摘要:

FARADAY DISCUSSIONS OF THE CHEMICAL SOCIETY NO67 1979 Kinetics of State Selected Species THE FARADAY DIVISION CHEMICAL SOCIETY LONDONOrganising Committee Dr. J. P. Simons (Chairman) Dr. A. R. Burgess Prof. R. J. Donovan Mrs. Y. A. Fish Prof. R. Grice Dr. D. M. Hirst Prof. J. C. Robb. Dr. I. W. M. Smith Dr. J. C. Whitehead Dr. D. A. Young ISBN: 0 85186 950 5 ISSN: 0301-7249 0 The Chemical Society and Contributors 1979 Printed in Great Britain by Fletcher & Son Ltd, NorwichA GENERAL DISCUSSION ON Kinetics of State Selected Species 9th, 10th and 11th April, 1979 A GENERAL DISCUSSION on Kinetics of State Selected Species was held at the University of Birmingham on 9th, 10th and 11th April, 1979. The President of the Faraday Division, Professor F. C . Tompkins, F.R.S., was in the chair: about 170 Fellows of the Faraday Division and visitors from overseas attended the meeting.Among the overseas visitors were : Prof. M. Alexander, U.S.A. Dr. J. M. Alvarino, West Germany Prof. F. J. Aoiz, Spain Prof. G. H. Atkinson, U S A . Dr. N. Basco, Canada Dr. R. R. Burke, France Dr. R. J. Buss, U.S.A. Dr. J. E. Butler, U.S.A. Prof. A. Cabello Albala, Spain Prof. F. Castano, Spain Dr. P. N. Clough, West Germany Dr. T . Darko, Sweden Prof. X. De Hemptinne, Belgium Dr. A. Ding, West Germany Mr. K. Eichler, West Germany Dr. H. Figger, West Germany Prof. F. Fleming Crim, U.S.A. Dr. R. Foon, Australia Prof. E. U. Franck, West Germany Prof. K. Freed, U.S.A. Prof. T. F. George, U.S.A. Prof. G. Giacometti, Italy Prof. A. Gonzalez Urena, Spain Prof. P.Gray, West Germany Dr. W. Hack, West Germany Prof. W. L. Hase, U.S.A. Dr. E. F. Hayes, U.S.A. Dr. L. Hellner, France Mr. V. J. Herrero, Spain Mr. H. Heydtmann, West Germany Dr. L. Holmlid, Sweden Prof. P. L. Houston, U.S.A. Prof. W. M. Jackson, U.S.A. Dr. W. Jakubetz, Austria Dr. B. Katz, Israel Prof. K. L. Kompa, West Germany Prof. I. Koyano, Japan Dr. P. J. Kunst, West Germany Mr. L. Lain, Spain Dr. C. Lalo, France Dr. S. Leach, France Dr. H. U. Lee, Wesr Germany Dr. S . R. Leone, U.S.A. Dr. M. R. Levy, U.S.A. Mr D. Lubman, U.S.A. Dr. K. Luther, West Germany Mr. J. P. Martin, France Dr. J. Masanet, France Prof. M. Menzinger, Canada Prof. J. Momigny, Belgium Mr. J. Paris, France Prof. J. C . Polanyi, Canada Prof. E. Poquet, France Dr. K. V. Reddy, U.S.A.Prof. H. Reiss, U.S.A. Dr. C. T. Rettner, U.S.A. Prof. S. A. Rice, U.S.A. Mrs. M. P. Roellig, U.S.A. Dr. G. Rotzoll, West Germany Prof. J. Santarnaria, Spain Prof. G. C . Schatz, U.S.A. Prof. J. L. Schreiber, U.S.A. Prof. D. W. Setser, U.S.A. Prof. P. E. Siska, U.S.A. Dr. J. J. Sloan, Canuda. Prof. F. M. G. Tablas, Spain Dr. K. Tanaka, Japan Dr. G. Venzl, West Germany Dr. J. Wanner, West Germany Dr. K. B. Whaley, U.S.A. Prof. R. N. Zare, U.S.A. Dr. R. Zellner, West GermanyA GENERAL DISCUSSION ON Kinetics of State Selected Species 9th, 10th and 11th April, 1979 A GENERAL DISCUSSION on Kinetics of State Selected Species was held at the University of Birmingham on 9th, 10th and 11th April, 1979. The President of the Faraday Division, Professor F. C . Tompkins, F.R.S., was in the chair: about 170 Fellows of the Faraday Division and visitors from overseas attended the meeting.Among the overseas visitors were : Prof. M. Alexander, U.S.A. Dr. J. M. Alvarino, West Germany Prof. F. J. Aoiz, Spain Prof. G. H. Atkinson, U S A . Dr. N. Basco, Canada Dr. R. R. Burke, France Dr. R. J. Buss, U.S.A. Dr. J. E. Butler, U.S.A. Prof. A. Cabello Albala, Spain Prof. F. Castano, Spain Dr. P. N. Clough, West Germany Dr. T . Darko, Sweden Prof. X. De Hemptinne, Belgium Dr. A. Ding, West Germany Mr. K. Eichler, West Germany Dr. H. Figger, West Germany Prof. F. Fleming Crim, U.S.A. Dr. R. Foon, Australia Prof. E. U. Franck, West Germany Prof. K. Freed, U.S.A. Prof. T. F. George, U.S.A. Prof. G. Giacometti, Italy Prof. A. Gonzalez Urena, Spain Prof.P. Gray, West Germany Dr. W. Hack, West Germany Prof. W. L. Hase, U.S.A. Dr. E. F. Hayes, U.S.A. Dr. L. Hellner, France Mr. V. J. Herrero, Spain Mr. H. Heydtmann, West Germany Dr. L. Holmlid, Sweden Prof. P. L. Houston, U.S.A. Prof. W. M. Jackson, U.S.A. Dr. W. Jakubetz, Austria Dr. B. Katz, Israel Prof. K. L. Kompa, West Germany Prof. I. Koyano, Japan Dr. P. J. Kunst, West Germany Mr. L. Lain, Spain Dr. C. Lalo, France Dr. S. Leach, France Dr. H. U. Lee, Wesr Germany Dr. S . R. Leone, U.S.A. Dr. M. R. Levy, U.S.A. Mr D. Lubman, U.S.A. Dr. K. Luther, West Germany Mr. J. P. Martin, France Dr. J. Masanet, France Prof. M. Menzinger, Canada Prof. J. Momigny, Belgium Mr. J. Paris, France Prof. J. C . Polanyi, Canada Prof. E. Poquet, France Dr. K. V. Reddy, U.S.A.Prof. H. Reiss, U.S.A. Dr. C. T. Rettner, U.S.A. Prof. S. A. Rice, U.S.A. Mrs. M. P. Roellig, U.S.A. Dr. G. Rotzoll, West Germany Prof. J. Santarnaria, Spain Prof. G. C . Schatz, U.S.A. Prof. J. L. Schreiber, U.S.A. Prof. D. W. Setser, U.S.A. Prof. P. E. Siska, U.S.A. Dr. J. J. Sloan, Canuda. Prof. F. M. G. Tablas, Spain Dr. K. Tanaka, Japan Dr. G. Venzl, West Germany Dr. J. Wanner, West Germany Dr. K. B. Whaley, U.S.A. Prof. R. N. Zare, U.S.A. Dr. R. Zellner, West GermanyCONTENTS Page 7 16 27 41 57 66 90 97 110 146 162 173 180 188 204 Polanyi Memorial Lecture by R. N. Zare TRANSLATIONAL EXCITATION Introductory Lecture: Efect of Translational Energy on Reaction Dynamics by R. Grice Reaction of Alkali Metal Atoms with Carbon Tetrachloride: Rainbow-like Couplings of Product Angle and Energy Distribution by S.J. Riley, P. E. Siska and D. R. Herschbach Electronic Excitation in Potentially Reactive Atom-Molecule Collisions by M. A. D. Fluendy, K. P. Lawley, J. McCall, C. Sholeen and D. Sutton Observation of a Condon Reflection Products State Distribution in the Collinear H + C12 Reaction by M. S. Child and K. B. Whaley Distribution of Reaction Products (Theory) : Part I2.--Microscopic Branching in H + XY -+ HX + Y , HY + X (X, Y = Halogens) by J. C. Polanyi, J. L. Schreiber and W. J. Skrlac F + H2 Collisions in the Presence of Intense Laser Radiation: Reactive and Non- Reactive Processes by P. L. DeVries, T. F. George and J.-M. Yuan Vibrational-mode-specijic Energy Consumption: Translational and Vibra- tional State Dependence of the Ba + N20 (vl, u2, u3) -+ BaO* + N2 Reaction by D.J. Wren and M. Menzinger GENERAL DISCUSSION VIBRATIO NAL-ROTATIO NAL EXCITATION Introductory Lecture: Chemical Reaction of Vibrationally Excited Molecules by C. B. Moore and I. W. M. Smith Molecular Beam Studies of Unimolecular Reactions C1, F + C2H3Br by R. J. Buss, M. J. Coggiola and Y. T. Lee Direct Measurement of Photoisomerization Lifetimes for Laser-excited Methylcycloheptatriene Molecules by H. Hippler, K. Luther and J. Troe Wavelength Dependence of Multiphoton Absorption and Dissociation of Hexafluoroace tone by W. FuD, K. L. Kompa and F. M. G. Tablas Reaction Dynamics of State-Selected Unimolecular Reactants: Energy Dependence of the Rate Coeficient for Methyl Isocyanide Isomerization by K.V. Reddy and M. J. Berry Infrared Multiple Phonon Excitation and Dissociation of Single Molecules by M. N. R. Ashfold, G. Hancock and G. Ketley212 221 255 273 286 297 306 316 329 343 363 366 Time-resolved Measurements on the Relaxation of OH(v = 1) by NO, NO2 and O2 by D. H. Jaffer and I. W. M. Smith GENERAL DISCUSSION ELECTRONIC EXCITATION Introductory Lecture: Analogy between Electronically Excited State Atoms and Alkali Metal Atoms by D. W. Setser, T. D. Dreiling, H. C. Brashears, Jr and J. H. Kolts Kinetic Study of Electronically Excited Carbon Atoms C(2'S0) by D. Husain and P. E. Norris Reactions of O(2' D2) and O(23PJ) with Halogenomethanes by M . C. Addison, R. J. Donovan and J. Garraway State-to-State Photochemical Reaction Dynamics in Polyatomic Molecules by K. F. Freed, M. D. Morse and Y. B. Band Pho tofragmen tation Dynamics and Reactive Collisions of Laser-excited Electronic States by S. L. Baughcum, H. Hofmann, S. R. Leone and D. J. Nesbitt Studies of BrCl by Laser-induced Fluorescence: Part 3.-Collision-$ree Dynamics of Quantum Resolved Levels in the Excited B3n (O$) State by M. A. A. Clyne and I. S. McDermid Crossed Beam Studies of Chem ilum inescen t Metastable A tom ic React ions: Excitation Functions and Rotational Polarization in the Reactions of Xe (3P2,0) with Br, and CCl, by C. T. Rettner and J. P. Simons GENERAL DISCUSSION Closing Remarks by S. A. Rice Index of Names

ISSN:0301-7249    

DOI:10.1039/DC9796700001

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY 369 Date 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1978 1978 1979 1979 Subject Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Photo-effects in Adsorbed Species Physical Adsorption in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Radiation Effects in Liquids and Solids Ion-Ion and Ion-Solvent Interactions Colloid Stability Structure and Motion in Molecular Liquids Kinetics of State Selected Species Oxidation For current availability of Discussion volumes, see back cover.Volume 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67GENERAL DISCUSSIONS OF THE FARADAY SOCIETY 369 Date 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1978 1978 1979 1979 Subject Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Photo-effects in Adsorbed Species Physical Adsorption in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Radiation Effects in Liquids and Solids Ion-Ion and Ion-Solvent Interactions Colloid Stability Structure and Motion in Molecular Liquids Kinetics of State Selected Species Oxidation For current availability of Discussion volumes, see back cover.Volume 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

