Potential Energy Surface Crossings in Organic Photochemistry Fernando Bernardi and Massimo Olivucci Dipartimento di Chimica "G.Ciamician" dell'Universita di Bologna Via Selmi 2 40 126 Bologna ltaly Michael A. Robb Department of Chemistry King's College London Strand London UK WC2R 2LS 1 Introduction As a result of complementary experimental and theoretical work in the last five years new aspects of the excited state behaviour of organic molecules have emerged. The most general of these is that low-lying intersections (crossings) between the photochemically relevant excited state and the ground state occur with a previously unsuspected frequency. Thus an organic molecule moving on an excited state potential energy surface has a high probability of entering a region of surface crossing during the excited state life- time. Such crossings conical intersections in the case of two singlet (or two triplet) surfaces or singlet-triplet surface intersec- tions provide a very efficient 'funnel' for radiationless deactiva- tion or for chemical transformation of the system (see for example the 'highlight' article by M. Klessinger'). As a consequence many of the 'textbook' models for the treatment of the photophysical and photochemical behaviour have been considerably refined. The purpose of this review is to outline the computational and experi- mental results that support this new view of photochemical reac- tivity. In textbooks the efficiency of internal conversion (IC) and intersystem crossing (ISC) is usually discussed in terms of the interaction between the vibrational energy levels of the ground and excited state potential energy surfaces using the Fermi Golden Rule. The traditional view of photochemical reactions (mainly due to the work of Van der Lugt and Oosteroffz) assumes that the absorption of a photon results in the generation of an excited state species (M"). This intermediate represents the precursor of the photoproducts (P) which are generated ilia decay to the ground state. This decay was predicted to take place at an woided cross- ing of the excited and ground state potential energy surfaces. At such an avoided crossing if the energy gap is larger than few kJ Fernando Bernardi is Professor of Organic Chemistry at the University of Bologna. He received his degree in Industrial Chemistrv at the University of Bologna in 1962 and studied with S.F. Boys in Cambridge (I969- f971). Hi5 research interats spun all aspects of theoretical organic chemistry. mol-I M* will rapidly thermalyse and the decay probability will be determined by the Fermi Golden Rule. Accordingly such processes are supposed to occur on the same timescale (several molecular vibrations) as fluorescence. Modem experimental measurements and new computational techniques are now providing results that challenge such models for understanding organic photochemistry. Issues such as the effi- ciency of IC at a surface crossing the competition with fluores- cence when an excited state barrier is present and the relationship between the molecular structure at the intersection and the struc- ture of the photoproducts provide the intellectual motivation for the experimental and computational investigation of various pho- tochemical reactions. The rate and the energy thresholds control- ling IC can now be experimentally measured by exploiting the advances in laser spectroscopic techniques that have pushed the time resolution of various experimental techniques below the picosecond timescale. Thus very fast IC processes and short excited state lifetimes can now be detected. For example many detailed experiments are available in the photophysics and photo- chemistry of conjugated hydrocarbons in solution or isolated con- ditions. Femtosecond excited state I ifetimes have been observed for simple dienes,< cyclohexadienes? hexatrienes,5 and in both free6 and opsin-bound7 retinal protonated Schiff bases. Experiments on isolated molecules in cold matrices or expanding jets have revealed the presence of 'thermally activated' fast radia- tionless decay channels in hexatrienes? octatetraene~~~'~) and aro- matic compounds (see refs. collected in ref. 1 I). While laser experiments provide information on the structure and energetics of the excited state potential energy surfaces controlling fast decay more traditional photochemistry such as quantum yield measure- ments provide information on the molecular structure of the decay Massimo Olivucci is Ricercatore at the Utziversity of Bolognu where he obtained his PhD in 1989. He u~usa post-doctoral fellow at King's College London I989- 1992. His research interests lie in the theoretical modelling of photochemistry. Michael Rohb is Prc$es.tor of Chemistry at King :s College London. He obtained his PhD from the University of Toronto in 1970 and was awarded the DSc from the University of London in I988. His research interests lie in the development of MC-SCF methods and appli- cations to chetnical reactivitv. Fernando Bernardi Massimo Olivucci Michael Robb 32 1 channel and on the product formation paths The detailed charac- terisation of the stereo- and regio-chemistry of the primary photo- products and transient intermediates their quantum yields and the effect of specifically designed sterically and rotationally hindered reactants on these quantitiesi2 is now possible An alternative view of photochemical reactions that is consistent with recent experiments was suggested more than 30 years ago by