore photophysics were probed using laser-induced —uorescence, multiphoton ionization, and other spectroscopic/dynamical probes.More recently, femtosecond timeresolved techniques have been applied to clusters of this type.4,5 A parallel eÜort has developed in the study of ionic clusters comprised of solvated charged chromophores.6 These experiments have an advantage over neutral cluster studies in that there is generally no ambiguity concerning the size of the cluster, an important issue if one is trying to probe size-dependent eÜects. Clusters of with Ar and have been of particular I2~ CO2 recent interest ; the photodissociation dynamics of these clusters have been studied in an elegant series of frequency and time-resolved experiments by Lineberger and coworkers. 7h14 We have undertaken studies of these clusters using a new experimental technique, femtosecond photoelectron spectroscopy (FPES), providing a picture of the photodissociation dynamics that in many ways complements the Lineberger experiments.Previously we have reported results on and clusters.15,16 Here new I2~ I2~(Ar)n results for clusters are presented and discussed in light of earlier experiments I2~(CO2)n on clusters. I2~(Ar)n Two types of experiments have been performed by Linebergerœs group on clusters of and other dihalides with and Ar.In the experiments on (see Fig. 1) the I2~ CO2 I2~ anion is photoexcited from the state to a repulsive electronic state, the X2&u ` A@ 2%1@2, g state, and the subsequent interactions between the recoiling photofragments and solvent 101102 Dynamics in molecular and cluster anions Fig. 1 Potential energy curves for low-lying electronic states of and Correlating atomic I2~ I2 .states are indicated to the right. The anion and state parameters are taken from X2 &u ` A2%3@2, g ref. 16. The anion state parameters are taken from ref. 37. Neutral state parameters are A@ 2%1@2, g from ref. 38»41. species (S) are probed. In one set of experiments7,8,13,17 the product masses from onephoton dissociation were determined.These experiments show that for small numbers of solvent species only ìuncagedœ ionic products of the type are produced, whereas I~(S)n for larger clusters stable products of the type dominate. These ìcagedœ products X2~(S)n result from recombination of the photofragments on a lower-lying, bound state of a I2~, process analogous to geminate recombination in solution.18 The second set of experiments9h11,14 used a two-photon pump-and-probe scheme with picosecond and, more recently, femtosecond lasers to perform time-resolved studies of the recombination dynamics in clusters of sufficiently large so that caging occurs.In these experiments I2~ the chromophore is dissociated with the pump pulse, and subsequent absorption of I2~ the probe pulse (of the same color) is monitored as a function of delay time.The experiments yield the overall time-scale for recombination and vibrational relaxation of the on its ground electronic state : 1.3 ps in the case of vs. 130 ps for I2~ I2~(CO2)16 , While the recovery of the absorption is monotonic for clusters, I2~(Ar)20 .14 I2~ I2~(Ar)n the results for have been interpreted in terms of ìcoherent recombinationœ of I2~(CO2)16 the photofragments occurring on the excited state of (see Fig. 1) ca. 2 ps A2%3@2, g I2~ after the pump pulse.9,10,14 In related work, the time-resolved recombination dynamics of in solution were studied by Barbara and co-workers via transient absorption in a I2~ variety of polar solvents.19,20 The absorption recovery times lie in the range of a few picoseconds, i.e.a similar time-scale to the clusters. I2~(CO2)n The –nite clusters have been considered in a series of theoretical papers in which molecular dynamics simulations are used to determine the equilibrium geometries of the clusters and track the dynamics subsequent to photodissociation of the dihalide chromophore. The original studies by Perera and Amar21 focused on the time-scales for recombination and solvent evaporation on the ground electronic state of the dihalide.More recent work by Batista and Coker22 and Parson and co-workers23h25 has considered the importance and time-scale of non-adiabatic electronic transitions that occur subsequent to photoexcitation. Parson in particular has emphasized the role of ìanomalous charge switchingœ in these clusters, in which the asymmetric charge distribu-B.J. Greenblatt et al. 103 tion on the two iodine atoms induced by solvation in the cluster ground state is reversed in the photoexcited state. The FPES experiments discussed here were undertaken to provide a more complete picture of the dissociation dynamics in clusters. In these experiments, the I2~(CO2)n I2~ chromophore is excited to the repulsive state by an ultrafast (ca. 80 fs) pump A@ 2%1@2, g pulse. The time-evolution of the cluster is monitored by photodetachment with an ultrafast probe pulse and measurement of the resulting photoelectron spectrum. At each pump»probe delay the photoelectron spectrum provides a ìsnapshotœ of the cluster dynamics, and is particularly sensitive to the local environment of the excess electron in the cluster.In contrast to Linebergerœs pump»probe experiments, FPES can be used to investigate clusters in which no caging and recombination occurs. When recombination does occur, FPES can reveal the electronic state of the dihalide at each delay time, along with the degree of vibrational excitation and the approximate number of solvent species remaining in the cluster. Results are reported here for two clusters : for I2~(CO2)4 , which almost no caging occurs, and in which caging is complete.I2~(CO2)16 , Experimental Although the FPES experiment has been described in detail elsewhere,15 several improvements have been made recently and are discussed below. Fig. 2 shows the apparatus. Cluster anions are generated by passing a mixture of 3% in Ar over CO2 I2 crystals at a backing pressure of 10»30 psig, expanding the gas mixture into a vacuum chamber through a piezoelectric valve running at a repetition rate of 500 Hz, and crossing the resulting free jet with a 1.5 keV electron beam just downstream of the nozzle.The resulting plasma cools collisionally to produce both positive and negative ions.After passing through a 5 mm diameter skimmer located 11 mm below the valve ori–ce, the negative ions are injected into a Wiley»McLaren time-of-—ight mass spectrometer26 by applying pulsed extraction and acceleration –elds perpendicular to the beam axis. The –nal beam energy varies between 800 eV and 1.7 keV, depending on the voltages used. A three-plate pulsed mass gate27 ensures that only anions of the desired mass interact with the lasers.The original source chamber of our apparatus has been divided into two regions to accommodate additional diÜerential pumping. Each region is now pumped by a Varian VHS-10 diÜusion pump with 4400 l s~1 pumping speed; this results in a considerably lower pressure in the region where the ion extraction pulses are applied.On their way to the laser interaction region, the anions pass through two additional diÜerentially pumped regions. The –rst diÜerential region is pumped by a Varian VHS-6 diÜusion Fig. 2 Schematic diagram of the apparatus. Shown are the ion source, time-of-—ight mass spectrometer, ìmagnetic bottle œ photoelectron spectrometer and re—ectron photofragment analyzer.104 Dynamics in molecular and cluster anions pump.The second diÜerential region and laser interaction region are each pumped by Varian V250 turbomolecular pumps. The base pressure in the –nal region is 1]10~9 Torr. Laser pulses cross the ion beam at the focus of a ìmagnetic bottle œ photoelectron spectrometer, which is based on the design of Cheshnovsky et al.27 However, a strong (0.8 T) permanent magnet, rather than an electromagnet, is used to produce the inhomogeneous magnetic –eld.It is located 9.5 mm below the beam axis, outside the vacuum chamber, and can be easily removed. A 1.3 m long solenoid –eld (20 G) guides the photoelectrons toward a 75 mm diameter dual microchannel plate detector. The arrival time distribution is recorded after each laser shot with a Stanford Research Systems SR430 multichannel scalar.Because of the inherently low resolution (ca. 250 meV) of a spectrometer which collects all of the electrons ejected from a fast-moving ion beam, a pulsed deceleration –eld is used to slow the ions down just before the interaction region.28,29 This results in an improvement in the electron energy resolution of up to a factor of four, with further improvements expected shortly.An in-line microchannel plate detector mounted on a retractable translator arm is used to record time-of-—ight mass spectra of the ion beam. We can also measure the photofragment mass spectra resulting from excitation of a particular cluster with the pump pulse alone. To do this, the primary ion detector is retracted, allowing the ions to continue into an oÜ-axis re—ectron7 which separates the daughter and parent ions.These are collected by another microchannel plate detector for photofragment mass analysis. Both types of mass spectra are recorded using a Tektronix TDS744A digitizing oscilloscope at a repetition rate of ca. 80 Hz. The pump and probe laser pulses are generated from a commercial femtosecond laser system. A Coherent Innova-90 Ar` laser pumps a Clark-MXR NJA-5 Ti : sapphire oscillator. Selected pulses are ampli–ed using a Clark-MXR regenerative ampli–er system that includes a pulse stretcher, a Ti : sapphire regenerative ampli–er pumped by a Nd : YAG laser running at a repetition rate of 500 Hz, and a pulse compressor. At 780 nm, the pump pulse wavelength, the pulse width and energy are 70 fs FWHM (sech2) and 1 mJ, respectively.About 80% of this beam is directed into a frequency tripling unit (CSK Optronics 8315A), resulting in a probe pulse at 260 nm with width and energy of 110 fs and 20 lJ, respectively. (The width of the probe pulse is measured by diÜerence frequency cross-correlation using a 300 lm thick KDP crystal.) The remainder of the 780 nm pulse passes through a computer-controlled variable delay line, and is then collinearly recombined with the probe pulse prior to entering the vacuum chamber.The polarization of the pump and probe pulses is perpendicular to the ion beam axis. For accurate determination of the temporal overlap of the pulses inside the vacuum chamber, two-color above threshold photodetachment (ATD) of I~ is used.30 Because the probe pulse wavelength is sufficient to detach electrons from ground state and clusters, the photoelectron spectra are not background- I2~(Ar)n I2~(CO2)n free.Background subtraction is accomplished by either alternating 20 s scans between the desired delay and a –xed, negative ([2 ps) delay, or by using an optical chopper (New Focus 3501).The chopper blocks the pump pulse every other laser shot, and the SR430 scalar performs shot-by-shot background subtraction. Background spectra are also collected concurrently at 80 Hz repetition rate with the TDS744A oscilloscope. These are stored and used for longer-time normalization of the spectra. Depletion of the ground state31 causes a bleach of the background-subtracted signal, which is com- I2~ pensated by adding a percentage of the background back to the spectra.Results Fig. 3 shows FPES spectra of bare for several pump»probe delay times. These I2~ spectra are taken using pulsed deceleration to slow down the ion beam; consequentlyB. J. Greenblatt et al. 105 Fig. 3 Femtosecond photoelectron spectra of bare with decelerated ion beam.The pump» I2~, probe delay times are indicated to the right of the spectra. Assignments of various features are indicated, and explained in the text. the electron energy resolution (ca. 100 meV) is substantially better than in our spectra reported and discussed previously.15 As the delay time increases, two broad features, A1 and shift toward lower electron energy and evolve into two sharp features, and A2, B1 at electron energies of 1.71 and 0.77 eV, respectively.Peaks and represent B2, B1 B2 photodetachment of the I~ photoproduct to the and states of atomic iodine, 2P3@2 2P1@2 respectively, whereas the broader features and at early times result from photo- A1 A2 detachment of the dissociating wavepacket on the anion state to the close A@ 2%1@2, g lying and states and the state of neutral No evolu- A@ 3%2u A3%1u (A1), B 3%0`u (A2) I2 .tion of the spectra occurs after 200 fs, indicating that dissociation of the bare ion is complete by this time. Femtosecond photoelectron spectra for are shown in Fig. 4, also with a I2~(CO2)4 decelerated ion beam. At short times, from 0.0 to 0.1 ps, the evolution of the photoelectron signal between 1.4 and 2.0 eV is similar to bare in that a broad feature (A) I2~, arises and shifts toward lower electron energy to form a narrower peak At lower (B1).energy, a second sharp feature arises on the same time-scale. and are separat- (B2) B1 B2 ed approximately by the spin»orbit splitting in atomic iodine (0.943 eV), and therefore appear to be analogous to the atomic I~ transitions in Fig. 3, although they are noticeably broader and shifted toward lower electron energy by 0.3 eV. By 0.2 ps, two new features are evident in the spectrum on the low energy side of and labelled B1 B2, C1 and with each of the new features occurring at 0.14 eV lower electron energy than C2 , the main peaks. By 0.5 ps, each doublet has evolved into a single broad peak and (D1 broadens and shifts toward lower electron energy from 0.3 to 2 ps, followed by a D2).D1 slight shift (0.05 eV) of the entire feature to higher energy between 2 and 200 ps.106 Dynamics in molecular and cluster anions Fig. 4 Femtosecond photoelectron spectra of (with decelerated ion beam). A simula- I2~(CO2)4 tion (» » ») of the 200 ps spectrum is shown superimposed on the experimental spectrum.Labelled features are discussed in the next. Mass distribution used in simulation : n\1, 23%; n\2, 39%; n\3, 30%; n\4, 8%. Fig. 5 shows femtosecond photoelectron spectra for In contrast to the I2~(CO2)16 . and spectra, no transitions to neutral electronic states correlating to I2~ I2~(CO2)4 are seen ; these are too high in energy for the probe pulse because of stabilization I(2P1@2) energy of the anion from the 16 solvent molecules initially.At 0.0 ps, the spectrum consists of a broad, symmetric feature (A) centered at 0.72 eV, which is analogous to the transient in the FPES of bare As the delay time increases, this feature rapidly I2~. disappears, while another broad feature (B) centered at 0.38 eV dominates the spectrum by 0.2»0.4 ps. By 0.7 ps, this feature appears as a shoulder on a lower energy feature, labelled C in Fig. 5; this shoulder steadily decreases in intensity and disappears by 4.0 ps. An additional high energy feature (D) is apparent starting at 0.7 ps between 0.5 and 1.7 eV. This feature increases in intensity to 1.6 ps, and from 1.6 to 10 ps shifts gradually toward lower electron energy. During this time, feature C shifts toward higher energy, coalescing with D into a single feature (E) by 10 ps.Discussion I2 ó(CO2)4 It is instructive to compare the FPES results for with those obtained for I2~(CO2)4 Lineberger and co-workers found that and I~(Ar) are the domi- I2~(Ar)6 .16 I~(CO2)2 nant products from the photodissociation of at 720 nm and at 790 I2~(CO2)4 I2~(Ar)6 nm, respectively.8,13 At 780 nm, we measure essentially the same distribution of products for using the re—ectron mass analyzer to separate the photoproducts I2~(CO2)4 from the pump laser alone.In spite of similar asymptotic product distributions for theB. J. Greenblatt et al. 107 femtosecond photoelectron spectra. Simulations (» » ») of spectra at 0.4 ps and Fig. 5 I2~(CO2)16 later based on parameters in Table 1 are shown superimposed on experimental spectra.Between 0.7 and 10 ps, the vertical scale is expanded for energies larger than 0.9 eV. Labelled features are discussed in the text. two anions, with essentially zero caging in both cases, the FPES spectra of I2~(CO2)4 diÜer signi–cantly from those for The spectra show that the bond I2~(Ar)6. I2~(Ar)6 I2~ breaks in approximately 200 fs, just as in bare The resulting ì I~œ features then shift I2~.toward higher electron energy from 240 to 1200 fs without otherwise changing in appearance, and do not evolve further after 1200 fs. This is due to a progressive weakening of the interaction between the I~ anion and the Ar solvent atoms as the charged photofragment leaves the cluster.24 In the spectra in Fig. 4, the narrow ì I~œ features, and are clearly I2~(CO2)4 B1 B2 , apparent at 0.1 ps. They are shifted by 0.30 eV toward lower electron energy from bare I~; this ìsolvent shift œ corresponds to 1.5 molecules.32 However, the appearance by CO2 0.2 ps of features and at lower electron energy indicates that the interaction C1 C2 between the I~ fragment and solvent molecules has increased between 0.1 and 0.2 ps, and the subsequent evolution of the doublets into the broad features and by 0.5 D1 D2 ps implies that this interaction strengthens further during this time.The spectra thus suggest that the I~ fragment does not monotonically move away from the solvent species, as was the case in Instead, it appears to initially pull away from the I2~(Ar)6 . cluster (0.1 ps) but then complexes with the solvent molecules (0.2»0.5 ps). These dynamics are consistent with the considerably deeper well in (212 meV)33 as I~… … …CO2 compared to I~… … …Ar (46 meV).34 Fig. 6 shows a ìcartoonœ of the dissociation dynamics. Parson and co-workers have performed molecular dynamics simulations on somewhat larger clusters which show eÜects similar to those implied by our I2~(CO2)n spectra.25 These calculations show that in the X state of the cluster there is an asymmetric charge distribution on the two I atoms; the molecules preferentially solvate CO2108 Dynamics in molecular and cluster anions Fig. 6 ìCartoonœ of dissociation dynamics in the cluster. Dark spheres indicate iodine I2~(CO2)4 atoms, and light elongated structures denote molecules.The symbols ((( ))) indicate vibra- CO2 tional excitation. the I atom with the larger negative charge. The situation is reversed upon excitation to the A@ state, an eÜect referred to as ìanomalous charge switchingœ.24 Consequently, once dissociation begins, the I~ fragment is relatively unencumbered by solvent molecules. Although the interiodine distance rapidly increases, the attractive force between the I~ and the molecules surrounding the I atom fragment is sufficient to prevent or at CO2 least slow down dissociation on the A@ state, and this attractive force results in the solvent atoms being drawn toward the I~.The resulting more symmetric distribution of solvent molecules induces non-adiabatic transitions to the lower-lying A or X state. This is accompanied by rapid, asymmetric solvation of the I~, leaving the neutral I fragment with its much weaker solvent interaction free to leave the cluster.These calculations therefore suggest that the rapid complexation of the I~ fragment and dissociation of the cluster as evidenced by the evolution of the sharp features and into the broader B1 B2 features and is associated at least in part with a non-adiabatic transition to one D1 D2 of the two lower-lying electronic states of the cluster.Little change in the spectra occurs after 2 ps, so these photoelectron spectra are attributed to clusters. In this time regime, the number of molecules sol- I~(CO2)n CO2 vated to the I~ fragment can be estimated by –tting the spectra to a distribution of photoelectron spectra ; these spectra have been measured previously32 and I~(CO2)n show that, for nO9, each molecule increases the electron binding energy by ca. 150 CO2 meV. The results of the best –t at 200 ps are shown superimposed on the experimental spectrum in Fig. 4; the assumed distribution is given in the caption. Note that the n\2 and 3 clusters constitute the bulk of the products at 200 ps, with n\2 being slightly dominant.This disagrees with the experimental mass distribution, in