ISSN:0301-7249    

DOI:10.1039/DC97967BX003

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Polanyi Memorial Lecture BY RICHARD N. ZARE Department of Chemistry, Stanford University, Stanford, California 94305, U.S.A. Received 16th May, 1979 Early workers in the field of chemical kinetics largely contented themselves with the measurement of reaction rates in terms of the concentrations of the interacting species. Michael Polanyi’s experimental efforts were directed along the same lines. Polanyi’s original idea was to form atomic or molecular beams of the reagents to be studied.’ These beams were to be arranged so that they crossed. A measurement of the product flux would give the cross-section of the reaction from which the reaction rate could be calculated. However, experimental methods of the 1920s precluded the use of such techniques and instead Polanyi relied upon the ingenious use of diffusion flames.Two reacting gases were admitted to opposite ends of a long glass tube. As they met, reaction was established. Some of the reactions produced visible chemilumines- cence; others led to the formation of nonvolatile products that adhered to the walls of the tube. From the length of the reaction zone one could estimate how many scattering collisions occurred before reaction, based on a knowledge of diffusion theory and gas kinetic cross-sections. This method was used by Polanyi and coworkers to determine about one hundred reaction cross-sections, mostly for reactions of alkali atoms with halogen-containing molecules.2 The cross-sections varied in size from a very tiny fraction of a gas kinetic collision cross-section to those much larger, so much larger that they might be figuratively compared to the size of a whale! These measurements were widely recognized to be of fundamental importance and were the precursors of extensive molecular beam studies of the very same ~ystems.~ However, even more than his experimental work, Polanyi distinguished himself among kineticists by his inquiry into the relationship between the values of these reaction cross-sections and the structures and dynamics of the interacting species.Polanyi was one of the first to seek an explanation in terms of the forces between the reaction partners during a collisional encounter. For the generic bimolecular reac- tion A + BC -+ AB + C , Polanyi adopted the theory of London (which we recognize today as the basis of the Born-Oppenheimer approximation) in which the nuclei of atoms move essentially according to the laws of classical mechanics under the potential given by quantum mechanics for some fixed ABC nuclear configuration.Together with H. Eyring, Polanyi constructed in 1931 a potential energy surface4 to describe the reaction H + H2 -+ H, + H. Using transition state theory developed in his laboratory, calculations were made of the reaction rate with this potential energy surface. The conceptual innovation was born that an understanding of the main topological features of the potential energy surface is the first step toward a qualitative understanding of the reaction dynamics. The potential energy surface was not purely theoretical; it employed empirical data in the form of the diatomic potentials of the reactants and products, Later8 POLANYI MEMORIAL LECTURE Sato' introduced parameters to control the form of the potential in the region where all three particles are strongly interacting.This so-called London-Eyring-Polanyi- Sat0 (LEPS) surface has become a touchstone against which all other potentials are compared. So the seeds were sown for the study of reaction dynamics, a field that has produced a bounteous harvest of new insights into how chemical reactions occur. The bulk reaction rate is a macroscopic property of the reaction, representing an average over all reagent and product variables. It has been very difficult, therefore, to extract information about the dynamics from its measurement alone. To achieve a deeper insight, we must select the state of the reagent molecules and detect the state of the products. This measurement of " state-to-state kinetics " is becoming possible by the use of ever increasingly sophisticated spectroscopic and molecular beam techniques. We gather here to celebrate the 25th anniversary of the Discussion " Fast Reactions", held in Birmingham in 1954.Since that time the dream of using molecular beam techniques to study the microscopics of reaction dynamics has not only been realized but has become a mature field, providing us with some of the most detailed informa- tion on how reagents are transformed to products during a reactive en~ounter.~ It is doubly fitting that we meet in Birmingham since this is the birthplace of the first reactive scattering beam experiments by Bull and Moon6 on alkali metal atoms with carbon tetrachloride.Indeed, we will hear at this Discussion a revival of the Bull and Moon " swatter technique " to accelerate reagents by means of a spinning bat as well as discussion on the same reactive scattering system that Bull and Moon first investi- gated. The fruit of our own labours also springs from the field Polanyi planted. I would like to share with you some recent results we have obtained on state-to-state reaction dynamics. The ideal chemical dynamics experiment in which angle, velocity and internal energy variables of both reactants and products are specified, can be approached best by a marriage between molecular spectroscopy and molecular beam techniques. One possible means of effecting this match is to use the method of laser induced fluorescence (LIF) for detection of the reaction products.' Here a tunable laser is scanned through an electronic absorption band of the product molecule.P branch 14 20 fnrhrm 13 5 1"' R branch 15 I I 20 3910 3900 3890 wavelecgth /A FIG. 1.-Excitation spectrum of N'1 X state (B2ZZ + X2z:) produced by 100 eV electrons (100 PA) on N2 (4 x Torr).R. N. ZARE 9 When the laser wavelength coincides with a specific transition between internal (vibrational-rotational) energy levels, a fraction of those molecules in the (u", J") level of the ground state are pumped to the (u', J') level of the excited electronic state. Once there, the excited molecules can re-emit their energy (fluoresce) and this fluorescence may be detected very sensitively.By recording the total undispersed fluorescence intensity as a function of laser wavelength, one obtains an excitation spectrum that is very similar to the absorption spectrum of the molecular species under study. Fig. 1 illustrates an excitation spectrum of N i taken in our laboratory by Allison and Kondow. The N i ions are formed by electron impact ionization of N2 under collision-free conditions. The spectral resolution in fig. 1 is provided by the narrow- ness of the bandwidth of the tunable laser. If rotational line strengths (Honl- London factors) and vibrational band strengths (Franck-Condon factors) are known or can be calculated, then relative populations of the internal levels of the ground state products may be derived from the excitation spectrum.For example, an analysis of fig. 1 shows that the rotational levels of the N2+ U" = 0 state are populated in a manner well characterized by a temperature (TR = 323 & 5 K). While LIF can be exceedingly sensitive, it does not enjoy universal applicability. The products must have a strong electronic absorption band in the region covered by presently available tunable lasers, its spectroscopy and radiative properties must be known and the fluorescence quantum yield must be appreciable. These restrictions usually limit LIF usefulness to diatomic and some selected small polyatomic molecules, but when the LIF detection method can be applied, the information obtained often is remarkably rich. OVEN CHAMBER w DRIVE LIGHT BAFFLE PHOTOM ULTl PL I ER 1 SIGNAL CHART BOXCAR RECORDER' I INTEGRATOR, , - 1 - I FIG.2.-Cutaway drawing of the beam-gas experimental setup. A swing-in mirror permits excita- tion of the HF molecules in the scattering chamber by two different light paths, one antiparallel, the other perpendicular to the probe laser beam.10 POLANYI MEMORIAL LECTURE For some time we have been examining the reactions M + HF -+ MF + H where M is an alkaline earth atom. This is an interesting family of reactions because it contains both exothermic and endothermic members and it typifies a transformation from a covalently-bound reagent to an ionically-bound product. The alkaline earth monofluorides have several strongly allowed electronic transitions in the visible, making their detection by LIF quite straightforward.The HF reagent can be con- trolled using a pulsed HF laser tuned to a selected vibrational-rotational level or using a seeded nozzle beam to enhance translational energy in a known manner. Fig. 2 shows a schematic view of the apparatus placed in a beam-gas configuration. A beam of alkaline earth atoms traverses a scattering chamber filled with HF gas at sufficiently low pressures (1 x lod4 Torr) that collisional relaxation of the products is negligible. The HF laser beam can be directed either along the metal beam or at right angles to it. The exothermic reaction Ba + HF -+ BaF + H; AH! = -18 kJ mol-' (2) occurs with a large cross-section without HF vibrational excitation. By subtracting 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 BaF ( v ' ) FIG.3.-Vibrational population distribution of the BaF product formed in the reaction Ba + HF for different HF reagent translational and internal energies. The arrows indicate the reaction exo- thermicity limits. (a) v(HF) = 0, T = 1.6 kcal mol-'; (b) v(HF) = 1 , T = 1.6 kcal mol-'; (c) v(HF) = 0, T = 10.2 kcal mol-'.R . N. ZARE 11 with the help of a difference circuit the BaF fluorescence intensity when the HF laser was off from the intensity when the HF laser was on, Pruett and Zare' obtained the BaF excitation spectrum resulting from reaction of Ba with HF(u = 1). Fig. 3 presents the relative vibrational populations of the products. Of the 46 kJ mol-I represented by the reagent HF vibrational excitation, some 57% appears as product vibration. In our laboratory, Perry and Gupta seeded an HF beam with He or H, and crossed it with an effusive Ba source (beam-beam configuration; see fig.4). Fig. 5 compares TO PUMPS BAFFLE ARM i TO PUMPS 1 1":"' DYE LASER BEAM FIG. 4.-Crossed beam set-up for studying the effect of HF reagent translational energy on product yield and product internal state distribution. the BaF excitation spectra obtained at high and low collision energies. At 43 kJ mol-' in collision energy, R1 bandheads appear which are not observed at the lower collision energy. The presence of these R1 bandheads signifies high product rotational excita- tion. At high collision energy, additional vibrational levels of BaF are populated but the product vibrational distribution continues to peak at v" = 0 (see fig.3). This contrasts with the effect of reagent vibration which shifts the peak of the distribution to v" = 6. The added 36 kJ mo1-l in collision energy is transformed into 51 % trans- lation, 28% rotation and 21% vibration of the product. Yet another important conceptual advance in this field is due in part to Michael Polanyi, namely, his son John. From a study of classical trajectories on LEPS surfaces J. C . Polanyi and coworkers9 have arrived at the general rule that additional reagent vibration, A V , appears as product vibration, A V', while additional collisional energy, AT, is transformed into product translational and rotational energy, AT'12 POLANYI MEMORIAL LECTURE B a F C2 I l l / , -I2 C ( 2 , 2 ) 500 5 02 504 dye Laser wavelength /nm FIG. 5.-Excitation spectra of the BaF product formed by the reaction Ba + HF +BaF + H at different relative initial kinetic energies.(a) <T> = 10.2 kcal mol-I; (6) <Ti = 3.7 kcal mol-'. + AR'. Our findings for Ba + HF are in qualitative but not quantitative agree- ment with these generalizations. The above studies have been extended to the endothermic reactions which do not proceed readily under thermal conditions. However, Karny and Zare'O have found that the rates of these reactions increase by at least four orders of magnitude when the HF is excited into its first vibrational state. Fig. 6 shows some sample excitation spectra. This reaction system offers the opportunity to compare the effectiveness of reagent vibration and translation in promoting an endothermic reaction at the same total energy.To date there is only one direct experimental comparison for an endothermic reaction. Brooks and coworkers" found for the marginally endothermic reaction that HCl(v = 1) has a reaction cross-section about ten times that of HCl(u = 0) with the same amount of translational energy. K + HC1+ KC1 + H ; AH = +6 kJ m01-~ (4)R. N. ZARE 13 A__. L ----- _I--- I______-l I 6490 6500 6510 6520 6530 6540 wavelength 1% FIG. 6.-Excitation spectra of the SrF product resulting from the reactions (a) Sr + HF(v = 1) and (b) Sr + HF(u = 0). To carry out the corresponding comparison for Sr + HF, the Ba + HF reaction is used as an internal reference standard. A mixed alkaline earth atom beam is pre- pared by combining equimolar quantities of barium and strontium.This beam is crossed with the seeded HF beam and the BaF to SrF product yields are compared. The same comparison is also made in the beam-gas configuration to determine the intensity ratio I[Sr + HF(u = l)] to I[Ba + HF(u = O)]. With the assumption that the cross section for the exothermic reaction Ba + HF does not change with collision energy, we find the preliminary value of the cross-section ratio at the same total energy: ( 5 ) a[Sr + HF(u = 1, ET = 7 kJ mol-I)] a[Sr + HF(u = 0, ET = 54 kJ mol-I)] - - 15. Eqn (5) should be no more uncertain than a factor of three. ;; 0 2 t -- average collision energy / k c a l mol-' FIG. 7.-FIuorescence intensity of SrF product as a function of relative initial kinetic energy. The quantity, AH,", reflects the present uncertainty in the heat of reaction.A deconvolution of this data to correct for the spread in collision energy and the variation of beam intensity with seeding ratio would accentuate both the rise and fall-off.14 POLANYI MEMORIAL LECTURE This result supports the generalization that vibration is more effective than trans- lation in promoting an endothermic reaction.I2 However, since Sr + HF is much more endothermic than K + HCl, one might have expected a larger ratio even though the potential energy surfaces may differ. Using the principle of microscopic reversi- bility, J. C. Polanyi, R. B. Bernstein and coworkers13 have obtained the above ratio for several endothermic reactions from studies of the reverse exothermic reactions. They find that at constant total energy, vibrational excitation of the reagent is typically two to three orders of magnitude more efficacious that translational energy in promot- ing endothermic reaction.Thus the Sr + HF reaction contrasts with these reactions in that translational energy is qualitatively more effective. Could it be that the Sr + HF reaction proceeds through a complex? Because of the divalent character of the alkaline earth atoms, the H-M-F configuration will lead to a well in the potential energy surface. This may cause reagent translational energy to be coupled more effectively to motion along the reaction coordinate. This would account for the relatively steep falloff in SrF product yield with relative initial translational energy above 50 kJ rno1-l (see fig.7). This type of complex may also be formed in the reaction Ba + HF which would help to explain the quantitative devia- tions from J. C . Polanyi’s generalizations, AV -+ AV’ and AT 3 AT’ + AR’. H S r * I F I/ 6500 6520 wavelength /A FIG. 8.-Excitation spectra for Sr + HF(u = 1, J = 1) with the HF molecule preferentially aligned perpendicular to the Sr atom approach direction (upper trace) or parallel to the Sr atom approach direction (lower trace). The dashed curves are computer simulations assuming a rotational tempera- ture of 800 K for all vibrational levels. The baselines are indicated for comparison purposes. For the J = 1 case, the HF molecules are prepared with a 3 + cos28 distribution, where 8 is the angle between the electric vector of the light beam and the internuclear axis of the molecule.R.N . ZARE 15 Yet subtler questions about the dynamics of the Sr + HF reaction can be posed and resolved experimentally with the help of laser preparation of the reagent. For ex- ample, Karny, Estler and Zare14 have demonstrated the importance of reagent rota- tion and orientation. The latter deserves special mention as it is a step from scalar to vector measurements characterizing the reactive c~llision.'~ The output of the HF laser is linearly polarized and the plane of polarization may be selected by means of a Fresnel rhomb (fig. 2). Thus the HF(u = 1 ) reagent molecules are prepared so that the Sr collision partner preferentially approaches the HF internuclear axis either in the collinear or broadside configuration, on the average.Fig. 8 shows the resultant excitation spectra for these two " average " collision geometries. It is clearly seen that broadside attack favours the population of higher vibrational levels in the SrF product. If one believes that attractive energy release is correlated with product excitation,16 then this result supports recent theoretical calculations ''918 indicating that the minimum energy path of the reactions of alkali and alkaline earth atoms with hydrogen fluoride proceeds through a highly bent configuration. There are many advantages to the preparation of oriented reagents by optical pumping: the degree of selection is high; the degree of selection is well defined; and the optical pumping process permits state selection as well as orientation.Clearly the study of reagent orientation upon chemical reactivity and product state distribu- tion is still a relatively uncultivated spot in Michael Polanyi's garden on which many flowers may bl00m.'~ It has the promise of allowing chemists to explore and control the stereodynamics of reaction pathways. Support from the Air Force Office of Scientific Research and the National Science Foundation is gratefully acknowledged. E. P. Wigner and R. A. Hodgkin, '' Michael Polanyi 1891-1976," Biographical Memoirs of Fellows of the Royal Society, 1977, 23, 413. M. Polanyi, Atomic Reactions (Williams and Norgate, London, 1932); M. G. Evans and M. Polanyi, Trans. Faraday SOC., 1939, 35, 178, 192, 195. M. R. Levy, Dynamics of Reactive Collisions, Progr. Reaction Kinetics, 1979, vol.10, nos. 1-2. S. Sato, J. Chern. Phys., 1955, 23, 2465. T. H. Bull and P. B. Moon, Disc. Faraday SOC., 1954, 17, 54. H. W. Cruse, P. J. Dagdigian and R. N. Zare, Faraday Disc. Chem. SOC., 1973,55277; R. N. Zare and P. J. Dagdigian, Science, 1974, 185, 739; J. L. Kinsey, Ann. Rev. Phys. Chem., 1977, 28, 349. J. G. Pruett and R. N. Zare, J. Chem. Phys., 1976,64, 1774. A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi and J. L. Schreiber, Faraday Disc. Chem. Soc., 1973, 55, 252. 4 H. Eyring and M. Polanyi, 2. phys. Chem. B, 1931,12,279. lo Z. Karny and R. N. Zare, J. Chem. Phys., 1978,68, 3360. l1 T. J. Odiorne, P. R. Brooks, and J. V. V. Kasper, J. Chem. Phys., 1971,55, 1980; J. G. Pruett, l2 M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969,51,1451. l3 K. G. Anlauf, D. H. Maylotte, J. C. Polanyi and R. B. Bernstein, J. Chem. Phys., 1969, 51, 5716; J. C. Polanyi and D. C. Tardy, J. Chem. Phys., 1969,51,5717. l4 Z. Karny, R. C. Estler and R. N. Zare, J. Chem. Phys., 1978,69, 5199. l5 D. A. Case and D. R. Herschbach, Mol. Phys., 1975, 30, 1537; J. Chem. Phys., 1976, 64, 4212; 1978,69, 150; D. A. Case, G. M. McClelland and D. R. Herschbach, Mol. Phys., 1978, 35, 541 ; G. M. McClelland and D. R. Herschbach, J . Phys. Chem., in prcss. l6 J. C . Polanyi, Accorints Chem. Res., 1972, 5, 161. l7 G. G. Balint-Kurti and R. N. Yardley, Faraday Disc. Chem. SOC., 1977, 62, 77. l8 Y. Zeiri and M. Shapiro, Chern. Phys., 1978, 31, 217. l9 See fig. 2 in D. R. Herschbach, Faraday Disc. Chem. SOC., 1973,55,233. F. R. Grabiner and P. R. Brooks, J. Chem. Phys., 1975,63, 1173.