the physicist Edward Telleri3 at the 20th Farkas Memorial Symposium He suggested that it was the electronic factors that may play the dominant role in the efficiency of radiationless decay Teller made two general observations (I) In a polyatomic molecule the non-crossing rule which is rigorously valid for diatomics fails and two electronic states even if they have the same symmetry are allowed to cross at a conical intersection (11) Radiationless decay from the upper to the lower intersecting state occurs within a single vibrational period when the system ‘travels’ in the vicinity of such intersection points On the basis of these observations Teller pro- posed that conical intersections may provide a common and very fast decay channel from the lowest excited states of polyatomics In the field of photochemistry Zimmermani4 and Michlt5 were the first to suggest independently that certain photoproducts originate from IC at a conical intersection Zimmermant4 and Michl l5 use the term ‘funnel’ for this feature In this review we will show that in agreement with the sugges- tions of Teller Zimmerman and Michl recent computational” l6 work when taken in conjunctionwith modern experimental studies indicates that the radiationless decay process does not occur via an excited state intermediate in many cases but rather through a conical intersection (1 e an unavoided surface crossing) between excited and ground states Radiationless decay at a conical inter- section implies that (a)the IC process will be 100% efficient (i e the Landau-Zerner17 decay probability will be unity) (b) any observed retardation in the IC or reaction rate (I e the competition with flurorescence) must reflect the presence of some excited state energy barrier which separates M* from the intersection structure and (c)in the case where the decay leads to a chemical reaction the molecular structure at the intersection must be related to the struc- ture of the photoproducts 2 The ’Physical Chemistry‘ of Conical Intersections The precise nature of the molecular mechanism that controls radia- tionless decay in polyatomics is a problem that has intrigued pho- tochemists and photophysicists for several decades An excited state species decays non-radiatively via internal conversion (IC) to a state of the same spin multiplicity and via intersystem crossing (ISC) to a state of different spin multiplicity In textbooks the effi ciency of IC and ISC is usually discussed in terms of the interaction between the vibrational energy levels of the two potential energy surfaces using the Fermi Golden Rule,i8 see eqn (1) where klhfis the rate of transition from initial (1) to final # states,W,and Wfare wavefunctions of initial and final states and pE is the density of states Upon simplification this term reduces approxi mately to eqn (2) where (x,Ixf>are Franck-Condon factors (i e vibrational overlaps) and plSC/lc is an electronic factor The efficiency of IC and ISC is often discussed in terms of Franck-Condon factors and plsc/lcis assumed to play a minor role The Landau-Zener model provides an alternative semi-classical model for radiationless decay As shown by Desouter-Lecomte and Lorquet,17 the probability of radiationless decay is given in eqn (3) where 6 is the Massey parameter given as eqn (4) CHEMICAL SOCIETY REVIEWS 1996 5= Wq) (4)LIsllg(s)l2Tr where q is a vector of nuclear displacement coordinates The term g(q) is the non-adiabatic coupling matrix element defined in eqn (6) while Iq I is the magnitude of the velocity along the reaction path q and AE is the energy gap between the two states IP and W2 Unless AE is less than a few kJ mol I the decay probability is van- ishingly small However as we approach a point where the surfaces actually cross the decay probability becomes unity To understand the relationship between the surface crossing and photochemical reactivity it is useful to draw a parallel between the role of a transition state in thermal reactivity and that of a conical intersection in photochemical reactivity ~~~ Reaction Co-ordinate Reaction Co-ordinate Scheme 1 In a thermal reaction the transition state forms a dynamical bottle- neck through which the reaction must pass on its way from reactants to products (Scheme la) A transition state separates the reactant and product energy wells along the reaction path A conical intersection (Scheme lb) also forms a structural bottleneck that separates the excited state branch of the reaction path from the ground state branch The crucial difference between conical intersections and transition states is that while the transition state must connect the reactant energy well to a single product well via a single reaction path an intersection is a ‘spike’ on the ground state energy surface (see inset in Scheme 1b) and thus connects the excited state reactant to two or inore products on the ground state via several ground state reaction paths The nature of the products generated following decay at a surface crossing will depend on the ground state valleys (reac- tion paths) that can be accessed from that particular structure Theoretical investigations of surface crossings have required new theoretical techniques based upon the ‘mathematical’ description of conical intersections and we now briefly review the central theoret- ical aspects The double cone shape of the two intersecting poten tial energy surfaces can only be seen if the energies are plotted against two special internal geometric