which I~(CO2)2 and comprise 75% and 7% of the products, respectively.35 This discrepancy I2~(CO2)3 may indicate that the time required to evaporate the last molecule is longer than CO2 the time window of the experiments (200 ps), in contrast to the results in which I2~(Ar)6 photoelectron spectra corresponding to the asymptotic ArI~ product were evident by 1.2 ps.16 This explanation could be tested by measuring spectra at much larger (ca.ns)B. J. Greenblatt et al. 109 delay times, which is feasible with a slight modi–cation to the apparatus. We note that the spectra used to –t the spectrum in Fig. 4 were taken for cold anions; the I~(CO2)n imperfect –t at 200 ps may be an indication that this spectrum is from vibrationally excited a necessary condition for further evaporation. I~(CO2)n , I2 ó(CO2)16 Previous work on photodissociation at 720 nm and 790 nm by Lineberger I2~(CO2)16 and co-workers8,9,35 shows 100% caging of the product, with 7 (720 nm) or 6.5 (790 I2~ nm) molecules lost, on average, via evaporative cooling as the recombines and CO2 I2~ vibrationally relaxes.Time-resolved experiments9,10,14 show that relaxation of the is I2~ complete on a time-scale of several picoseconds, with the exact value depending on the photodissociation wavelength. Similar experiments on also show 100% caging, I2~(Ar)20 but the product mass distribution is bimodal, split approximately evenly between bare and 13,35 The channel is attributed to recombination on the X I2~ I2~(Ar)WnX/11.I2~ state of and the FPES study of shows that the other channel is due to I2~, I2~(Ar)20 recombination on the A state ; this state apparently survives for at least several I2~ microseconds, the time-scale of the Lineberger experiments. The FPES experiments on also show that the time-scales for vibrational energy relaxation on the A and I2~(Ar)20 X states of are 35 and 200 ps, respectively.The role of the A state in the dynamics of I2~ clusters following photoexcitation appears to be quite diÜerent. From the I2~(CO2)16 product mass distributions, it is clear that there is no asymptotic trapping on the A state. On the other hand, the time-resolved measurements by Lineberger show evidence for ìcoherent recombinationœ on the A state at pump»probe delays around 2 ps.With this background, we now consider the interpretation of the spectra I2~(CO2)16 in Fig. 5. There are several trends in these spectra to be understood: (1) the evolution and eventual disappearance of feature B from 0.2 to 4 ps ; (2) the appearance of features C and D starting at 0.7 ps; and (3) the eventual coalescence of these two features by 10 ps.The second and third trends are similar to eÜects seen in the FPES of and I2~(Ar)20 are attributed to vibrational relaxation of the chromophore on the X state potential I2~ energy curve. As shown in Fig. 7, photodetachment from a highly vibrationally excited anion state results in well separated high and low energy features in the photoelectron spectrum corresponding to transitions from the inner and outer turning points, respectively, of the vibrational wavefunction on the state to the state of I2~ X2&u ` X1&g ` neutral As the vibrationally relaxes, the inner and outer turning points coalesce, I2.I2~ as will the two corresponding features in the photoelectron spectrum. Hence, the –rst appearance of the high energy feature D indicates that recombination on the X state has occurred by 0.7 ps, resulting in highly excited The subsequent coalescence of fea- I2~.tures C and D by 10 ps represents the time-scale over which vibrational relaxation is complete. We note that a full coalescence of the analogous features in the I2~(Ar)20 FPES does not occur, because all of the Ar atoms evaporate before the relaxes to its I2~ vibrational ground state.In the evaporation of each molecule removes I2~(CO2)16, CO2 considerably more energy from the cluster (ca. 240 vs. 73 meV),13,35 so can easily I2~ relax to its ground vibrational state without evaporation of all the solvent molecules. This process of vibrational relaxation and solvent evaporation can be treated more quantitatively by simulating the FPES at various delay times in order to determine the average level of vibrational excitation and the number of solvent molecules remaining on the cluster as a function of time.To do this one needs to know how much each CO2 molecule increases the electron binding energy of the We have measured photoelec- I2~. tron spectra of several clusters using the probe laser alone, and –nd an I2~(CO2)n average increase of 80 meV per molecule [signi–cantly less than the 140 meV shift CO2 for Assuming this to be independent of the vibrational state, the simula- I~(CO2)n].I2~ tions in Fig. 5 can be generated using a range of vibrational levels and cluster sizes, the110 Dynamics in molecular and cluster anions Fig. 7 Simulated state v\0 and v\20 vibrational wavefunctions, and photoelectron I2~ X2&u ` spectra average values of which are given in Table 1.Thus, for example, at 1.6 ps, the simulations assume a broad vibrational level distribution (16OlO55, SlT\32) and 13»14 molecules solvating the cluster, moving to a much colder distribution (0OlO17, CO2 SlT\3) and 11»12 molecules by 10 ps. The –t is quite good, except at energies CO2 O0.4 eV in the spectra between 0.7 and 2.9 ps; this is discussed below.The simulations indicate 4»5 molecules have evaporated by 200 ps, and that CO2 the chromophore is largely vibrationally relaxed, with SlT\3. This means nearly I2~ all the available energy from relaxation on the X state has been transferred to the various solvent vibrational and librational modes.However, comparison with the photofragmentation study by Vorsa,35 in which the dominant product fragments are indicates that solvent evaporation is not complete by 200 ps. Thus, at 200 I2~(CO2)9, 10 , ps, the remaining excess energy is distributed among the solvent modes, and the timescale for further solvent evaporation is likely to be described statistically. The incomplete evaporation by 200 ps is consistent with recent simulations by Faeder and Parson, who predict minimum time-scales of several hundred ps for complete evaporation.36 We next consider the interpretation of feature B.This feature is a distinct peak at 0.2 and 0.4 ps, but from 0.7 to 2.9 ps it appears more as a shoulder in the spectra around 0.4 eV. At 0.2 ps, it is reasonable to assign feature B to newly formed within the I~(CO2)n cluster ; the shift from bare I~ is equivalent to solvation by 8»9 molecules.This CO2 number does not re—ect the number of molecules in the cluster, only the average CO2B. J. Greenblatt et al. 111 Table 1 Average values of parameters used to –t the FPES spectra I2~(CO2)16 between 0.7 and 200 ps time/ps SlTa SEvibTb/eV SnTc 0.7 40.5 0.482 14.5 1.0 40.5 0.482 14.5 1.6 32.1 0.396 13.5 2.9 17.5 0.231 13.5 4 7.3 0.104 11.7 6 4.8 0.071 11.5 10 3.1 0.049 11.5 200 3.1 0.049 11.5 a Average vibrational level.b Average vibrational energy. c Average number of molecules. CO2 number close enough to the I~ to interact with it. There are two possible interpretations to the subsequent evolution of this feature. One can consider this evolution as a steady decrease of intensity of feature B from 0.4 to 2.9 ps and attribute this decrease to depletion of solvated I~ via recombination on the X state to form vibrationally excited I2~.Alternatively, the change in appearance of feature B from a distinct peak at 0.4 ps to a shoulder at 0.7 ps can be interpreted as recombination on the A state, with the disappearance of the shoulder between 0.7 and 4 ps due to leakage out of the A state and onto the X state.According to this mechanism, which is depicted in the ìcartoonœ in Fig. 8, recombination on both the X and A state occurs starting around 0.7 ps, but no population remains on the A state by 4.0 ps. The second mechanism is more in line with Linebergerœs experiments and Parsonœs simulations,25 both of which suggest that recombination on the A state plays a role in the overall dynamics.In contrast to the photodissociation of the stronger I2~(Ar)20 , interactions with the solvent molecules are likely to shorten the lifetime of this CO2 excited state signi–cantly, consistent with disappearance of the shoulder by 4 ps. It would also be somewhat surprising for the solvated I~ to persist for several picoseconds, given that recombination in occurs in 1 ps, and all other processes common to I2~(Ar)20 both clusters occur more rapidly in clusters with We therefore favour the mecha- CO2 .nism involving some short-lived recombination on the A state. However, to really distinguish the two mechanisms it is necessary to have a better understanding of the A state and how molecules in that state interact with solvent molecules.I2~ CO2 Conclusions Time-resolved photodissociation studies of clusters have been per- I2~(CO2)n/4, 16 formed using femtosecond photoelectron spectroscopy (FPES). The spectra I2~(CO2)4 show that the I~ photofragment initially moves away from the cluster, but the attractive interaction between the I~ and molecules is sufficiently strong that the I~ is pre- CO2 vented from escaping.Instead, from 0.2 to 0.5 ps, it is drawn toward the solvent molecules and complexes with several of them. This diÜers from the scenario for I2~(Ar)6 photodissociation, in which the attraction between the I~ and Ar atoms is sufficiently weak that the anion solvent interaction decreases monotonically subsequent to photodissociation of the chromophore.The FPES of for times greater than 0.7 I2~ I2~(CO2)4 ps appear to be from a distribution of clusters, with the n\2 and 3 clusters I~(CO2)n present in approximately equal amounts as long as 200 ps after the dissociation pulse.112 Dynamics in molecular and cluster anions Fig. 8 ìCartoonœ of cluster evaporation and recombination dynamics.Symbols are I2~(CO2)16 identical to those in Fig. 6. Comparison with photofragment ion mass spectra taken several microseconds after dissociation indicates that solvent evaporation is incomplete at 200 ps. In the FPES experiment allows us to follow a complex series of events I2~(CO2)16 that occurs subsequent to photodissociation of the chromophore. Dissociation I2~ results in a partially solvated I~ chromophore which can be distinctly observed out to 0.4 ps.We interpret the spectra at longer times to indicate that recombination occurs on both the A and X states of Recombination on the A state is short-lived, and by 4 ps I2~. only the X state is populated. Starting at 0.7 ps, we can monitor the process of vibrational relaxation on the X state and the accompanying evaporation of solvent molecules.We –nd vibrational relaxation to be largely complete by 10 ps, but solvent evaporation is not complete even by 200 ps. The role of the A state is the most uncertain component of our interpretation and requires further experimental and theoretical investigation. This work is supported by the National Science Foundation under Grant No.CHE- 9710243 and the Defense University Research Instrumentation Program under Grant No. F49620-95-1-0078. References 1 R. E. Smalley, L. Wharton and D. H. Levy, J. Chem. Phys., 1978, 68, 671. 2 R. J. Le Roy and J. S. Carley, Adv. Chem. Phys., 1980, 42, 353.B. J. Greenblatt et al. 113 3 N. Halberstadt and K. C. Janda, Dynamics of Polyatomic van der W aals Clusters, Plenum, New York, 1990. 4 J. J. Breen, D. M. Willberg, M. Gutmann and A. H. Zewail, J. Chem. Phys., 1990, 93, 9180. 5 Q. L. Liu, J.-K. Wang and A. H. Zewail, Nature (L ondon), 1993, 364, 427. 6 A. W. Castleman, Jr. and K. H. Bowen, Jr., J. Phys. Chem., 1996, 100, 12911. 7 M. L. Alexander, N. E. Levinger, M. A. Johnson, D. Ray and W. C. Lineberger, J. Chem. Phys., 1988, 88, 6200. 8 J. M. Papanikolas, J. R. Gord, N. E. Levinger, D. Ray, V. Vorsa and W. C. Lineberger, J. Phys. Chem., 1991, 95, 8028. 9 J. M. Papanikolas, V. Vorsa, M. E. Nadal, P. J. Campagnola, J. R. Gord and W. C. Lineberger, J. Chem. Phys., 1992, 97, 7002. 10 J. M. Papanikolas, V. Vorsa, M. E. Nadal, P. J. Campagnola, H. K. Buchenau and W. C. Lineberger, J. Chem. Phys., 1993, 99, 8733. 11 D. Ray, N.E. Levinger, J. M. Papanikolas and W. C. Lineberger, J. Chem. Phys., 1989, 91, 6533. 12 A. M. Sanov and W. C. Lineberger, 1997, unpublished work. 13 V. Vorsa, P. J. Campagnola, S. Nandi, M. Larsson and W. C. Lineberger, J. Chem. Phys., 1996, 105, 2298. 14 V. Vorsa, S. Nandi, P. J. Campagnola, M. Larsson and W. C. Lineberger, J. Chem. Phys., 1997, 106, 1402. 15 B. J. Greenblatt, M.T. Zanni and D. M. Neumark, Chem. Phys. L ett., 1996, 258, 523. 16 B. J. Greenblatt, M. T. Zanni and D. M. Neumark, Science, 1997, 276, 1675. 17 M. E. Nadal, P. D. Kleiber and W. C. Lineberber, J. Chem. Phys., 1996, 105, 504. 18 D. E. Smith and C. B. Harris, J. Chem. Phys., 1987, 87, 2709. 19 A. E. Johnson, N. E. Levinger and P. F. Barbara, J. Phys. Chem., 1992, 96, 7841. 20 P. K. Walhout, J. C. Alfano, K. A. M. Thakur and P. F. Barbara, J. Phys. Chem., 1995, 99, 7568. 21 L. Perera and F. G. Amar, J. Chem. Phys., 1989, 90, 7354. 22 V. S. Batista and D. F. Coker, J. Chem. Phys., 1997, 106, 7102. 23 J. M. Papanikolas, P. E. Maslen and R. Parson, J. Chem. Phys., 1995, 102, 2452. 24 J. Faeder and R. Parson, J. Chem. Phys., 1998, in press. 25 N. Delaney, J. Faeder, P. E. Maslen and R. Parson, J. Phys. Chem. A, 1997, 101, 8147. 26 W. C. Wiley and I. H. McLaren, Rev. Sci. Instrum., 1955, 26, 1150. 27 O. Cheshnovsky, S. H. Yang, C. L. Pettiette, M. J. Craycraft and R. E. Smalley, Rev. Sci. Instrum., 1987, 58, 2131. 28 L.-S. Wang, H.-S. Cheng and J. Fan, J. Chem. Phys., 1995, 102, 9480. 29 H. Handschuh, G. Gantefor and W. Eberhardt, Rev. Sci. Instrum., 1995, 66, 3838. 30 M. D. Davidson, B. Broers, H. G. Muller and H. B. van Linden van den Heuvell, J. Phys. B, 1992, 25, 3093. 31 M. T. Zanni, T. R. Taylor, B. J. Greenblatt, B. Soep and D. M. Neumark, J. Chem. Phys., 1997, 107, 7613. 32 D. W. Arnold, S. E. Bradforth, E. H. Kim and D. M. Neumark, J. Chem. Phys., 1995, 102, 3510. 33 Y. Zhao, C. C. Arnold and D. M. Neumark, J. Chem. Soc., Faraday T rans., 1993, 89, 1449. 34 I. Yourshaw, Y. Zhao and D. M. Neumark, J. Chem. Phys., 1996, 105, 351. 35 V. Vorsa, PhD Thesis, University of Colorado, Boulder, 1996. 36 J. Faeder, N. Delaney and R. Parson, personal communication, 1997. 37 E. C. M. Chen and W. E. Wentworth, J. Phys. Chem., 1985, 89, 4099. 38 D. R. T. Appadoo, R. J. Leroy, P. F. Bernath, S. Gerstenkorn, P. Luc, J. Verges, J. Sinzelle, J. Chevillard and Y. Daignaux, J. Chem. Phys., 1996, 104, 903. 39 X. N. Zheng, S. L. Fei, M. C. Heaven and J. Tellinghuisen, J. Chem. Phys., 1992, 96, 4877. 40 J. W. Tromp and R. J. Le Roy, J. Mol. Spectrosc., 1985, 109, 352. 41 F. Martin, R. Bacis, S. Churassy and J. Verges, J. Mol. Spectrosc., 1986, 116, 71. Paper 7/05890J; Received 12th August, 1997

ISSN:1359-6640    

DOI:10.1039/a705890j

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss., 1997, 108, 115»130 Excited state dynamics in clusters of oxygen Runjun Li, Karl A. Hanold, Mark C. Garner, A. Khai Luong and Robert E. Continetti University of California, San Diego, Department of Chemistry and Biochemistry, 9500 Gilman Drive, L a Jolla, CA 92093»0314, USA Considerable insights into the dynamics of both ionic (photodissociation) and neutral (dissociative photodetachment) decomposition pathways of O4~ and have been gained using photoelectron and photofragment trans- O6~ lational spectroscopy in a fast-ion beam.The data at 532 nm reveal a O4~ novel process involving sequential photodetachment of an electron with a near-zero binding energy from photodissociating Studies of at O4~. O6~ 532 nm reveal that addition of a third to the core leads to a dra- O2 O4~ matic change in the photodissociation dynamics, producing highly vibrationally excited photofragments not observed in the case of At O2~ O4~. 355 nm, both and yield vibrationally excited photofragments, O4~ O6~ O2~ as observed by autodetachment of the nascent At O2~ (vP5)]O2]e~. 266 nm, photofragment time-of-—ight (TOF) measurements on and O6~ show that the dynamics of dissociative photodetachment in are O4~ O6~ only slightly perturbed relative to The anisotropic product angular O4~.distribution previously observed in is observed to persist in the three- O4~ body neutral decomposition The origins O6~]hl]O2]O2]O2]e~. of these diverse phenomena in and are discussed. O4~ O6~ 1 Introduction An understanding of the evolution of chemical dynamics in neutral and anionic clusters as a function of cluster size has been pursued as it may yield essential insights into condensed-phase dynamics.1,2 Recent advances in this area have included translational energy spectroscopy studies of the photodestruction of cluster ions,3,4 and more recently time-resolved photodestruction5 and photoelectron spectroscopy studies6 of the reaction dynamics of cluster ions.These studies have begun to probe the in—uence of solvation on the reaction dynamics in small clusters, including the important caging eÜect well known from the condensed phase in which the solvent prevents separation of the nascent photofragments. We are interested in studying reaction dynamics in both neutral and anionic clusters of oxygen. Oxygen clusters and liquid oxygen have a complicated chemistry due to numerous low-lying electronic states.In this work we combine measurements of photofragment time-of-—ight spectra and photoelectron kinetic energy measurements to probe the photodissociation and dissociative photodetachment (DPD) dynamics of small anionic clusters of oxygen. We –nd that the dynamics of the neutral DPD pathway are aÜected only slightly by addition of an to while the branch- O2 O4~, ing ratio for the ionic photodissociation pathway is increased, with a dramatic change in dynamics at 532 nm. The oxygen dimer anion, provides an interesting test case for the study of the O4~, in—uence of cluster size on reaction dynamics.Small anionic clusters of oxygen appear to form around the unusually stable dimer anion of oxygen, In high-pressure mass O4~.spectrometry experiments, Hiraoka showed that is bound relative to O4~ O2(3&g~) by 0.46^0.02 eV.7 Addition of a third to form however, was ]O2~ (2%g) O2 O6~, 115116 Excited state dynamics in oxygen clusters found to release only an additional 0.11 eV, consistent with electrostatic interactions. Posey et al.recorded the photoelectron spectrum of at 532 nm which was found to O4~ be devoid of –ne structure with the exception of the characteristic peaks of photo- O2~ detachment.8 This showed that photodissociation was an important channel at that wavelength, with the nascent produced in the primary photodissociation under- O2~ going photodetachment by a second photon: O4~]hl]O2]O2~(2%g) O2~(2%g)]hl]O2(3&g~, 1*g)]e~ DeLuca et al.later studied the photodestruction of and higher clusters at 1.06 O4~ lm, and observed signi–cant photodissociation of nP3, in the absence of a (O2)n~, strong absorption in They interpreted these results in terms of a charge-transfer- O4~.9 to-solvent absorption in which the excess electron was transferred from the core to O4~ the ìsolventœ Han and Johnson carried out studies of the nascent vibrational O2.O2~ distribution (v\0»3) from photodissociation of clusters by photoelectron spec- (O2)n~ troscopy at 1064 and 532 nm.10 At 1064 nm, they found a vibrational distribution consistent with a vibrational temperature of 2600 K. Detailed analysis of the 532 nm data was not reported in their paper. There have also been a number of detailed studies on electron attachment to neutral clusters of oxygen by Maé rk and co-workers, in which the primary event is electron capture by a single molecule within the cluster environ- O2 ment.11,12 In our laboratory we have carried out a further series of experiments designed to clarify the photochemistry of These studies have shown that undergoes two O4~.O4~ limiting photodestruction processes in the wavelength range from 532 to 262 nm: photodissociation and dissociative photodetachment (O4~]hl]O2~]O2) (O4 ~ Both processes occur on repulsive excited state potential ]hl]O2]O2]e~).13h15 