ISSN:0301-7249    

DOI:10.1039/DC9796700007

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

TRANSLATIONAL EXCITATION Effect of Translational Energy on Reaction Dynamics BY ROGER GRICE Chemistry Department, University of Manchester, Manchester M13 9PL Received 14th February, 1979 1. INTRODUCTION Some of the first molecular beam studies on the effect of initial translational energy on reactive scattering were concerned with the reactions of alkali metal atoms. The use of effusive beam sources severely limited the range of translational energy which could be explored by velocity selection of the alkali metal beam with a slotted disc velocity selector. However, the low intensity of the alkali metal atom beam resulting from such an arrangement is compensated by the high efficiency of surface ionisation detection which can be used with alkali metal species. An earlier Faraday Discussion included a summary' of reactive scattering data on the K + CHJ reaction which exemplifies the range of information which may be obtained by these techniques.Similar results have been obtained2 for the K + Iz, RbF, CsF, HCl reactions. The relatively simple electronic structure of the potential energy surface imposed by the prevalence of ionic interactions in alkali metal atom reactions often permits inter- pretation3 of the reactive scattering data in terms of simple but effective models of the reaction dynamics. A particularly compelling example of the power of such models is illustrated by the lucid interpretation4 of the reactive scattering of alkali metal atoms by carbon tetrachloride molecules presented at this Discussion. The effect of initial translational energy on the dynamics of some non-alkali-metal reactions has been studied using effusive beam sources.The reactions of hydrogen atom^^*^ with halogen molecules, of fluorine atoms6 with hydrogen chloride and oxy- gen atoms' with iodine molecules have been studied using low pressure microwave discharge sources to produce low energy beams and thermal dissociation sources to produce higher energy beams. The reaction of fluorine atoms with deuterium mole- cules has been studied' as a function of initial translational energy by varying the temperature of the nozzle source of the deuterium beam. This technique is possible in this case only because the deuterium molecules are much lighter than the fluorine atoms, which are produced by effusion from a nickel oven and velocity selected by a slotted disc velocity selector.These early studies represent a pioneering stage which is now being transformed by the development of supersonic nozzle beams of atoms and free radicals seeded in inert buffer gases. These sources provide intense beams with narrow velocity distri- butions which can be readily varied by changing the molecular weight of the buffer gas. The measurement of angular and velocity distributions of reactive scattering from these beams is greatly assisted by the use of cross-correlation time-of-flightR . GRICE 17 analysis in place of the much less efficient conventional time-of-flight m e t h ~ d . ~ ' ~ Full contour maps of the differential reaction cross-section can now be measured as a function of initial translational energy for an increasing range of reactions.Particu- larly when these differential reaction cross-sections are augmented by measurements of product internal state distributions, they should provide a basis for the develop- ment of models for non-alkali-metal reaction dynamics. Since the electronic struc- ture of the reaction potential energy surface for non-alkali-metal species is often more complicated than that of alkali-metal species, we may expect that such comprehensive experimental information will be necessary for substantial theoretical progress to be made. 2. ADVANCES IN EXPERIMENTAL TECHNIQUE The production of supersonic alkali-metal atom beams seeded in inert buffer gas may be achieved9*'' in a manner analogous to the production of seeded beams of stable molecules," by the admission of buffer gas to a heated oven which maintains an appropriate alkali-metal vapour pressure.Supersonic beams of unstable atoms seeded in inert gases may be generated by thermal dissociation of diatomic molecules diluted by a high pressure of buffer gas in a high temperature oven constructed of inert materials. In this way, supersonic beams of hydrogen,12 fluorine13 and other halogen l4 atoms have been produced respectively from tungsten, nickel and graphite ovens. An alternative method of generating supersonic atom beams involves the use of a high pressure discharge through a dilute mixture of a diatomic precursor in excess inert buffer gas. A supersonic oxygen atom beam was first produced in this manner from a radio-frequency discharge by Miller and Patch." A microwave discharge source16 has been used in our laboratory to produce supersonic oxygen and chlorine atom beams.Oxygen atom beams seeded in He and Ne cover the energy range E = 13-35 kJ mol-' with Mach numbers M = 5-7 and intensities of (1-5) x lo1' atom sr-' s-l. A radio frequency oxygen atom discharge source has recently been developed at Berkeley17 which gives a higher degree of dissociation but is much more elaborate and more susceptible to discharge through the source chamber residual gas and hence requires higher pumping speed. Direct current discharge sources have been used to produce supersonic beams of hydrogenI8 and nitrogen l9 atoms. Thus an extensive range of supersonic atom beam sources suitable for studying the transla- tional energy dependence of reactive scattering is now available and we may expect supersonic free radical sources to be available in the near future.Depending upon the masses of the accelerated species and the buffer gas and also the temperature of the source, seeded nozzle beams will generally be the method of choice for producing molecular beams in the energy range 5-200 kJ mol-'. However, the use of rotor accelerated beams is enjoying a revivalZo after prolonged neglect following the pioneering work of Bull and Moon.21 The absence of buffer gas in rotor accelerated beams may offer advantages in some experiments, though the intensity is generally much lower than seeded nozzle beams. At energies above those which can be achieved by seeded nozzle beam sources > 400 kJ mol-', the charge exchange source becomes the method of choice.The velocity compression technique outlined at this DiscussionZ2 offers a method of maximising the rather low intensities available from this type of source in time-of-flight experiments. The single pulsing method of time-of-flight analysis used with a mechanical chop- per d i s ~ ~ , ~ in reactive scattering measurements or with voltage modulation of a charge exchange source," suffers from a very low duty factor, typically < 5%. This may be improved substantially by use of the pseudo-random cross-correlation time-of-flight18 TRANSLATIONAL EXCITATION method which enjoys a duty factor ~ 5 0 % . The cross-correlation method was first used by Hirschy and Aldridge23 to measure the velocity distribution of an Ar beam but its application to the measurement of velocity distributions of reactive scattering has followed 24-26 only recently.The implementation of the cross-correlation method in our laboratory 27 involves a mini-computer interface which drives a pseudo random chopper disc in synchronism with the advance of the channel address register. Time- of-flight data are stored in a random access memory which permits narrow channel widths 2 300 ns with negligible dead time Z S ns between channels. Data are transferred periodically to the minicomputer which performs the deconvolution and analysis of the accumulated data. The improved efficiency of data retrieval together with the higher intensity of reactive scattering and well defined kinematics provided by supersonic nozzle beams permits direct inversion28 of laboratory data to obtain a full contour map of the differential reaction cross-section.3. RECENT STUDIES OF REACTION DYNAMICS The systems so far studied with supersonic seeded beams and cross-correlation time-of-flight analysis show a wide range of reaction dynamics with differing depend- ence on initial translational energy. The improved resolution of the differential reaction cross-section and its dependence on initial translational energy is now providing much more detailed information and models of reaction dynamics which have been used to explain more limited data are becoming inadequate. The com- pleteness which is now attainable may be judged from the contour map of the differen- tial reaction cross-~ection,~~ shown in fig.1, for the 0 + CS, reaction with 0 atoms 0 cs2-02 *cs FIG. 1.-Polar contour map of 0s flux from 0 + CS2 with 0 atoms seeded in He as a function of centre-of-mass scattering angle 8 and velocity u, at an initial translational energy E = 38 kJ mol-'. Incident 0 atom direction is denoted by 0 = O", incident CS2 direction 0 = 180".R . GRICE 19 seeded in He buffer gas giving an initial translational energy E = 38 kJ mol-'. In this case, velocity distributions measured at 27 laboratory scattering angles have been inverted directly to obtain a contour map of the differential reaction cross-section covering the full range of centre-of-mass scattering angle 8 = 0 - 180". The re- action follows a stripping mechanism whereby 0s product scattering peaks in the forward direction 8 = 0" with respect to the incident 0 atom beam.There is a constant intensity in the backward hemisphere which is lower than that of the forward peak by a factor x3.5. This reaction has also been s t ~ d i e d ~ ~ , ~ ' at lower initial translational energy E = 13 kJ mol-' using an 0 atom beam seeded in Ne. The differential reaction cross-section was found to be ~ n a l t e r e d ~ ~ . ~ ' over this range of initial translational energy when proper account of the variation in total energy avail- able to reaction products Etot is taken into account by calculating the fraction of this energy disposed into product translation. The reaction of C1 atoms with Br, mole- cules has been studied3' using C1 atoms seeded in He and Ar to cover the translational energy range E = 28-74 kJ mol-'.This reaction also exhibits a stripping mechan- ism with BrCl product scattered very sharply into the forward direction 8 < 40" and very little product scattered at wider angles. Hence these stripping reactions are each governed by an attractive potential energy surface with exoergicity released in the entrance valley. The sharpness of forward peaking for the C1 + Br2 reaction reflects its low exoergicity ADo = 25 kJ mol-' compared with the initial translational energy. In contrast the 0 + CS, reaction has a higher exoergicity ADo = 87 kJ mol-.l which exerts a greater influence on the reaction dynamics and maintains the intensity of wide angle scattering. In both cases the reaction dynamics indicate that reaction occurs in collisions with impact parameters at least comparable to the hard sphere collision diameters b 3 A. However, the small values of the total reaction cross- sections Q = 3-14 A2 indicate the presence of a significant orientation require- ment32*33 for each of these reactions.at an initial translational energy E = 31 kJ mol-', also gives OCl product scattering in the forward direction, The reaction of 0 atoms seeded in He with C1, 0 C l 2 ' 0 ~ * C I - -200 100 m s-1 FIG. 2.-Polar contour map of OC1 flux from 0 + C12 with 0 atoms seeded in He as a function of centre-of-mass scattering angle 8 and velocity u, at an initial translational energy E = 31 kJ mol-I.20 TRANSLATIONAL EXCITATION as indicated by the contour map of the differential reaction cross-section shown in fig.2. However, the lower intensity data at wide angles 8 2 50" have a product trans- lational energy lower than that in the forward direction by a factor x 3 . Analysis of additional laboratory angular distribution data which were not included in deter- mination of the contour map of fig. 2, indicates the presence of a minor peak in the backward direction (8 = 180") with a relative height 0.3 j-- 0.1. More limited meas~rements~~ with 0 atoms seeded in Ne at an initial translational energy E = 13 kJ mol-1 indicate that the height of the backward peak increases to 0.55 & 0.15. Thus the reaction appears to proceed via a short-lived collision complex35 whose life- time increases with decreasing initial translational energy.However, the osculating complex assumes that all collision complexes are bound by a hollow on the potential energy surface and that the product translational energy distribution is independent of scattering angle. Clearly this is inappropriate to the 0 + Clz reaction which might more properly be regarded as consisting of a stripping com- ponent arising from collisions at large impact parameters and wide angle scattering arising from collisions at smaller impact parameters. The displacement reactions 0 + CF,I -&I+ CF, 7 100 m s-1 FIG. 3.-Polar contour map of 0 1 flux from 0 + CFJ with 0 atoms seeded in He as a function of centre-of-mass scattering angle 8 and velocity u, at an initial translation energy E = 32 kJ mol-'. of F and C1 atoms with vinyl bromide molecules36 also appear to proceed via a short- lived complex and do show a modest variation in product translational energy with scattering angle, with higher energies in the forward and backward directions.As shown in this Di~cussion,~~ such a modest variation in product translational energy can be explained in the context of the osculating complex model by considering the coupling of product angular and translational energy distributions which is enforced by conservation of the total angular momentum of the complex. The iodihe atom abstraction reactions of F atoms seeded in Ar and He with CHJ molecules13 also proceed via a short-lived collision complex whose life-time depends on initial trans- lational energy. In this case, the product translational energy distribution is found to be independent of scattering angle to within the accuracy of the experimental data, in accord with the simplest version35 of the osculating complex model.The iodine atom abstraction reaction of 0 atoms with CFJ has been studied3'p3* using 0 atoms seeded in He and Ne to cover the range of initial translational energyR. GRICE 21 E = 14-32 kJ mol-'. The contour map of fig. 3 shows that the differential reac- tion cross section for 0 atoms seeded in He is essentially isotropic. However, the contour map of fig. 4, showing the differential reaction cross-section for 0 atoms seeded in Ne, indicates that 01 reactive scattering favours the backward hemisphere with respect to the incident 0 atom direction, at lower initial translational energy.This rebound mechanism suggests that reaction occurs only at small impact parameters in lower energy collisions but that the maximum impact parameter for reaction increases slightly with initial translational energy. The angular distributions of re- active scattering are in accord with a hard sphere scattering whereby product repulsion arises from induced repulsive energy release4' at small inter-nuclear distances. This model predicfs4O the conversion of initial translational energy into product trans- lational energy for the thermoneutral 0 + CF31 reaction, as is found to be roughly the 1100 1000 4 900 t 80° 4 70° 0 + CF,I -QI + CF, 100 m 5-1 FIG. 4.-Polar contour map of 0 1 flux from 0 + CFJ with 0 atoms seeded in Ne as a function of centre-of-mass scattering angle 8 and velocity u, at an initial translational energy E = 13 kJ mol-'.case for the average values of these energies. However, the product translational energy distributions for 0 + CF31 are strongly skewed with respect to the initial translational energy distribution as illustrated in fig. 5 for 0 atoms seeded in He. This suggests that there is also substantial energy exchange with internal modes of the CF3 radical and this is confirmed by the product translational energy distributions also shown in fig. 5 for the reactions41 of 0 atoms seeded in He with C2F51 and C3F71 molecules. The energy disposed into product translation decreases as the complexity of the departing radical increases along the series CF3, C2F5, C3F7 despite the increasing reaction exoergicity 42 along this series. Clearly transfer of energy to internal modes of the departing radical is becoming more effective as the complexity of the radical increases; an effect which has also been observed39 in the reactions of alkali metal atoms with alkyl iodides.The angular distributions shown in fig. 5 are nominally isotropic for all these I atom abstraction reactions with 0 atoms seeded in He, though with some indication of sideways peaking particularly for C2F51. The reaction of 0 atoms with tetrafluoroethylene molecules22 TRANSLATIONAL EXCITATION 1 .o X 3 d c 0.0 t c 0.5 t I 0 .o !# 0 30 60 90 120 150 180 c.m. angle, 8 / O I - 0 30 60 90 120 translational energy, ['/ kJ rnol-' FIG. 5.-Product angular and translational energy distributions for the reaction of 0 atoms seeded in He with perfluoroalkyl iodide molecules.The arrow indicates the initial translational energy E = 32 kJ mot-'. (-) CF31, (- - -) c3&I and ( 0 *) C2FSI. is presently being using 0 atoms seeded in He to give an initial translational energy E = 31 kJ mol-l. This reaction is of particular interest since it involves the cleavage of a carbon-carbon double bond rather than the exchange of single bonds in the metathetical reactions which have so far been studied in molecular beam experi- ments. Preliminary results shown in fig. 6 indicate that the angular distribution favours the forward hemisphere and the product translational energy distribution accounts for only a small fraction of the very large total energy available to reaction products E,,, = 430 kJ mol-'.Thus it is possible that the reaction produces an electronically excited triplet CF2(3BI) rather than the ground singlet CF2(lA1), as suggested by recent discharge flow and flash photolysis experiment~.~~ The transla- tional energy dependence of the total cross-section for the H, D + Br, reactions has been measured l2 using a supersonic H or D atom beam and laser induced fluorescenceR . GRICE 23 0 20 40 60 80 100 120 140 160 180 c.m. angle, 8 / O 0 50 100 150 200 250 translational energy, U kJ mol-' FIG. 6.-Product angular and translational energy distribution for the reaction of 0 atoms seeded in He with tetrafluoroethylene molecules at an initial translational energy E = 31 kJ mol-'. detection of the Br atom products.The cross-section depends on initial relative velocity rather than translational energy. In addition to the use of seeded beams of reactive atoms and free radicals, beams of stable molecules seeded in inert gasesz5 continue to be used to explore the trans- lational energy dependence of chemical reactions. This is well exemplified by the study of the Ba + N,O reaction reported4s at this Discussion, where electronically excited BaO* is detected by chemiluminescence measurements. The reactions of B and Ho atoms with N,O molecules, which also yield chemiluminescent products BO* and HoO*, have been studied46 as a function of translational energy using evaporation of a thin B or Ho film by an intense pulsed laser to produce an energetic atom beam.The endoergic reaction of Hg atoms with I, molecules has been studied4'24 TRANSLATIONAL EXCITATION using Hg atoms seeded in H2 driver gas to cover the energy range E = 87-250 kJ mol” and is found to proceed via a long-lived collision complex. Similarly, the reaction of SbFS seeded in H, and He driver gases with a range of organic halide molecules has been to yield ionic products due to abstraction of a halide anion by the SbFS molecule. Collisions at very high energies are usually dominated by inelastic collisions to the exclusion of reaction as illustratedz2 in this Discussion. However, the collisional dissociation 49 of CsCl molecules by energetic inert gas atoms (A = Ar, Kr, Xe) seeded in Hz exhibits an associative dissociation channel in the threshold region A + CsCl -+ ACs+ + C1-.(2) Associative and reactive ionisation has been observeds0 for the reactions of a large range of metal atoms M with Oz molecules, where the metal beam is produced by sputtering and velocity selected by a slotted disc velocity selector M + O2 -+ MOz+ + e- --f MO+ + 0 + e-. Carbon atoms also shows0 reactive ionisation with 0, molecules. (3) 4. THEORETICAL INTERPRETATION The increasing scope and accuracy of experimental measurements of the depend- ence of reactive scattering on initial translational energy offers both a challenge and an opportunity to further theoretical investigations. The theoretical problem divides into two parts; first the determination of the potential energy surface for the reaction and secondly the description of scattering in terms of nuclear motion over the surface.Progress in the determination of potential energy surfaces was reviewed at a recent Faraday Discussion (62) and requires little further comment here, other than to note the construction of an empirical potential energy surfaces1 for the Hg + I2 reaction which has been adjusted to agree with the main features observed in reactive scattering experiments 47 on this system. The diatomics-in-molecules method has been useds2 to calculate a potential energy surface for the Ff + H2 reaction and the valence bond methods3 for the H + Br, reaction. While the quantitative accuracy of such calcula- tions may be uncertain, they have the important property of correctly including the topology32 of the potential energy surface.Paradoxically, the empirical s1 and semi-empiricals2 methods have the advantage over ab initio methodss3 that the surfaces may be adjusted to fit experimental observations. The correlation of ex- perimental data and the reaction potential energy surface has traditionally relied on Monte Carlo calculations of classical trajectories for the nuclear motion. This method continues to be refineds4 and is exemplified in this Discussions5 by a detailed study of H atom migration in the dynamics of the H + ICl reaction and its dependence on reactant translational energy. In contrast, quantum mechanical calculations of the nuclear motion have often inspired more awe than physical insight. Thus it is particularly reassuring to see semi-classical methods of quantum mechanics being applied further to classical trajectory calculations in this Di~cussion.~~ This approach identifies quantum phenomena in a physically appealing manner which is more apt for the interpretation of experimental results.It is also stimulating to see calcu- lations presented at this Discussions7 of the effect of intense non-resonant laser irradia- tion on the dynamics of the F + H2 reaction; perhaps this is a case where theory will provoke experimental measurements. New problems of theoretical interest are being posed by the increase in experi-R . GRICE 25 mental measurements on the reaction dynamics of polyatomic systems. In the reactions of atoms with triatomic molecules, the disposal of energy into product rotation is not restricted by the conservation of total angular momentum as in the reactions of atoms with diatomic molecules.Models based on Walsh molecular orbital theory have been proposed 2938 to rationalise product rotational excitation, as arising from excitation of bending modes of the transition state followed closely by scission of the bond about which bending occurs. In reactions with more than three atoms in the transition state, many internal modes of vibration and internal rotation influence the reaction dynamics. When the collision complex lives for many rota- tional periods, energy is equilibrated equally over all accessible modes subject to conservation of angular momentum and the theory of unimolecular reactions may be applied59 with some success. However, collision complexes which persist for only a fraction of the rotational period do not achieve complete energy equilibra- tion and differing internal modes may be expected to have differing effects on the reaction dynamics.As the number of modes involved increases, the reaction dy- namics differ increasingly from the simple models appropriate to the reactions of atoms with diatomic molecules since the dynamics must be averaged over the phases of many modes. At present there is little theoretical work to provide guidance in the analysis of polyatomic reaction dynamics proceeding via a short-lived transition state. However, the increasing scope and detail of experimental measurements may now provide adequate information for the interpretation of these more complicated and chemically more representative systems, R.B. Bernstein and A. M. Rulis, Faraday Discussion Chem Soc., 1973, 55, 293. ' K. T. Gillen, A. M. Rulis and R. B. Bernstein, J. Chem. Phys., 1971,54,2851; S . Stolte, A. 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Schugerl, Rev. Sci. Znstr., 1975,46, 1656. l1 N. Abauf, J. B. Anderson, R. P. Andres, J. B. Fenn and D. G. H. Marsden, Science, 1967, 155, 997. J. W. Hepburn, D. Klimek, K. Liu, J. C. Polanyi and S. C. Wallace, J. Chem. Phys., 1978, 69, 4311. l3 J. M. Farrar and Y. T. Lee, J. Chem. Phys., 1975,63, 3639. l4 J. J. Valentini, M. J. Coggiola and Y. T. Lee, Rev.Sci. Znstr., 1977, 48, 58. l5 D. R. Miller and D. F. Patch, Reu. Sci. Znsfr., 1969, 40, 1566. l6 P. A. Gorry and R. Grice, J. Phys. E, 1979, 12, 857. l7 Y. T. Lee, personal communication. l9 R. W. Bickes, K. R. Newton, J. M. Herman and R. B. Bernstein, J. Chem. Phys., 1976, 64, 'O C. T. Rettner and J. P. Simons, Faraday Disc. Chem. Soc., 1979, 67, 329. 'l T. H. Bull and P. B. Moon, Disc. Faraday SOC., 1954, 17, 54. 22 M. A. D. Fluendy, K. P. Lawley, J. McCall, C. Sholeen and D. Sutton, Faraday Disc. Chem. 23 V. L. Hirschy and J. P. Aldridge, Reu. Sci. Znsfr. 1971, 42, 381. K. R. Way, S. C. Yang and W. C. Stwalley, Rev. Sci. Znstr., 1976, 47, 1049. 3648. Soc., 1979, 67, 41.26 TRANSLATIONAL EXCITATION 24 P. A. Gorry, C. V. Nowikow and R. Grice, Chem. Phys. Letters, 1977,49, 116.25 J. J. Valentini, M. J. Coggiola and Y . T. Lee, Faruday Disc. Chem. SOC., 1977, 62, 232. 26 H. Haberland, W. von Lucadou and P. Rohwer, Ber. Bunsenges. phys. Chem., 1977, 81, 150. 27 C. V. Nowikow and R. Grice, J. Phys. E, 1979,12, 515. 28 P. E. Siska, J. Chem. Phys., 1973, 59, 6052. 29 P. A. Gorry, C. V. Nowikow and R. Grice, Mol. Phys., 1979, 37, 329. 30 P. A. Gorry, C. V. Nowikow and R. Grice, Chem. Phys. Letters, 1978, 55, 19; J. Geddes, 31 J. J. Valentini, Y. T. Lee and D. J. Auerach, J. Chem. Phys., 1977, 67,4866. 32 D. J. Mascord, P. A. Gorry and R. Grice, Faraday Disc. Chem. SOC., 1977, 62, 255; P. A. 33 R. C. Estler and R. N. Zare, J. Amer. Chem. SOC., 1978,100, 1323; Z. Karny, R. C. Estler and 34 P. A. Gorry, C. V. Nowikow and R. Grice, Mol.Phys., 1979,37, 347. 35 G. A. Fisk, J. D. McDonald and D. R. Herschbach, Disc. Furuduy SOC., 1967,44,228. 36 R. I. Buss, M. J. Coggiola and Y. T. Lee, Faraduy Disc. Chem. SOC., 1979,67,162; J. T. Cheung, J. D. McDonald and D. R. Herschbach, J. Amer. Chem. SOC., 1973, 95, 7889. 37 P. A. Gorry, C. V. Nowikow and R. Grice, Chem. Phys. Letters, 1978, 55, 24. 38 P. A. Gorry, C. V. Nowikow and R. Grice, Mol. Phys., 1979,38, in press. 3 9 J. L. Kinsey, G. H. Kwei and D. R. Herschbach, J. Chem. Phys., 1976,64,1914. 4 0 A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi and J. L. Schreiber, Furuday Disc. 41 J. H. Hobson, R. J. Browett, P. A. Gorry and R. Grice, to be published. 42 E. N. Okafo and E. Whittle, Int. J. Chem. Kinetics, 1975,7,273, 287. 43 P.A. Gorry, R. J. Browett, C. V. Nowikow and R. Grice, to be published, 44 S. Koda, Chem. Phys. Letters, 1978, 55, 353; D. S. Hsu and M. C. Lin, Chem. Phys., 1977, 45 D. J. Wren and M. Menzinger, Faraday Disc. Chem. SOC., 1979, 67, 97. 46 S. P. Tang, N. G. Utterback and J. F. Frichtenicht, J. Chem. Phys., 1976, 64, 3833. 4 7 T. M. Mayer, B. E. Wilcomb and R. B. Bernstein, J. Chem. Phys., 1977, 67, 377. 48 A. Auerbach, R. J. Cross and M. Saunders, J. Amer. Chem. SOC., 1978, 100,4908. 49 S. H. Sheen, G. Dimoplon, E. K. Parks and S. Wexler, J. Chem. Phys., 1978,68,4950. P. N. Clough and P. L. Moore, J. Chem. Phys., 1974, 61,2145, Gorry and R. Grice, Faraday Disc. Chem. SOC., 1977,62, 318, 320. R. N. Zare, J. Chem. Phys., 1978, 69, 5199. Chem. SOC., 1973,55, 252. 21, 235. C. E. Young, P. M. Dehmer, R. B. Cohen, L. G. Pobo and S. Wexler, J. Chem. Phys., 1976, 64, 306; 65, 2562; G. P. Konnen, A. Haring and A. E. De Vries, Chem. Phys. Letters, 1975, 30, 11. 51 T. M. Mayer, J. T. Muckerman, B. E. Wilcomb and R. B. Bernstein, J. Chem. Phys., 1977, 67, 3522. 52 J. Kendrick, P. J. Kuntz and I. H. Hillier, J. Chem. Phys., 1978, 68, 2372. 53 P. Baybutt, F. W. Babrowicz, L. R. Kahn and D. G. Truhlar, J. Chem. Phys., 1978,68, 4809. 54 J. C. Polanyi and N. Sathyamurthy, Chem. Phys., 1978, 33, 287. 55 J. C. Polanyi, J. L. Schreiber and W. Skrlac, Furuday Disc. Chem. SOC., 1979, 67, 66. 56 M. S. Child and K. B. Whaley, Furuday Disc. Chem. SOC., 1979, 67, 57. 5 7 P. L. DeVries, T. F. George and J. M. Yuan, Faraduy Disc. Chem. SOC., 1979, 67, 90. 58 R. Grice, M. R. Cosandey and D. R. Herschbach, Ber. Bunsenges. phys. Chem., 1968,72, 975. 59 G. Worry and R. A. Marcus, J. Chem. Phys., 1977, 67, 1636; R. A. Marcus, Ber. Bunsenges. phys. Chem., 1977,81, 190; J. M. Farrar and Y. T. Lee, J. Chem. Phys., 1976,65, 1414; S . A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Letters, 1972, 12, 564; L. Holmlid and K. Rynefors, Chem. Phys., 1977,19,261.