coordinates of the molecule (x,and x in Scheme 2) The coordinate x is the gradient difference vector given in eqn 6 while x2 is the gradient of the interstate coupling vector see eqn (7) x = (c;(g)c,) (7) where C and C are the configuration interaction (CI) eigenvectors in a CI problem and H is the CI hamiltonian The vector x2 is POTENTIAL ENERGY SURFACE CROSSINGS IN ORGANIC PHOTOCHEMISTRY -M A ROBB ETAL parallel to the non-adiabatic coupling given in eqn (5) These geo- metric coordinates form the so called ‘branching space’ As we move in this plane away from the apex of the cone the degeneracy is lifted (see Scheme 2a) and ground state valleys must develop on the lower cone In contrast if we move from the apex of the cone along any of the remaining n -2 internal coordinates (where n is the number of degrees of freedom of the molecule) the degeneracy is not lifted This space of n -2 internal coordinates the ‘intersec- tion space’ is a hyperline consisting of an infinite number of conical intersection points (see Scheme 2b) n-2 dimensional intersection-space 2-dimensional state branching-space Scheme 2 Often the chemically relevant conical intersection point is located along a valley on the excited state potential energy surface Figure 1 illustrates a two-dimensional model example Here two potential energy surfaces are connected via a conical intersection This inter- section appears as a single point (CI) since the surfaces are plotted along the branching space (x x2) The intermediate M* is reached by relaxation from the Franck-Condon region (FC) and it is sepa- rated from the intersection point by a transition state (TS) In this case the molecular structure of the intersection and the reaction pathway leading to it can be studied by computing the minimum energy path (MEP) connecting FC to M* and M* to CI using the standard intrinsic reaction coordinate (IRC) method l9 However there are situations where there is no transition state connecting M* to the intersection point or where an excited state intermediate on Figure 1 Model conically intersecting potential energy surfaces plotted along the branching space (x 3,) The arrows indicate the direction of the minimum energy path connecting the FC point to the photoproducts P and P’ M* is the excited state intermediate and TS is a transition state con necting M* to the conical intersection (CI) the upper energy surface does not exist In such situations mech- anistic information must be obtained by locating the lowest lying intersection point along the n -2 intersection space of the mole- cule The practical computation of the molecular structure of a conical intersection energy minimum can be illustrated by making an analogy with the optimization of a transition structure As illus-trated in Scheme la a transition structure is the highest energy point along the path joining reactants to products and the lowest energy point along all the n -1 directions orthogonal to it One can opti- mize such a structure by minimising the energy in n -1 orthogo-nal directions and maximising the energy in the remaining direction corresponding to the reaction path The technique for locating the lowest energy intersection point** exploits the fact that the branching space directions x and x2play a role analogous to the reaction path at the transition state Accordingly the lowest energy point on a conical intersection is obtained by minimising the energy in the n -2 dimensional intersection space (x,x xn),which preserves the degeneracy (see Scheme 2b) The techniques outlined above provide information on the struc- ture and accessibility of the intersection point which controls the locus and efficiency of IC The evolution of ground state photo- products following decay ~’iasuch an IC channel requires a study of the possible ground state relaxation process Observe the shape of the ground state surface in the region of the conical intersection in Figure 1 The double cone in this case is ‘elliptic’ and two sides are steeper than the others This situation is typical of many cases and relaxation valleys develop more quickly in these directions We have recently implemented a method to locate and characterize all the relaxation directions that originate at the lower vertex of the CI cone 2’ The MEP starting along these relaxation directions defines the ground state valleys which determine the possible relaxation processes and the photoproducts This information is structural (i e non-dynamical) and provides insight into the mechanism of photo- product formation from vibrationally ‘cold’ excited state reactants such as those encountered in many experiments where slow excited state motion or/and thermal equilibration is possible (in cool jets in cold matrices and in solution) In many cases such structural or static information is not suffi- cient The excited state may not decay at the minimum of the conical intersection line Alternatively the momentum developed on the excited state branch of the reaction coordinate may be suffi- cient to drive the ground state reactive trajectory along paths that are far from the ground state valleys In such cases a dynamics treatment of the excited state/ground state motion is required For small systems a parametrised potential can be developed and full semi-classical quantum dynamical treatment is possible 22 In our own work:? we have used classical dynamics with a parametrised hybrid quantum-mechanical/force-field (MMVB the molecular