energy surfaces, leading to large translational energy release and highly anisotropic product angular distributions.The photodissociation studies14 con–rmed the bond dissociation energy for and also demonstrated that the lowest energy photodissociation O4~]O2~]O2 channel at wavelengths less than 532 nm yields excited and ground state O2(1*g) products.This shows that the ground electronic state of is most likely a O2~(2%g) O4~ doublet state since the dissociation of a quartet state into a singlet and doublet is spinforbidden.The photodissociation dynamics exhibit a marked wavelength dependence. At both 523 and 532 nm, photodissociation yields a very narrow photofragment distribution : 90% v\0) and 10% O2(1*g , v\0)]O2~ (2%g, O2(1*g , v\0)]O2~ (2%g , v\1), with low rotational excitation. At 349, 355, 262 and 266 nm, however, the photofragments were found to be vibrationally and rotationally excited.In addition, evidence for the production of electronically excited products was observed at 262 nm. O2(1&g `) The photodissociation product angular distributions at all wavelengths were found to be strongly peaked along the electric vector, with an anisotropy parameter b16 ranging from 1.8 to 2.0 as the photon energy increases. These results showed that there are several optically allowed low-lying repulsive states of accessed by a parallel tran- O4~ sition from the ground state.The studies of dissociative photodetachment (DPD) have revealed considerable insights into both the structure of and the repulsive states of At 532 nm, we O4~ O4 . recorded high resolution photoelectron»photofragment energy correlation spectra for the DPD of Measurement of photoelectron and photofragment kinetic energies in O4~.coincidence revealed vibrationally resolved total translational energy release spectra for the process v)]e~. Structural information on gas- O4~]hl]O2(3&g~, v)]O2(3&g~, phase was obtained from this measurement of the correlated product vibra- O4~ O2 tional distribution using a simple Franck»Condon simulation of the overlap of theR.L i et al. 117 vibrational wavefunctions of two perturbed molecules with two free ground state O2 O2 molecules. The simulation showed that two equal OwO bond lengths of 1.272 in ” with a longer bond distance inferred, was most consistent with the experi- O4~, O2wO2 mental results. The narrow rotational distributions observed in this experiment indicated that the structure is probably characterized by a high symmetry.15 The O4~ observation of non-Franck»Condon photodetachment processes at 349 nm13 and excited state products at 349, 355 and 266 nm17 has shown that O2(1*g)]O2(3&g~) there are also several repulsive states of neutral optically accessible from the O4 O4~ ground state.Recently, an extensive set of high-level ab initio calculations on the ground and excited states of has been completed by Aquino et al.18 Using the complete-active- O4~ space]second-order perturbation theory (CASPT2) method,19 they have obtained predictions for the structure, electron affinity, bond dissociation energy and vibrational frequencies of The large aug-cc-pVTZ basis,20 known to give reliable values for O4~.electron affinities of –rst-row atoms and molecules, was used.These calculations predict that the equilibrium structure of has symmetry with a electronic ground O4~ D2h 2Au state. The stability of with respect to is calculated to be ca. O4~ O2(3&g~)]O2~(2%g) 0.50 eV, in reasonable agreement with the experimental quantities.14 The calculations show that the electronic structure of is a notoriously multi-con–gurational O4~ problem; however, the ground state may be rationalized in terms of the dominant 2Au con–guration by considering overlap of the anti-bonding orbitals of and as pg O2 O2~ shown in Fig. 1. Aquino et al.18 have also examined the doublet excited states of In particular, O4~. they have located three excited states optically accessible from the ground state of 2Au via a parallel transition (polarized along the x-axis in symmetry as shown in O4~ D2h Fig. 1). Fig. 2 shows a pseudo-diatomic schematic view of these excited states in terms of Fig. 1 Qualitative molecular orbital model for the ground state of The symmetry 2Au O4~. D2h axes and theoretical predictions of the bond lengths are also shown.118 Excited state dynamics in oxygen clusters Fig. 2 Schematic ground and dipole-allowed excited-state potential energy surfaces for The O4~. adiabatic correlations for the low-lying doublet excited states are shown, with experimental energetics14 for the dissociation channels. The relative energies of the and excited states 2B3g 2Au are from theoretical calculations18 as described in the text. the distance. Electric-dipole absorption along the x-axis can occur to repul- O2wO2~ sive excited states, with one at 0.66 eV above the ground state correlating to 2B3g products. There is a second repulsive excited state correlat- O2(3&g~)]O2~ (2%g) 2B3g ing to products at 2.0 eV above the ground state.Excitation to this O2(1*g)]O2~ (2%g) state may explain the observation at 532 nm of this channel with low vibrational excitation.Finally, at 4.5 eV above the ground state is a repulsive state. This state 2Au becomes vibronically allowed with excitation of the vibration of The vibra- b3u O4~. b3u tion lengthens one OwO bond while shortening the other one, breaking the sym- D2h metry and resulting in localization of the excess electron on the incipient Thus, this O2~. state might be expected to be strongly coupled to the photodissociation reaction.The calculated energy of this state is too high to explain the observation of highly vibrationally excited products at 355 nm (3.5 eV). This seems to be a possibility worthy of further consideration, however, as involvement of this state may provide an explanation for the sharply diÜering photodissociation dynamics in at 532 and 355 nm.O4~ In the present work, we aim to experimentally address the in—uence on the reaction dynamics of the addition of a third molecule to form We also provide addi- O2 O6~. tional information on the photodissociation dynamics of Theoretically, the O4~. O6~ cluster is an open question, as no calculations known to us have been carried out on the structure of this cluster to date.As mentioned above, though, it is known experimentally that the third is bound much more weakly than the dimer binding energy. The O2R. L i et al. 119 in—uence of clustering on these photodestruction pathways will be addressed via a combination of photoelectron and photofragment translational spectroscopy. The eÜect on the photodissociation channel is studied by examination of the photoelectron spectra of and Photoelectron spectra can provide information on the photodissociation O4~ O6~.channel in two ways. As shown by Johnson and co-workers,8h10 sequential photodetachment of photofragments can provide insights into the nascent dis- O2~(v\3) tribution of The second way is due to the facile autodetachment of O2~(v\0»3). Given a photoelectron spectrometer with good low-electron-energy trans- O2~(v[3).mission, the characteristic autodetachment peaks of can be observed as a tell-tale O2~(v) sign of highly vibrationally excited Initial studies of the photofragment energy and O2~. angular distributions produced in the DPD of are also presented, as studied by O6~ time-of-—ight spectroscopy and interpreted via Monte Carlo simulations. 2 Experimental The dissociative photodetachment spectrometer used in these experiments has been previously described in detail,13,21 and only a brief overview will be given here. Oxygen cluster anions are produced in a pulsed supersonic expansion at a repetition rate of 1 kHz by electron impact on either pure or 2»5% seeded in He»Ne with a 1 keV O2 O3 electron beam. Anions are formed by secondary electron attachment processes and cooled by collisions in the expansion.The anions pass through a skimmer to enter a diÜerentially pumped chamber, are accelerated to beam energies of 2.5»4 keV, and massselected by time-of-—ight. In the interaction region the ion packet is intercepted orthogonally by the linearly polarized 100 ps pulsed output of a mode-locked, Q-switched, cavity-dumped Nd : YAG laser using the harmonics at 532, 355 or 266 nm.The laser was focused to a spot of ca. 0.5 mm diameter, yielding —uences of ca. 700 MW cm~2 at 532 nm and ca. 200 MW cm~2 at 355 and 266 nm. The laser electric vector, E, was rotated with respected to the beam velocity using a half-wave plate. The laboratory kinetic energy and recoil angle of photodetached electrons are determined by time-of-—ight using a time- and position-sensitive photoelectron detector.21 The photoelectron recoil angle must be measured to allow correction for the large Doppler eÜect in the fast ion beam.The center-of-mass electron kinetic energy (Ek, e) resolution is ca. 4%*E/E. Calibration using the photodetachment of showed peak- O2~ position accuracy of \5 meV from eV at 532 nm and \10 meV from 1 to Ek, e\0.2»2 3 eV at 355 nm.The use of a short-pulse laser allows these measurements to be made with an extremely short (7.5 cm) —ight path. This facilitates the transmission of low energy electrons meV), allowing studies of vibrationally autodetaching (Ek, e\200 O2~. If the ion or neutral dissociates after photon absorption, the photofragments recoil out of the beam over a 0.95 m —ight path and impinge on a two-particle time- and position-sensitive detector. In the case of two-body dissociation, photofragments are determined to originate from a single dissociation event by checking for conservation of linear momentum in the center-of-mass frame.In experiments on however, three O6~, products are anticipated, so the primary observable from the photofragments is the O2 time-of-—ight (TOF) spectrum on the two halves of the detector.The overall time-of- —ight distribution can be measured and simulated, however. Measurements were made of neutral-only photofragment TOF distributions by electrostatically de—ecting any residual ions and ionic photofragments out of the beam path after the laser interaction region. 3 Results 532 nm photoelectron spectra : and O4 ó O6 ó In Fig. 3 photoelectron spectra from and are shown in the bottom and top O4~ O6~ frames, respectively. Both photoelectron spectra are dominated by a broad feature120 Excited state dynamics in oxygen clusters Fig. 3 Top frame: photoelectron spectrum of at 532 nm. Autodetachment peaks are labelled O6~ vA\5, 6, 7 and sequential photodetachment peaks from shown in the ]5 trace.The peaks O2~ labelled v@\0, 1, 2, 3, 4 correspond to photodetachment of to the labelled state of O2~(vA\0) The peaks labelled vA\1, 2, 3 correspond to photodetachment of to The O2. O2~(vA) O2(v@\0). –t to the broad DPD feature and sharp autodetachment peaks was used to extract an estimate of the relative cross sections for production of Bottom frame: photoelectron spectrum O2~(vAP5). of at 532 nm.Sequential photodetachment peaks from shown in ]10 trace. Note peak O4~ O2~ at the photon energy (hl). peaking at 0.7 and 0.6 eV This feature has been shown in our previous (O4~) (O6 ~). studies of to be due to DPD on a repulsive neutral surface : O4~ O4~]hl]O2(3&g~) It is likely that the origin of this feature is identical for with the ]O2(3&g~)]e~.O6~, third produced in the electronic ground state. Beyond that, however, the spectra O2 show considerable diÜerences. The –ne structure observed in the spectrum (see O4~ ]10 trace) originates from the primary photodissociation process O4~]hl]O2(1*g , followed by photodetachment of the photofragment v\0)]O2~(2%g ,v\0,1) O2~ with a second photon.8,13,15 The features in the photoelectron spectrum at 0.15 and 0.35 eV also arise from the photodetachment of nascent and an additional small peak O2~ reproducibly appears at the photon energy (2.33 eV).In the case of photoelectron»photofragment coincidence experiments have been O4~, carried out.15 These experiments allow the photoelectron spectrum of nascent pho- O2~ tofragments at 532 nm to be studied in greater detail by examining only photoelectrons produced in coincidence with photodissociation events characterized by kinetic energy release, in the range 0.7 to 0.9 eV.This spectrum is shown in the middle frame of ET , Fig. 4, and the photoelectron spectrum of free is shown in the bottom frame for O2~ reference.The peak positions for the photodissociated agree well with the photo- O2~ electron spectrum of free There is, however, a dramatic diÜerence between the O2~. relative intensities of the and manifolds and those of free As O2(3&g~) O2(1*g) O2~. discussed below, this is likely to be due to the molecular-frame photoelectron angular distribution for and the fact that the products of the O2~]hl]O2]e~ O2]O2~ photodissociation are strongly aligned by a parallel electronic transition with bB1.8.13R. L i et al. 121 Fig. 4 Top frame: photoelectron spectrum for as shown in Fig. 3. Middle frame: energy- O4~ gated photoelectron spectra of at 532 nm, found by binning only photoelectrons produced in O4~ coincidence with photofragment translational energy release eV.Bottom frame: 0.7\ET\0.9 photoelectron spectrum of free with product electronic and vibrational states identi–ed O2~, O2 with the combs. The peak at the photon energy is also present in this gated photoelectron spectrum, showing that this is a two photon process : the –rst photon initiates the photodissociation of and the second photon ejects an electron with a near-zero binding O4~, energy.This feature was also observed in the earlier work of Han and Johnson10 and was assigned to photodetachment of However, the coincidence measure- O2~(v\3). ment of the photofragment translational energy release show that this cannot be true energetically. Possible origins of this novel feature will be discussed further below. In the spectrum in the top frame of Fig. 3 the peak at the photon energy is no O6~ longer distinct ; however, the region from 2.0 to 2.3 eV is considerably more congested due to the production of vibrationally excited in the photodissociation of as O2~ O6~, previously discussed by Han and Johnson.10 These features are labelled as vA\1, 2 and 3 in the ]5 trace on the –gure. The most striking diÜerence from the spectrum, O4~ however, is the appearance of the prominent sharp peaks at 0.19, 0.30 and 0.41 eV labelled as vA\5, 6 and 7.These peaks can be energetically identi–ed as resulting from the autodetachment of vibrationally excited 6 and O2~ : O2(v@\0)^O2~(vA\5, 7).22,23 The –t to the spectrum allows an estimate of the magnitude of the autodetachment features to be extracted, yielding a vibrational distribution in vA\5 : 6 : 7 of 0.5 : 0.3 : 0.2, respectively. The autodetachment peaks have FWHMB50 meV.These photoelectron spectra con–rm that a large change in the photodissociation dynamics producing occurs when an is added to the core. The eÜect on the DPD O2~ O2 O4~122 Excited state dynamics in oxygen clusters process, however, appears to be minimal based on the small change in the photoelectron spectrum. 355 nm photoelectron spectra : and O4 ó O6 ó The 355 nm photoelectron spectra for and are shown in Fig. 5. The O4~ O6~ O4~ spectrum, in the bottom frame, is dominated by two broad continua, the feature A with a peak at 1.95 eV and a secondary maximum at 1.73 eV and the broad feature B rising below 1.2 eV. The feature A has been previously shown to be due to DPD to ground state molecules.13 The two maxima in A arise from the photoelectrons produc- O2(3&g~) ed in the DPD processes and the nearly degenerate O2(v\0)]O2(v\1)]e~ O2(v\ and channels.These features are not 1)]O2(v\1)]e~ O2(v\0)]O2(v\2)]e~ observed in the photoelectron at 532 nm due to the underlying photodetachment O4~ signal of as shown in Fig. 4. The broad feature B has been shown to be due to O2~ DPD to the new open channel producing There is addi- O2(3&g~)]O2(1*g)]e~.13 tional –ne structure superimposed on B at eV.The peak positions are the Ek, e\0.7 same as those observed for in the 532 nm data, indicating that these features Ek, e O6~ also correspond to vibrationally autodetaching 6, O2~ : O2(v@\0)]e~^O2~(vA\5, 7, 8). This observation of autodetaching at 355 nm in the photodissociation of is O2~ O4~ not surprising based on previous photofragment translational spectroscopy measurements in this laboratory.14 These earlier experiments showed that was produced O2~ with a wide range of internal excitation.Once again taking advantage of photoelectron» photofragment coincidence measurements on at 355 nm, these autodetachment O4~ Fig. 5 Top frame: photoelectron spectrum of at 355 nm. The autodetachment peaks are O6~ labelled vA\5, 6, 7, 8. The –t to the broad DPD feature and sharp autodetachment peaks was used to extract an estimate of the relative cross-sections for production of Bottom O2~(vAP5). frame: photoelectron spectrum of at 355 nm. Autodetachment peaks are seen as labelled in O4~ top frame.R. L i et al. 123 Fig. 6 Energy-gated photoelectron spectra of at 355 nm, found by binning only photoelec- O4~ trons produced in coincidence with photofragment translational energy release eV. The ET[1.1 –t to the broad DPD feature and sharp autodetachment peaks was used to extract an estimate of the relative cross-sections for production of O2~(vAP5). features can be examined by generating a spectrum from only those events with ET[1.1 eV.17 The spectrum in Fig. 6 shows the autodetachment peaks from more clearly O4~ due to discrimination against the ì direct œ DPD electrons produced in coincidence with lower events. The –t to the spectrum provides an estimate for the intensity of the ET (vA\5, 6, 7, 8) vibrational state of 0.48 : 0.35 : 0.09 : 0.08, respectively.The autode- O2~ tachment peak widths are similar to those observed in the spectrum at 532 nm. O6~ The photoelectron spectrum is shown in the top frame of Fig. 5. The broad O6~ continua, A and B, are very similar to the spectrum, suggesting that DPD to both O4~ and occurs in as well. The O2(3&g~)]O2(3&g~)]e~ O2(3&g~)]O2(1*g)]e~ O6~ third, weakly bound is presumably produced in the electronic ground state.The O2 features are shifted to lower electron kinetic energies (higher electron binding energies) than in by approximately 100 meV. The striking feature in the spectrum, however, O4~ is the prominence of the autodetachment peaks in This suggests that the photo- O6~. dissociation cross-section is signi–cantly higher in than in at this wavelength.O6~ O4~ The vibrational distribution does not appear to show a great diÜerence between the two species, however. The –t to the autodetachment peaks in the spectrum indicates a v\5 : 6 : 7 : 8 distribution of 0.59 : 0.25 : 0.11 : 0.05. Compared to the results on it O4~, appears that the third reduces the vibrational excitation of photoproducts at O2 O2~ 355 nm. 266 nm photoelectron spectra The 266 nm photoelectron spectra for and are shown in Fig. 7. The energy O4~ O6~ resolution is degraded at this wavelength due to the large photoelectron kinetic energy and no signi–cant diÜerences are observed between the two species. Feature B, shown to originate from in is larger than feature A, a change O2(3&g~)]O2(1*g)]e~ O4~,17 from the ratio observed at 355 nm.Recent experiments have shown that this is due to the higher photon energy accessing new repulsive states of correlating with these O4 excited molecular products in DPD.17 Previous studies of the photodissociation of O4~ have shown that the photodissociation cross-section is reduced to only ca. 10% of the DPD channel at 266 nm. Given this low cross-section and the rising laser-correlated124 Excited state dynamics in oxygen clusters Fig. 7 Top frame: photoelectron spectrum of at 266 nm. Bottom frame: photoelectron spec- O6~ trum of at 266 nm. The rising signal below 0.5 eV is due to laser-correlated photoelectrons. O4~ photoelectron background at eV, it is not surprising that autodetachment or Ek, e\0.5 sequential photodetachment features are not observable in the spectra. 