ISSN:0301-7249    

DOI:10.1039/DC9796700016

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Reactions of Alkali Metal Atoms with Carbon Tetrachloride Rainbow-like Coupling of Product Angle and Energy Distributions BY STEPHEN J. RILEY,? PETER E. SISKA~ AND DUDLEY R. HERSCHBACH Department of Chemistry, Harvard University, Cambridge, Massachusetts 021 38, U.S.A. Received 9th April, 1979 Velocity distributions of alkali metal chlorides reactively scattered from crossed thermal beams of K, Rb or Cs and CC14 have been measured over the range 100-lo00 m s-' at laboratory angles from 10 to 100" with respect to the parent alkali beam. The differential cross sections for reactive scat- tering in the centre-o_f-mass system show strong coupling between the peak position of the product angular distribution 6' and the final relative translation91 energy E', and vary markedly with the identity of the alkali metal atom.For a given alkali metal, 6' shifts to smaller angles as E' increases, and as K -+ Rb -+ Cs the entire pattern shifts toward the forward hemisphere. These properties suggest an analogy to the rainbow effect familiar in elastic scattering. The product distributions can be simu- lated by a simple dynamical model. The most important features are the reaction probability as a function of initial impact parameter, the repulsive force causing dissociation of the unstable CC4- intermediate formed by transfer of the alkali metal valence electron, and the T --f V, R energy transfer induced by release of this repulsion during formation of the product bond. The product velocities obtained 25 years ago for Cs + CC14 by Bull and Moon agree with our data within z 10 %.Molecular beam chemistry in the " early alkali age " drew encouragement from the remarkable pioneering experiment of Bull and M0on.l They bombarded a stream of Cs vapour at right angles by a pulsed, accelerated CCl, beam produced by " swat- ting " with a paddle attached to a high speed rotor. Signal pulses from scattered Cs or CsCl were recorded by a surface ionization detector. Although there was no direct means to distinguish between Cs and CsCI, the observed pulses were attributed to reactively scattered CsC1, on the basis of time-of-flight analysis and blank runs with the CCl, replaced by Hg vapour. These experiments were not emulated, however, and indeed were wrongly discounted in contemporary reviews, evidently because it was expected that elastic scattering must always outweigh reactive scattering.We have previously shown2 that the contrary holds for Cs + CC1, in the pertinent angular region and hence Bull and Moon should be vindicated. On this Silver Jubilee occa- sion, we report a quantitative reactive scattering study which reaffirms the results of Bull and Moon and also reveals a strong correlation between the product scattering angle and translational recoil energy. A correlation between the preferred direction of recoil of the products and the magnitude of the reaction cross-section was one of the earliest themes to emerge from molecular beam experiments and trajectory studies of reaction dynamics. For CHJ, reaction is limited to small impact parameters and most of the alkali halide scatters backwards (" rebounds ") with respect to the incident alkali metal beam.For t Present address : Department of Chemistry, Yale University, New Haven, Connecticut 06520, $ Present address : Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsyl- U.S.A. vania 15213, U.S.A.28 REACTIONS OF ALKALI METAL ATOMS WITH CCl, Br,, reaction at large impact parameters is domiflant and most of the product goes forward (" stripping "). For CC14, the reaction cross-section is of intermediate size and the product peaks sideways, giving a conical angular distribution about the direction of the initial relative velocity ~ e c t o r . ~ Velocity analysis experiments likewise show a nice contrast. The product translational energy is large for the CH31 case4 and small for the Br, case;' the angular distributions do not change much with the product translational energy or with the identity of the alkali metal atom.For the CC14 case, we find a contrary trend: the preferred direction of the product shifts for- wards rapidly as the translational recoil energy increases and also as K + Rb -+ Cs. Similar product angle-energy coupling is often found in nuclear physics, where it is usually associated with an angular momentum restriction6 or with the effect of a Coulomb barrier.7 Also, a theoretical study of the H + H2 reaction' predicts that the product distribution shifts from backwards-peaked to a forward-directed cone as the collision energy (about equal to the product recoil energy in this case) is increased to values 2-5 times the barrier height.In all these examples the form of the product angle-energy correlation resembles the " rainbows " of elastic scattering. EXPERIMENTAL CONDITIONS The apparatus and experimental procedures are described elsewhere. The reactant beams, which intersect at 90°, emerge from ovens mounted on a platform that is rotated to scan the scattering angle. A two-filament surface ionization detector is used to distinguish reactively scattered MCl from the nonreactively scattered M atoms. The velocity distribu- tions are measured with a small, slotted-disc analyser.'' The resolution is 20 % (f.w.h.m.) and velocities from 20 to 1000 m s-' can be conveniently measured. Parent beam para- meters are given in table 1 . To facilitate kinematic calculations, the observed number density distributions are fitted to a functional form, P(u) = (u/6)" exp ((n/m)[l - ( ~ / 0 ) ~ ] } .TABLE 1 .-VELOCITY DISTRIBUTIONS IN PARENT BEAMSO beam T,/K T,/K a/m s-' 6/m s-' n, ml nz mz cs Rb K CCI4 623 553 281 376 4.5 3.2 10.4 1 .o 623 543 348 456 11.7 0.7 10.9 0.9 653 613 527 712 9.8 0.8 5.3 1.5 328 - 190 235 2.2 3.2 3.1 1.8 Temperatures Tu and TL refer to the upper (source) and lower (supply) chambers of the alkali metal beam oven. The quantity a = (2kTu/M)+ is the most probable velocity for a Maxwell-Boltzmann velocity distribution. Other parameters are defined in eqn (1); subscript 1 refers to u < 6, subscript 2 to v > 8. The D parameter represents the peak velocity and the exponents n and m are obtained from a least-squares fit to the data points.(For a Maxwell-Boltzmann beam, D = o! and n = rn = 2.) The CC14 beam velocity distribution was measured in an auxiliary experiment employing the negative surface ionization technique." The usual surface ionization filaments were replaced with an activated, thoriated tungsten filament of low work function, and the filament bias was reversed so that negative ions could be collected. Beam modulation and phase-sensitive detection were employed to suppress contributions from background electron emission. Under these conditions, a CCI4 beam yields C1- ions with z 1.5 % efficiency.S . J . RILEY, P . R . SISKA AND D . R . HERSCHBACH 29 RESULTS AND KINEMATIC ANALYSIS Fig. 1 shows velocity distributions of reactive scattering at several laboratory (LAB) angles.The relative intensities at the various angles were determined by normalizing the integrated flux (area under the velocity scan) at each angle to the total flux as measured in the previous angular distribution experiment^.^ The peak veloci- ties shift rapidly with laboratory angle, much more so than for any other alkali metal 0 500 1000 0 500 1000 lab velocity / m s-l 0 5 00 1000 FIG. 1 .-Velocity distributions of reactively scattered alkali metal chloride at indicated laboratory angles, for reactions of (a) Cs, (b) Rb and (c) K with CC14. The parent alkali metal beam is directed at 0”, the CCI4 beam at 90”. Open circles are experimental points, solid curves are smoothed data. Dotted curves show distributions back-calculated from the nominal centre-of-mass cross-section of eqn (3), dashed curves from the least-squares fitted polynomial expansion of eqn (4).The ordinate scale is such as to assign 10 units to the largest experimental peak for each reaction (60” for K, 50” for Rb, 30” for Cs).30 REACTIONS OF ALKALI METAL ATOMS WITH cc1, system so far studied. A distinct bimodal structure is also present, again varying strongly with angle. The low velocity components correspond approximately to the LAB velocity of the centre-of-mass in each case. The observed intensity at a particular LAB velocity and angle, ILAB(v, 6), is re- lated to the differential reaction cross-section in the c.m. system, Icm(u, 0), by an aver- age over the parent beam distributions. This is given by ILAB(V, 8 ) = dmdvl jomdv2ni(vi)nl(vz) vJIcm(u, 8>, (2) where v1 and v2 are the velocities of the reactant beams, n, and n, the number densities, V = ( u l + uZ)* the initial relative velocity, and J = v2/u2 is the Jacobian factor for the c.m.-+ LAB flux transformation. In previous work Icm(u, 8) has been extracted by approximate iterative methods which usually assume the velocity and angle de- pendence to be separable. Such methods proved utterly unsuccessful for the CC14 reactions. This led to the development of two much more efficient procedures, neither of which involves assuming separability of the velocity and angle dependence. The first method merely carries out the LAB -+ c.m. transformation directly by selecting a single representative velocity in each of the parent beams in order to define the transformation uniquely.Then, aside from a normalization factor, The resulting " nominal " c.m. cross-section depends to some extent on the velocities used for the parent beams. However, trial calculations using synthetic data con- firm that, for values of v1 and v2 near the most probable velocities of the parent beams, the nominal result provides a good approximation to the true cam. cross-section. A " best fit " nominal cross-section can be determined by varying v1 and v2 and back- calculating ILAB(v, 0 ) for comparison. Table 2 gives " best fit '' parameters. TABLE 2.-vELOCITY PARAMETERS FOR KINEMATIC ANALYSIS' system u1 u2 UO cs + cc14 450 260 250 Rb + CCl, 500 200 400 K + CC14 800 187 800 Units are m s-l; ul(alkali metal) and v4(CC12) are velocities of the parent beams used in the nominal kinematic transformation of eqn (3); uo is the width parameter for the least-squares fitted polynomial expansion of eqn (4).The second method employs the c.m. --+ LAB transformation with Icm(u, 6) repre- sented by a convenient functional form, Icm(u, 6) = exp [ - ( u / u , ) ~ ] 2 ai juku$. (4) ij Here u, = u cos 6, u, = u sin 6 are the Cartesian coordinates of the c.m. velocity vector. The gaussian factor causes the cross-section to vanish as u +- 00, at a rate governed by the width parameter, uo. The coefficients a i j in the polynomial factor are determined by a least-squares fitting procedure, which compares the transformed and velocity-averaged intensity computed from eqn (2) and (4) with the observed LAB data.Computational details and an analysis of the method are presented else- where,12 including criteria for choosing the size of the coefficient matrix, aij. A 6 x 6S . J . RILEY, P . E . SISKA A N D D. R . HERSCHBACH 31 matrix was used here. The only free parameter in this procedure is uo, and it may be varied to optimize the fit. The result is not strongly dependent on the choice of uo. Table 2 includes the values adopted, which are z 10 % lower than the peak velocity of the nominal c.m. cross-section. Fig. 1 shows the LAB distributions backcalculated from both the nominal and least squares c.m. cross-sections. As expected, the nominal cross-section tends to be too broad and incapable of reproducing fine structure, since it incorporates the velocity averaging inherent in the experiment.Yet the quality of the fit obtained with the nominal method is much better than any achieved using the previous iterative approxi- mations. The least squares method reproduces the data more closely; the standard error of fit is 2.7 % for Cs, 5.1 % for Rb and 3.4 % for the K data. Also, whereas the nominal method deteriorates at the " edges " of the data (at high velocities and at 10 and looo), the least-squares method provides smooth extrapolations beyond those regions. Fig. 2 shows c.m. differential cross-sections, plotted as angular distributions for various c.m. velocities. The similarity between the nominal and least-squares results again indicates the value of the quick and essentially trivial nominal procedure.The most striking aspect of these distributions is the strong coupling between c.m. velocity and angle. As the product exit velocity increases, the peak of the angular distribution shifts rapidly to smaller scattering angles. The width of the angular distribution also decreases as the exit velocity increases. Another notable feature is the rapid drop in intensity on the small angle side of each peak, in contrast to a more gradual fall-off towards large angles. Fig. 3 shows the flux distribution of final relative translational energy of the products, E' (for MC1 us. CCl,) at various angles. Aside from normalization, this is given by P(E', 8) = Icm(u, O ) / U . ( 5 ) The abscissa scale is in terms of the fraction, ftrans = E'/Etot, of the total available energy, E,,, = E + Eint + ADo.Here E and Ei,, are representative initial relative translational and internal energies of the reactants. ADo is the reaction exoergicity obtained from the MCI and Cl-CC1, bond dissociation ene~gies.'~.'~ Values for the K/Rb/Cs cases are: E = 6.3/6.7/8.4; Eint = 2.5 (diatomic approximation); ADo = 155/134/138 kJ mol-'. The corresponding fraction of energy appearing as vibrational and rotational excitation of the products is given byfint = 1 - ftrans. The strong coupling between the product translational energy and scattering angle is again evident in these distributions. The " mountain ridge " or locus of largest intensity is indicated by a dashed curve. The deviation of these loci from a circle is another measure of the coupling. Also evident is the marked shift to higher exit velocities and wider scattering angles as Cs -+ Rb -+ K.The contour maps show evidence of some low velocity structure at small angles. This structure corresponds to the bimodal form of the LAB velocity distributions where it is enhanced by the u2/u2 Jacobian in the c.m. -+ LAB transformation of eqn (2). The low velocity structure is likewise enhanced in the energy distributions by the u-' factor in eqn (9, as indicated by the dashed portions of the curves in fig. 3. However, in the contour maps it is a relatively minor feature and will not be considered here. The low velocity region in c.m. space is the region most severely " washed out " by velocity averaging, and a reliable quantitative determination of such structure cannot be obtained without resorting to velocity selection of the parent beams.Fig. 4 displays contour maps of the c.m. cross-section.32 REACTIONS OF ALKALI METAL ATOMS WITH cc1, 1 . 0. c.m. scattering angle, 8 /O FIG. 2.-Angular distributions of reactively scattered alkali metal chloride for various velocities u in the centre-of-mass (c.m.) system, for reactions of (a) Cs, (6) Rb and (c) K with CCI.,. By convention, 0" refers to the initial c.m. direction of the reactant alkali metal atom velocity, 180" to the CCI4 c.m. velocity. Dotted curves show results from nominal kinematic transformation, dashed curves those obtained from the least-squares procedure.S . J . RILEY, P . E . SISKA AND D . R . HERSCHBACH 33 f int 1.0 0.9 0.8 0.7 0.6 0.5 1.0 0.5 0 rr H ; 1.0 L - Y- Y Q z U .- In c al T) 3 x 0.5 4 )I 0 1.0 0 .5 C 0 0.1 0.2 0 . 3 0.4 0.5 fraction of product energy in translation, ftrans FIG. 3-Energy distributions at various c.m. scattering angles for alkali metal chloride product, derived from the least-squares fitted polynomial cross-sections, for reactions of (a) Cs, (6) Rb and (c) K with CC14. Upper abscissa scale gives fraction of available energy appearing in internal excitation, lower scale that in relative translation of products.34 REACTIONS OF ALKALI METAL ATOMS WITH cc1, 90" 0" 90' FIG. 4.