mechanics valence bond method) This method employs a ‘direct’ procedure for solving the equations of motion and avoids the tedious and often unfeasible parametrisation of an analytical expression of a multidimensional energy surface The trajectory- surface-hopping algorithm of Tully and Preston (see ref 23 for details) is used to propagate excited state trajectories on to the ground state in the region of a conical intersection 3 Reaction ’Funnels’ in the Photochemistry of T-T* and n-n* States The application of different spectroscopic techniques to low tem- perature samples of ‘isolated’ conjugated molecules has begun to provide very detailed information on the excited state dynamics of these organic systems In Figure 2 we illustrate the results of two different experiments The first experiment (Figure 2a) is due to Kohler and coworkerslO who recorded the fluorescence lifetime of S ,(2A,) all-trans-octa- 1,3,5,7-tetraene (all-trans OT) as a function of the temperature In this experiment the all-tram OT molecules are isolated in a molecular cavity of frozen hexane and do not inter- act with each other From Figure 2(a) one can see that at tempera- tures above 200 K the fluorescence lifetime drops dramatically indicating fast decay of the excited state molecules to the ground 324 CHEMICAL SOCIETY REVIEWS. 1996 100 200 Temperature/ K (a) -n qr50 I?$ -1003CD Radiationless 0CD-50 Y 13 -0 5 I 0 1000 2000 3000 4000 A EnergyAbove the Origin / cm-’ Figure 2 ‘Opening’ of a fast radiationless decay channel in all trans octate traene in (a) matrix isolated conditions (b) in a expanding cool jet state This event was assigned to the opening of a thermally acti- vated efficient radiationless decay channel with a barrier height of ca 1500 cm-(1 1 9 kJ mol-I) The second experiment (Figure 2b) is due to Christensen Yoshihara Petek and coworkers,’ who reported the fluorescence decay rate of S all-trans OT molecules measured in free jet expansion as a function of the excitation energy These authors propose that cis-trans isomerisation is responsible for the radiationless decay channel which opens up at ca 2 I00 cm I (25 kJ mol I) excess energy The data from both experiments can be explained using the model surface shown in Figure la In both experiments the fluorescence lifetime decreases slowly and almost linearly by increasing the S I excess vibrational energy until an energy threshold is reached and a dramatic decrease in excited state lifetime is observed Similar observations have been documented In other conjugated molecules In S benzene there is a ca 3000 cm I (35 9 kJ mol I) threshold for the disappearance of S fluorescence (see ref I I) This observation is assigned to the opening of a very efficient radiation- less decay channel (termed ‘channel 3’) leading to the production of fulvene and benzvalene In S cyclohexadiene which is produced via a fast decay from the spectroscopic S state there must be a small barrier (ca 4 kJ mol I) to decay to S since the photoprod- ucts of the ring-opening reaction are detected a few picoseconds after initial excitation Ab initio CAS-SCF and multi-reference MP2 show that the topology of the first (T-+) excited state energy surface is indeed consistent with the model surface shown in Figure I (except for cyclohexadiene in which there is no transition structure between the excited state energy minimum and the intersection pointlhfl Thus the observed energy thresholds which are well reproduced in theoretical computations correspond to the energy barriers which separate an excited state S intermediate from a S ,/Soconical intersection point The molecular system spends very little time in the neighbour- hood of geometries characterised by conical intersections Thus such geometries are not amenable to direct experimental observa- tion and can only be derived from theoretical computations The optimized conical intersection structures for all-trans OT S benzene and S cyclohexadiene intersections are collected in Figure 3 Comparison of these structures reveals common struc- tural and electronic features Each structure contains a triangular Figure 3 Structures of S ,/So conical intersections in conjugated hydrocar bons showing the -(CH),-kink (framed) (a) all trans octatetraene. (b) benzene (c) cyclohexadiene Interatomic distances are in 8 arrangement of three carbon centres corresponding to a -(CH),-kink of the carbon skeleton in all-trans OTIhh and benzene“ and to a triangular arrangement of the -CH and -CH-CH terminal frag- ments in cyclohexadiene 16(’ The electronic structure in each case corresponds to three weakly interacting electron5 in a triangular arrangement which are loosely coupled to an isolated radical centre (this is delocalised on an ally1 fragment in all-trans OT and benzene and localised in cyclohexadiene) This type of conical intersection structure appears to be a general feature of conjugated systems and has been documented in a series of polyenes and polyene radicals The electronic origin of this feature can be under- stood by comparison with H where any equilateral triangle con- figuration corresponds to a point on the D,/D conical intersection in which the three H electrons have identical pairwise interactions Moving from conjugated hydrocarbons to other classes of organic molecules the electronic structure of the lowest lying inter- section changes We now have detailed results on the Paterno-Buchi reaction,’& a,P-enonesI&’ the oxadi-n-methane and [ 1 ,.?J-acyl sigmatropic rearrangements of /3,y-enones,16p azo-compounds (diazomethanel ’”) and photorearrangement of acyl- cyclopropenes to furans I6x While hydrocarbon photochemistry typically involves a low energy covalent state the photochemistry of bichromophoric (C=O and C=C) compounds is complicated by the competition between triplet 3( r-n-) pathways and singlet ](T-7.r) and triplet ’(n-n-) pathways The novel feature of our results is the discovery of points in the surface where all four states are degenerate This feature rationalises the singlet-triplet photochem- istry in a novel way The new features that arise in bichromophoric (C=O and C=C) compounds can be illustrated with the structure of the So/S conical intersections found in a,p-enones In this case the first singlet POTENTIAL ENERGY SURFACE CROSSINGS IN ORGANIC PHOTOCHEMISTRY -M A ROBB ETAL 325 Figure 4 Low lying intersections in CIS acrolein (a) Sl(n-+)/So conical intersection (b) Tl(r-+)/S0 triplet/singlet crossing excited state is not a v-7F state but an n-+ state where the lone- pair orbital n becomes singly occupied This fact alone results in an electronic and molecular structure which is very different from the -(CH),-kink seen in conjugated hydrocarbons The case of cis-acroleinl6" is instructive (see Figure 4a) The S,/S conical inter- section has a 90" twisted terminal CH and corresponds to a diradical with radical centres on CH and 0 with a central C-C double bond (1 34 A) This structure corresponds to a point of degeneracy between the n-+ and ground state because the radical centres do not interact with each other and with the central .sr-bond Thus in this structure the S state and the l(n-7F) state differ only in a 90" rotation of the position of the singly occupied orbital on the oxygen Since the position of this radical centre is isolated from the CH radical centre the states have the same energy The structure of the S,/Soconical intersection in acrolein ration- alises the observed wavelength dependent photochemistry of a,P-enones Direct irradiation with 310 nm light produces cis-trans double bond isomerisation exclusively In contrast irradiation with 250 nm light produces a mixture of isomerisation and ring-closure products The 310 nm photochemistry comes from the enone TI triplet state Computations on acrolein demonstrate that this state is populated by ISC from the initial S (n-+) excited state molecule to a TI (.sr-+) diradical intermediate the structure of which is shown in Figure 4b The 3( n-+) diradical intermediate is not gen- erated directly but involves decay through successive SJT and a T,/T intersections The T intermediate is located at a T,/S inter- section and is the precursor of the photoproducts which are gener- ated via a slow ISC process The stability and structure of this diradical correlates nicely with the observed phosphore~cence~~ and lack of production of the four-membered ring oxetene upon >300 nm irradiation 25 In fact while the two radical centres are located on two vicinal carbons the carbonyl bond is fully formed Consequently relaxation to the Sostate can only result in a@-enone formation structure via cis-trans motion The production of oxetane requires a very different decay point which is assigned to the Si/So conical intersection described above The fact that 250 nm radiation is required for populating this decay channel is consistent with the fact that this is located at least 40 kJ mol above the initial S struc ture 4 Butadiene Photochemistry Beyond the Woodward-Hoffman rules The cyclisation of butadienes and ring-opening of cyclobutenes are textbook examples of pericyclic reactions The stereochemistry of both thermal and photochemical pericyclic reactions can be pre- dicted on the basis of the Woodward-Hoffman (WH) rules l8 Despite the fact that the success of these rules has been demon- strated in many cases it is not obvious why they work in the case of the photochemistry of polyenes The WH rules predict the stere- ochemistry of the motion on the (HOMO-LUMO singly excited) I B spectroscopic state (see Figure 5a) However the spectroscopic investigation7 of short polyenes shows that after photoexcitation these systems decay to a lower lying doubly excited (2A,) state Thus the photoproducts must originate from this state via IC Why is the 'disrotatory ' stereochemistry predicted for the spectroscopic state of s-CISbutadiene not lost on the 2A state? Further while a rigid disrotatory stereochem is try has been experimental 1y observed for the s-CISbutadiene ring-closure Leigh et a1 26 have demon- strated that the reverse photoreaction the ring-opening of cyclobutene occurs with a low degree of stereospecificity About 20 years ago Van der Lugt and OosterofP proposed that along distinguished disrotatory and conrotatory ring-closure coor- dinates the 2A state has two deep minima The observed disrota- tory stereochemical preference was then explained on the basis of a higher rate of IC at the disrotatory 2A minimum (see arrows in Figure 5a) owing to a substantially smaller excited statelground state energy gap in this point The recent computational re-investi gation of the interplay between the 2A dark state potential energy surface the lB surface and the lA ground state surface of S-CI~ butadiene rationalises its photo-stereochemistry16/fIn Figure 5b we show the energy profiles along the reaction paths computed for the first two excited states of s-cis butadiene Upon relaxation