266 nm neutral photofragment TOF spectra The dynamics of DPD in at 266 nm have been examined by recording photofrag- O6~ ment TOF spectra. The translational energy and angular distributions for have O4~ previously been reported, and show that DPD occurs via a parallel transition at all photofragment kinetic energies. At 266 nm the photofragment translational energy release in the DPD of peaks at 0.8 eV and has appreciable intensity out to 1.5 eV.O4~ The angular distribution is characterized by an anisotropy parameter b that rises from 0.8 to approach the asymptotic value of 2.0 at the higher kinetic energies where signi–- cant photodissociation is known to occur.14 Given the anisotropic product angular distribution, coupled with a large kinetic energy release, photofragment TOF spectra for recorded with the E vector of the laser along the ion beam exhibit a winged O4~ Doppler pro–le.The photofragment TOF spectra for show the same characteristic O6~ shape, as shown in Fig. 8. This –gure shows the TOF distribution for the neutral photofragments from recorded at a beam energy of 4.0 keV. The TOF is plotted relative O6~ to the nominal arrival time of the beam at 10.8 ls.The primary diÜerence between O6~ the TOF spectrum and the spectrum (not shown) is the observation of the O6~ O4~ small peak at the beam velocity of This feature must be due to the ìthirdœ O6~. O2 , which, given the similarity in energy and angular distributions to is evidently a O4~, spectator which plays little role in momentum conservation in the primary dissociation of the core.O4~ To further quantify the similarity between the and TOF spectra, Monte O4~ O6~ Carlo simulations were carried out.14 In these calculations, it was assumed that a two-R. L i et al. 125 Fig. 8 TOF spectrum of neutral photofragments and recorded at 266 nm with a beam energy O6~ of 4 keV. The nominal arrival time of the center-of-mass is 10.8 ls.The laser E vector was horizontal (along beam axis). The dashed-line –t shows the simulation of the high-energy-release channel, and the dotted line –t shows the low-energy-release channel from interaction with ìO4~œ the spectator O2 . body DPD of is followed by a two-body interaction between one O4~]O2]O2]e~ of the fast photofragment and the third, spectator, The DPD of was O2 O2.O4~ modelled using the photofragment energy and angular distributions reported for this process at 262 nm in ref. 14. In the subsequent collision between one of the fast O2 photofragments and the spectator the translational energy release is taken to be O2 , \0.1 eV and peak at 0 eV in the simulation. As the solid line simulation shows, the agreement between the DPD center-of-mass energy and angular distributions and O4~ the result is striking.No adjustable parameters were used in this –t other than the O6~ fraction of the spectator detected. Most of the spectator is not detected in this O2 O2 con–guration due to the beam-block at the center of the detector. These results show that the DPD of is described very well as a two-body dissociation of the core, O6~ O4~ with a negligible perturbation by the third The most noticeable diÜerence between O2 .the solid line simulation and the data is the larger signal observed at ^200 to ^300 ns. This is signal produced from the high energy part of the photofragment translational energy release distribution, which contains contributions from ion photodissociation.14 This may indicate an increase in the photodissociation branching ratio at 266 nm as well. 4 Discussion The photoelectron and photofragment results presented here reveal contrasting eÜects of the clustering of with on the photodestruction dynamics of the core. O2 O4~ O4~ O4~ itself is a very interesting species which undergoes photodissociation and DPD at the wavelengths studied in this work.The evidence presented here indicates that addition of a third increases the relative photodissociation cross-section at 532 and 355 nm. O2 More importantly, the third causes a drastic change in the photodissociation O2 dynamics at 532 nm, yielding substantial vibrational excitation in the product, as O2~ shown by the autodetaching v\5, 6 and 7 states of observed at low in the O2~ Ek, e photoelectron spectra.The continua in the photoelectron spectra associated with DPD, on the other hand, show little change upon clustering with an additional Further- O2 . more, the TOF spectra recorded for DPD at 266 nm reveal that the translational energy126 Excited state dynamics in oxygen clusters and angular distribution for the DPD of are virtually unchanged from The O6~ O4 .third is truly a spectator with respect to photoexcitation leading to DPD. O2 Autodetachment dynamics of O2 ó The observation of autodetaching states of nascent is analogous to the recent O2~ observation of vibrationally autodetaching formed in dissociative electron attach- O2~ ment to reported by Allan et al.24 As noted by Allan et al., autodetachment provides O3 a novel probe of the product state distribution in an ionic dissociation yielding an autodetaching molecular anion. The autodetachment peaks observed in the photoelectron spectra for at 532 and 355 nm and at 355 nm are dominated by maximum *v O6~ O4~ autodetachment transitions, i.e.In fact, no identi–able O2(v@\0)]e~^O2~(vA\5). peaks associated with other transitions were observed, although given that this signal is on top of a large DPD background, it is unlikely that small peaks associated with other transitions would be easily observable.Autodetachment is known to produce inherently non-Franck»Condon vibrational distributions as it results from a breakdown in the Born»Oppenheimer approximation. As discussed by Schulz, autodetachment in a system like which involves a d-wave (l\2) continuum electron, often favors maximum O2~, kinetic energy photoelectrons, as the higher energy electron more readily tunnels through the l\2 centrifugal barrier.25 The autodetachment features provide a novel probe of product vibrational distributions since autodetaches with a O2~ O2~(vP4) quantum yield of unity.Observation of photodetachment by a second photon, O2~(vO shown in the 532 nm data, certainly provides a measure of the rela- 3)]hl]O2]e~, tive population of those low-lying vibrational states, however, the intensity of this signal is dependent on the square of the laser —uence.Further studies of the product vibra- O2 tional distribution in the autodetachment of will be of value in extraction of O2~(v[3) detailed vibrational distributions from the data presented here.Photodissociation of O4 ó These experiments provide interesting new insights into the photodissociation dynamics of At 355 nm, the observation of vibrational autodetachment of con- O4~. O2~(v[5) –rms the previous photofragment translational spectroscopy results which indicated the production of with signi–cant internal excitation at that wavelength.The peak O2~ widths for all of the autodetachment features are observed to be of the order of 50 meV. In the absence of rotational broadening or other perturbations, observation of a 20 meV splitting arising from the spin»orbit states of could be expected.26 Further eÜorts to O2~ determine the rotational distribution of the will require a consideration of the O2~ propensity rules for vibrotational transitions in autodetachment.27 The energy-gated photoelectron spectra recorded at 532 nm reveal two novel results. The –rst concerns the change in intensity for the and channels relative O2(3&g~) O2(1*g) to free The origin of this eÜect is most likely due to the fact that the nascent O2.O2~ produced in the photodissociation of is strongly aligned.It is well known that O4~ photoelectrons produced in coincidence with the formation of are character- O2(3&g~) ized by a highly anisotropic laboratory angular distribution peaked perpendicular to the electric vector of the laser, while those corresponding to are nearly isotropic.28 O2(1*g) The lowest partial wave allowed in photodetachment is a p-wave (l\1).29 This and the higher partial waves will interfere above threshold and will in general lead to an anisotropic molecular frame photoelectron angular distribution as well.30 Given the restricted detection geometry in the current experiments, in which photoelectrons are only detected when they recoil into a 20° cone above the ion»laser interaction region, detection of the nearly isotropic photoelectrons produced in coincidence with is O2(1*g) favored.R.L i et al. 127 The more novel result, however, is the observation of a small photoelectron peak at the photon energy. The appearance of this feature at a photofragment translational energy release of 0.8 eV shows unambiguously that the photodetachment process which gives rise to this feature occurs on the repulsive ionic surface correlating to O2(1*g) after the photofragment repulsion has been determined.In Rydberg states ]O2~(2%g) of neutral atoms and molecules and dipole-bound states of negative ions31,32 it is common to see photoelectrons at nearly the photon energy; however, this is not expected in the case of At the risk of some speculation, consider the following O4~. scenario.The excess electron in is delocalized over the two moieties, as shown O4~ O2 by experimental17 and theoretical results.18 As the moieties begin to separate in the O2 photodissociation event a point is reached beyond which the electron is localized on one of the Just before localization occurs, some part of the electronic wavefunction may O2 . be in a region of near-zero electron binding energy by analogy to the asymptotic limit of electron transfer between and at large distances, which requires the electron to O2 O2~ enter the continuum.If a second photon intercepts the dissociating complex in this con–guration, the photoelectron could be ejected with the full photon energy in a twoelectron transition : O4~]hl][O4~]*]hl ]O2(3&g~, v)]O2(3&g~, v)]e~(Ek, e\hl).The timescale over which this sequential photon absorption would have to occur is by necessity on a timescale of tens of femtoseconds. The distance in is calcu- O2wO2 O4~ lated to be 2.15 At a kinetic energy of 0.8 eV, this distance will increase by 1 in ca. ”. ” 30 fs. For this feature to be observed with both nanosecond10 and picosecond lasers, then, the cross-section would have to be large.We hope to examine the —uencedependent behavior of this feature using a shorter pulse (100 fs»1 ps) laser in the near future. Photodissociation and dissociative photodetachment dynamics of O6 ó The origin of the large change in the photodissociation dynamics between and O4~ O6~ at 532 nm constitutes an interesting question. As mentioned in the introduction, DeLuca et al.9 interpreted the photodissociation of in the absence of a signi–cant absorp- O6~ tion in at 1064 nm in terms of a charge-transfer-to-solvent model.The current O4~ measurements by no means rule out such a mechanism at 1064 nm or any other wavelength. However, the observations in our laboratory of direct photodissociation of O4~ on at least three repulsive ionic states14 suggests that it is worthwhile to consider the change in dynamics in terms of a perturbation of the repulsive states of the molecular anion by the addition of a third, weakly bound Additional evidence in favor of O4~ O2 .this interpretation comes from the marked similarity in the photodissociation dynamics of and at 355 nm. Photodissociation of both species yields high vibra- O4~ O6~ O2~ tional excitation at 355 nm.In the introduction the possible role played by the vibronically allowed repulsive 2Au state in the photodissociation of and the production of highly vibrationally excited O4~ at 355 nm was discussed. Given the similarity of the photodissociation dynamics of O2~ at 532 and 355 nm to the 355 nm photodissociation dynamics of it is logical O6~ O4~, to consider a common origin for this behavior.The third might stabilize this repul- O2 sive state in the cluster relative to the ground state. This stabilization could O4~ …O2 allow photoexcitation of this state at 532 nm in leading to the production of O6~, v). The energetics of this process in must be carefully con- O2(1*g)]O2~(2%g, O6~ sidered, however. Photodissociation of at 532 nm produces O4~ O2(1*g)]O2~(2%g) with a maximum excess energy of 0.89 eV, of which 0.8 eV appears in translation.Thus, for the highest vibrational state of energetically allowed is v\7 (0.89 eV O4~, O2~128 Excited state dynamics in oxygen clusters above the zero point). However, Hiraoka has determined the binding energy of to O2 to be ca. 0.11 eV.7 This result is consistent with the photoelectron spectra, and is O4~ likely to be chie—y due to stabilization of the ground state relative to the photodissociation asymptote.This shift is sufficient to rule out the production of O2~(v\7) from the photodissociation of at 532 nm. O6~]O2(3&g~)]O2(1*g)]O2~(2%g) A second explanation for the photodissociation dynamics of at 532 nm is that O6~ the clustering of onto opens up the energetically most stable photodissociation O2 O4~ channel, producing at 532 nm.Given that this product channel 2O2(3&g~)]O2~(2%g) must be operative to explain the photodissociation results reported by DeLuca et al.9 at 1064 nm in this is plausible. As shown in Fig. 2, two dipole-allowed repulsive O6~, states in correlate to this asymptote.Excitation to the state will occur via a O4~ 2B3g parallel transition, while the state is reached by a perpendicular transition. In 2B2g future measurements, we hope to determine the photofragment anisotropy for photodissociation of which should provide further insights into the possible role played O6~, by these lower-lying repulsive states in both and O4~ O6~. The increase in the photodissociation branching ratio relative to DPD as the third is added to may be evidence for charge-transfer-to-solvent processes similar to O2 O4~ those invoked by DeLuca et al.9 in their studies below the photodetachment threshold for at 1064 nm.The additional could serve to ìcageœ the photodetached electron O6~ O2 by capture to form vibrationally excited as shown by the electron attachment O2~, studies of neutral clusters by Maé rk and co-workers.11 The electron attachment O2 studies have shown that this process is only efficient for eV, so it is possible Ek, e\0.4 that this process may consume the low energy electrons produced in the DPD of A O6~.second aspect of caging in the photodissociation of oxygen clusters is also worth consideration.A hard collision between the nascent produced in photodissociation of O2~ the core with the third might be expected to lead to vibrational excitation. The O4~ O2 transfer of several quanta in such a collision is unlikely, however.33 Furthermore, the near-two-body dynamics observed in the DPD of at 266 nm indicate that col- O6~ lisional interactions with the third are likely to be negligible.In the future, we will O2 carry out measurements of the vector correlations between the photofragments and photoelectrons produced in the photodestruction of If there are signi–cant inter- O6~. actions with the third after photon absorption, by either a photodetached electron or O2 the nascent little or no angular correlation will be observed between the products.O2~, In contrast to the eÜect on the photodissociation dynamics, the dynamics of DPD appear to be only slightly perturbed by the addition of an to at 266 nm. As the O2 O4~ TOF measurements presented above show, DPD of is a pseudo-two-body process, O6~ with minimal momentum transfer to the third While no calculations have been O2 . carried out on the structure of to date, this observation alone can provide limited O6~ structural insights.At 266 nm, it is known that DPD in occurs via a parallel O4~ transition, with the photofragments strongly peaked along the electric vector. The preservation of this behavior in argues that the third must lie out of the plane of the O6~ O2 core, so the rapidly recoiling molecules produced in DPD of the core have only O4~ O2 a minimal nearly elastic interaction with the third O2 . 5 Conclusions Although the addition of a third to the molecular anion has only a small eÜect O2 O4~ on the ion stability, it is found to have a dramatic eÜect on the dynamics of ionic photodissociation. This is in marked contrast to the small eÜect observed on the dynamics of DPD. Further work, both experimental and theoretical, is required to fully describe the photodestruction processes at work in the anionic clusters of oxygen.While calculations of the electronic structure of these systems are difficult, reliable calculations for have –nally become available. Even in the case of there have been no O4~ O4~R. L i et al. 129 theoretical studies of the dynamics of DPD and ionic photodissociation. An important test of the electronic structure and future dynamical studies of oxygen anions will be to explain in detail the dramatic eÜects on the photodissociation dynamics induced by the addition of an oxygen molecule to O4~.Experimentally, further studies are in order to clarify the nature of three-body dissociation in This system is small enough to permit a detailed examination of the O6~.dynamics by a coincidence measurement of the energy and angular distributions of all the photofragments We have built an apparatus which will allow (O2]O2]O2]e~). such measurements on this and other three-body cluster and molecular dissociation processes to be carried out. Such measurements should reveal the detailed nature of the partitioning of momentum among the three products, and should also provide the O2 information required to distinguish between the charge-transfer-to-solvent mechanism proposed by DeLuca et al.,9 and any role played by direct dissociation on the perturbed repulsive states of the molecular anion ìsolvatedœ by If the charge-transfer-to- O4~ O2 .solvent model is correct, it is doubtful that a large anisotropy in the O2]O2]O2~ product angular distributions will be observed.By carrying out these detailed measurements we plan on contributing to the growing understanding of the transition between gaseous and condensed phase systems. In addition, we hope that by providing a more detailed understanding of the chemistry of oxygen clusters, speci–c new insights into the chemistry of solid and liquid can be gained.O2 We thank Drs. Aquino, Walch and Taylor for sharing the results of their calculations on prior to publication, and for many useful discussions. R.E.C. is a Camille Dreyfus O4~ Teacher-Scholar, A.P. Sloan Research Fellow and a Packard Fellow in Science and Engineering. This work was supported by the US Air Force Office of Scienti–c Research under Grant F49620-96-1-0220.A.K.L. was supported by AFOSR AASERT Grant F49620-97-1-0387. References 1 J. M. Farrar, in Cluster Ions, ed. T. Baer, C. Y. Ng and I. Powis, Wiley, New York, 1993, pp. 243»317. 2 A. W. Castleman, Jr. and K. H. Bowen, Jr., J. Phys. Chem., 1996, 100, 12911. 3 J. T. Snodgrass, C. M. Roehl and M. T. Bowers, Chem. Phys. L ett., 1989, 159, 10; T. Nagata and T. Kondow, J. Chem. Phys., 1993, 98, 290. 4 A. B. Jones, A. L. M. Buxey, P. R. Jukes, J. A. Smith and A. J. Stace, J. Chem. Phys., 1995, 103, 474. 5 V. Vorsa, S. Nandi, P. J. Campagnola, M. Larsson and W. C. Lineberger, J. Chem. Phys., 1997, 106, 1402. 6 B. J. Greenblatt, M. T. Zanni and D. M. Neumark, Science, 1997, 276, 1675. 7 K. Hiraoka, J. Phys. Chem., 1988, 89, 3190. 8 L. A. Posey, M. J. DeLuca and M. A. Johnson, Chem. Phys. L ett., 1986, 131, 170. 9 M. J. DeLuca, C. C. Han and M. A. Johnson, J. Chem. Phys., 1990, 93, 268. 10 C. C. Han and M. A. Johnson, Chem. Phys. L ett., 1992, 189, 460. 11 S. Matejcik, A. Kiendler, P. Stamp—i, A. Stamatovic and T. D. Maé rk, Phys. Rev. L ett., 1996, 77, 3771. 12 T. D. Maé rk, K. Leiter, W. Ritter and A. Stamatovic, Phys. Rev. L ett., 1985, 55, 2559. 13 K. A. Hanold, C. R. Sherwood and R. E. Continetti, J. Chem. Phys., 1995, 103, 9876. 14 C. R. Sherwood, K. A. Hanold, M. C. Garner, K. M. Strong and R. E. Continetti, J. Chem. Phys., 1996, 105, 10803. 15 K. A. Hanold, M. C. Garner and R. E. Continetti, Phys. Rev. L ett., 1996, 77, 3335. 16 R. N. Zare, Mol. Photochem., 1972, 4, 1. 17 K. A. Hanold, M. C. Garner and R. E. Continetti, unpublished work. 18 A. Aquino, S. P. Walch and P. R. Taylor, personal communication. 19 K. Andersson and B. O. Roos, in Modern Electronic Structure T heory, Part 1, ed. D. Yarkony, World Scienti–c Publishing, Singapore, 1995. 20 R. A. Kendall, T. H. Dunning and R. J. Harrison, J. Chem. Phys., 1992, 96, 6796. 21 K. A. Hanold, C. R. Sherwood, M. C. Garner and R. E. Continetti, Rev. Sci. Instrum., 1995, 66, 5507. 22 M. J. Travers, D. C. Cowles and G. B. Ellison, Chem. Phys. L ett., 1989, 164, 449. 23 K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure IV . Constants of Diatomic Molecules, Van Nostrand, New York, 1979, pp. 506»507.130 Excited state dynamics in oxygen clusters 24 M. Allan, K. R. Asmis, D. B. Popovic, M. Stepanovic, N. J. Mason and J. A. Davies, J. Phys. B: At. Mol. Opt. Phys., 1996, 29, 3487. 25 G. J. Schulz, Rev. Mod. Phys., 1973, 45, 423. 26 M. Allan, J. Phys. B: At. Mol. Opt. Phys., 1995, 28, 5163. 27 U. Hefter, R. D. Mead, P. A. Schulz and W. C. Lineberger, Phys. Rev. A, 1983, 28, 1429. 28 M. W. Siegel, R. J. Celotta, J. L. Hall, J. Levine and R. A. Bennett, Phys. Rev. A, 1972, 6, 631. 29 K. J. Reed, A. H. Zimmerman, H. C. Andersen and J. I. Brauman, J. Chem. Phys., 1976, 64, 1368. 30 D. Dill, J. Chem. Phys., 1976, 65, 1130. 31 R. L. Jackson, P. C. Hiberty and J. I. Brauman, J. Chem. Phys., 1981, 74, 3705. 32 C. G. Bailey, C. E. H. Dessent, M. A. Johnson and K. H. Bowen, Jr., J. Chem. Phys., 1996, 104, 6976. 33 X. Yang, J. M. Price, J. A. Mack, C. G. Morgan, C. A. Rogaski, D. McGuire, E. H. Kim and A. M. Wodtke, J. Phys. Chem., 1993, 97, 3944. Paper 7/05823C; Received 8th August, 1997