-Contour map of differential cross-sections for reactively scattered alkali metal chlorides, obtained from least-squares procedure, for reactions of ( a ) Cs, (b) Rb and (c) K with CC&. The intensities are normalized to 100 and contour lines are shown for each 10 units.Tick marks along radial lines appear every 100 m s-l. Open circles and dashed curves indicate the " mountain ridge ", or locus of maximum intensity. Table 3 compares the LAB velocity of CsCl in the Bull and Moon experiments with that computed from our least-squares c.m. cross-section. The velocity of the CC14 beam was taken to be that of the paddle tip with a thermal distribution super- imposed. The Cs beam, also thermal, was given a cosine distribution of directions about 0". The calculated LAB velocity distributions of CsCl scattered at 80, 90 and 100" were averaged to approximate the degree of collimation used by Bull and Moon, and multiplied by two additional factors of velocity to correspond to time-of-flight signal pulses.The agreement is better than 10 %, certainly as good as could be ex- pected in view of the approximations required and uncertainties about precise ex-S . J. RILEY, P. E. SISKA AND D. R . HERSCHBACH 35 TABLE 3.4OMPARISON WITH BULL AND MOON'S EXPERIMENT' rotor tip speed product pulse speed Bull and Moon calc. 1.52 4.7 2.92 4.9 4.33 5.2 6.52 6.7 4.6 5.1 5.6 6.2 Units are lo2 m s-l. perimental conditions. The fact that the agreement remains good at all four rotor speeds is of particular interest, since our calculations assume Icm(u, 0) does not vary significantly with the initial relative translational energy of the reactants. This varies from ~ 4 . 2 to 24 kJ rno1-I in the Bull and Moon experiments, according to the observed speed of the CCI, pulses.RAINBOW MODEL In elastic scattering, rainbow structure usually results from an attractive potential well. However, a repulsive barrier can also produce a rainbow which is similar in all respects except that the rapid fall-off in intensity occurs toward narrow angles rather than wide angles." This is just the behaviour observed for the CC1, reactions. Since elastic rainbows of the usual kind are observed for these systems,I6 any barrier in the reactant trajectory would have to occur rather late in the entrance channel. Indeed, the electron transfer which governs the reactions appears more likely to intro- 0 0 1 2 5 10 20 reduced recoil energy, K FIG. 5.-Rainbow plot for the Morse and Lennard-Jones potentials [ref. (18) and (19)], and for the H + H, reaction [circles, ref.(S)] and deuteron stripping reaction [squares, ref. (7)]. For the H + Hz reaction, the characteristic energy E is taken as 0.4 eV, the minimum saddle-point height for the potential surface used in ref. (8). For the ( d , p ) reaction, the points are shifted an arbitrary amount, corresponding to an E of 25 MeV.36 100 50 \ aD' a; w (31 C tl 0 a t 3 .- E! 20 10 I I I I I I I I REACTIONS OF ALKALI METAL ATOMS WITH Cc& 1 1 1 A 0 0 O O 0 O O 0 0 0 0 0 A A A 0 0 0 0 A A A FIG. 6.-Rainbow plot for reactive scattering of K(O), Rb (0) and Cs (A) atoms from CCI, derived from the least-squares fitted polynomial cross-sections. duce a barrier in the exit ~hanne1.I~ The venerable Evans-Polanyi discussion of curve-crossing suggests the barrier height would vary with the product bond strength and thus would decrease in the order K 21 Rb > Cs.Semiclassical theory shows the rainbow structure is governed by an Airy function form factor, with the rainbow angle 0, located on the " dark " side at a point where I(0) sin 0 has 44 % of its peak inten~ity.'~ At high energies, Or becomes inversely proportional to the ratio K = E / E of the collision energy to the well depth or barrier height. Fig. 5 com- pares the &(K) functions computed for a Morse potential16 and a Lennard-Jones (12, 6) potential" with the high energy approximation for the latter case, 0, = 2/K. This shows the angle-energy correlation depends only weakly on the form of the potential. Data points are included for two reactions which are definitely governed by repulsive barriers: a (d, p ) deuteron stripping reaction and the H + Hz reaction.8 The notion of" reactive rainbows " appears to have some merit for these systems.Fig. 6 presents a similar plot for M + CCl,, derived by applying the usual analysis for elastic scattering" to our product distributions. The rainbow model looks dubi- ous, since Or varies more like the inverse square root rather than the inverse first power of the energy. The slopes increase at large E'. This is suggestive because the same trend is noticeable in fig. 5 at low energies; a barrier causes a negative deviation from the K - l line in contrast to the positive deviation caused by a potential well. The curvature thus may indicate that the recoil energies for the CCl, systems are too low Fig.5 and 6 examine the heuristic notion of " reactive rainbows ".S . J . RILEY, P . E . SISKA A N D D . R . HERSCHBACH 37 to show the characteristic K-’ behaviour. If fig. 6 does pertain to rainbow scattering, the relative position of the curves indicates that the barrier height decreases in the order K > Rb > Cs (and the relative heights are roughly in the ratio 5: 3 : 1). This phenomenological rainbow analysis does not deserve much credence. However, it has led to a rather simple model which appears to give a comprehensive account of the reaction dynamics for the CC14 systems as well as the CH41 and Br, systems. DYNAMICAL MODEL There is now a large repertoire of reactive scattering models that are more tractable than full-scale classical trajectory calculations and call for much less information about the potential surface.21 Although we did not find a previous model suitable for the CCl, reactions, the treatment outlined here borrows from several such models; we refer to it as eclectic (to avoid a crowd of acronyms).Our model deals specifically with the electron transfer process, A + BC --f A+ + B-C -+ A+B- + C, and has four main components : the deflection function is taken as the sum of reactant and product portions, 0, + O,, each governed by a two-body central force potential. In the entrance channel the BC bond is fixed at its equilibrium distance for the ground vibrational state; in the exit channel AB is fixed at the r-centroid distance corresponding to its vibrational excitation.The entrance channel potential Vi, is determined from a 2 x 2 secular determinant. The diagonal elements represent covalent (Lennard-Jones) and ionic (Rittner) interactions and the off-diagonal element contains the ionic-covalent coupling term.23 The exit potential V,,, prescribes the decomposition of the transient B - C ion-molecule and is determined from dissociative electron attachment data. 24 (2) As in the DIPR the switch between the entrance trajectory and the exit trajectory is abrupt and the repulsive energy release is evaluated from a Franck- Condon approximation in analogy to photodissociation.26 (3) As in the infinite-order-sudden appro~imation,’~ the collision mechanics is much simplified by fixing the angle between the molecular axis and the radius vector from the collision partner to the molecular centroid.This angle is denoted by q in the entrace channel and 11’ in the exit channel. Thus, only a single representative geometry is specified for the ABC complex at the switchover point. (4) As in the “ half-collision ” model for photodissociation,28 the partitioning of the abruptly released repulsive energy between relative translation E’ of AB and C and internal excitation Elint of AB is estimated from an impulsive approximation akin to the Landau-Teller model for translational-to-vibrational energy With this eclectic model, we find rainbow-like reactive scattering can readily be obtained. The most important factors involved are the range of the reaction proba- bility P,(b) as a function of initial impact parameter; the transition-state geometry ; and the T --f V, R energy transfer induced by the repulsive energy release. Two formulae suffice to describe the role of these factors.The differential cross-section is given by (1) As in the extended optical Here x = 0, + 0, is the classical deflection function; y(rBc) is the initial vibrational wavefunction; I 8E’/2rBcl is a Jacobian factor, the slope of the repulsive potential of the B-C ion at the initial bond distance. All quantities are computed for various38 REACTIONS OF A L K A L I METAL ATOMS WITH CCl, fixed rBC values and the cross-section is then averaged. The energy transfer is given by E&,/Eb = 4 sin2 p cos2 p sin2 (8,’/2)N(p). (7) Here Eh is the sum of the initial relative kinetic energy and the repulsive energy available for disposal in the products (Eb would be E’ in the absence of energy transfer); cos’p = (m,/m,,)(m,/m,,) is a kinematic mass factor, with p the skew angle for axes which diagonalize the kinetic energy.30 The function H(p) is given by Harris;28 it specifies the deviation from adiabaticity in terms of the ratio p of the collision duration to the vibrational period of the product molecule.In the impulsive limit, p = 0 and H = 1. In this limit, eqn (7) is Mahan’s formula for T -+ V transfer in collinear collisions,29 except for the sin2 (0:/2) factor, which in effect inserts an impact parameter. This important factor involves the product contribution to the scattering angle (the zero superscript again indicates a value obtained without including energy transfer).As usual in impulsive models,’* Ei,, may be resolved into vibrational and rotational components using the transition state geometry. Eqn (6) exemplifies the essentially geometrical character 22 of the correlation be- tween the preferred direction of product recoil and the magnitude of the reaction cross- section. If P,(b) is sufficiently long-ranged, the reactants can swing around each other in grazing collisions and the exit repulsion cannot overcome the strong preference for forward scattering that results from the b/sin 0 factor. If P,(b) is shorter-ranged, only closer collisions give reaction and the repulsion then kicks the products apart sideways or backwards. Likewise, for noncollinear transition-state configurations, certain angular regions become inaccessible due to the combined effects of exit repul- sion and angular momentum conservation, Eqn (7) also provides a strong dependence on initial impact parameter.When b is large and the products tend to scatter forwards, the energy transfer delivers more of the exit repulsion into translation whereas the opposite occurs at small impact parameters which favour backward scattering. The magnitude of the effect depends strongly on the mass factors and the adiabaticity parameter. This energy transfer is the major factor governing the rainbow-like coupling of the product angle and energy distributions in the CC14 reactions. Since E’ is thereby enhanced for the more- forward-scattered products which carry large centrifugal angular momentum, the exit parameter b’ shows a maximum as a function of b and hence produces a minimum in the part of BP governed by the exit energy transfer.Although this does not yield axlab = 0, it does give a local minimum in axlab which serves to focus the product intensity in the corresponding angular range. Thus, the eclectic model produces “ energy-transfer rainbows”. Product angle-energy contour maps obtained from the model simulate the experi- mental results quite well for the CCl,, CHJ and Br2 reactions. Fig. 7 shows such maps for the CCl, case. As with any such model, there is considerable leeway in the choice of some parameters, The most reassuring aspects are the comprehensive character of the agreement and trends governed by nonadjustable parameters : the atomic masses.Thus, for the CCl, systems the mass dependence of eqn (7) accounts for the variation seen in the E‘ against 0 coupling with change of alkali metal atoms, including the lithium reaction which shows only weak ~oupling.~’ This also accounts for the modest but definite E’ against 8 coupling seen in the Br, reactionsI2 and the lack of such coupling in the CH,I case., For our nominal choice of potential para- meters, we find for the CC14 systems a somewhat bent M/ \C configuration c1S . J . RILEY, P . E . SISKA A N D D . R . HERSCHBACH 39 9 0' ( a ) 120" t 60' 60' ( b ) 90" 120' T / 5 I O0 FIG. 7.-Contour maps for reactively scattered alkali metal chlorides calculated from the eclectic model. Notation and format as in fig. 4. ( a ) Cs + CC14, (b) Rb + CC14, (c) K + CC14.(with q z 20°, q' z l 5 O ) enhances substantially the rainbow-like behaviour of the scattering. Such features suggested by the model invite closer study by means of trajectory calculations. It is fitting that the molecular dynamics of the CCl, reactions seem to involve spinning and swatting, much as in the apparatus of Bull and Moon. Support of this work by the National Science Foundation is gratefully ack- nowledged. T. H. Bull and P. B. Moon, Disc. Faraday Sue., 1954,17, 54. D. R. Herschbach, in Chemical Lasers, Appl. Optics Suppl., 1964, 2, 193. K. R. Wilson and D. R. Herschbach, J. Chem. Phys., 1968,49, 2676. R. B. Bernstein and A. M. Rulis, Faraday Disc. Chem. Soc., 1973, 55, 293. J. H. Birely and D. R. Herschbach, J. Chem. Phys., 1966, 44, 1690.40 REACTIONS OF ALKALI METAL ATOMS WITH Cc14 S.T. Butler, Proc. Roy. SOC. A, 1951, 208, 559. M. Karplus and K. T. Tang, Disc. Faraday SOC., 1967, 44, 56. S. J. Riley and D. R. Herschbach, J . Chem. Phys., 1973, 58, 27. ' L. C. Biederharn, K. Boyer and M. Goldstein, Phys. Rev., 1956,104,383 and work cited therein. lo R. Grice, Ph.D. Thesis (Harvard University, 1967). l1 A. Persky, E. F. Greene, and A. Kuppermann, J. Chem. Phys., 1968,49, 2347. l3 L. Brewer and E. Brackett, Chem. Rev., 1961, 61,425. l4 T. L. Cottrell, The Strengths of Chemical Bonds (Butterworth, London, 1958). l5 K. W. Ford and J. A. Wheeler, Ann. Phys. (N.Y.), 1959,7, 249. l6 R. M. Harris and J. F. Wilson, J. Chem. Phys., 1971, 54, 2088. P. E. Siska, J. Chem. Phys., 1973, 59, 6052 and work cited therein. M. G. Evans and M. Polanyi, Trans. Faraday Soc., 1938,34, 1 1 ; J. C. Polanyi, Chem. Phys. Letters, 1967, 1, 421. R. B. Bernstein, in Atomic Collision Processes, ed. M. R. C. McDowell (North Holland, Amsterdam, 1964), p. 895. l9 E. A. Mason, R. J. Munn and F. J. Smith, J. Chem. Phys., 1966,44,1967. 2o E. F. Greene, G. P. Reck and J. L. J. Rosenfeld, J. Chem. Phys., 1967,46, 3693. 21 J. C. Polanyi and J. L. Schreiber, in Physical Chemistry, An Aduanced Treatise, vol. VIA, Kinetics of Gas Reactions, ed. W. Jost, (Academic Press, New York, 1974), p. 383. 22 D. R. Herschbach, Adv. Chem. Phys., 1966, 10, 319; J. L. Kinsey, G. H. Kwei and D. R. Herschbach, J. Chem. Phys., 1976, 64, 1914. 23 R. Grice and D. R. Herschbach, Mol. Phys., 1974,27,159; R. W. Anderson and D. R. Hersch- bach, J. Chem. Phys., 1975, 62, 2666; S. A. Adelman and D. R. Herschbach, Mol. Phys., 1977, 33, 793. 24 W. E. Wentworth, R. George and H. Keith, J. Chem. Phys., 1969, 51, 1791. See also S. M. Lin, D. J. Mascord and R. Grice, Mol. Phys., 1974, 28,975. 25 P. J. Kuntz, M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969, 50,4623. 26 D. R. Herschbach, Faraday Disc. Chem. SOC., 1973, 55, 233. 27 R. T. Pack, J. Chem. Phys., 1974, 60, 633; D. Secrest, J . Chem. Phys., 1975, 62, 710; L. W. Hunter, J . Chem. Phys., 1975, 62, 2855. 28 K. E. Holdy, K. C. KIotz, and K. R. Wilson, J. Chem. Phys., 1970,52,4588; R. M. Harris and D. R. Herschbach, J. Chem. Phys., 54, 3652. 29 B. H. Mahan, J. Chem. Phys., 1970,52, 5221. 30 F. T. Smith, J. Chem. Phys., 1959, 31, 1352. 31 D. D. Parrish and R. R. Herm, J. Chem. Phys., 1971,54,2518; C . M. Sholeen and R. R. Herm, J . Chem. Phys., 1976, 65, 5398.