from the FC region the photoexcited molecule undergoes a barrierless relax ation leading ultimately to decay to the 1A I ground state There are two successive intersection points involved in the relaxation process The first intersection occurs between the spectroscopic 1 B state and the dark 2A state and is located in the vicinity of the FC region This IS consistent with spectroscopic studies on isoprene (2 methylbutadiene),3 which indicates that the 1B state is depopulated on a timescale of 10 fs owing to fast internal conversion to the nearby 2A state The second intersection involves a conical inter section between the 2A and the lA state which will be entered after 2A geometric relaxation Thus photoproduct formation occurs after 2A decay following solvent cooling of the initially hot molecule The 1 B path which describes the relaxation from the FC region (see arrows in Figure 5b) involves a disrotatory motion of the ter- minal methylenes in agreement with the prediction of the WH rules However both a disrotatory and a conrotatory reaction path exist on the 2A potential energy surface which ends in the same 2Al/lA crossing region However while the disrotatory path is barrierless the conrotatory path has a barrier (due mainly to steric effects) and it is located 30 kJ mol higher in energy Thus the (energetically preferred) structural evolution of the system along the 2A energy surface will also be disrotatory but for a reason unrelated to the WH theory Simply the conrotatory motion on the 2A surface is hindered by a barrier The original Van der Lugt and Oosteroff model (arrows in Figure 5a) can now be refined Our computations and experimental work indicate the existence of a disrotatory I B,/2A I crossing in butadienes However there are no CHEMICAL SOCIETY REVIEWS 1996 i F=i disrotatory Figure 5 Butadiene photochemistry (a) WH state correlation diagram The arrows represent the Van der Lugt and Oosteroff mechanism (b) Computed MEP from the S (1 B2) FC structure of s cis butadiene to the S (2A,)/S conical intersection Full lines and light lines represent the energy profile along the dis- rotatory and conrotatory MEP respectively The terminal hydrogen atoms in the structures have been highlighted to indicate the stereochemistry true 2A minima and the lowest energy point on the 2A state is a conical intersection Direct irradiation of s-cis butadienes is known to yield a mixture of cis-trans isomerisation and cyclisation photo product^^^ In a 20 K matrix Squillacote et af have measured the ratios of double-bond cis-trans isomerisation s-cis>s-trans isomerisation ring-closure and reactant back-formation The structure of the computed 2A,/IA conical intersection and the energy profiles of the four relaxation paths that begin at the apex of this conical intersection are shown in Figure 6 Neglecting the effect of dynamical factors which may in principle control the efficiency of the different relax- ation processes it is obvious that double-bond cis-trans isomerisa-tion ring-closure and reactant back-formation will be competitive We have not been able to locate a path leading to the cyclopropyl- methylene diradical which is a precursor of bicyclobutane This observation is consistent with the fact that this product has not been seen experimentally Our theoretical prediction which suggests that the photoreactivity of s-cis butadiene involves simultaneous twist- ing motion about the central C-C bond and one of the original double bonds (see Figure Sb) has been experimentally tested by Leigh et af using a series of C-C ring-locked butadienes l2 Their experiments show that the yield for double-bond isomerisation is indeed affected by the size of the ring blocking the C-C s-cis>s-truns rotation The reaction paths illustrated in Figures 5 and 6 also provide an explanation for the lack of stereochemistry observed in cyclobutene (CB) ring-opening reactions 26 (The WH rules predict a disrotatory stereochemistry) The experimental observations can be explained by assuming that the CB ring opens on the 1B2state In this way CB photolysis would yield 1B2 s-cis butadiene which decays to the dark 2A state following the pathway illustrated in Figure Sb The CB final photoproducts must originate via decay at the same 2A I/1A conical intersection and will follow the relaxation paths shown in Figure 6 It is then obvious that since decay at this point involves concurrent butadiene formation and double-bond cis-trans isomerisation the production of a stereospecific (disrota- tory) ring-opening product is impossible Thus the loss of stereo- chemistry IS due to the unuvoiduble concurrent cis-trans isomerisation and butadiene formation 5 Towards a Dynamic View of Photochemical Processes Benzene and Azulene In our preceding discussion of butadiene photochemistry we have shown how excited state and ground state relaxation paths can provide structural (I e non-dynamical) information on the mech- anism of product formation associated with radiationless deactiva- tion A more realistic picture of these processes requires the description of the reaction dynamics obtained from the computation and analysis of non-adiabatic trajectories We now illustrate this point with some results on benzene and azulene The lifetime of the S state of vapour phase benzene drops dra- matically when the vibrational excess energy overcomes a ca 3000 cm-I (35 9 kJ mol I) barrier In contrast recent spectroscopic investigations have demonstrated