ISSN:1359-6640    

DOI:10.1039/a705823c

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss., 1997, 108, 131»138 Direct detection and spectroscopy of O4* Holly M. Bevsek, Musahid Ahmed, Darcy S. Peterka, F. Cortney Sailes and Arthur G. Suits* Department of Chemistry, University of California, Berkeley and Chemical Sciences Division, L awrence Berkeley National L aboratory, Berkeley, CA 94720, USA We have produced and directly detected a metastable state of tetraoxygen in a molecular beam, both by means of a dc discharge and by photodissociation of ozone in the collision region.The produces a complex O4* spectrum from which general conclusions may be made about its energetics and structure. The detection proceeds through a (1]1) resonant photoionization process in the vicinity of 300 nm, implying an energy for this species about 4 eV above that of two isolated molecules.A predominance of O2 peak frequency diÜerences in the range 411»419 cm~1 supports a cyclic D2d geometry as predicted by ab initio calculations, although a de–nitive judgment on the structure of awaits further study. O4* The existence of a stable, covalent molecule has been debated since Lewis –rst made O4 this hypothesis in 1924.1 Although the weakly bound dimer was identi–ed in the (O2)2 1960s,2 the search continued for a cyclic structure that would have enhanced stability due to pairing of the two unpaired electrons in oxygenœs highest occupied molecular p2p * orbital.The possibility of a metastable cyclic oxygen polymer is strengthened by considering the well known stability of sulfur rings. This system is also interesting since could be used as a high energy density material (HEDM) due to its energetic c-O4 dissociation to two ground state molecules: O2 O4 ]2O2 ; *rH\[48 kcal mol~1 based on the assumption3 of normal OwO single bonds in and neglecting ring strain O4 contributions.The –rst theoretical attempt to determine whether a stable cyclotetraoxygen species exists was undertaken by Adamantides et al.4 They found a minimum at the SCF-CI level in the potential surface for a geometry with approximately equal OwO bond D2d lengths of ca. 1.4 close to that of a normal OwO single bond. Calculations at a ”, higher level of theory were later undertaken by Schaefer and co-workers,3 con–rming the geometry. Harmonic vibrational frequencies (see Table 1) were calculated along D2d with the barrier to dissociation. This value was found to be about 6 kcal mol~1, implying that is too unstable to be useful as a HEDM.Several other calculations5h7 have O4 been performed to determine whether a branched form of could exist. Such a D3h O4 state was found to exist approximately 2 eV above the geometry; however, it was D2d also found to be unstable with respect to dissociation.A comparison of the various calculations on may be found in Fig. 1. O4 In spite of its instability, several attempts to produce have been made. Helm and O4 Walter9 have used charge transfer neutralization of to form in O4 ` O4 non-(O2)2 geometries ; however, they only detected the dissociation products. Production of O2 O4 * Email: agsuits=lbl.gov 131132 Detection and spectroscopy of O4* Table 1 Predicted harmonic vibrational frequencies for the geometry of from ref. 4 D2d O4 assignment frequency/cm~1 symmetry ring stretch 877 A1 ring deformation 783 B1 OwO stretch 678 E ring deformation 793 B2 ring pucker 396 A1 in non-dimer con–gurations was also performed by Continetti and co-workers10 using the dissociative photodetachment technique with Again, only the dissociation O4~.O2 products were observed, although they did not perform detection in the plane of the O4~ beam. Recently, Jacox and co-workers11 have attempted to produce species by c-On Fig. 1 Energetic comparison of several calculations O4H. M. Bevsek et al. 133 codepositing with at 5 K. Although interesting species such as and O3 Ne*(3PJ) O3~ possibly an complex were observed, there was no evidence for formation of O2… … …O4 ` any species.Recently, we have produced metastable containing more than 4 eV c-On O4* above the energy of 2 molecules, consistent with predictions for A description O2 c-O4 . of how we prepare this species and preliminary –ndings follow. Experimental A schematic diagram of the experiment is given in Fig. 2. Neat was passed through a O2 Proch»Trickl12 piezoelectric pulsed valve.The pulsed (200 ls) beam then passed O2 through the center of two stainless steel electrodes, one at ground potential and the second at ]3»5 kV. The ground plate was approximately 3 mm from the nozzle, and grounded to it. The pulse of between the electrodes produced an arc discharge which O2 extended back to the nozzle ori–ce (as evidenced by widening of the ori–ce after many hours of use).The beam was then skimmed and travelled 6 cm where it was intersected by the unfocussed, frequency doubled output of a pulsed dye laser (Spectra-Physics, PDL-1) pumped by a Nd : YAG laser (Quantel, 592). The laser —uence was typically 1 mJ cm~2 or less. Resonance enhanced multi-photon ionization (REMPI) produced O4 ` ions which were accelerated through a 20 cm time-of-—ight tube.The ions struck a microchannel plate and the secondary electrons were accelerated towards a phosphor screen. The phosphorescence was detected by a photomultiplier tube, and the resulting voltage displayed on an oscilloscope. REMPI spectra were collected by passing the O4 ` signal through a boxcar integrator and scanning the ionization wavelength.Interestingly, we discovered that was also produced when 5% seeded in He O4* O3 was photodissociated by focused 266 nm light at the nozzle of the pulsed valve. Replacing the ozone mixture with pure still produced but at approximately half the O2 O4*, signal intensity. Spectra collected using this method of preparation were identical in O4* Fig. 2 Experimental schematic diagram134 Detection and spectroscopy of O4* the spectral region scanned (300»315 nm) to those in which the was formed with the O4* discharge. Thus it appears that is produced by ozone photodissociation in the O4* environment of the supersonic expansion, providing a second pathway for the formation of O4* . Results and Discussion Typical time-of-—ight mass spectra with the discharge on and oÜ are displayed in Fig. 3. Mass calibration was performed using the signal visible in Fig. 3, and later by mixing O2 He and Ar with and observing the non-resonant He* and Ar* signals. We have O2 examined the region from 276 to 332 nm and these spectra, produced using a neat O2 beam, are displayed in Fig. 4. This spectrum shows many intense peaks which are discussed in detail below.A power dependence study was performed to investigate the energetics of this system; the results are shown in Fig. 5. The data are an average of the power dependence of four peaks in the 320»325 nm spectral region. Note the linear dependence which is obtained for the –rst three points, after which some saturation apparently occurs. A linear least-squares –t to the data prior to saturation (dashed line) yields a slope of 0.92, consistent with a (1]1)REMPI process with saturation of the ionization step.An overall linear –t to all of the data (solid line) yields a slope of 0.80. The spectrum in Fig. 3 allows us to make some general statements about the energetics of the initial and intermediate states. The fact that we see vibrational structure out to 327 O4* nm indicates that the initial state extends at least up to 4.1 eV above 2 while the O2 , intermediate state extends up to 7.9 eV.The evidence thus indicates that these spectra represent a metastable form of containing substantial internal energy relative to two O4 molecules. O2 Alternative explanations for the intense spectra are not satisfying : possible can- O4 ` didates include higher polymers of oxygen that undergo dissociative ionization to give Although this explanation cannot be rejected absolutely, since there is no evidence O4 `.to support the existence of higher oxygen polymers, the simpler explanation is preferred. Ions in the beam are de—ected by the ion optics and do not survive into the probe Fig. 3 Time-of-—ight spectra from an molecular beam with the discharge on (dashed line) and O2 oÜ (solid line).Laser power is 1 mJ pulse~1 at 306 nm.H. M. Bevsek et al. 135 Fig. 4 (1]1)REMPI spectrum of from 276 to 332 nm. Laser power is 800 lJ pulse~1. O4* region, so they cannot account for the observed spectra. These spectra were not observed in beams in the absence of oxygen or ozone nor with the discharge oÜ.By assuming a typical peak velocity of the beam to be 8]104 cm s~1 one can O4* estimate a lower bound to the lifetime of 80 ls, although it may be much longer. These spectra imply both the existence of the metastable and an excited intermediate state O4* or states through which the resonant detection occurs. Furthermore, the narrowness of the spectral peaks indicates that the REMPI intermediate state must also have a relatively long lifetime, precluding strong predissociation of the intermediate state.The spectrum is quite congested which is surprising considering the high symmetry expected for this system. Hot bands and combination bands are expected with a hot Fig. 5 Power dependence of four peaks in the 320»325 nm spectral region.Solid line is a O4* linear least-squares –t to the entire data set ; dashed line is a linear least-squares –t to the –rst three points. Power density is measured in J cm~2 pulse~1.136 Detection and spectroscopy of O4* discharge source, although it is doubtful that all the peaks observed are due to excitations from only two or three fundamental frequencies. Deviations from the orbitalsymmetry selection rules are known to occur when highly symmetric species undergo Jahn»Teller distortion,13 and it is possible that this is the case with Furthermore, O4* .the geometry of the intermediate state or states is unknown and there could be as many as six excited vibrational modes, the maximum allowed for a tetra-atomic system. In light of this, we have measured the frequency diÜerence between 99 peaks and looked for commonly occurring diÜerences.Table 2 summarizes the peak-to-peak frequency diÜerences along with their recurrence. There are naturally many other frequently occurring diÜerences as would be expected with a total of 4851 peak diÜerences ; we chose to examine only those with 18 or more repetitions within the range 300Ol/cm~1O2000 for simplicity.The conclusions we reach are therefore clearly tentative, and a more de–nitive discussion must await further studies. Based on the 22 most commonly occurring frequency diÜerences, we can make several observations. The two most often discovered diÜerences are 437 and 801 cm~1 with 24 recurrences each. Together, the peaks comprising these diÜerences account for 12 of the strongest peaks in the spectrum (see Table 3 for a listing of the peaks).The 801 cm~1 frequency diÜerence has the additional feature of a four-peak progression occurring at 35 652 cm~1 (280.49 nm), 34 853 cm~1 (286.93 nm), 34 054 cm~1 (293.65 mm), and 33 254 cm~1 (300.72 nm). Furthermore, a frequency diÜerence of 1599 cm~1 is observed and is mostly made up of weak- and medium-intensity peaks, suggesting it might be an overtone of 801 cm~1.This suggests that this frequency is a fundamental mode of and could either be the OwO stretch or ring deformation mode O4*, l3 l4 calculated by Schaefer and co-workers.4 No such ìovertoneœ was found for the 437 cm~1 frequency. Closer examination of the frequency diÜerences in Table 2 reveals some relations among these frequencies.The 1639 cm~1 frequency, for example, can be obtained within Table 2 Commonly occurring frequency diÜerences in the REMPI spectrum O4* frequency/cm~1 repetitions 312^1 18 329^1 22 340^1 18 382^1 18 386^1 20 404^1 22 411^1 22 437^1 24 447^1 20 497^1 18 537^1 18 633^1 18 732^1 18 801^1 24 816^1 24 836^1 18 941^1 20 1159^1 22 1599^1 22 1639^1 22 1813^1 18 1954^1 22H. M.Bevsek et al. 137 Table 3 Frequencies and wavelengths of the most often repeated frequency diÜerences *l/cm~1 frequency/cm~1 wavelength/nm 437 34 792 34 355 287.42 291.08 34 145 33 709 292.87 296.66 33 244 32 807 300.81 304.81 32 680 32 247 307.57 311.75 32 487 32 048 307.82 312.03 32 088 31 653 311.64 315.93 31 726 31 288 315.20 319.61 31 430 30 992 318.17 322.66 31 369 30 933 318.79 323.38 31 244 30 807 320.06 324.60 31 221 30 783 320.30 324.85 801 35 783 34 982 279.46 285.86 35 652 34 853 280.49 286.92 35 144 34 343 284.54 291.18 34 944 34 145 286.17 292.87 34 853 34 054 286.95 293.65 34 054 33 254 293.65 300.72 32 088 31 288 311.64 319.61 32 077 31 278 311.75 319.71 31 861 31 061 313.86 321.95 31 430 30 628 318.17 326.50 31 411 30 612 318.36 326.67 error limits from a sum of the 801 cm~1 and 835 cm~1 frequencies.Similarly, the sum of the 329 cm~1 and 403 cm~1 frequencies gives 732 cm~1, 339 cm~1 and 497 cm~1 gives 836 cm~1, 403 cm~1 and 410 cm~1 gives 816 cm~1 and the 941 cm~1 frequency can be obtained by adding 403 cm~1 and 536 cm~1. Of course, any one of these ìcombinationsœ could also indicate a diÜerence band, i.e., 1639 cm~1 could be a fundamental frequency, producing 801 cm~1 by subtraction of 835 cm~1.Again, without further studies the experimental vibrational frequencies of remain an open question. O4* Perhaps the most important feature of the spectrum is a proliferation of frequency separations in the 411»419 cm~1 range. The 411^1 cm~1 diÜerence is listed in Table 2 since it met the criterion of a minimum of 18 recurrences ; however, there are 12 recurrences of a 415^1 cm~1 and 16 recurrences of a 419^1 cm~1 diÜerence.The 415 cm~1 diÜerence is especially striking as it corresponds to the diÜerence of the two very intense peaks at 302.13 nm and 305.96 nm and at 284.03 nm and 287.42 nm. This frequency range is also very close to the predicted3 value of the pucker mode c-O4 l5 and the observed range could be the result of anharmonicity.If this is indeed a fundamental mode, the geometry is essentially con–rmed, as the smallest frequency D2d expected for a structure should be greater than 495 cm~1, the out-of-plane bending D3h vibration of planar SO3 .14 The mechanism of formation of the molecule is of course a matter of speculation, but it is likely that the discharge produces a critical combination of a plasma rich in excited molecules and rapid supersonic cooling.Although the evidence for this as Lewisœ O2 O4* cyclic molecule is certainly incomplete at this stage, this remains the most plausible explanation for the observations. Other experiments currently underway include direct VUV probing of the beam, photoelectron spectroscopy and two color spectroscopy experiments. These should provide a more complete picture of the properties of this interesting molecule.138 Detection and spectroscopy of O4* Conclusions We have produced and directly detected a metastable state of tetraoxygen both by means of a dc discharge and by photodissociation of ozone in the collision region of a molecular beam.We have determined the detection to proceed through a (1]1)REMPI process, and have recorded the spectrum from 278 to 327 nm. The produces a O4* O4* complex spectrum from which general conclusions may be made about the structure of A predominance of peak frequency diÜerences in the range 411»419 cm~1 supports O4*. a geometry, as predicted by Adamantides et al.4 and Schaefer and co-workers.3 D2d Other commonly occurring diÜerences compare well with this assignment, although a de–nitive judgement on the structure of awaits further study, which we are pursuing.O4* H.M.B. acknowledges valuable discussions with Prof. R. Bartlett, Dr R. Copeland, Dr C. Dressler, Prof. Y. T. Lee and Prof. J. Lombardi. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the US Department of Energy under Contract no.DE-AC03-76SF00098. References 1 G. N. Lewis, J. Am. Chem. Soc., 1924, 46, 2027. 2 R. E. Leckenby and E. J. Robbins, Proc. R. Soc. L ondon A, 1965, 265, 389. 3 (a) E. T. Seidl and H. F. Schaefer, J. Chem. Phys., 1988, 88, 7043; (b) K. M. Dunn, G.E. Scuseria and H. F. Schaefer, J. Chem. Phys., 1990, 92, 6077; (c) E. T. Seidl and H. F. Schaefer, J. Chem. Phys., 1992, 96, 1176. 4 (a) V. Adamantides, D. Neisius and G. Verhaegen, Chem. Phys., 1980, 48, 215; (b) V. Adamantides, Chem. Phys., 1980, 48, 221. 5 I. and E. W. Nilssen, Chem. Phys. L ett., 1989, 157, 409. R‘egen 6 M. Hotokka and P. Pyykkoé , Chem. Phys. L ett., 1989, 157, 415. 7 E. Ferreira, P. Gardiol, R. M. Sosa and O. N. Ventura, J. Mol. Struct., 1995, 335, 63. Note added in proof: recent high level calculations –nd the form at ca. 4.2 eV, A. Korkin, M. Nooijen, J. D. Watts D3h and R. J. Bartlett, unpublished work. 8 R. Lindh and L. A. Barnes, J. Chem. Phys., 1994, 100, 224. 9 H. Helm and C. W. Walter, J. Chem. Phys., 1993, 98, 5444. 10 (a) C. R. Sherwood, M. C. Garner, K. A. Hanold, K. M. Strong and R. E. Continetti, J. Chem. Phys., 1995, 102, 6949; (b) K. A. Hanold, M. C. Garner and R. E. Continetti, Phys. Rev. L ett., 1996, 77, 3335. 11 C. L. Lugez, W. E. Thompson and M. E. Jacox, J. Chem. Phys., 1996, 105, 2153. 12 D. Proch and T. Trickl, Rev. Sci. Instrum., 1989, 60, 713. 13 D. C. Harris and M. D. Bertolucci, Symmetry and Spectroscopy, Dover, New York, 1989. 14 V. E. Bondybey and J. H. English, J. Mol. Spectrosc., 1985, 109, 221. Paper 7/05535H; Received 30th July, 1997

ISSN:1359-6640    

DOI:10.1039/a705535h