ISSN:0301-7249    

DOI:10.1039/DC9796700027

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Electronic Excitation in Potentially Reactive Atom-Molecule Collisions BY MALCOLM A. D. FLUENDY, KENNETH P. LAWLEY, JOHN MCCALL, CHARLOTTE SHOLEEN AND DAVID SUTTON Department of Chemistry, University of Edinburgh, Edinburgh EH9 355 Received 1 1 th December, 1978 Inelastic differential scattering cross sections for the system potassium + alkyl halide have been measured in the small angle region for Ex between 20-1000 eV". Electronic excitation of both colli- sion partners is seen together with vibrational excitation of the alkyl halide. Evidence is adduced suggesting that excitation occurs by either of two paths corresponding to the preliminary transfer of an electron in the entrance channel or as the colliding pair recedes. A harpooning model incorporating bond stretching in the negative molecular ion is developed that agrees well with most of the observations.A large number of exit channels are open in the collision system alkali atom + alkyl halide at higher energies. They include: M + RX-+ M + RX(RX7) elastic (inelastic) (0 - + M X + R reaction (ii) -+ M+ + RX- chemi-ionisation (iii) -+ M* + RX M +RX*) electronic excitation - + M + R + X dissociation. (v) The first two processes have been extensively investigated at thermal collision energies 1*2 and are well known examples of the electronic harpooning mechanism, subsequent chemical reaction occurring at thermal energies by ionic combination. The chemi-ionisation channel is less well explored3 but provides direct evidence for non-adiabatic behaviour at the ionic/covalent surface crossing.The importance of an ionic surface in coupling ground and excited electronic states of the atom is con- firmed by collision-induced fluorescence ~tudies.~ In the work described here continuing the programme outlined in a previous Faraday Discus~ion,~ we have eliminated the reaction channel by working at high relative kinetic energies and choosing a heavy halogen atom, iodine. Equally im- portant from the point of view of analysis, by confining scattering observations to very small angles ( 5 5") the K atom trajectories are essentially rectilinear and of con- stant velocity. Nevertheless, because the forward momentum is high, interesting regions of the potential inside the harpooning radius can be probed by these small deflections. Electronic excitation of several eV is readily observed.42 ATOM-MOLECULE COLLISIONS EXPERIMENTAL APPARATUS The apparatus used in this work is shown schematically in fig.1. The beam of fast alkali atoms was produced initially as ions by surface ionization and electrostatic focusing. The ion beam was then pulse modulated, using a velocity compression technique described else- where,6 so that the energy loss resulting from a collision could be recorded by measurement of the flight time of the scattered atom and hence the post-collision states of the atom and molecule inferred. After modulation the ion beam was neutralised in a vapour cell and any remaining ions deflected away. r a d i a t i o n heater source oven Gtjst aff son ~~ ~~ t a r g e t beam reservoir r collimating array 3 cross beam chopper motor vapour c e l l ion dump collision zone plates collimating slits f cross beam filament porous tungsten disc t.0.f pulsing lens collimating array flexible bellows / detector detect o r assembly FIG.1 .-Schematic representation of apparatus. The fast neutral beam then intercepted a slow target beam of molecules formed by effusion from a capillary array in a well defined collision zone. This beam was also modulated (at 47 Hi) and the target flux continuously monitored by a gauge placed directly below the collision zone. Potassium atoms scattered from this region were ionised on a cool W wire and detected uia a scintillator and photomultiplier. The detector could be varied in angle with a precision of &0.002". Atom arriirals located in angle by the detector position were arranged to stop a 50 MHz clock running in synchronism with the pulse modulation so that the flight time could be recorded.The collection of data and the operation of the experiment were controlled by an on-line computer.' The signal collection and experimental control arrangement are shown schemati- cally in fig. 2. Hard copy log and graphical output facilities were provided to allow operator intervention, DATA COLLECTION A N D ANALYSIS Count rates are very low in this experiment (<0.01 counts s-l) and periods of E 12 h were required to collect sufficient counts at the widest angles. Data collection thus took place over periods of about five days. During this time the main beam arrival time profile was checked at intervals under program control and data collection suspended and the operator.) DEC 11/45 I run delay C& ? delay ,flip f lop - '/ 1 i l o B i, -tr7 - ready -T multiplexe d a t a target modulator r filament I monitor stepper angle drive encoder modulation r e lay drivers t i a 0.0.c. i modulation I display rp 4-1 logging teletype teletype f l i p fi scaler 4 I 4 I ] clock c" divider44 ATOM-MOLECULE COLLISIONS alerted if any significant changes in the beam fluxes or other operating conditions took place. The angular scan was made automatically to a predetermined sequence, angle changes being initiated automatically when a set precision had been reached. The data reported in this paper were accumulated over a period of about eighteen months during which time the equipment was removed from one building to another and a number of small changes made.Partly as a result the time location of the primary beam pulse varied by as much as 30 ns between different experiments. The data were therefore adjusted in time so as to be relative to the unscattered beam arrival as measured in each experiment. Any accompanying variation in the pulse width was corrected by a process of deconvolution and reconvolution to a standard pulse width, the stability of these operations being checked by trials with synthesised noisy data. Inconsistencies of this type between different experimental runs rather than counting statistics account for most of the noise seen in the results. After these adjustments had been made in the laboratory frame the data were transformed into the c.m.frame using the most probable laboratory velocities. RESULTS These results are most compactly presented as c.m. contour maps showing the variation in the product of the scattered intensity and the square of the scattering angle, Z(x)x2, as a function of the variable z (t = collision energy x scattering angle, Ex) and the post-collision velocity. The contour map in fig. 3 shows such a plot for K + Ar and illustrates the energy b 4 1 2 scattering angle 1 deg FIG. 3.-K + Ar scattering at 108 eV c.m. collision energy. The thick lines indicate energy losses of 0.0 and 1.6 eV (centre of mass frame).M. A . D . FLUENDY, K . P . LAWLEY, J . MCCALL, C . SHOLEENANDD. SUTTON 45 resolution since in this E region the scattering is at least 98 % elastic.The island of intensity at slow exit velocities is due to the K4' isotope present at ~6 % abundance. The other contour maps in fig. 4-6 show similar plots for methyl and propyl iodide at various initial collision energies. In comparison with the K + Ar data considerable inelasticity, particularly at the wider angles, is immediately apparent and can be seen to onset at specific Ex. + .- u 0 0, w - I 0 5 scattering angle I deg 2 FIG. 4.-K + CH,I scattering at 164 eV collision energy. The thick lines indicate energy losses of 0.0, 1.6 and 3.47 eV (centre of mass frame). Cuts through the surface show the intensity of scattered K atoms as a function of the energy lost by them in collision are perhaps more suggestive. A number of ex- amples computed by averaging together several sets of independent observations in a narrow range of angle are shown in fig.7 and 8. The solid curves on these figures show the results of a deconvolution procedure using the 0" profile as a reference profile. The peaks are sharpened by this process but can already be distinguished in the unprocessed data ; moreover, independent angular scans yield peaks which move smoothly with angle as in fig. 9-1 1 . The enhanced scattering profiles prepared in this way are combined to yield similarly sharpened contour maps as shown in fig. 12 and 13. Time of flight data of this type are of limited value in molecular systems because it is not possible to associate a given velocity change in the K atom with a specific exit channel, owing to the number of closely spaced energy states.Thus, in the K + RI system the K ionisation continuum starts at 4.34 eV and there is a near con-46 ATOM-MOLECULE COLLISIONS tinuum of vibration-rotation states in each electronic level of RI. Table 1 summarises the relevant information for K and CH31 (C3H,I is similar). In view of this continuum of vibronic levels, it is remarkable that discrete energy losses are observed at least up to 10 eV at the largest angles of scattering. r. u 0 0, > + .- d 0 5 3 d 1; :j -5 7 62 0 2 scattering angle / deg and 3.47 eV (centre of mass frame). FIG. 5.-K + CHJ scattering at 81 eV collision. The thick lines indicate energy losses of 0.0, 1.6 DISCUSSION At scattering angles x 5 5", the momentum transfer perpendicular to the incident velocity is small (x = final transverse momentum/incident forward momentum).The various small-angle approximations are valid and the momentum changes in the forward direction cancel on the incoming and outgoing halves of the trajectory. Under these conditions the maximum energy transferable to vibration/rotation of the molecular partner is where X = I or R, the end struck, and a " forceless " oscillator has been assumed. The maximum energy thus transferred at the angles of observation will be <0.5 eV, far smaller than most of the observed energy loss channels. The extensive vibronic energy transfer that is observed can only occur if the potential energy surfaces areM . A . D . F L U E N D Y , K . P . LAWLEY, J . MCCALL, C . SHOLEEN A N D D . SUTTON 47 profoundly modified in the course of the collision.The source of this alteration is clearly the crossing onto the ionic state. The harpoon model, equivalent to adiabatic behaviour at the ionic/covalent crossing, is well established as the mechanism for chemical reaction in many alkali metal systems at thermal energies. At the collision energies of the present experiments the reactive channel is essentially closed because the fast K+ ion cannot accelerate the c .- u 0 aJ > L I 61 0 3 scattering angle / deg and 3.47 eV (centre of mass frame). FIG. 6.-K + C3H71 scattering at 166 eV collision. The thick lines indicate energy losses of 0.0, 1.6 I- ion sufficiently rapidly to capture it before leaving the ionic surface. The residual electronic excitation is like the grin on the face of the Cheshire Cat, the aftermath of a much more profound electronic rearrangement.We develop a model to account for the broad features of the observed scattering in two stages. As a first approximation, the collision is assumed to be isotropic and sudden with respect to the R-I motion, i.e., the R-I bond is clamped at its equilibrium value throughout the collision. The behaviour of the various diabatic potential sur- faces can then be displayed solely as a function of the K-I coordinate, fig. 14(a). The vertical electron affinity of the alkyl iodides is sufficiently small (-0.9 eV) for the ionic state to intersect all the K* channels (including the ionised continuum) and thus to provide a route for populating these states. Excited electronic states of RI, except the A state, lie above the dissociation limit of K+RI- (5 eV) and must then be populated48 ATOM-MOLECULE COLLISIONS by a different mechanism. We speculate that an excited charge transfer state is involved but the mechanism will not be discussed here.The only important adjustable parameter in these potentials is the short range repulsion behaviour of the ionic state and the coupling matrix elements at the various crossings. Whatever the values of the parameters, some simple consequences arise because any exit channel can be reached via two paths, according to whether or not the electron is transferred on the first passage of the ionic/covalent crossing. 0 energy loss /eV FIG. 7.-Energy loss profiles observed at various scattering angles for K + CH31 at 81 eV collision energy.The dashed curves are observed values and the solid lines their deconvolution. (a) 61, (b) 122 and (c) 203 eV". The predictions of this model (using the potentials shown, the Landau-Zener approximation and the classical small-angle formulae to evaluate the cross-sections) are compared with experiment at 164 eV in fig. 15, the energy loss data being par- titioned in accord with the asymptotic energy losses assuming only electronic excitation. The model is partially successful, especially in predicting the narrow angle thresh- olds of K* and CHJ* ( A ) state onsets. If the route to these states involved a cross- ing on the respulsive wall of the potential, the angular threshold would appear at much larger angles and the intervention of a strongly attractive surface is unambiguous.The model is less satisfactory in predicting the change in angular onsets of the vari- ous channels with incident energy. These thresholds are seen to occur at lower E values in the 81 eV data, whereas the basic model necessarily predicts constant Ex values (assuming straight line trajectories). More important differences are seen inM. A . D . FLUENDY, K . P . LAWLEY, J . MCCALL, C . SHOLEEN A N D D . SUTTON 49 111 I: I 6 O energy loss /eV I FIG. 8.-Energy loss profiles observed at various scattering angles for K + CH31 at 164 eV collision energy. The dashed curves are observed values and the solid line their deconvolution. (a) 75, (6) 450 and (c) 900 eV". the energy loss spectrum where the model only permits energy losses corresponding to the electronic states of the separated species.The observations (e.g., fig. 7 and 8) show a much larger number of discrete energy loss processes, some of them (those < 1.6 eV) not being assignable at all to electronic excitation. The most serious assumption of the basic model lies in the neglect of the internal motion of the target molecule. s, changes in the C-I bond distance can occur which greatly alter the vertical electron affinity and hence the posi- tion of the ionic/covalent crossing. Such effects have been discussed by other workers8 in connection with chemical reaction and chemi-ionisation. The initial crossing at R1 yields CHJ- in a strongly repulsive state [fig. 14(b)], assuming a vertical transition.As the C-I bond stretches on the ionic surface, the ionic/covalent crossing moves to larger R values (fig. 16) and on the return of the electron a large amount of energy can be dumped in the Me-I vibration. The extent of such energy transfer clearly depends on the time spent on the ionic surface and ranges from zero if the motion at R1 is diabatic (electron not transferred) to actual dissociation of the Me-I bond if the MeI- surface is sufficiently repulsive. Since there are in general two classical paths leading to a particular angle of deflection (if b < &), corresponding to diabatic or adiabatic motion at R1, each electronic exit channel should be accompanied by two distinct peaks in the time of arrival spectrum. During the collision lifetime, typically50 ATOM-MOLECULE COLLISIONS Our second model, then, is to permit relaxation of the C-I bond in the ionic state by introducing a term Vio"(RR-I) = A exp [-a(& - RkO?)] (2) into the total potential energy.The I-K interaction remains coulombic and there is no K-R interaction. One result emerges immediately from this model. If the para- meters in Vion(&) are taken to be those of the isolated ion,' far too much vibrational excitation is predicted even in the ground electronic exit state. In fact, we would have a runaway situation with extensive bond dissociation (and probably chemi-ionisation). In practice (fig. 9-1 1) the vibrational energy gain in both the ionic K and K* channels is quite small ( z 1 eV) and almost constant with Ex after the threshold.The CHJ- ion is thus perturbed by the passing K+ ion and we can very crudely incorporate this effect in the model by making a adjustable. However, even this degree of freedom is not sufficient for the data to be fitted; if the vibrational energy gain in the K* (ionic) channel is fitted, too little energy loss occurs in the ground state channel. In qualitative terms, the initial acceleration of the methyl group after 2 x F - :I 2 - 0, - * 0 0 0 v u v " " 0°C 0 1: L 1 I I I I I I I I 0 500 1000 t IeV deg FIG. 9.-Plot showing the location of the peaks observed in the energy loss measurements as a function of the reduced scattering angle, z. CH31 + K 164 eV collision energy. 0 FIG. 10.-Plot showing the l m i o n of peaks observed in the energy loss measurements. CH31 + K at 81 eV collision energy.M .A , D. FLUENDY, K . P. LAWLEY, J . MCCALL, c . SHOLEEN AND D. SUTTON 51 I -- 6 300 t l e V d e g 0 FIG. 11 .-Plot showing the location of peaks observed in the energy loss measurements. C3H71 + K at 166 eV collision energy. I I I I 1 1 2 3 4 5 scattering angle I deg FIG. 12.-Contour plot showing CH31 + K scattering as a function of energy loss and c.m. scattering angle at a collision energy of 164 eV and after enhancement by deconvolution. Thick lines are drawn at energy losses of 0.0, 0.86, 1.6 and 2.8 eV.52 ATOM-MOLECULE COLLISIONS v) 0 x d al 1 060 1.720 scattering angle /deg FIG. 13.-Contour plot showing CHJ -+ K scattering as a function of energy loss and scattering angle at a collision energy of 81 eV and after enhancement by deconvolution.Thick lines are drawn at energy losses of 0.0, 0.72, 1.4, 2.0 and 3.2 eV. electron transfer seems to be rapid, but the repulsion soon drops almost to zero. The functional form of eqn (2) must be wrong and the dependence of Vion on RMeK should be introduced. This could be interpreted as due to the repulsion of the departing Me group by the K+ ion, or the change in bond order of MeI- due to partial back transfer of the electron to K+. Nevertheless, relaxation of the Me-I bond on the ionic surface is a key step in the collision process. Besides leading to extensive vibrational excitation, the deflection of trajectories sampling the ionic surface will depend on the extent of R-I relaxation during the collision. The angular thresholds for all electronic processes fed by the ionic surface will not thus scale with Ex, and will also depend upon the reduced mass of RI.These effects can be seen in fig. 17, where the energy losses calculated from this TABLE I.-EXCITED STATES OF K AND CH3I K energy /eV CHSI energy/eV 42s, 0.0 X(%) 0.0 42P3,; 1.62 A* 3.47* 52s+ 2.61 B, C(E) 6.10, 6.16 3’D;,4 2.67 D, ( E ) 6.77 5’P+,; 3.06 E, 7.30 I.P. 4.34 Rydberg states Rydberg states F, G 9.4, 9.8 LIP. 9.54 * Onset of continuous adsorption; peak at 4.5 eV.M . A . D. FLUENDY, K . P . LAWLEY, J . MCCALL, C . SHOLEEN AND D. SUTTON 53 R I i FIG. 14.-(a) Isotropic diabatic potential model for K + RI interaction. (b) CHd and CHJ* potentials. Dashed curves show the perturbation used to obtain the approximate fit described. FIG.15.-Isotropic sudden model; comparison with observations for CHJ + K at 164 eV. model are displayed against the corresponding scattering angle. In the Ex region around 150 eVo, particularly at 81 eV collision energy, a rainbow feature can be seen where two branches for the ionic ground state scattering coalesce. The invariance of vibrational excitation with angle of scattering is a remarkable feature of the plots and again points to a relatively small shift of the ionic/covalent seam with changing transit time over the surface. Finally, the differential cross sections for the channels identified are displayed, together with the model predictions, in fig. 18 and 19. The observed very narrow angle elastic scattering is normalised to the model.54 ATOM-MOLECULE COLLISIONS FIG.1 &--High energy trajectories on an ionic/covalent surface. Two trajectories are shown, corre- sponding to different initial kinetic energies (EA < EB). The crossing point on the outward path (R,) is very sensitive to E. In case A, Rz is so large that dissociation or ionisation would result. The K trajectory in real space is inset. I I 3- > : 2 - cn lA 0 - , * ----- - - - __ M . . . . . . . . . . . . . . . . . . M - * - - - * . . - ..... ..... .- * _----- -- . . . . . . . . . . . 0 500 1000 - ,elastic I elasticN T l e V d e g FIG. 17.-Comparison of observed (0) and bond stretching model predictions (M) for the energy loss as a function of reduced scattering angle. The subscript I indicates motion on the neutral surface. Model and experiment are in accord in predicting an increasing energy loss as the mass of R decreases and as the collision lifetime increases.Dashed curve, 81 eV Mel; solid curve, 164 eV MeI; dotted curve, 166 eV PrI.M . A . D . FLUENDY, K . P . LAWLEY, J . MCCALL, C . SHOLEENANDD. SUTTON 55 SO00 m u - D N ;? 5 - - - b ' t / e V deg - .- "'4 t P T - , -I A A 0 500 1000 t / e V deg 2750r FIG. 18.-Differential cross-sections for K + CH3I at 164 eV. (0, 0 ) ground state N, I; (A, A) K* (4p) N, I ; (0, 1) CH31* ( A ) N, I. Lines are the model fit (-) N and (- - - -) I. 0 3 000 T t eV deg FIG. 19.-As for fig. 18, but at 81 eV. T I e V deg CONCLUSIONS Our conclusions as to the processes involved may be summarised with reference to fig. 14(a) as follows: (a) Each electronic exit channel is accompanied by two vibrational channels, one with small or zero internal energy change, the other with substantial vibrational excitation.These two channels correspond to, respectively, diabatic or adiabatic (harpooning) behaviour at the first crossing R1. Both channels are important in the experimental energy range. (b) The negative ion state involved is a repulsive state, but with rather different characteristics from the isolated RI- ion. In particular, the amount of bond stretch- ing is less than expected (at least in the configuration probed in the bound state exit channels) and points to some containment of the alkyl group. ( c ) The differential cross section summed over all discrete exit channels (ground plus excited states) is approximately constant over the x range from 0.5 to 5" (LAB).This strongly suggests that continuum processes (bond dissociation and ionisation), unless they onset at very small angles of deflection, play a negligible role at impact parameters 5 0 L j .56 ATOM-MOLECULE COLLISIONS ( d ) The excitation of the A state of CH31 is observed to have two energy loss con- tributions and angular thresholds, but these have less intensity than in the K* channel. An ionic surface again probably intervenes because of the small angular thresholds. But even without bond stretching, the ground state K+CH31- surface would lead to a crossing at GZ 50 A on the outward branch, at which point the coupling matrix element between the two states would be essentially zero. Some electronic excitation of the negative ion may be involved, i.e., harpooning to a different empty orbital. (e) Discrete energy losses >5 eV are observed and these must correspond to electronic excitation of the alkyl iodide. Since these energy levels are above the energy of the separated K+RI- ion pair, the ground state ionic surface cannot be involved in their coupling. J. L. Kinsey, Molecular Beam Reactions (M.T.P. Int. Rev. Sci., Physical Chemistry, 1972) ser. 1, vol. 9. M. E. Gersh and R. B. Bernstein, J . Chem. Phys., 1972, 56, 6131. A. P. M. Baede, Charge Transfer between Neutrals at Hyperthermal Energies, Adv. Chem. Phys., (Wiley, Chichester, 1975), vol. 30. V. Kempter, Electronic Excitation in Collisions between Neutrals, Ado. Chem. Phys., (Wiley, Chichester, 1975), vol. 30. M. A. D. Fluendy, K. P. Lawley, J. M. McCall and C. Sholeen, Faraday Disc. Chem. SUC., 1977, 62, 149. J. M. McCall and M. A. D. Fluendy, J . Phys. E, 1978,11,631. ed. R. A. Rosner, B. K. Penney and P. N. Clout (Advance, London, 1975). W. E. Wentworth, R. George and H. Keith, J. Chem. Phys., 1969,51, 1791. ’ M. A. D. Fluendy, J. H. Kerr, J. M. McCall and D. Munro, On-line Computing in the Laboratory, * J. A. Aten, G. A. H. Lanting and J. Los, Chem. Phys., 1977,19,241.