that the S state of the pseudo- aromatic molecule azulene has a sub-picosecond lifetime arising from a nearly barrierless fast deactivation process Our recent ab initio computations' rationalise these data and have confirmed that in both molecules a S ,/So conical intersection occurs on the S potential energy surface Non-adiabatic dynamics from benzene23 and azuleneI6' S states give new insight into the quantum yield of prefulvene in the case of benzene and suggest that one may observe coherent vibrations on the ground state of azulene In Figure 7 we show that the S poten-tial energy surfaces of benzene and azulene have different shapes in the region of the conical intersections For S benzene there is a sub- stantial barrier separating an excited state intermediate from the conical intersection region In contrast azulene shows a 'sloped' conical intersection which is slightly higher than the intermediate region Our dynamics studies have been carried out with the MMVB technique discussed in ref 23 Comparison of the MMVB energy and molecular structures of benzene and azulene with the corresponding ub initio parameters (see Figure 7) indicates a good qualitative agreement The computed non-adiabatic dynamics are thus expected to be qualitatively correct In the case of benzene our objective was to understand the origin of the very low quantum yield (cu 0 02) for the production of ben- zvalene Figure 7(a) shows that there is an S transition structure with a geometry that is virtually identical to the optimized intersec- tion Thus there will be two possible types of trajectory that pass POTENTIAL ENERGY SURFACE CROSSINGS IN ORGANIC PHOTOCHEMISTRY -M. A. ROBB ETAL. Table 1 Quantum yield of prefulvene as a function of the initial momentum (excess energy) along the reaction path Excess energy Hopped trajectories (%) Prefulvene yield (%) kJ mol-1 12.9 48 0.0 22.5 100 0.0 25.1 100 2.7 27.6 100 3.1 32.6 100 2.0 37.7 100 2.7 41.8 100 11.3 48.5 100 22.3 0 2 4 6 8 MEP(a.u.) Figure 6 Energy profiles along the computed MEP describing the relax- ation from the S,/Soconical intersection point to the s-cis butadiene pho- toproducts. The terminal hydrogen atoms in the structures have been highlighted to indicate the stereochemistry. through the conical intersection region trajectories that follow the reaction path between the S minimum and the prefulvene structure and trajectories that return to the So minimum after a surface hop. The quantum yield corresponds to the ratio of the numbers of tra-jectories leading to the prefulvene as a function of the total. In our simulation the initial conditions were designed to select trajectories approaching the intersection region. There are two variables asso- ciated with the initial conditions (a)the value of the initial kinetic energy (momentum) along the reaction path and (b)the value of the initial vibrational kinetic energy randomly distributed among the normal modes orthogonal to the reaction path. The effect of the initial momentum along the reaction path is shown in Table 1 which lists the percentage of trajectories that A hopped during the simulation and the percentage that terminated in the prefulvene region for a range of excess kinetic energies. The very small computed yield of prefulvene shows a general increase as the kinetic energy rises. The experimental quantum yield at 253 nm is 0.016 which rises slightly to 0.037 at 237 nm. These results are remarkable for two reasons. First we manage to reproduce the characteristic low quantum yield observed experimentally. Secondly we find that the dynamics associated with passage through the conical intersection can be interpreted using simple classical arguments. If the excess energy is directed along the reac- tion coordinate leading to prefulvene the quantum yield increases. If the excess kinetic (vibrational) energy is directed orthogonal to the reaction coordinate the quantum yield decreases (see Table 2). Thus sampling a larger area of the potential surface at higher kinetic energies produces trajectories that are no longer confined to the bottom of the reaction ‘valley’. Rather the initial kinetic energy will be distributed into a variety of vibrations and not just be directed toward the prefulvene region. The anomalous fluorescence of azulene -emission from S rather than S -was first recognised by Beer and Longuet-Higgins forty years ago (see refs. in 16i). Femtosecond laser studies and spectroscopic linewidth measurements have now established that complete internal conversion from S to the ground state takes place in less than a picosecond. Ab initio computations show how such ultra-fast decay can be explained by the So/S conical inter- section represented in Figure 7(b). The molecular dynamics studies suggest that the decay can take place before a single oscillation 1.JI 1.39 [1.49] c 1.49 [1.47] S1 t ,/ benzene Figure 7 Conically intersecting potential energy surfaces in benzene and azulene. (a) Shape of the S and So energy surfaces in benzene. The arrows repre- sent the MEP connecting S benzene to the product well via the conical intersection. (b) S and S,,energy profiles along the S path from the FC structure of azulene. The ab inirio and MM-VB (in square brackets) geometrical parameters and energies are reported in A and kJ mol-I respectively. Table 2 Quantum yield of prefulvene as a function of the initial vibrational kinetic energy (AE,,,) randomly distributed among the normal modes orthogonal to