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Faraday Discuss., 1997, 108, 139»159 Rydberg states in quantum crystals NO in solid H2 Franco Vigliotti,a Majed Chergui,a Meinrad Dickgiesserb and Nikolaus Schwentnerb a Institut de Physique des Sciences, de L ausanne, Expeç rimentale, Faculteç Universiteç CH-1015 L ausanne, Switzerland b Institut Experimentalphysik, Freie Berlin, Arnimallee 14, D-14195 Berlin, fué r Universitaé t Germany Fluorescence, excitation and —uorescence depletion spectra of the lowest Rydberg states of NO trapped in matrices are reported.The absorption H2 bands are shifted by about 0.58 eV to the blue of the gas phase energy. They are strongly broadened and exhibit an asymmetry by a blue wing. The —uorescence bands are signi–cantly narrower, with a red wing, and lie very close to the gas phase energy.The absorption lineshape can be accounted for by the large extension of the ground state wavefunction, due to the strong contribution of the zero point motion in the lattice. The absorption» H2 emission Stokes shift is interpreted in terms of ìbubbleœ formation around the Rydberg excited molecule. A moment analysis of the absorption and emission bands in the harmonic approximation shows that most of the absorption»emission Stokes shift is used up as energy to create the ìbubbleœ around the excited molecule.The —uorescence depletion spectrum yields Rydberg»Rydberg transitions very close to the gas phase energy. This, together with the —uorescence spectra, indicates that the molecule is in a quasi-free, gas-phase-like state in the expanded cage.The excitation spectra and the —uorescence depletion spectra indicate a severe compression of the Rydberg series of NO in matrices, which can be accounted for by a large H2 negative electron affinity of solid Concerning the intramolecular energy H2 . relaxation in NO, it is found that the Rydberg%valence relaxation processes follow much the same pattern as observed in rare gas matrices for the lower valence states.For the higher valence states, a photochemical route is suggested. For the vibrational relaxation by *v\2 in the A state and for the C»A electronic relaxation, intermolecular energy transfer processes between NO molecules are invoked, which occur in the sub-ns timescale. I Introduction There is intense interest in describing the energy storage and energy release properties of solid hydrogen in a large class of applications such as rocket propulsion1 and fusion technology.In this context, laboratory studies of impurity doped solid hydrogen can deliver information at a microscopic level using the impurity as a local probe of the structure and dynamics by means of its spectroscopy. This has led to an increase in such studies over the past few years.1 These studies also take place in the background of the eÜorts aimed at a fundamental description of quantum properties such as super—uidity (for helium), tunnelling, zero point motions, etc., and their eÜects on chemical reactivity, using spectroscopic techniques.2 With the advent of ultrafast laser techniques it is now possible to study dynamic properties of condensed phase systems with great accuracy.3 139140 Rydberg states in quantum crystals The description, at a microscopic level, of the dynamic response of a crystal strongly driven out of equilibrium by an ultrashort laser pulse should provide much insight into the ongoing dynamics in such systems.We have recently started a femtosecond pump» probe study of the dynamic response of rare gas crystals following excitation of Rydberg states of impurities.4 The choice of such excitations stems from the fact that the Rydberg electron has an extended orbital, of the order of the nearest neighbour distance, and therefore there is a strong short range repulsive interaction with the closed shell rare gas atoms at the equilibrium con–guration of the ground state.From the knowledge gathered on rare gas solids, it is found that the repulsive interaction of the Rydberg electron with the rare gas matrix scales with the matrix cage radius,5,6 i.e. the smaller the cage (in going from Xe to Ne), the larger is the repulsive interaction. This interaction manifests itself in strong blue gas-to-matrix shifts and severe broadening of the Rydberg absorption bands.6 This leads to ìbubbleœ formation around the excited impurity and Rydberg —uorescence is strongly Stokes shifted with respect to absorption as a consequence.5 The increase in the cage radius is estimated to represent an increment by as much as 20% of the cage radius in the ground state, following photoexcitation to their Rydberg states of Xe impurities in Ar clusters7 or NO impurities in Ar matrices8 according to recent molecular dynamics (MD) simulations.ìBubbleœ formation is an ultrafast process occurring on the timescale of picoseconds.4,7,8 The extent of the cage relaxation results from an equilibrium between repulsion due to the Rydberg electron and the cohesive forces of the crystal. Thus, for the soft Ne crystal the cage expansion is more important than for the heavier rare gas solids.5 In liquid He it has been predicted that the ìbubbleœ radius reaches ca. 17 for an electron in the —uid.9 ” With a nearest neighbour distance of 3.8 for solid close to that of solid Ar, ” H2 ,1 we would anticipate a blue shift in absorption close to that for Ar matrices (about 0.8 eV) just on the basis of the cage size.In addition to the cage size, it is important to also consider the electron affinity of the solid. Indeed, for solids such as Ne and Ar, is V0 V0 ca. 0.5 and 0.0 eV, respectively.6 In solid most estimates scatter from H2 , V0B1.0»3.3 eV,10h13 while experimental values are in one case, eV, determined by –tting V0B[1.2 a Wannier exciton series to the absorption bands of Xe atoms in solid and in the H2 ,14 other case, eV, from photoluminescence transitions of electrons over a solid V0B]3.5 surface.15 Most of these reports point therefore to a strong repulsion of electrons by H2 the crystals.However, the few studies available on the Rydberg absorption in hydro- H2 gen matrices1,14 show that the gas-to-matrix shift amounts to about 0.6 eV, i.e. signi–- cantly less than in Ar matrices and this trend is con–rmed in the present report.Solid has a bulk compressibility modulus six times larger than Ne and we expect cage H2 expansion due to ìbubbleœ formation to be more signi–cant. The signature of such a process can be obtained by performing conventional spectroscopic studies as in the case of rare gas matrices.5 To our knowledge, there is no report on the —uorescence of impurities in solid while this is not the case for solid Although the absorption of H2 D2 .1,16 the –rst Rydberg state of Xe has been observed in solid the —uorescence of Xe- H2 ,14 doped solid excited by 2 keV electrons, is characterised by emission of the H2or D2 , XeH or XeD complex, and the atomic Xe Rydberg —uorescence is missing.17 This paper reports on Rydberg absorption and —uorescence of NO trapped in solid as well as H2 —uorescence depletion experiments which provide information about the fate of higher Rydberg states of the impurity in the solid.18 We will also discuss some of the intramolecular relaxation mechanisms therein involved and compare them with the data gathered on rare gas matrices.19 II Experimental The experiments were carried out using laser excitation in Lausanne and Synchrotron radiation in Berlin.F.V igliotti et al. 141 II(a) Laser experiments For the laser induced —uorescence study, the samples were grown by condensing a gaseous mixture of NO and (dilution 3 : 1000) onto a liquid helium cooled H2 MgF2 window at O 4 K in a vacuum chamber (less than 5]10~9 mbar at room temperature).Gas purity was 99.995% for and 99.95% for NO. Once the deposition was completed H2 and for a temperature of 4.0 K, the pressure in the chamber was 5]10~7 mbar. Further lowering of the temperature to 3.0 K led to a pressure decrease to about 10~8 mbar. Therefore, the measurements were taken at 3.0^0.2 K. Raising the temperature just above 10 K resulted in loss of the samples.A(v\1) was excited with the ArF laser line at 193.3 nm and A(v\0) was pumped at 210.2 nm by stimulated Raman shifting of the 193.3 nm beam in a Raman cell –lled with at 6 bar. Fluorescence was dispersed by a 0.5-m monochromator equipped with H2 a 1200 gr mm~1 grating and detected by a UV photomultiplier. For the —uorescence depletion experiment (described in more detail in ref. 18), the A-Rydberg state was populated as described above, while scanning over the Rydberg» Rydberg transitions was achieved by means of an optical parametric oscillator (OPO), pumped by the third harmonic of an injection-seeded Nd: Yag laser. The OPO tuning range was 450»700 nm (signal wave) and 720»1680 nm (idler wave). Its linewidth was 0.2 cm~1 spectral and 5 ns temporal.The detected signal is the loss of —uorescence intensity of the initially excited A-state as a function of OPO wavelength. The experiments were carried out at a repetition rate of 20 Hz for the A-Rydberg excitation and 10 Hz for the Rydberg»Rydberg transition to monitor shot-to-shot —uctuations of the ArF laser as well as the loss of NO —uorescence due to sample destruction over long-term irradiation.The PM photocurrent (—uorescence signal) and the photodiode signal from the OPO laser were analysed by a gated boxcar averager or a fast oscilloscope. The OPO pulse was delayed by 10»20 ns with respect to the ArF laser pulse to ensure re-excitation of the A(v\0) level from a fully relaxed cage con–guration and to avoid overlap between the pump and probe pulses.II(b) Synchrotron experiments For recording the excitation spectra of the NO —uorescence, tuneable synchrotron radiation was used at the 3NIM-2 station at BESSY. The sample preparation was identical to that described above [Section II(a)], with the exception that the cryostat was limited to temperatures P4.2 K. This rather high temperature for solid combined with the H2 , temperature gradient inside the sample caused the loss of more than 75% of the sample in less than 30 min.To prevent this, a pure Ar layer was condensed on top of the solid sample. The resulting samples were found to be stable with respect to desorption for H2 more than 30 min after deposition. The excitation spectra of the A(0) and A(1) —uorescence were recorded by tuning the detection monochromator to one of the A(0,vA) or A(1,vA) bands and recording its intensity as a function of excitation wavelength.The excitation spectra give information about relaxation pathways giving rise to the detected —uorescence, as we will see later. The experimental set-up has been described elsewhere.20 Brie—y, synchrotron radiation is dispersed by a 3-m normal incidence monochromator, and the dispersed radiation is focused onto the sample after the exit slit of the monochromator. The focal point on the sample serves as an entrance slit to a secondary 0.25-m Ebert monochromator, used to analyse the —uorescence light.The vacuum ultraviolet (VUV) excitation spectra were corrected for the transmission of the primary monochromator. In addition, an FTIR spectrometer of 0.5 cm~1 resolution is connected to the sample chamber via a set of mirrors.The IR radiation from a Standard Globar source (imaging range: ca. 500»7500 cm~1) is sent on the sample by the same optics as the synchrotron beam. The142 Rydberg states in quantum crystals Fig. 1 FTIR spectrum of a freshly grown sample of 0.3% NO in matrices at 4.2 K H2 transmitted IR beam is then collected after the sample and recorded by the spectrometer.In order to check for sample quality, IR spectra of the NO-doped samples were H2 recorded. A typical spectrum in the region of the NO fundamental is shown in Fig. 1 for a fresh sample. The attribution of bands is based on the assignment previously proposed for the IR absorption spectrum of NO in Ne matrices.21 The bands labelled I and II were attributed to monomers in single- and di- or tri-substitutional sites, respectively. In matrices, the peaks are shifted by ca. 1 cm~1 to the red with respect to the Ne case, H2 but the intensity of peak I to peak II is reversed compared to Ne. The peaks at 1868.8» 1777 cm~1are assigned to the and cis-dimer modes, while the 1859.7 cm~1 band is l1 l5 attributed to the van der Waals (vdW) dimer.The vdW-dimer band is strongly reduced relative to the cis-dimer bands, as compared to the Ne case. In addition, relative to the intensity of the monomer peaks, the contribution of cis-dimer bands is enhanced compared to Ne matrices. Obviously, NO dimers are formed more efficiently in the softer H2 matrices. This feature plays an important role in dipole»dipole energy transfer processes as will be shown below.III Results III(a) Laser experiments The 193.3 nm laser line falls on the broad A(v\0) absorption band in Ar and Ne matrices.5,6 Fig. 2(a) shows the —uorescence spectrum obtained upon ArF laser excitation. A progression appears which can easily be identi–ed as the A(1,vA) —uorescence with an origin band peaking at 215.5 nm, i.e.slightly to the red of the gas phase energy by ca. 15 meV. A weaker progression is also present in Fig. 2(a), which is the sole one to appear when exciting at 210.2 nm [Fig. 2(b)]. It corresponds to the A(0,vA) progression, also slightly shifted to the red of the gas phase energy. The bands of both progressions are asymmetric with a red wing and their full width at half maximum (FWHM) is about 350 cm~1.Improving the resolution to 0.1 nm does not reveal any –ne structure. Furthermore, no valence emission bands are observed in either case when searching in the j[300 nm region where they appear in rare gas matrices.19 Fig. 3 shows the —uorescence decay curves obtained for both progressions. They can be –tted by monoexponentials with a lifetime of 185^15 ns for A(v\0) (i.e.close to the gas phase valueF. V igliotti et al. 143 Fig. 2 Fluorescence spectrum of 0.3% NO in matrices at 3.5 K, upon laser excitation at 193.3 H2 nm (a) and at 210.2 nm (b). Resolution is 0.5 nm. of about 200 ns22) and 65^5 ns for A(v\1). The risetime of the —uorescence was limited by the pulsewidth of the laser in both cases, even for A(v\0) —uorescence upon 193.3 nm excitation [Fig. 2(a)]. In matrices, the 193.3 nm (6.41 eV) excitation clearly excites the A(v\1) level H2 predominantly and 210.2 nm (5.9 eV) excites exclusively the A(v\0) level. This points to the fact that the Rydberg bands of NO in are not as blue shifted compared with NO H2 in Ar matrices. In the latter, excitation energies of 6.35 and 6.64 eV would be needed in order to reach the A(v\0) and A(v\1) band maxima, respectively. The presence of a weak A(v\0) —uorescence upon 193.3 nm excitation might suggest a non-radiative A(v\1)]A(v\0) channel.This cannot be the case, as the risetime of A(v\0) —uorescence upon 193.3 nm excitation is O 15 ns (i.e. limited by the laser pulsewidth), while the decay time of A(v\1) is 65 ns. The latter results from the combination of the pure radiative rate of 5.0]106 s~1 and the non-radiative rates, which we therefore estimate to about 107 s~1.Thus, we believe that the presence of A(v\0) —uorescence upon 193.3 Fig. 3 Fluorescence decay curves of the A2&`»X2% (0,vA) bands (a) and A2&`»X2% (1,vA) bands (b) of NO in matrices at 3 K H2144 Rydberg states in quantum crystals nm irradiation is due to excitation of the blue tail of its absorption band which probably overlaps the A(v\1) absorption band at its red wing.This interpretation is con–rmed by the synchrotron radiation measurements described in Section III(b). Fig. 4 shows a typical —uorescence depletion spectrum, common to both A(0) and A(1) —uorescence. Two prominent dips show up at ca. 1.03 and 1.1 eV and a weaker one at ca. 1.17 eV. This spectrum is similar to the one already reported for NO in Ar matrices.18 We can safely assign the –rst doublet to the *v\0 transitions from the A state to the C and D states, which are separated by ca. 0.1 eV in the gas phase. The shoulder at ca. 1.17 eV is attributed to the *v\0 transition from the A(3sr) state to the E(4sr) state.It is interesting to note that even though the A»C and A»D energy splitting is close to the gas phase one, the A»E splitting is dramatically reduced by ca. 0.9 eV with respect to the gas phase value. On the other hand, the FWHM of the A»C, A»D and A»E bands are ca. 700, 450 and 450 cm~1 respectively. This is signi–cantly smaller than the linewidth observed by vertical excitation of Rydberg states from the ground state, as we will see in the following section.The diÜerence in bandwidths of these transitions is still unclear. III(b) Synchrotron experiments The excitation spectra of A(v\0) and A(v\1) —uorescence, which are comparable to absorption spectra, are shown in Fig. 5 and the A(0,0) absorption and emission bands are compared in Fig. 6 on the same energy scale.The A(0) and A(1) absorption maxima exhibit a blue shift of ca. 0.58 eV with respect to the gas phase and a severe broadening. The FWHM is ca. 1900 cm~1, in good agreement with the predictions mentioned above [Section III(a)]. The A(0)^X(0) absorption band shows an asymmetry with a broader blue wing [Fig. 6]. It is interesting to note that the matrix-shift of Rydberg transitions of NO in is substantially smaller than that observed in Ar matrices.On the other hand, H2 the broadening is more severe and is substantially larger than in Ne matrices where the bands are the broadest of all rare gas matrices. Superimposed on the A(1) absorption band in Fig. 5(b) are two sharp bands which can be identi–ed as the valence transitions B2% (7,0) and (8,0).These valence contributions are also present (but weaker) in the A(v\0) —uorescence. These features will be explained in Section IV(c). Fig. 5(a) shows that above the A(0,0) absorption band, a broad quasi-continuous absorption shows up, Fig. 4 Depletion spectrum, in the 0.9»1.25 eV region, of the NO A(v\0) —uorescence in solid H2 (see text for assignment of bands)F. V igliotti et al. 145 Fig. 5 Excitation spectrum of the A(v\0) —uorescence (a) and A(v\1) —uorescence (b) of NO in matrices H2 starting from about 6.5 eV with a shoulder at 6.7 eV and a maximum at ca. 6.9 eV. Starting just to the red of the latter, a series of sharp dips appear, which can be identi–ed as transitions to the valence B 2% and B@ 2* states. They are shifted to the red by ca. 150 cm~1 and ca. 300 cm~1, respectively, compared to the gas phase. The fact that the valence absorption appears as minima rather than maxima will be discussed below. Returning to the shoulder at ca. 6.7 eV, it is identi–ed as the red wing of the A(2,0) absorption band, on the basis of the vibrational spacings of the A state and of the bandwidths. On the other hand, the steep rise to the maximum at ca. 6.9 eV can, by comparison with similar data in rare gas matrices, only be assigned to absorption to the next higher Rydberg level, C2%(v\0). This is con–rmed by the excitation spectrum of Fig. 5(b) where the A(1,0) band shows up at low energies, followed at higher energies by a shoulder at ca. 6.9 eV and a steep rise peaking around 7.2 eV. Again, on the basis of vibrational spacings and bandwidths, the shoulder can be identi–ed as the red wing of the A(3) absorption band, and the steep rise as the red wing of the C(1,0) absorption Fig. 6 A(0,0) band of NO in matrices in absorption and emission. The broken line represents H2 the gas phase energy.146 Rydberg states in quantum crystals Table 1 Maxima (E) and FWHM (C) of the Rydberg absorption bands of NO in matrices, obtained from excitation spectra (Fig. 5) and from —uorescence H2 depletion spectra (Fig. 4) transition gasc Emax abs *Eabs d Cabs *Eem Cem X2%»A2&`a 5.480 6.064 ]0.584 0.235 [0.0034 0.043 X2%»C2%a 6.494 6.894 ]0.395 0.235 X2%»D2&`a 6.604 7.03 ]0.426 0.235 A2&`»C2%b 1.014 1.03 ]0.016 0.077 A2&`»D2&`b 1.128 1.10 [0.028 0.062 *E is the gas-to-matrix shift in absorption (abs) and in emission (em), respectively. All entries are in eV.a From excitation spectra. b From —uorescence depletion spectra. c E. Miescher and K. P. Huber, Int. Rev. of Science, Physical Chemistry (2), Vol. 3, Butterworths, London, 1976, p. 3. d DiÜerence with the corresponding gas phase values. band. Taking the known lineshapes for the A(v@,0) bands and assuming the same width for the C2%(v@,0) and D2&`(v@,0) bands, we simulated the Rydberg absorption keeping the energies of the C(v@,0) and D(v@,0) band maxima as adjustable parameters [for the A(v@[0,0) bands, these energies are inferred from the vibrational spacing of the A state].The result yields a blue gas-to-matrix shift of ca. 0.40 and ca. 0.43 eV for the C and D states, respectively, i.e.substantially smaller than for the A state in all matrices and for the C state in rare gas matrices, except Xe.6 In addition, vibrational splittings for the C and D states are inferred from the –t in very good agreement with their gas phase vibrational spacings. Returning to Fig. 5(b), just as for Fig. 5(a), sharp bands due to valence transitions appear in the spectrum but this time, the B(v@\7»14,0) bands appear as maxima rather than minima, while the bands above ca. 7.4 eV all appear as minima, just as in Fig. 5(a). A comparison of the valence bands in the 6.7»7.3 eV region shows that the valence bands appear as maxima in the excitation spectrum of the A(1) —uorescence [Fig. 5(b)], whereas they appear as minima in that of the A(0) —uorescence [Fig. 5(a)]. However, for the B(vP13) bands, the pro–les are anomalous with a long red wing and a sharp blue wing reminiscent of the Fano pro–les already observed for NO in rare gas matrices.23 The data contained in Fig. 2»6 are summarised in Tables 1 and 2. The main results are : (1) Rydberg absorption is less blue shifted in matrices than in rare H2 gas matrices (except Xe), whereas the bandwidths are much larger in (Table 2).