ISSN:0301-7249    

DOI:10.1039/DC9796700041

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Observation of a Condon Reflection Products State Distribution in the Collinear H + C1, Reaction BY M. S. CHILD -f AND K. B. WHALEY~ Theoretical Chemistry Department, University of Oxford, 1 South Parks Road, Oxford Received 5th December, 1978 A classical and semiclassical investigation of conditions required for the observation of a Condon reflection pattern in the products state distribution for the collinear H + C12 reaction is reported. Both vibrational and translation excitation of the reactants are considered. The use of semiclassical arguments in this context is justified by a high level of agreement with exact quantum mechanical results, although a significant threshold anomaly remains to be investigated. Competition with the inelastic channel above a certain threshold, which decreases with increasing reactant vibrational quantum number, is found to invalidate any simple Condon reflection prediction.The nature and importance of this competition is shown to be simply characterisable in terms of the properties of certain trapped trajectories, or nascent transition states, in the products valley of the potential surface. 1 . INTRODUCTION An important question for this General Discussion is what part quantum mechanics should play in the theory of reaction dynamics. Two obvious answers are in the treatment of the reaction threshold and of the resonances displayed by the collinear H + H2 reaction1y2 for example. Quantum mechanical interference can also yield a Condon reflection pattern in the product vibrational state distribution, whereby the distribution can in principle mirror the oscillatory form of the reactant wavefunction either as a function of product quantum number at given energy, or as a function of energy at given quantum n ~ m b e r .~ The former is clearly apparent in exact quantum mechanical results for the H + C1, rea~tion.~ It is also inevitably predicted by a variety of Franck-Condon models for the reaction me~hanism.~’ The experimental situation is less dear. A bimodal distribution from reactant state n = 1 has been reported for the H + C12 reaction,’ but this may be explicable on other than quantum mechanical grounds.10 While we recognise that the rotational degrees of freedom cannot be ignored in any direct comparison with experiment, we beIieve that the possi- ble observation of a Condon reflection products state distribution is sufficiently inter- esting to merit a detailed study of the conditions for its occurrence in a collinear model.The method of investigation is by classical and semiclassical mechanics, using the LEPS potential employed in previous classical l1 and quantum mechanical calcula- tions. Our purposes are (a) to examine the validity of available uniform semiclassical approximations 3~12-14 in a reactive context, (b) to identify the optimum conditions for observation of a Condon reflection distribution and (c) to discuss the branching between reactive and inelastic scattering, which is expected to invalidate any simple Condon reflect ion prediction. Emphasis is placed throughout on the disposition of relevant trajectory end points in reactant and product internal phase space.A particular “ barred ” representation l5 7 Visiting Fellow 1978-79. Institute for Advanced Studies, Hebrew University, Jerusalem, Israel. 0 Present address : Department of Chemistry, Harvard University, Cambridge, Mass., U.S.A.58 PRODUCT DISTRIBUTION FROM H + clz familiar to workers in the semiclassical field is employed in order to yield a picture which is independent of the choice of translational coordinate. This pictorial approach first clarifies the origin of any interference structure in the products state distribution; hence the conditions for its observation are readily understood. It also shows how the growth of the reaction zone in reactant space first grows to encompass successive quantum states as the energy increases, and then distorts and even begins to shrink as the advent of complex or snarled trajectories leads to increasing competition with the inelastic channel.Until the last few months the only approach to mapping this competition has been by laboriously noting the fate of many hundred traject~ries,l'-'~ but Pechukas and Pollak20 have recently shown how in principle knowledge of certain trapped trajec- tories on the potential surface may be used to generate such a map in a simple way. Families of such trapped trajectories have been identified for the H + H2 system2, and its isotopic variants,22 but the present paper contains the first report of their existence on a strongly exothermic surface. This is also the first practical implementation of the proposed mapping scheme.20 Our overall purpose is therefore to discuss the effects of both vibrational and trans- lation reactant excitation on the reaction dynamics. The results are specific to the H + Cl, system, but the general principles apply to any collinear atom-diatom reaction.2 . CONDON REFLECTION STRUCTURE Fig. 1 may be used to illustrate the principles behind the general Condon reflection prediction3 and to understand the requirements for its observation. It illustrates in product phase space the outcome of a set of classical trajectory calculations from a given reactant quantum state at a given energy [C12(n = 0) at E = 0.4 eV]. A special modified angle-action representation, outlined in the Appendix, was adopted to obtain this symmetrical picture, but it has no effect on the physical significance of the dia- gram.The key features are that the translate C; of the n,th reactant orbit necessarily encloses the same area [(n, + +)h] as the quantised orbit itself, and that the semi- 1 G1a.u. Cl' ,la.u. FIG. 1.-Reactive trajectory end points in the products phase space at E = 0.4 eV (0.0147 a.u.). Cz is the product phase space orbit for n2 = 5, C; the translate of the reactant orbit for nl = 0. The shaded area determines the semiclassical phase difference between the two nl = 0 to nz = 5 root trajectories. The axes B and are defined in the Appendix.M. S. CHILD AND K. B . WHALEY 59 classical phase responsible for the interference between the two root trajectories contributing to a particular transition is given by the relevant shaded area in the diagram (applicable to the n, = 0, n2 = 5 transition in this case).The root trajec- tories themselves appear as intersections between C', and C,. The observation of Condon reflection structure as a function of product quantum state requires first that successive quantised orbits should cut off areas lying between 0 and (n, + 4)h. This is impossible if C; encloses the origin for example, in which case the reflection pattern would remain undeveloped, just as in diatomic spectroscopy a fully developed pattern within the discrete spectrum requires an adequate separation between the potential wells. A second requirement is that C; should suffer only two intersections with any given C2. The existence of more than two root trajectories would lead to higher interference structure.Finally the contour Ci should be com- plete, implying no significant branching between reactive and inelastic scattering. Similar arguments apply to the variation of a given n, -+ n2 transition probability as a function of energy, because C; will typically move outwards as the energy in- creases, again cutting off an increasing area between 0 and (n, + +)h. Only the second two requirements then apply, but they are much less easily satisfied, particularly for excited reactant states, due to increasing competition with the inelastic channel at higher energies. The nature of this competition for the H + C1, system is discussed in detail in section 4. 3. SEMICLASSICAL TRANSITION PROBABILITIES An extensive comparison between semiclassical and available exact quantum mechanical r e s ~ l t s , ~ was performed in order to test the above semiclassical con- clusions, and to assess the reliability of specific uniform approximations, namely Airy,12 Bessel,13 Laguerre l4 and h a r m ~ n i c .~ The semiclassical calculations were performed in the conventional way 23 with the semiclassical phases deduced from the action integrals along the trajectories. Our only computational contribution is to use the constraints imposed by the phase space picture in fig. 1 to solve a troublesome phase discontinuity problem.2k27 This discontinuity occurs during a transformation of phase between Cartesian and angle action representations, which is applied in the initial and final asymptotic region^.^**^^ It arises because the necessary classical generator involves inverse tri- gonometrical functions, which are returned by any computer routine as the principal value.Such discontinuities may cause errors of &(2n, + 1)n & (212, + 1)n in the phase difference between the contributing trajectories. Fig. 1 implies however that the maximum phase difference is (n, + +)n, because the total area of Ci is (n, + +)h or (2n, + l)nh, and the Airy12 and Bessel13 approximations require that the area of the smaller of the two divisions of C; by C2 should be adopted; the Laguerre14 and har- monic* approximations give the same result for either of the two areas. Hence the correct phase difference is obtained simply by adding or subtracting terms (2n, + 1)n (2n + 1)n and (2n2 + 1)n to the raw value returned by the program until the answer lies between 0 and (n, + 4)~.Given this procedure the results obtained by the different approximations are in agreement with 5 x. The Laguerre result is given below. Fig. 2 gives a comparison between the exact quantum mechanical and semi- classical results for all classically allowed transitions from the n, = 0 and n1 = 1 reactant states at energies for which the trajectories are 100 % reactive. Three features may be noted. First the semiclassical results are in good qualitative agreement with the exact Similar Bessel results are available in the l i t e r a t ~ r e . ~ ~60 PRODUCT DISTRIBUTION FROM H -/- clz results for all transitions. The quantitative agreement is typically within 0.05 probability units for transitions from the n, = 0 state, and within 0.1 probability units for the n, = 1 state.The right hand sections of the diagram show that the agreement is certainly sufficient to confirm the Condon reflection behaviour observed in the quantum mechanical results4 which also extend to n1 = 2. PO n 4 n f/eV A 0.3 0.2 0.1 * 0.1 t / e V n :::I 0.5 P,, 0.4 ::;h 0.1 1 2 3 4 5 6 7 n ( b ) FIG. 2.-Comparison between exact (solid line) and semiclassical (dashed line) transition probabilities for (a) nl = 0, (b) nl = 1. The right hand section of each diagram gives the distribution as a function of nz at E = 0.32 eV (0.117 a.u.). Points are the quantum mechanical and circles the semiclassical Secondly the major semiclassical anomaly occurs at threshold for each state al- though it is much weaker than that observed for the H + H2 reaction.31 This is tentatively attributed to neglect of possible complex trajectories (arising from complex reactant angle variables) in the construction of the uniform approximation.The available uniform approximations all require only two root trajectories but the non- sinusoidal shape of the quantum number n2 against initial angle q1 curve in fig. 3 while admitting only two real roots, suggests the possibility of nearby complex roots. A similar anomaly observed in spectroscopic applications of the uniform Airy approxi- mation3’ has recently been removed by use of a four transition point appr~ximation.~’ Finally, the energy range amenable to the semiclassical analysis, and hence to a firm prediction of Condon reflection behaviour, is sharply reduced in going from n, = 0 to n1 = 2.This reduction occurs at low energies due to the increasing threshold, and at higher energies due to the more rapid onset of competition with the inelastic channel for higher reactant quantum numbers. The factors underlying this competition are discussed in the following section in relation to the number and loca- tion of possible trapped trajectories on the potential surface. values.M. S . CHILD AND K . B . WHALEY 6 - 4- 2 - 61 1 - - I I I "2 FIG. 3.-Variation of the product quantum number n2, with modified reactant angle g1 (see Appendix for nl = 1 at E = 0.22 eV (0.0081 a.u.). 4. EXISTENCE AND SIGNIFICANCE OF TRAPPED TRAJECTORIES P e ~ h u k a s ~ ~ and, more recently, Pechukas and Pol1ack2O have underlined the im- portance of the number and location of certain periodic trajectories trapped between equipotentials of the surface.We therefore first demonstrate the existence of such trajectories for the H + C1, system and then discuss their significance for the present investigation. This is the first such study for a strongly exothermic reaction, previous investigations having been limited to the H + H2 system21 and its isotopic variants.22 Fig. 4 shows one such trajectory at E = 0.20 eV and the four most important of a possibly infinite family at E = 0.35 and E = 0.50 eV. Also shown in the lower part of each diagram is the map in reactant phase space of trajectory end points obtained by applying a small perturbation in the reactants direction at successive points along the single trapped trajectory in fig.4(a) and the two outermost trajec- tories in fig. 4(b) and (c). The single trapped trajectory, passing close to but not necessarily through the saddle point, constitutes the strict transition at this energy, and the translate of the trajectory into the reactant phase space divides this space into reactive and inelastic scattering regions. Transition state theory is exact under these conditions, with the microcanonical reaction probability given by the ratio of the reactive area to the total area within the available energy shell. Finally the percentage classical reactivity coefficient for a given quantum state is simply the fraction of the relevant orbit lying within the reaction zone.Thus the threshold for 100 % classical reactivity occurs at an energy such that the reaction zone just encloses the orbit in question. The appearance of further trapped trajectories at higher energies complicates the picture, [fig. 4(b) and (c)]. The most significant of these additional trajectories for the present discussion is the one closest to the products region, because it acts as the ultimate point of no return. Some trajectories therefore passing through the first " transition state " may fail to reach it. Hence it provides a division between the " directly reactive " and the " complex " or " snarled " trajectories. As expected in view of the complex nature of these trajectories the effect of a smaII perturbation of this product side trajectory in the reactant direction is not always to lead to reactants, but our calculations show as in fig.4(b) and 4(c) that the resulting translate forms a closed, or almost closed contour in reactant phase space, lying necessarily inside the The significance of this diagram will now be discussed. The low energy case depicted in fig. 4(a) is relatively simple.62 PRODUCT DISTRIBUTION FROM H + c12 - - - - - - - - - - - I I I I I I I 5 10 x1a.u. x/a.u. FIG. 4.-Trapped trajectories and division of the reactant phase space at (a) E = 0.2 eV (0.0074 a.u.), (b) E = 0.35 eV (0.0129 a.u.) and (c) E = 0.5 eV (0.0184 a.u.). Potential contours are given at intervals of 0.01 a.u. from -0.06 to 0.04 a.u. The axes are given by x = rHCl -I [mCl/mHCI]rCICl y =.[(mH + 2mc1)/4 mH]+rclcl. The boundary of each phase space picture is determined by the available energy. A' and B' denote the reactant contours asymptotic to the outer trapped trajectories A and B, respectively. Fig. 4(a) is divided into an inner, direct reactive, and an outer, direct inelastic, scattering region. The intermediate shaded region in fig. 4(b) and (c) belongs to the complex trajectories.M. S. CHILD AND K. B . WHALEY j2a.u. I 63 T1a.u. I ( b ) j1a.u.64 PRODUCT DISTRIBUTION FROM H -/- c12 translate of the reactant trapped trajectory. This provides a division of the available space into three parts, direct reactive, complex and direct inelastic, a division which would otherwise require a laborious examination of the nature and fate of several hundred traject~ries.'~-'~ The deeply incursive part of the inner curve at E = 0.35 eV [fig.4(b)] was in fact first charted in this way. The curve obtained is indistinguishable by eye from that shown in fig. 4(b). The significance of these results in relation to the previous discussion, is that the increasing incursion of the " complex " area into the reaction zone is directly respon- sible for the increasing preponderance of inelastic scattering at higher energy, particu- larly since, for the present system, most complex trajectories appear to be ultimately non-reactive. The effect is most marked for the higher reactant quantum numbers because the shape of the incursion cuts more deeply into this part of the reactant phase space. It therefore appears that the dominant features of the reaction may be understood without reference to the central, dashed periodic trajectories in fig.4(b) and 4(c). These differ in nature from the outer trajectories in that trajectories starting from neighbouring points on the equipotential appear to run towards and then cross them, whereas those starting close to the outer ones always diverge away from them. It is conjectured that the former are closely associated with the observation of reactivity bands 17-19,25,35 and also possibly with the existence of quantum mechanical reso- nances.'P2 Many questions related to the existence of stable classical motions in regions far from the saddle point remain, however, to be investigated. 5. CONCLUSIONS Existing semiclassical theory based on real classical trajectories from states which are 100 % reactive has been tested, and shown to be typically accurate to 5-10 %.The most serious anomaly occurs at threshold. The energy range over which such calculations can be performed, and hence over which a firm prediction of Condon reflection behaviour can be made, decreases sharply with increasing reactant vibrational state, due to significant branching between reactive and inelastic scattering. The ranges found in the present study are 0.15-0.5 eV at n, = 0 and 0.2-20.32 eV at n, = 1. It has been shown that the present H + CI2 surface can support not merely a single " transition state trapped trajectory " passing close to the saddle, but that at higher energies whole families of such trajectories exist.These provide insight into the occurrence and nature of complex or snarled trajectories. They also offer a simple device for mapping the reactant phase space into direct reactive, direct inelastic, and complex trajectory end points. The authors are grateful for stimulating discussions with Dr. P. M. Hunt and One of them (M.S.C.) wishes to acknowlege the hospitality of the Dr. E. Pollack. Hebrew University, Jerusalem where the final part of this work was completed.65 M . S . CHILD AND K . B . WHALEY APPENDIX The conventional modified angle variable 1 5 9 1 6 q is defined in terms of the true angle q,36 the local vibrational frequency o, and the translational coordinate R, momentum P and reduced mass m Q = q - mcoR/P. An associated modified coordinate r‘ and momentump may be defined by substituting for q in the appropriate formulae for the type of oscillator in que~tion,~’ which is a Morse oscillator in the asymptotic parts of a LEPS surface.Any semiclassical results are, however, invariant to a further modification of the form because the Jacobian [(t, n)/(q, n)] is unity. The definition 4 = Q + y ( 4 y ( n 2 ) = - 3 [ q a ( n 2 ) + qb(n2)1 (3) where qa(n,) and q b ( n 2 ) are the modified angles derived from the two root trajectories from the given n, to any n2, has been used to obtain the symmetric representation in fig. 1. S. F. Wu and R. D. Levine, Mol. Phys., 1971, 22, 881. D. J. Diestler, J. Chem. Phys., 1972, 56, 2092. M. S. Child, Mol. Phys., 1978, 35, 759. M. Baer, J. Chem. Phys., 1973, 60, 1057.M. J. Berry, Chem. Phys. Letters, 1974, 27, 73. U. Halavee and M. Shapiro, J. Chem. Phys., 1976,64,2826. B. C. Eu, Mol. Phys., 1976, 31, 1261. G. C. Schatz and J. Ross, J. Chem. Phys., 1977, 66, 1021, 1037. A. M. G. Ding, L. J. Kirsch, D. S. Perry and J. C. Polanyi, Faraday Disc. Chem. Soc., 1973, 55, 252. lo C. A. Parr, J. C. Polanyi, W. H. Wong and D. C. Tardy, Faraday Disc. Chem. SOC., 1973, 55, 308. l1 P. 3. Kuntz, E. M. Nemeth, J. C. Polanyi and C. E. Young, J. Chem. Phys., 1966,44, 1168. l2 J. N. L. Connor and R. A. Marcus, J. Chem. Phys., 1971, 55, 5636. l3 J. R. Stine and R. A. Marcus, J. Chem. Phys., 1973, 59, 5145. l4 M. S. Child and P. M. Hunt, Mol. Phys., 1977, 34,261. l5 W. H. Miller, J. Chem. Phys., 1970, 53, 3578. l6 W. H. Wong and R. A. Marcus, J. Chem. Phys., 1971,55, 5663. l7 J. S. Wright, K. G. Tan and K. J. Laidler, J. Chem. Phys., 1976, 64, 970. J. S. Wright and K. G. Tan, J. Chem. Phys., 1977, 66, 104. l9 K. G. Tan, K. J. Laidler and J. S. Wright, J. Chem. Phys., 1977, 67, 5883. 2 o P. Pechukas and E. Pollak, J. Chem. fhys., 1977, 67, 5976. 21 E. Pollak and P. Pechukas, J. Chem. Phys., 1978,69, 1218. 22 D. I. Sverdlik and G. W. Koeppl, Chem. Phys. Letters, 1979, in press. 23 C. C. Rankin and W. H. Miller, J. Chem. Phys., 1971, 55, 315a. 24 J. M. Bowman and A. Kuppermann, Chem. Phys., 1973, 2, 158. 25 J. W. Duff and D. G. Truhlar, Chem. Phys., 1974, 4, 1 . 26 J. W. Duff and D. G. Truhlar, Chem. Phys., 1975,9,243. 27 S . J. Fraser, L. Gottdiener and J. N. Murrell, Mol. Phys., 1975, 29, 415. 28 W. H. Miller, J. Chem. Phys., 1970, 53, 1949. 2 9 R. A. Marcus, J. Chem. Phys., 1973, 59, 5135. 30 K. B. Whaley, B.A. Pt II Thesis (Oxford University), unpublished. 31 J. M. Bowman and A. Kuppermann, J. Chem. Phys., 1973,59, 6524. 32 0. Atabek and R. Lefebvre, J. Chem. Phys., 1978, 67,4983. 33 P. M. Hunt and M. S. Child, Chem. Phys. Letters, 1979, in press. 34 P. Pechukas in Dynamics of Molecular Collisions, Part B, ed. W. H. Miller (Plenum Press, New 35 J. W. Duff and D. G. Truhlar, Chem. Phys. Letters, 1976, 40, 251. 36 H. Goldstein. Classical Mechanics (Addison-Wesley, N.Y., 1950). 37 D. G. Truhlar, J. A. Merrick and J. W. Duff, J. Amer. Chem. Soc., 1976, 98, 6771, York, 1976), chap. 6.