the reaction path The effect is shown for two values of the initial momentum along the reaction path (excess energy) Prefulvene yield (%) Excess energy Excess energy (27 6 kJ mol I) (43 1 kJ mol I) 0 00 12 7 II 3 0 002 121 68 0 003 20 10 5 0 004 23 86 0 005 08 74 0 006 04 70 0 007 04 51 0 008 00 47 E = Hartree units (1 E = 2626 kJ mol I) AEhmit (a u) m 0001 7.5 8.5 9.5 10.5 11.5 12.5 13.5 Time S1-> SO hop occurred / fs Figure 8 Azulene dynamics simulations distribution of hop times with small and large initial vibrational excess energies (AEII,) through the intersection space is completed The results of this sim- ulation are summarised in Figure 8 The average time taken to reach the hopping region is always ca 10 fs and it is the time dispersion that increases with the available kinetic energy at the hop At low kinetic energies (0 001 a u ) nearly all (observe the single peak in Figure 8) of the surface hops occur within the first half vibrational- period of their excited state lifetime (trajectory A in Figure 7b) At higher initial energies there is a much wider spread of crossing times with two clear peaks corresponding to hops earlier and later than those observed at lower energy The second peak therefore corresponds to molecules that decay after having completed the first half of a vibration along the relaxation coordinate (trajectory B in Figure 7b) 6 Concluding Remarks Excited state reactivity is controlled by three factors (a)the pres- ence and magnitude of barriers in the excited state branch of the reaction coordinate (6) the dynamics of IC or ISC as the system returns to the ground state and (c)the nature of ground state reac- tion pathways that are populated following IC or ISC The concept of the ‘photochemical funnel’ introduced by ZimmermanI4 and Michl Is can now be substantiated via both computational and exper- imental investigations Advances in computer and laser technology CHEMICAL SOCIETY REVIEWS 1996 and the introduction of new computational and experimental methodologies are yielding a new mechanistic picture of photo- chemical reactions This picture is based upon the idea that single or successive low-lying intersections provide the bottlenecks con- trolling the evolution of a photoexcited molecule from the FC region to the photoproduct valleys Both theory and experiment now indicate that such intersection mechanisms are a general feature in photochemical reactivity problems Acknowledgements This research has been supported in part by the EPSRC (UK) under grant numbers GR/J25 123 GR/H58070 and GR/K048 1 1 We are also grateful to NATO for a travel grant (CRG 950748) 7 References I See references collected in M Klessinger Angew Chem Int Ed Engl,l995,34,549 2 W TA M Van der Lugt and L J 0osteroff.J Am Chem Soc 1969 91,6042 3 M 0 Trulson and R A Mathies J Phys Chem 1990,94,5741 4 See (a)P J Reid S J Doig S D Wickham and R A Mathies J Am Chem Soc 1993,115,4754and references cited therein (b)S Pullen L A Walker 11 B Donovan and R J Sension Chem Phys Lett ,1995 242,415 5 D R Cyrand C C Hayden,J Chem Phvs 1996,104,771 6 H Kandori Y Katsuta M Ito and H Sasabe J Am Chem Soc ,1995 115,2669 7 Q Wang R W Schoenlein L A Peteanu R A Mathies and C V Shank. Science 1994,266,422 8 H Petek A J Bell R L Christensen and K Yoshiara. SPIE 1992. 1638,345 9 H Petek A J Bell Y S Choi K Yoshiara B A Tounge and R L Christensen J Chem Phvs ,1993,98,3777 10 B E Kohler,Chem Rev 1993,93,41 11 I J Palmer I N Ragazos F Bernardi M Olivucci and M A Robb J Am Chem SOC ,1992,115,673 12 W J Leigh and A Postigo,J Chem SOC Chem Commun ,1993,1836 13 E Teller Isr J Chem ,1969,7,227 14 H E Zimmerman J Am Chem SOC,1966,88,1566 15 J Michl ,J Mol Photochem ,1972,243 16 (a)P Celani S Ottani ,M Olivucci F Bemardi and M A Robb J Am Chem Soc ,1994,116 10141 (b)P Celani M Garavelli S Ottani F Bernardi M A Robb and M Ol~vucci J Am Chem Soc 1995,117 11584 (c) I J Palmer 1 N Ragazos F Bemardi. M Olivucci and M A Robb J Am Chem Soc 1994 116. 2121 (6) M Reguero M Olivucci F Bernardi and M A Robb,J Am Chem SOC,1994,116 2103. and references cited therein (e) S Wilsey M J Bearpark F Bernardi M Olivucci and M A Robb J Am Chem Soc 1996. 118 176 v> see N Yamamoto F Bernardi A Bottom M Olivucci M A Robb and S Wilsey J Am Chem Soc ,1994,116,2064,and references cited therein (8)S Wilsey M J Bearpark. F Bernardi M Olivucci and M A Robb,J Am Chem Soc ,1996,111press (h)P Celani F Bernardi M Olivucci and M A Robb,J Chem Phvs ,1995,102,5733,(1) M J Bearpark F Bernardi S Cliffort M Olivucci M A Robb B R Smith and TVreven J Am Chem SOC 1996,118,169 17 M Desouter Lecomte and J C Lorquet J Chem Phys ,1977,71,4391 18 A Gilbert and J Baggott ‘Essentials of Molecular Photochemistry’ Blackwell Scientific Publications. Oxford 1991 19 M L McKee and M Page in ‘Reviews in Computational Chemistry’ ed K B Lipkowiz and D B Boyd 1993,4,35 20 I N Ragazos M A Robb,F Bernardi and M Olivucci Chem Phys Lett 1992,197,217 M J Bearpark M A Robb and H B Schlegel Chem Phys Lett ,1994,223,269 2I P Celani ,M A Robb M Garavelli F Bernardi and M Olivucci Chem Phys Lett 1995,243.1 22 H Koppel W Domcke and L S Cederbaum Adv Chem Phys ,1984 57,59 23 B R Smith. M J Bearpark M A Robb F Bernardi and M Olivucci Chem Phys Lett ,1995,242,27 24 R S Becker K Inuzuka and J King,./ Chem Phys 1970,52,5164 25 L E Friedrich and G B Schuster,J Am Chem SOC ,1972,94,1193 26 W J Leigh and K Zeng,J Am Chem Soc 1991,113,2l63 27 M Squillacote and T C Sample J Am Chem SOC 1990,112,5546