(2) H2 Table 2 Absorption gas-to-matrix shifts (*E) and FWHM (C) of the lowest Rydberg states of NO in and rare gas matrices, together with the electron affinity and the positive ion polariza- H2 (V0) tion energy of the solids (P`) Ne Ar Kr Xe H2 gas transition E *E C *E C *E C *E C *E C X»A2&` 5.48 0.97 0.18 0.857 0.12 0.62 0.09 0.4 0.08 0.584 0.235 X»C2% 6.494 0.85 0.14 0.83 0.085 0.55 0.1 0.33 0.05 0.395 0.235 X»D2&` 6.608 0.9 0.145 0.85 0.1 0.57 0.07 0.34 0.06 0.426 0.235 V0 1.5 0.4 [0.5 [0.4 1.0»3.5a [1.2b V0]P` P0c B[1.0c B[1.4c B[1.9c [2b All entries are in eV.The sum represents the shift of the impurity ionization potential in V0]P` the solid (see text). a Ref. 11»15. b Ref. 10. c Ref. 6.F. V igliotti et al. 147 Rydberg —uorescence occurs with a large absorption»emission Stokes shift of ca. 0.6 eV, which points to an extensive lattice rearrangement around the excited molecule. (3) Both absorption and emission lineshapes are asymmetric in matrices, contrary to rare gas H2 matrices.6 (4) The Rydberg»Rydberg A»C and A»D transitions induced from the cagerelaxed A state con–guration are only slightly shifted from their gas phase values.This, together with a similar result from the —uorescence bands, points to a weak perturbation of the molecule by the environment, in the relaxed cage state. (5) A(v\0) —uorescence can be excited via relaxation from A(v\2) [but not A(v\1)], C(v\0) and higher lying Rydberg levels which make up the continuous absorption. (6) A(v\1) —uorescence can be excited via relaxation from A(v\3) [but not A(v\2)], C(v\1) [but not C(v\0)], and all higher lying Rydberg levels which make up the continuous absorption.(7) There are weak peaks due to the low lying valence levels B(v\7»9) in the excitation spectrum of the A(v\0) —uorescence. Higher lying valence levels give rise to a negative contribution which appears as dips in the excitation spectrum.(8) Peaks appear from the low lying valence levels B(v\7»14) in the excitation spectrum of A(1) —uorescence, but they turn into a negative contribution (i.e. dips) for the high lying B@(v\0,1, . . .) valence levels. (9) Finally, there is no valence emission. The excitation spectrum of total —uorescence was also recorded with the hope of detecting weak valence emission, but none could be found.This points to a complete quenching of the lowest valence states B2% and a 4% to the ground state of NO or to matrix species. IV Discussion DiÜerent types of results are obtained from the present study: (a) spectroscopic data, (b) cage expansion, and (c) intramolecular non-radiative relaxation and energy transfer among NO molecules.In the following, we will discuss these classes of results separately. IV(a) Spectroscopy From Table 1, we see that the A(v@,0) band maxima of NO in matrices are shifted by H2 ca. 0.58 eV to the blue of the gas phase energy. This shift is very close to that reported for Al1 and Xe10 in hydrogen matrices, but is signi–cantly smaller than the matrix shift reported for NO in Ne and Ar matrices.5,6 On the other hand, the FWHM increases signi–cantly with respect to these matrices.From Fig. 6, we also infer an absorption» emission Stokes shift of ca. 0.6 eV measured from maximum to maximum. It is comparable to the one obtained for NO in Ar, but signi–cantly less than that for NO in Ne matrices.5 We will –rst consider the absorption bandshapes in relation to available data on the van der Waals complexes. In molecular beam studies,24 vertical excitation of the NO»Rg complex (Rg\He, Ne, Ar) was carried out and absorption was recorded by detecting the —uorescence of the NO fragment.Because of the strong change in equilibrium con–guration between ground and excited states of the complex, the excitation reaches the continuum part of the excited state potential surface of the complex and leads to absorption bands shifted to the blue, as compared to the monomer energy. It is interesting to note that the gas-to-matrix shifts and FWHM for NO A2&` in Ar, Ne5,6 and matrices re—ect the same trends as observed for NO A2&` complexed with Ar, H2 Ne and He atoms.24 That is, the shifts increase slightly from Ar to Ne then decrease signi–cantly for (He) in the complex.On the other hand, the bandwidths increase H2 signi–cantly from Ar to (He) via Ne. These comparisons stress the connection H2 between the molecule trapped in the crystal and when complexed with only one solvent148 Rydberg states in quantum crystals species. The origin of the large bandwidth in the matrix is due to the large zero point H2 (ZP) motion in the ground state.This was checked by constructing an NO»Ne potential for the ground state, with the well depth derived by the method of Parmenter and co-workers25 and taking the equilibrium distance equal to the Ne»Ne equilibrium distance. We generated the ground state wavefunction for the lowest level of the van der Waals complex, and using the re—ection method and the experimental A(v\0) Rydberg absorption band, we generated a repulsive potential of Born»Mayer type that would mimic the repulsive interaction between NO A2&` and Ne.Replacing Ne by the H2 , ground state wavefunction spans a much larger region in space because of ZP motion of and the increased bandwidth from Ne to is fully accounted for by this feature of H2 H2 the ground state.The resulting absorption bandwidth in going from Ne to is H2 however asymmetric to the low frequency side rather than to the high frequency side, as observed in the experiment. This is due to the fact that the ground state wavefunction has more density spreading at large distances than at short ones. This two-body (NO»Ne) approach was improved by generating a quasi-harmonic potential for the ground state considering an Ne»NO»Ne chain.The re—ection method was used again to reproduce the Rydberg absorption pro–le and to generate a repulsive potential for the excited state in Ne matrices. Substituting for Ne leads to a ground state wavefunc- H2 tion that is again signi–cantly more extended, but now symmetric. Upon application of the re—ection principle, keeping the excited state potential unchanged, the absorption band is signi–cantly broadened and shows now an asymmetry to the blue as we observe in our spectra [Fig. 6]. This stems from the fact that the repulsive part of the excited potential cannot be approximated by a constant slope over the spatial extension of the ground state wavefunction. This approximation is only valid in the case of Ne and heavier rare gas atoms because the ground state wavefunctions are much more localised in space.Accordingly, the experimental Rydberg absorption bands in rare gas matrices have nearly perfect gaussian lineshapes.6 Turning now to the issue of the shifts, we have given in Table 2 the absorption energies and gas-to-matrix shifts of the A2&`, C2% and D2&` states of NO in H2 matrices (Fig. 5, 6) and in rare gas matrices.5,6 The weaker matrix shift of the vertical excitation energies in matrices as compared to rare gas matrices (except Xe)6 is H2 surprising if we consider the predicted large positive values.11h15 It should be noted V0 that a nearly similar gas-to-matrix shift was reported for the case of the Rydberg transition 4s(2S)^ 3p(2P) of Al in matrices1 and for the electronic excitation of Xe in H2 H2 and What are the reasons for the weaker blue shifts as compared to rare gas D2 .10 matrices ? (a) One possibility could be that the nearest neighbour distance is signi–cantly larger than in rare gas matrices, and the ground state wavefunction samples a softer part of the excited state potential surface.This is surely the case for the NO(A)»He van der Waals complex,24 where the ground state equilibrium is at large enough distances that in absorption, softer parts of the NO (A)-He potentials are reached.This argument should not hold in the case of NO in matrices if we assume that the distance is not H2 NO»H2 too diÜerent from the distance in the solid. Indeed, the gas-to-matrix shift of the H2»H2 A state is larger in Ar and Kr matrices (Table 2) that have similar or even larger nearest neighbour distances than solid The assumption of nearly equal distance H2.NO»H2 and nearest neighbour distance is justi–ed on the basis of similar situations in H2»H2 rare gas matrices8 and of the resemblance of the IR absorption spectra (Fig. 1).21 It is also con–rmed by the similarity of the valence absorption spectra (Fig. 5 and ref. 6) of NO in with those in rare gas matrices. Indeed, a red gas-to-matrix shift of ca. 150 H2 cm~1 is found for the B»X transition (Fig. 5) while the same transition exhibits a red shift of ca. 100 cm~1 in Ne matrices and ca. 200 cm~1 in Ar matrices.26 These shifts are an indication of the stabilisation of the molecule in the matrix cage.Should the ground state molecule already be in a very loose cage (or even in a ìbubbleœ state), one wouldF. V igliotti et al. 149 expect valence transition energies of NO in matrices very close to their gas phase H2 value. We therefore do not favour the hypothesis of a very loose cage for explaining the weaker blue shift of the Rydberg transition of NO in matrices.H2 (b) The large ZP energy in the ground state. The diÜerence in ZP energy of the NO»Ne and pair potentials described above is ca. 16 cm~1. When summed NO»H2 over 12 neighbours, it amounts to a mere ca. 170 cm~1. It can therefore not explain the weaker blue shift of the Rydberg transition of NO in matrices. H2 (c) One could think of a speci–c interaction of the NO A state with the matrix H2 with an enhanced attractive contribution which would result in a weaker gas-to-matrix shift than in the rare gas matrices (except Xe).This argument does not hold since, as mentioned before, similar gas-to-matrix shifts are found for quite diÜerent systems such as Al1 or Xe10 in matrices. We would therefore seek the origin of the shift in a H2 property intrinsic to the crystals rather than in some speci–c interaction between NO H2 and the matrix.H2 In order to understand the Rydberg absorption in a rare gas matrix or in a molecular crystal, one has to consider that the ionization energy of the dopand will be EG i shifted from its gas phase value according to (IG) EGi \IG]P`]V0 (1) where is the medium polarization energy induced by the positive ionic core of the P` dopand, while is the electron affinity of the solid or the energy of the bottom of the V0 conduction band relative to the vacuum level.has been determined, for solid P`]V0 and for solid rare gases,27 from the convergence of the Rydberg absorption series H2 10 of dopands, interpreted as a Wannier excitonic series, from photoemission studies on pure and doped rare gas solids or from the threshold of photoconductivity.27,28 The best estimates6 for rare gas solid are given in Table 2.For solid the sole experimen- H2 , tal estimate was obtained from a –t of the Xe absorption series by the Wannier formula.10 Just on the basis of eqn. (1), one would expect a red shift of the Rydberg states for Ar, Kr and Xe matrices. This is indeed the case for high-n states in rare gas —uids, where it was found that the red shift of the Rydberg states as a function of rare gas density re—ects that of the ionization potential.28 This is not unexpected as the high-n Rydberg states have very extended orbital radii which can embed a large number of rare gas solvent species.Thus, the Rydberg state in the solvent can be regarded as having two energy contributions, the ion polarization energy and that of the elec- (P`) tron This is not the case for low-n Rydberg states which are known to be signi–- (V0).cantly blue shifted in both rare gas matrices (Table 2) and rare gas —uids.27h29 For such states, two eÜects will combine which will contribute energy positively. First, the small size of the orbital means that in most cases efficient shielding of the ionic core by the Rydberg electron occurs and the core polarization contributions will be (P`) reduced.Secondly, the size of these orbitals is typically of the order of the nearest neighbour separation, so that a strong overlap with the electronic cloud of the –rst shell of solvent species occurs. A repulsion ensues by virtue of the Pauli exclusion principle. Even if is negative such as in solid Kr and Xe (Table 2), there will still be a repulsive V0 positive contribution to the total energy because the Rydberg electron is forced into the electronic cloud of the rare gas atoms whereas the values correspond to an adiabatic V0 electron affinity of the solid (i.e. when the electron is in equilibrium with its environment).Nevertheless, an increasing can only infer a larger blue gas-to-matrix V0 shift as actually observed for NO (Table 2) in rare gas matrices or for several other dopands.27 In this sense, the large positive values calculated for solid in ref. 11»15 V0 H2 do not continue the trend observed in rare gas solids, since is larger than in solid Ne, V0 whereas the gas-to-matrix shift is much weaker (Table 2).On the other hand, adopting the experimental value of eV from ref. 10 would bring the matrix shifts V0\[1.2 H2 more in line with the trends, at least qualitatively.150 Rydberg states in quantum crystals Fig. 7 Con–guration model in the harmonic approximation. The diÜerent symbols are speci–ed in the text. We have another reason to suspect that will be negative for solid and this V0 H2 relates to the —uorescence depletion spectrum of Fig. 4. In this spectrum, the transition energy from the A(3sr) state to the E(4sr) state is signi–cantly reduced with respect to the gas phase (by ca. 0.9 eV). This corresponds to a drastic compression of the n\3» n\4 splitting in the Rydberg series. A compression was also observed in Ar matrices,18 although weaker (ca. 0.5 eV). In addition, if we consider that the A(v\0) level has nearly the gas-phase energy in the relaxed ìbubbleœ state (see below), this would mean that the Rydberg E state is shifted to lower energies in matrices. This red shift H2 suggests a red shift of the ionization potential of the dopand and thus a negative It is V0 . interesting to note that the spectrum of Fig. 4 bears a strong resemblance to a similar spectrum for NO in Xe matrices30 and that for both solids and Xe) the (H2 P`]V0 value is nearly the same. Since the value of eV for solid was inferred from V0\[1.2 H2 the value of [2 eV, we adopt the former as a more realistic value for the P`]V0 electron affinity of solid It would however be necessary to check the value H2 . P`]V0 of solid by photoemission or photoconductivity measurements. H2 IV(b) Cage expansion The origin of the large Stokes shift (Fig. 6) is a structural rearrangement around the molecule due to diÜerent equilibrium con–gurations of the X2% ground state and the A2&` Rydberg state with the matrix species.As mentioned above, the blue matrix shifts of the Rydberg absorption bands are caused by the repulsive interaction of the extended Rydberg orbital with the matrix species.The lattice relaxation which ensues takes place in such a way as to minimize the repulsive overlap. If we assume that the molecule is in a substitutional site of the lattice and consider that the 3sr orbital of the A state is H2F. V igliotti et al. 151 nearly spherical, it is likely that, as a –rst event after photoexcitation, the matrix species are radially pushed outwards to reduce the overlap of the wavefunctions, thus leading to formation of a nearly spherical ìbubbleœ.Such a situation has recently been described using MD simulations for the case of Xe in clusters7 and for NO in Ar crystals.8 At Arn this stage, a lineshape analysis as performed for NO in rare gas matrices5 would be useful to obtain an estimate of the energy released in ìbubbleœ formation and of the coupling of the optical transition to the lattice phonons.A rough estimate of the Stokes shift of ca. 600 meV with a typical phonon energy of ca. 9 meV for solid shows H2 31 that approximately 70 phonons are created in an absorption»emission event due to lattice rearrangements. In general, a con–guration coordinate model in the harmonic approximation (Fig. 7) is used to relate the spectroscopic information to the potential energy surfaces of the diÜerent electronic states of the dopand in the matrix. The diÜerent linewidths in absorption and emission (Fig. 6), although we are in the T \0 K limit, require both linear and quadratic coupling terms, i.e. diÜerent equilibrium con–gurations and diÜerent phonon frequencies for the ground and excited states.This case which is illustrated by Fig. 7, is used together with the method of moments. The nth moment being de–ned by: Mn\/~= `= (+u)nI(+u) d(+u) /~= `=I(+u) d(+u) (2) yields the centre of gravity of the bands, the higher moments are taken with respect M1 to this centre. is related to the half-widths.The so-called Huang»Rhys factors (or M2 electron»phonon coupling strengths) correspond to the displacement *q (Fig. 7). Se , Sg are related to the diÜerences in the phonon frequencies in the excited (e) and Be , Bg ground (g) states, respectively, and is the zero phonon (or adiabatic transition E0 energy). The four independent parameters (or and needed to describe E0 , Se Sg), +ue +ug the potential surfaces are derived from the four available moments M1A , M2A , M1 E , M2 E (A, absorption, E, emission ; see Table 3), via a system of four equations.5,32 The quadratic coupling terms (B), the displacement (*q) and the electron»phonon coupling constants are determined through the previous parameters via :32 (Se , Sg) Se\*q2 ue2 2+ug (3) Sg\*q2 ug2 2+ue (4) Be\ ue2[ug2 ug2 (5) Bg\ ug2[ue2 ue2 (6) The results of this moment analysis for the lineshapes in Fig. 6 are given in Table 4, together with the relaxation energies in the excited state ELR e \Se +ug , ELR g \Sg +ue , (absorption) and in the ground state (emission) potential surfaces. From Tables 3 and 4, one can note the following points : (a) the sum of relaxation energies in the excited state and the ground state is 0.64 eV and should correspond to the Stokes-shift. The latter should be taken as (Table 3) rather than *ESt\M14[M1 E the energy separation between band maxima, because the bands are asymmetric.Therefore, the moment analysis yields a Stokes-shift of 0.632 eV which is close to the value derived from the total relaxation energy (b) Table 4 shows that most of the ELR e ]ELR g .152 Rydberg states in quantum crystals Table 3 Experimental –rst, second and third moments given by eqn.(2) for the A(0,0) band of NO in matrices H2 absorption emission M1A M2A M3A M1 E M2 E M3 E 49 186 cm~1 845 286 cm~2 2.5]108 cm~3 44 088 cm~1 36 355 cm~2 [3.8]106 cm~3 (6.098 eV) (5.466 eV) Stokes shift is taken up by i.e. it goes in blowing the electronic ìbubbleœ in the ELR e , excited state.The small value of points to a very shallow potential in the ground as ELR g compared to the excited state. Furthermore, the similarities of the emission energy to that of the gas phase and of the A»C and A»D energies from the —uorescence depletion experiment (Table 1) point to a situation where the molecule is only slightly perturbed by the environment after cage relaxation.This in turn suggests the existence of a rather large ìbubbleœ in which the molecule is in a quasi-free, nearly gas-phase-like state. (c) *q, in eqn. (3) and (4), is a measure of the displacement of the equilibrium con–guration coordinate in the ground and excited states. It is related to the spatial rearrangement *r by: *r\ *q M1@2 (7) where M has to be chosen according to the symmetry of the rearrangement.If we consider the initial deformation to be a spherical expansion, then it is plausible that will ELR e be equally distributed among the 12 nearest neighbours and M\12m , where m is the mass of an molecule. This yields *rB1 Thus, cage expansion in solid is more H2 ”. H2 dramatic than that which is found for NO in Ne matrices.5 This is not surprising in view of the fact that solid has a bulk modulus six times larger than that of solid Ne.(d) H2 The consistency of the treatment is con–rmed by the less than order of magnitude agreement between the experimental third order moments (related to the asymmetry of the bands, see Table 3) and those calculated33 by means of the derived and Se , Sg , +ue +ug values (Table 4).(e) From the data of Tables 1»4, we can estimate the relaxation energy in the C2%(v\0) level as a result of lattice rearrangement. Indeed, if we refer to Table 1, we see that the A»C splitting is ca. 0.83 eV on the basis of the excitation spectra (Fig. 5). This corresponds to the splitting before cage relaxation around the A state has occurred (Fig. 7). The A»C splitting from the —uorescence depletion experiment (Fig. 4), i.e. after cage relaxation around the A state has been completed, is 1.03 eV (Table 1). From the relaxation energy in the excited A state, we can now estimate the cage relaxation energy needed for the C state. This energy amounts to ca. 0.27 eV, which is about half that for the A state. The smaller value is not too surprising as the C state is less subject to repulsive interactions than the A state, as can also be seen from the matrix Table 4 Parameters of the electron»phonon coupling of Rydberg transitions in matrices, derived from the H2 moment analysis by means of eqn.(3)»(6) (see text) +ug/ +ue/ E0/ ELR e / ELR g / meV meV Se Sg eV eV eV 7.4 13.9 67 10 5.6 0.5 0.14F. V igliotti et al. 153 shifts in absorption (Table 2) and therefore, less work is needed to accommodate the system in a relaxed matrix cage. A similar treatment for the D state yields a relaxation energy of ca. 0.33 eV, close to that of the C state. IV(c) Non-radiative relaxation by intramolecular and energy transfer processes From the observations, we can distinguish the following types of non-radiative energy relaxation processes also represented in Fig. 8: (i) Rydberg]valence relaxation for the A(1) state is suggested by the lifetime shortening which is observed and con–rmed by the model below. On the other hand, there is an almost total lack of A(0)]valence transition, again, as suggested by the lifetime measurements. (ii) Rydberg^valence relaxation mechanisms which result either in maxima or in dips for the valence bands in the Fig. 8 Energy level diagram of the lowest Rydberg and valence states of NO in solid and H2 intra- and inter-molecular energy relaxation processes (see text). The Rydberg levels in absorption and emission are represented by their corresponding lineshapes. The ladder of B2% levels on the right hand side shows those levels that are involved in energy transfer processes.154 Rydberg states in quantum crystals excitation spectra of A(0) and A(1).(iii) Vibrational relaxation in Rydberg states which, within the A state occurs by jumps of two vibrational quanta, i.e. A(2)]A(0) and A(3)]A(1) (Fig. 5 and 8). In addition, electronic Rydberg»Rydberg relaxation from the C state to the A state can occur for *v\0, i.e.C(0)]A(0) and C(1)]A(1) (Fig. 5 and 8). These processes are attributed to intermolecular energy transfer among NO molecules. IV(c) (1) Rydberg%valence relaxation. In the following, we will show that point (1) can be understood on the basis of already existing models for non-radiative Rydberg%valence relaxation in rare gas matrices.19 Indeed, it has been established that excitation of A(v\0) –rst leads to an ultrafast cage expansion (ìbubbleœ formation) process and that it is only once the –nal relaxed cage equilibrium con–guration has been reached that Rydberg]valence non-radiative relaxation comes into play.This is understandable since the cage relaxation process takes place on a timescale of picoseconds4 while the Rydberg-valence relaxation takes place on a timescale of nanoseconds.19 A model based on the Fermi golden rule was used in ref. 19, which predicts the rate constants k for radiationless transitions from the A2&` (v@) levels to near resonant a 4%, b 4&~ and B2%(v) valence levels. The rate is given by: k\2n o V p @ o2 +2up (8) with o V p @ o2\oCSl@ o lTSp@ o 0T o2 (9) C represents the coupling matrix element (electrostatic spin»orbit or Coriolis), which is known for all pairs of Rydberg-valence states in the gas phase;19,23,34 o Sl@ o lT o2 are the intramolecular Franck»Condon factors between pairs of A(v@) levels and valence B, b and a(v) levels with which they are in near resonance; o Sp@ o 0T o2 represents the Franck» Condon factors for the coupling to lattice phonons, and is the number of p@\(*E/+up) phonons of energy in the –nal state necessary to bridge the gap *E to the initial +up state (i.e.relaxed Rydberg level). The value o Sp@ o 0T o is usually evaluated in the harmonic approximation but in ref. 19 its value was directly extracted from the experimental lineshapes. The same model works for valence]Rydberg relaxation. In the following, we will adopt the same procedure as in ref. 19 and calculate, using eqn. (4) of ref. 19(b), the phonon Franck»Condon overlap between a Rydberg emission band of FWHMB50 meV and a valence line whose width is 5 meV, taken directly from Fig. 5. Both lineshapes are approximated as gaussians. Finally, we need the energy of the valence levels of NO in solid Based on a red shift of ca. 150 cm~1 for the B levels, we have shifted H2 .all B, b and a levels by the same amount with respect to their gas phase values. Using eqn. (8) and (9) and taking cm~1 for solid we have computed the non- hup\73 H2 ,31 radiative rates for the possible pairs of near-resonant Rydberg-valence levels involving the A(0) and A(1) levels. The valence levels in energy resonance with A(0) and A(1) are apparent in Fig. 8 and the pairs of levels with the largest rates are given in Table 5. It appears that the A(0)]a(6) rate is 37 s~1 and cannot compete with the measured rate of 5.5]106 s~1 for radiative decay of A(0). The A(1)]b(0) and A(1)]a(8) rates are of the order of 105 s~1 and can also not compete with the radiative decay. On the other hand, the A(1)]b(1) rate of ca. 3]107 s~1 can account for the 107 s~1 measured rate. The above non-radiative Rydberg]valence mechanism is identical to that observed in the case of rare gas matrices.19 Thus, the efficiency of Rydberg]valence relaxation is mainly modulated by the Franck»Condon overlaps of resonant Rydberg-valence level pairs.The resonance condition is determined by the energy of the Rydberg level in theF. V igliotti et al. 155 Table 5 Most important calculated non-radiative intramolecular Rydberg%relaxation rates and comparison with measured rates (see text for details of calculation) initial –nal kcalc nr / kmeas/ state state s~1 s~1 A(0) a(6) 3.7]101 5]107 A(1) a(8) 5]105 5]107 A(1) b(0) 6]105 B107 A(1) b(1) 3]107 B107 A(2) b(3) B1010 A(3) b(5) B1010 C(0) B(9) B1010 C(1) B(11) B1012 B(8) A(2) 2.3]106 B(9) A(2) 3]107 relaxed cage. As a consequence, since NO in matrices has the lowest relaxed Rydberg H2 energy of all matrices,5 it has the highest yield of Rydberg —uorescence from A(0). IV(c) (2) relaxation in the A state.The jumps by two vibrational quanta in Dø= 2 the A(2)»A(0) and A(3)»A(1) relaxation (Fig. 5) cannot be explained in terms of intramolecular vibrational relaxation (radiative or non-radiative) within the A state.Neither can they be enhanced by an exchange with vibrational energy (as there would be an H2 energy mismatch of ca. 500 cm~1). On the other hand, based on the Stokes shifts, the cage relaxation brings the energy of the A(2) and A(3) levels in resonance with the unrelaxed A(0) and A(1) levels, respectively (Fig. 8). Therefore, a Foé rster»Dexter dipole» dipole energy transfer may occur which populates the unrelaxed NO sites to their Rydberg A(0) and A(1) levels.Such a process has already been reported for NO in Ar and Kr matrices.19 It is also con–rmed by the fact that in the excitation spectrum of A(1) —uorescence [Fig. 5(b)] we noticed that the contribution of the A(3,0) band increases, relative to that of the other bands, over a longer period of time. This is caused by desorption of molecules, which increases the concentration of NO molecules in the H2 sample.From Table 5, however, it can be seen that A(2) and A(3) can be quenched to valence states at a rate of ca. 1010 s~1 in the most efficient channels. Therefore, in order for these levels to be able to populate A(0) and A(1) by energy transfer, respectively, the A(2)]A(0) or A(3)]A(1) intermolecular transfer rates must compete with the above rates for intramolecular relaxation.An essential ingredient for calculation of the Foé rster»Dexter transfer rate is the concentration of NO in the crystal. Since this is H2 not known, we proceed just as we did in ref. 19, i.e. we determine the concentration for which intermolecular energy transfer competes with intramolecular non-radiative decay for the A(3) and A(2) levels (Table 5).The dipole»dipole energy transfer rate is given by:19 KT\ 3 29n6cn6q2R6l6 FC[A(2)]X(0)] Æ FC[X(0)]A(0)]]P fem Æ fabs dl (10) l is the transition frequency, q is the pure radiative lifetime (200 ns), FC are the Franck» Condon factors and is the overlap integral of the normalised lineshapes for / fem Æ fabs dl156 Rydberg states in quantum crystals the donor and acceptor, respectively.Using eqn. (10) with the experimental parameters, we arrive at critical concentrations of ca. 1%. This is quite reasonable even though the gas was doped with a partial pressure of 0.3% NO. Indeed, (a) the sticking coefficient H2 of NO is substantially higher than that of molecules, (b) the gradual desorption of H2 molecules with time causes an increase in NO concentration, and (c) the softness of H2 the matrices makes diÜusion of NO molecules easier, so that there might be several H2 sites with close lying NO molecules, as con–rmed by IR measurements (Fig. 1). IV(c) (3) Electronic RydbergñRydberg non-radiative relaxation. From Fig. 5, we also see contributions of higher (C 2%, D2&`) Rydberg states to the —uorescence of A(v\0) and A(v\1). If we concentrate on the case of the C(0)]A(0) channel [Fig. 5(a)], it is clear that no valence levels feed population to A(v\0) —uorescence. The presence of the B(7»10) bands in its excitation spectrum [Fig. 5(a)] is due to their resonance [Fig. 8] with the A(2) band and their quenching to it.The latter then transfers population to A(0) via dipole»dipole energy transfer as described in the preceding paragraph. The contribution of higher Rydberg states to the A(v\0) —uorescence can therefore not be channelled via the valence states manifold. Another possibility would be a channelling of the energy down to C(0) followed by a radiative C(0)]A(0) cascade in the IR around 1 lm.If this were the case, then a radiative C(0)]X(vA) cascade should also be observable. Indeed the C»X(0,vA) —uorescence has an oscillator strength which is larger than the C»A(0,vA) —uorescence.35 We searched carefully for C»X(0,vA) bands both under direct excitation of C(0) using synchrotron radiation and by sequential excitation with lasers via the A(v\0) level.In both cases they were missing, which rules out the possibility of a C»A radiative cascade. The lack of C(v\0) radiative deactivation is not surprising as it is crossed by a number of valence states and in particular, it is strongly coupled to the B2% state via an electrostatic interaction yielding an electronic coupling matrix element of 1380 cm~1.34 The efficient quenching of the C state is con–rmed in Table 5 by calculations similar to those performed in Section IV(b) for the case of the A]valence relaxation.In the case of the C state, by comparison with the data for the A state, we assume that most of the Stokes shift is contained in the excited state relaxation. In Table 5 we have listed the most efficient channels. Considering a pure radiative decay rate of 5]107 s~1 for C(0) in the gas phase, it is clear from it that C(0) cannot decay radiatively in matrices.H2 According to Fig. 8, the last possibility that remains for a C(0)]A(0) relaxation to occur is one which combines two steps of dipole»dipole energy transfer : C(0)]A(2) and A(2)]A(0). The second has been discussed in the previous paragraph. The –rst can be envisaged because from the cage relaxation energy of the C state estimated in Section IV(b) we –nd that the relaxed C(0) level is in resonance with the unrelaxed A(2) level.In order for the C(0)]A(2) dipole»dipole energy transfer process to occur, it must have a rate that competes with the C(0)]valence intramolecular non-radiative relaxation rates of 109»1010 s~1 (Table 5). For the estimates of the dipole»dipole transfer rate, we use eqn.(10), assuming an emission lineshape for C(0) similar to that of A(0) (Fig. 6). For the pure radiative lifetime we take the gas phase lifetime of 20 ns.35 Finally, we assume an NO concentration of ca. 1%, as inferred from the A(2)]A(0) and A(3)]A(1) energy transfer rates [Section IV(b)]. We –nd a C(0)]A(2) transfer rate of ca. 1010 s~1 (Table 6). This is sufficient to compete with the C(0)]valence non-radiative relaxation. Since the A(2)]A(0) energy transfer is quite efficient and can to a certain extent compete with the A(2)]valence relaxation, the C(0)]A(0) relaxation channel can therefore be explained. We believe however that the energy transfer step C(0)]A(2) probably overwhelms the intramolecular C(0)]valence relaxation.Indeed in Fig. 5(b) the C(0) band is missing in the excitation spectrum of the A(v\1) —uorescence, although the latter can be populated by valence states.F. V igliotti et al. 157 Table 6 Calculated intermolecular dipole»dipole energy transfer rates (Foé rster»Dexter) (see text for details) donor acceptor K/s~1 A(2) A(0) 109 A(3) A(1) 9]108 C(0) A(2) 7]1010 C(1) A(3) 1]1011 B(7) A(1) 106»107 A(2) 106»107 B(8) A(1) 106»107 A(2) 105»106 Similar processes can be invoked to explain the occurrence of the lowest valence contributions to the A(v\0) and A(v\1) —uorescence excitation spectra (Fig. 5). Indeed, Foé rster»Dexter processes involving the B state and the ground state can give rise to transfer rates to the lower levels of the A state of the order of ca. 106 s~1 (Table 6 and Fig. 8). On the other hand, these valence contributions cannot be explained simply by direct non-radiative depopulation to the A state, some of the calculated rates being too small. IV(c) (4) Contributions of higher valence states. The manifestation of valence transitions as dips or maxima for the A(0) —uorescence can be rationalised in the following way: (1) As mentioned above, the weak positive contribution of the B(v\7»9) levels is probably due to energy transfer processes, as well as their depopulation to the A(2) level (Table 5) which then transfers energy to A(0) by a Foé rster»Dexter process [see Section IV(b)].(2) All B(vP10) levels appear as dips. This is due to the fact that they do not contribute to the A(0) —uorescence and therefore the molecules that are excited to these levels act as –lters to Rydberg excitation.(3) These dips indicate that the B(vP10) levels are depopulated to the ground state by a route which avoids A(0). It is interesting to note that, even for the B levels in resonance with C2% and undergoing strong con–guration mixing with it, the relaxation to the valence manifold is more efficient than to the Rydberg state continuum.We now turn to the case of A(1) —uorescence: it is surprising that just the valence bands due to B@ absorption appear as dips similar to the higher B bands in the case of A(0). If these states cascade down the valence manifold as is the case in rare gas matrices,19 then they should appear as maxima. That they have a negative contribution points to another relaxation route.This can either be a photochemical route or a radiative decay. Concerning the latter case, no sign of other emission bands appeared upon excitation in the valence dips. The photochemical route is favoured but it is not clear what nature it should have. If it is an intramolecular predissociation process, it can only occur via the A@2&` purely repulsive state but the latter crosses the B@ state above 8.5 eV.We therefore believe that it is a photochemical reaction with the matrix species H2 which is selective to this state. V Conclusions In this contribution complete characterisation of the spectroscopy and of the intramolecular and intermolecular energy relaxation processes involving Rydberg states in a158 Rydberg states in quantum crystals quantum crystal has been attempted on a model system consisting of NO trapped in an crystal.H2 As far as the spectroscopy is concerned, it has been found that the Rydberg states are blue shifted in matrices with respect to their gas phase energies, but that the magni- H2 tude of the shift is signi–cantly less than in the case of rare gas matrices (except Xe).On the other hand, the absorption bands are much broader than in rare gas matrices and they exhibit an asymmetry on the blue wing, whereas the emission bands are narrower than in all rare gas matrices and lie very close to the gas phase energy. The connection of the data in Ne, Ar and matrices with the data obtained in molecular beam studies H2 is stressed.In matrices, the broadening and asymmetry of the absorption band can H2 be accounted for by the large zero point motion of the ground state wavefunction. It is argued that the weaker blue shift as compared to rare gas matrices points to an electron affinity for solid that is large and negative, contrary to most theoretical predic- H2 tions.11h14 This, combined with the Rydberg —uorescence depletion spectra suggest that the value of eV obtained previously10 is more realistic for The P`]V0B[2 H2 .Rydberg —uorescence takes place with a large absorption»emission Stokes-shift which suggests the formation of a ìbubbleœ or microcavity around the excited molecule, as already discussed for rare gas matrices.5 A moment analysis based on a con–guration coordinate model in the harmonic approximation suggests that most of the Stokes energy is used up to blow the ìbubbleœ in the excited state.The A»X —uorescence energy and the A»C and A»D transition energies obtained from the —uorescence depletion experiment, in the case of the relaxed cage, are very close to the gas phase energies. Therefore, it appears that the ìbubbleœ state corresponds to a quasi-free, almost gasphase- like state of the molecule.Finally, intramolecular relaxation mechanisms have been investigated for NO in matrices. It appears that Rydberg%valence non- H2 radiative relaxation follows the same pattern as observed in the case of rare gas matrices (Fig. 8).19 On the other hand, no valence emission is observed suggesting that valence states are efficiently depopulated non-radiatively to the ground state of NO or to the H2 species.Results on the real-time probing of the dynamics of ìbubbleœ formation using femtosecond pump»probe techniques4 have recently been obtained and preliminary results are presented in ref. 36 and 37. We would like to thank V. A. Apkarian and E. Sarraf for useful discussions. The assistance of G.Zerza during the laser experiment is also acknowledged. We would like to thank the technical staÜ at BESSY for its backing. References 1 M. E. Fajardo, S. Tam, T. L. Thompson and M. 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Chem., submitted. Paper 7/05434C; Received 29th September, 1997

ISSN:1359-6640    

DOI:10.1039/a705434c

出版商:RSC    

年代:1997

数据来源: RSC