ISSN:0301-7249    

DOI:10.1039/DC9796700057

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Distribution of Reaction Products (Theory) Part 12.-Microscopic Branching in H + XY --+ HX + Y, HY + X (X, Y = Halogens) BY J. C. POLANYI, J. L. SCHREIBER $ AND W. J. SKRLAC t Department of Chemistry, University of Toronto, Toronto M5S 1A1, Canada Received 29th December, 1978 3D trajectory studies are reported for several potential energy surfaces that could serve as models for the reaction H + ICI. This reaction exhibits macroscopic branching to give HCl + I or HI + CI. The surfaces yielded product energy distributions suggestive of significant bimodality in the HCI product, but not the HI; i.e., there was evidence of microscopic branching for the macroscopic branch involving reaction with the more electronegative of the halogen atoms, X. All of the surfaces were characterised by a barrier to approach of H at the C1 end of IC1, but attraction at the I end, in conformity with evidence from molecular beam studies regarding the stability of complexes HYX in contrast to HXY (electronegativity xx > xu).Extensive calculations were performed on one of these surfaces for room temperature (T,",AN, = 300 K) and elevated translational temperature (T,"RANS = 2685 K). The findings were in qualitative accord with the bimodal vibration-rotation distributions of HX observed in infrared chemiluminescence studies of reactions of the type H + X Y . The bimodal distribution could be identified with two dynamically different paths for HCI formation (microscopic branching). The HCI formed with the lower internal energy, Ein,, resulted from reaction of H directly at the C1 end of ICI, whereas the HCI formed with higher Eint was produced by migra- tion of H from the I to the Cl, following a lingering interaction of H with I.Migration occurred late in the encounter, by insertion of H into the extended I-C1 bond. The collision energy dependence of these two microscopic branches (" direct '' and " migratory ") differed notably. The probability of direct reaction, since it involved barrier-crossing (E, = 1.6 kcal mol-'), increased steeply with col- lision energy, whereas the probability of the migratory dynamics fell (E, = 0 kcal mol-' from the I end). As a consequence the HC1 product vibration-rotation distribution altered markedly in going from ETORANS = 300 to 2685 K, in qualitative accord with the findings from an infrared chemilumi- nescence study.By contrast the energy distribution for the other product, HI, showed insignificant bimodality at 300 K, and no dramatic change in product vib-rotational distribution in going to 2685 K; microscopic branching appeared to be negligible for reaction to form HI. This paper presents a model study of the reactions of hydrogen atoms with inter- halogens, XY. The objective was to gain qualitative insight into some of the gross features of these reactions, which have recently become apparent. Two prominent features are the following: (only the first of these features was known when the present calculations were begun). (1) There is a tendency for reaction with one atom of XY (e.g., -+ HX) to yield a bimodal product energy-distribution, and reaction with the other (-+ HY) to yield a " normal " product energy-distribution similar to that observed in reactions H + Y2 --+ HY + Y.The bimodality in the HX product distribution has been termed " microscopic branching ", in order to distinguish it from the " macroscopic branch- ing" to yield the different chemical species, HX and HY. It appears that the $ Present address : Franklin and Marshall College, Lancaster, Pennsylvania 17604, U S A . t Present address: Lumonics Research Ltd, 105 Schneider Rd., Kanata, Ontario K2K lYE, Canada.J . C . POLANYI, J . L . SCHREIBER A N D W . J . SKRLAC 67 halide which gives the anomalous product distribution is the one which contains the more electronegative of the atoms, i.e., the electronegativities are characteristically xx xY.1-3 (2) At moderately enhanced collision energy the anomaly in the HX product ._ energy-distribution, i.e. the microscopic branching, is no longer obser~ed.~ The experiments which have yielded this type of information have been principally infrared chemiluminescence studies. These included studies of the reaction H + ICl + HCl + I, which exhibited marked bimodality in the product energy-distribution for HCl with 300 K reagent~l-~ and no bimodality with the same reagents at 2685 K (mean collision energy % 10 kcal m ~ l - ' . ~ A molecular beam investigation of the closely-related reaction D + ICl--+ DCl + I at a similar enhanced collision energy gave no evidence of bimodality in the product di~tribution.~ The same was true of the product angular and translation energy distribution from a beam study of the alternative macroscopic branch, D + ICl- DI + C1, at the same enhanced collision energy.'j Experimental information for the H + XY reaction H + BrCl with thermal (300 K) reagents is more complete, since both macroscopic branches were amenable to study by infrared chernilumine~cence.~ Reaction with the more electronegative halogen atom (Cl) gave rise to molecular product (HCl) with a bimodal product energy distribution, i.e. this macroscopic branch exhibited microscopic branching.The other macroscopic branch, by contrast, did not; the chemiluminescence from the HBr product was indicative of a singly-peaked product energy-distribution resembling (though not identical to) that for HBr formed in the reaction H + Br,.Experiments on this system at enhanced collision energy have not yet been reported. The reaction is H + CIF -+ HF + C1 or HC1 + F.7 Once again both macroscopic branches were studied in detail. In this case (cf. H + ICl and H + BrCl) the C1 atom was the less electro- negative of the halogen atoms in XY. As had been predicted the HC1 exhibited a unimodal distribution resembling the product of H + C12+ HC1 + C1, whereas the HF product energy distribution had an anomalous form characteristic of micro- scopic branching. Bimodality of product energy-distribution is not unique to the systems H + XY. In earlier experimental work bimodality over product vibrational excitation appeared to be present for H + C12f -+ HCl + C1 (the dagger indicates vibrational excita- tion).' The theoreticaI interpretation, based on 3D cIassicaI trajectory studiess9l0 in- volved a type of branched pathway across the potential-energy hypersurface, i.e., Cl,t in its contracted vibrational phase reacted by way of compressed intermediate configurations, and C12t in its extended phase reacted through stretched intermediate configurations.' This represents a species of microscopic branching.There was also experimental evidence for a bimodal distribution over product rotational energy states. This was observed in the hot-atom reactions C1 + HI --+ HC1 + I ' v l l and H + C12+ HC1 + C1,* as well as in the thermal reaction H + SC1, -+ HC1 + SC1.12 This phenomenon has not yet been the subject of a theoretical study. The model proposed in each cases*1'*12 involved, once again, the existence of two characteristic paths across the potential-energy hypersurface.The paths, in these cases, were conceived of as being a direct path in which the attacking atom A reacted with the end of BC to which it makes its first approach, e.g., A + BC-+ ABC+ AB + C, and an alternative " indirect " path in which A interacted first with (say) C and thereafter migrated to B, i.e., A + CB --+ ACB -% CAB -+ C + AB; i.e. the same chemical products but in different states of excitation (m indicates migration). In the case of the hot-atom reactions the migration stemmed, presumably, from A further reaction H + XY has been studied recently.68 DISTRIBUTION OF REACTION PRODUCTS momentum initially present in the attacking atom A, which caused A to skip (like a stone on water) from one end of CB to the other.The picture outlined in the previous paragraph was speculative. The speculation rested on frequent observation of migratory encounters in early (2D and 3D) trajec- tory studies involving a variety of approximations to the potential-energy hypersurface for reactions of alkali metal atoms with halogens, M + XY.', The system H + XY, which inspired the present study, offered an opportunity for examining the viability of the " direct " versus " migratory " hypothesis in a case where an observed bi- modality of product internal excitation lent particular credence to the microscopic- branching model. A preliminary report on the present 3D trajectory work has already appeared.14 The findings indicated that the direct, as compared with the migratory, hypothesis was indeed a possible one.The trajectory results were in general accord with our earlier c o n J e c t ~ r e ~ * ~ * ~ * ~ ~ * ~ ~ that the part of the product with lower internal excitation involved predominantly direct reaction, with a lower average impact parameter (b), whereas the product exhibiting higher internal excitation derived to a significant extent from migratory encounters characterised by a higher value of (b). The trajectory results indicate that there exists a dynamical link between the macro- scopic and microscopic branching.', The conceptual basis for this link is easily e~ernplified.~ If the approach of A to the B end of BC involves a significantly lower activation barrier than does approach of A to the C end, then (a) AB will be formed by direct reaction and in good yield, whereas (b) AC will be formed by migration plus direct reaction, i.e., AC can exhibit microscopic branching.The total yield of AC will depend on the sum of the probabilities of migration from B plus direct reaction at C. However, until the factors governing the likelihood of migration are made explicit, the interdependence of macroscopic and microscopic branching will involve a weak link. It is interesting, nonetheless, to set this deterministic picture alongside the alterna- tive viewpoint that stems from information theory.15 We have not applied informa- tion theory in the present paper. Ref. (3) shows that the simplest formulation of information theory is insufficient to account for the (macroscopic) branching ratio in H + BrCl. An important contributory cause is likely to be the failure of information theory in its customary formulations to include the effect of differing activation bar- riers for reaction at either end of the molecule under attack.A recent study suggests that this omission can be serious even in the case that the molecule under attack involves chemically similar atoms, the branched reaction being F + HD -+ HF + D or DF + H.16 The conception of alternative direct and migratory reaction dynamics has been employed in a recent beam plus gas study of the system Ba + CF,I -+ BaI + CF3.17 Laser-induced fluorescence indicates a vibrational distribution in BaI that is bimodal. The reaction is postulated to proceed by two mechanisms; direct reaction at the I end of ICF3 with lower (b), and migratory reaction from CF, to I with higher (b).The former process causes BaI to rebound in the backward direction; the latter causes the BaI to be scattered forward with higher vibrational excitation. Similarly it has been proposed l8 that the marked difference in dynamics observed I 9 l t 0 between K + ICH3 -+ KI + CH, and K + CF31 -+ KI + CF, could be due to direct reaction with backward scattering of KI in the former case and migratory reaction with forward scattering of KI, K + CF31 --+ K+CF3-I _", CF3 + K'I-, in the latter case. The most facile migration would be expected to be that of a light atom between slowly-moving heavy atoms.I4 In the reaction H + YX, with which the present paper and its precursors dea1,2v3p14 the light atom is the attacking one, and the inter-J .C . POLANYI, J . L . SCHREIBER AND W. J . SKRLAC 69 mediate HYX (xx > x y ) holds together amply long enough for H to migrate from Y to X. It has recently been pointed out2' that, if X is incident on YH, the same dynamics should apply. Specifically the proposal is that in the reaction Cl + HI -+ HCI + I the atomic motions can be described as C1 + H I 5 ClIH -+ CIHI+ HCl + I, where m indicates, once again, migration of the H. In atomic reactions with polyatomic molecules the attacking atom may react at more than one site to give chemically identical but energetically distinguishable product species. This " alternative site " branching has much in common with macroscopic branching, since it does not involve differing modes of approach to the identical atom, but single modes of approach to differing regions of the molecule under attack.Alternative site branching is exemplified by the case of HF formed in the reaction of F + HCOOH and also F + HCH0.22 One can envisage more complicated situations in which the attack at a given site on the polyatomic can occur by alternate dynamics (e.g., directly or through migration) with the consequence that true microscopic branching is superimposed on alternative site branching. POTENTIAL ENERGY SURFACES AND METHOD OF CALCULATION The dynamics of the model H + XY reaction were assumed to be governed by a single potential energy surface. While energetically allowed, the reaction path H + IC1+ HC1 + I*, producing electronically excited I atoms, is ~nimportant.~ The form of this single potential surface was obtained from the extended London- Eyring-Polanyi-Sat0 (LEPS) equation, used in many previous studies of hydrogen- halogen reactions.23 In this formulation, the interaction potential of the triatomic system is determined by the spectroscopic constants of the diatomic fragment mole- cules, and the " Sat0 parameters ", Si, associated with the three bonds i-HX, HY, XY.Since the HICl system showed the most dramatic bimodality of the systems then studied, the spectroscopic constants of this system were used to specify the potential and the corresponding masses were employed in dynamical calculations. The parameters are listed in table 1 [following the notation of ref. (24), with 3/3 = '/3 in all cases].TABLE 1 .-PARAMETERS EMPLOYED TO GENERATE POTENTIAL ENERGY SURFACES ~~ ~~ parameters common to all surfaces (D, F, G and H) HI IC1 HCI 'Dlkcal mol- 73.78 50.30 106.41 y / A - 1.750 1.847 1.868 re/A 1.604 2.321 1.275 ~~ parameters specific to individual surfaces surface S I C , S"C, E,(H + CII+ HCl t I) E,(H + IC1+ HI + C1) AL(H + CII + HCI + I)/% &(H -t IC1+ HI + Cl)/% S H I A 0.7 0.0 0.2 0.00 0.00 53.6 88.8 B 0.7 0.0 0.0 1.68 0.00 50.0 87.9 C D 0.7 * 0.7 -0.2 -0.1 0.05 0.025 1.52 1.59 0.00 0.00 24.3 37.5 71.6 85.370 DISTRIBUTION OF REACTION PRODUCTS A variety of potential surfaces, differing only in the values of the Si, were con- sidered. Basing our studies on the hypothesis described in the previous section we selected the Si so as to produce surfaces with an attraction between H and the I end of ICl, but a barrier to approach of H toward the C1 end of ICI.Exploratory compu- tations pexformed by C. A. Parr in this laboratory gave evidence of direct and migra- tory trajectories on several surfaces of this type, including surface A of this paper. The work was not, however, pursued to the point where a statistically meaningful product energy distribution was obtained. The classical barriers for the four surfaces on which dynamical calculations were performed are given in table 1, along with a crude measure of product energy release, All% [ref. (24) and references therein]. Typical of the surfaces considered is surface D. Fig. 1 gives the customary collinear cuts through this potential surface.The contours show the barrier to approach of H toward C1 along the ClI axis [fig. l(a)], and the long range attraction of I toward H [fig. l(b)]. For each of the four surfaces considered, classical trajectory calculations were performed to determine the product energy distributions in the two product channels. The initial conditions were selected to simulate a 300 K thermal distribution of re- I I 1 I I 1 1 - 1.0 2.0 3.0 4 .O 5 .O 6 .O [ , / A 20 10 5 2 1 1 2 5 10 20 30J . C . POLANYI, J . L . SCHREIBER AND W. J . SKRLAC 71 FIG. 1.-Collinear potential energy plots of surface D: (a) H i- C11+ HC1 + I, (b) H + IC1+ HI + C1. Note the substantial differ- ence in appearance. For (a), there is a barrier in the entry valley, while in (6) the entry valley is Both plots are presented in skewed and scaled coordinates.characterised by a long-range attraction. agent translational energies and internal states. Trajectories were begun at an initial separation of H from the XY centre of mass of 8 A. The range of impact parameters was subdivided into 0-4 and 4-6 A, and stratified sampling procedures were used to compute all averaged product distribution^.^^ Integrations were performed with a fixed step size fourth-order predictor-corrector numerical integration algorithm of the Adams-Moulton type26 with a step size of 3.0 x The effect of reduced step size on the outcomes of these trajectories is discussed below. A substantial fraction of the trajectories computed in the 300 K batch showed complex behaviour associated with migration of H between I and C1.A detailed s.72 DISTRIBUTION OF REACTION PRODUCTS study of the effect of reduced step-size on the outcome of selected complex trajectories was made. This showed that, while the values of the product energies (V’, R’, T’) for a given product (say HCl) were unaffected by reduction of the step size below 3.0 x s, the nature of the product in some of the trajectories changed as the step size was reduced (ie., HI became the product, for the example cited). A step size of 0.75 x s proved adequate, in the group of 2000 trajectories that were re-run, to give product identity and product attributes invariant with further reduction of step size. s one third of the complex trajectories leading to HC1 switched either to HI or to unreactive outcomes.However, a comparable number of other trajectories, which had given HI or no reaction at the larger step size, gave HCl at the reduced step size. Product distributions for the two groups were compared, and found to be similar. All the conclusions reported here are based on the large step size batch; the calculations using a reduced step size would, we believe, not differ in any significant aspect. Fig. 2 shows the product vibration-rotation distributions obtained for HCl from preliminary studies of surfaces A, B and C, and a more extensive study of surface D which will be described below. While the sample sizes are modest ((100 reactive trajectories for all but surface D), it is clear that all of these surfaces show a more complicated product distribution than has been observed either experimentally or computationally for H + X2 systems.The presence of HC1 in quite high rotational levels is particularly notable. The product distribution of the 300 K H + X2 series is characterised by low product rotational energies (e~perimentally~’?~~ and theoretic- Since the HC1 product distribution from surface D showed the greatest similarity to the experimentally observed distribution from the H + ICl reaction, it was used as the subject of more extensive calculations. In excess of twelve thousand trajectories were run using the initial conditions described above. In addition, three thousand trajectories were run with initial conditions simulating H atoms produced from a 3000 K oven, reacting with IC1 in a 300 K thermal distribution of internal states (effective translational temperature; T&ANs = 2685 K).These latter conditions simulated the reagent energy in experiments of Hudgens and M~Donald.~ At the step size 0.75 x >. ally 8,23,29 - 31 RESULTS ROOM TEMPERATURE The bimodality in product vi bration-rotation energy distribution suggested by preliminary calculations on surface D was confirmed by the more extensive calcula- tions. Fig. 2(D) is the result of the large-scale calculation, done for a 300 K distribu- tion of energies, on surface D. Fig. 3 shows the product translational energy against T’ distribution for both the HC1 and the HI product as given by the 300 K calculation on surface D. The HCl dis- tribution shows a marked peak at low T’ (low product translational energy and conse- quently high internal energy, vibration plus rotation, V’ + R’ = Eint).There is also a broad shoulder on the distribution, extending out to high T’ (low Ef,,). No such bimodal stiucture is apparent in the T‘ distribution for the HI product. We have divided the HC1 products into the two groups suggested by fig. 3(a), for the sake of further discussion. Those with T’ < 15 kcal are termed “ high Eint ”, and those with T’ > 15 kcal, “ low Ef,, ”. These two groups differ notably in other aspects of their product distributions, as summarised in table 2. In fig. 4(a) and 4(6) we show the “ triangle plot ” of fig. 2, surface D, separated into triangle plots for theJ . C . P O L A N Y I , J .L . SCHREIBER A N D W . J . SKRLAC 73 6ot -0 10 20 30 LO 50 60 R'lkcal mot-' 0 10 20 30 LO 50 60 R'l k c a l mol-' - I 0 d E d a u Y ..\ L 0 10 2 0 30 40 50 60 50 LO 30 20 10 ~~~ 0 10 20 30 LO 50 60 R ' / k c a l mol-' R ' l k c a l mol-' FIG. 2.--" Triangle plots " giving product vibration-rotation energy distributions for HCl product of H + ClI, obtained from 3D classical trajectory calculations using potential energy surfaces A, B, C and D (characterised in table 1). In all cases initial conditions were selected to simulate a 300 K thermal distribution of collision energies and reagent CII internal states. Bimodality is apparent to a greater or lesser degree in the results of all four calculations. Variation of the surface parameters had the effect of varying the relative proportions of products from the two microscopic branches, and of altering the product vibrational excitation of the " direct " branch at the left of each triangle. high Ei,, and low Ei,, components of the HCl product.The distribution for the low Ei,, group [fig. 4(b)] is similar to that of HCl produced by H + C12.27 The distribution of the high Elnt group [fig. 4(a)] is markedly different, resembling that for HC1 produced by Cl + H1.25932 Fig. 5 shows the vibration-rotation distribution of the HI product for this same calculation. There is a single " ridge " of high probability extending from Y' = 30, R' = 0 to Y' = 0, R' = 10 kcal mol-'. Our statistics do not permit us to say whether the small double peak along this ridge is real. It is of interest to examine the contributions of the low E;,, and high ,Tint com- ponents to the overall distribution of HCI over product vibration, u ' ; this is shown in fig.6. The vibrational distribution of the high Ei,, group is broader, and is74 DISTRIBUTION OF REACTION PRODUCTS displaced to significantly higher vibrational levels than that of the low Eint group. The two distributions overlap considerably, and the bimodality only evidences itself as a shoulder on the overall HCl distribution. While surface D predicts bimodality of product distribution similar to that of the experimentally observed distribution, it fails to match the experimental di~tribution.~ The ratio between the total amounts in the low Ei,, and high Eint groups is 0.72 for 1 I la 1 - I 0 5 10 15 20 25 30 35 1 FIG.3.-Product translational energy distributions from H + ICI, for a 300 K thermal distribution of initial conditions : (a) relative translational energy distribution of HCl + I, (6) relative translational energy distribution of HI + C1 (the T’ were the exact values computed for each trajectory; cf. fig. 4). In (a) the low T‘component of the HCl + I distribution corresponds to high internal excitation (high ,!?in*), and is associated with large values of V’ and/or R’. The high T’ portion corresponds to low Eint, and hence to lower V’ and R‘. No structure is apparent in the distribution of the HI + CI relative translation in (b). T ’ / kcal mol-’ surface D, while experimentally a similar division of the product HCl into two groups gave a ratio of only 0.25.As noted in the Introduction we regard surface D as no more than a model capable of giving us qualitative insight into some of the gross features of reactions H + XY. For completeness, fig. 6(b) shows the product vibrational distribution of HI. It is essentially flat over the range u’ = 0-2, with no significant indication of bimodal structure along the length of the “ ridge ” mentioned in the discussion of fig. 5. There are no experimental data regarding k(u’) for the HI product of H + ICl. The angular distributions of both HCl and HI are found to be broad and structure- less (fig. 7). While no experimental evidence is available on the angular distributions for this range of collision energies, higher energy data, discussed below, suggest thatJ .C . POLANYI, J . L . SCHREIBER AND W . J . SKRLAC 75 R’/ kcal rnol -’ 50 LO 30 20 10 0 10 20 30 LO 50 60 R ’ / kcal mol -’ FIG. 4.-Triangle plots of product vibration-rotation energy distributions of the (a) high ,Tint and (6) low Eint components of the HCl + I product of H + CII, with 300 K thermal initial conditions. The T’ values indicated on these two triangle plots, and all other such plots, are approximate values determined on the assumption of a fixed total energy in all products (this assumption is not precisely correct for a thermal distribution of initial conditions).76 DISTRIBUTION OF REACTION PRODUCTS 30c 0 R'kcal mol -' FIG. 5.-Product vibration-rotation energy distribution of the HI + Cl product of H + ICl with 300 K thermal initial conditions.In contrast to the results shown in fig. 1 for surface D, the HI product shows no marked division into low and high EinC fractions. the angular distributions are probably poorly represented by the results of these calcu- lations. As noted below, this should have little effect on the observations regarding the broad features of microscopic branching mechanisms. HIGH TEMPERATURE The results of the 2685 K batch of trajectories, intended to mimic the experimental conditions of Hudgens and M~Donald,~ are shown in figs. 8-1 1. While the HI product translational energy, T', distribution is hardly altered, the HCl distribution has been considerably changed. Only one peak is apparent, with a maximum at x 30 kcal mol-'. The maximum in the large peak (high EinJ of the 300 K HCl T' distribution, shown previously in fig.3, was below 10 kcal mol-', while that of the broad shoulder at 300 K (low Eint) was between 20 and 30 kcal mol-l. As is discussed below, the high Eint group has decreased markedly in importance with increasing translational temperature, so that the T' distribution is dominated by the low Eint group. This observation is supported by the general form of the HC1 vibration-rotation distribution [fig. 9(a)]. The 2685 K triangle plot closely resembles that obtained ex- perimentally at similarly enhanced collision energy for the reaction H + C12+ HCI + C1.* Since it is the low Eint component of the (300 K) HC1 product distribu- tion [fig. (4b)l that resembles H + C12+ HCl + C1, it is reasonable to suppose that it is the " low Eint " mechanism that is the dominant one at 2685 K.The significance of this proposition, as well as further evidence to support it, will emerge from the more detailed analysis to be found in the following section. Once again we find that our model surface (surface D) is only qualitatively in3 . C . POLANYI, J . L . SCHREIBER AND W . J . SKRLAC 77 o Oi2 0.4 I- T 1.0 x - E -L \ e - 0.5 - - 0 1 2 3 4 V ' FIG. 6.-Relative distribution among vibrational states, of products of H + IC1 with 300 K thermal initial conditions. (a) HCl product (-). The component distributions for low Eint (---) and high Eint (- -) are also shown, normalised so that the sum of the two equals the overall distribution. (Note that f; values indicated on the upper scale are determined in the approximation of a fixed total energy).(b) HI product. To within one standard deviation, the populations of u' = 0, 1 and 2 are all equal for HI.78 DISTRIBUTION OF REACTION PRODUCTS accord with experiment. Hudgens and McDonald4 found that the bimodality shown in fig. 1, surface D, of the present study [and more clearly in fig. 4(a) and (b)] was still discernible in the HCl product of the reaction H + ICI at 2685 K. Our surface D, as noted above, yields an excessive fraction of the low &'nt component at 300 K (roughly 3 times too Much relative to the high Eint, when compared with experiment); consequently at 2685 K the enhanced importance of the low Eint mechanism has the result that this component completely overshadows any contribution from the high 0.4 / a ) 1.c I I I I 0 40 80 120 160 I I I I 8,t,;, I I I 1 160 120 80 LO 0 e f h o l FIG. 7.-Product differential cross-sections for H + ICI with 300 K thermal initial conditions. (a) HCl product: overall (-), low El,,, (- - - -), high Eint (- -). No discernible difference is obtained between the angular distributions of the two fractions. (b) HI product. Eint mechanism that may be hidden in the product energy-distribution recorded in fig. 9(a). The important observation for the present model-study is that the shift toward a greater contribution of the low Eint dynamics at the higher translational temperature is clearly evident in the experimental The product vibration-rotation distribution of HI [fig. 9(b)] shows no such sub- stantial change with increasing translational temperature.The change that does occur is that the mean fraction of the total energy entering product vibration decreases (from 0.34 to 0.22) and the fraction entering rotation and translation increases corre- spondingly (see table 2). This is in accord with the normal pattern of behaviour noted experimentally and theoretically for a number of simple reactions [e.g., ref. (8) and (31)]. The effect of increased TTORaNs on the distribution over u' is shown for the HC1J . C . POLANYI, J . L . SCHREIBER AND W . J . SKRLAC 79 product in fig. lO(a). Once again the finding is in accord with the notion that the low Eint mechanism for HCI formation dominates at 2685 K on surface D. The maximum of the curve of relative k(u’) lies between u’ = 2-3.This corresponds to a modest downward shift from the low El,, distribution pictured in fig. 6(a), which peaks at u’ = 3-4. It does not resemble the high El,, curve of fig. 6(a), at u‘ = 5-6. I I I , , , I ! I , , , , T y kcal mol -’ 0 10 20 30 4 0 50 60 FIG. 8.-Product relative translational energy distributions for H + ICI with 2685 K thermal initial conditions: (a) HCI product, (6) HI product. The maximum in the HCI distribution has shifted from 10 kcal mol-’ [fig. 3(a)] to 30 kcal mo1-’, while the HI distribution is practically unchanged. The k(u’) for HI [fig. 10(b)] at 2685 K have also shifted to lower levels as compared with k(u’) at 300 K [fig. 6(b)]. Since table 2 shows that the cross-section for reaction has dropped by an order-of-magnitude (Le., the rate constant has dropped to 0.4 times) we conclude that this decrease has mainly affected the levels v’ = 2-3.The angular distributions at the higher translational temperature (fig. 11) are again flat and featureless ; they resemble the lower temperature results. The experi- mental findings for the higher energy range show the HC1 product to be primarily backward ~ c a t t e r e d , ~ ~ much like H + C1, at the same energy, while the HI product (as judged from the DI angular distribution obtained from D + TC1) is sideways peaked. Computational studies by McDonald29 and by Blais and Truhlar3* on the effect of potential anistropy on the angular distribution in systems with a L + HH mass - -80 DISTRIBUTION OF REACTION PRODUCTS R ' / kcal mol -' I bl 30 - 0 10 20 30 R'/ kcal mol -' FIG. 9.-Product vibration-rotation energy distributions for H + 1C1 with 2685 K thermal initial conditions: (a) HCI product, (b) HI product.There may be bimodality in (b). Bimodality is no longer apparent in (a).J. C . POLANYI, J . L . SCHREIBER AND W . J. SKRLAC 81 combination suggest a close connection between these two aspects, but little connec- tion between potential anisotropy and product energy distribution from their surfaces which exhibit repulsive energy release. We expect that the same conclusions would apply to the more complex trajectories we have observed, as the HICl " complexes " do not appear to rotate significantly during the period of close interaction, so that the direction of separation of HC1 and I is still determined in large measure by the angle between the initial ICl bond orientation and the initial direction of approach by the H [see also ref.(34)-(36)]. Appropriate modification of the angular anisotropy of surface D might produce the experimentally observed scattering patterns without significantly altering the prod- uct energy distributions of the two microscopic branches. In fact these latter attri- butes are also in need of alteration if the experimental findings for H + ICl are to be matched quantitatively. DISCUSSION Separation of the HC1 product into a low internal energy (" low Eint ") and a high internal energy (" high Eint ") components, on the basis of fig. 3, permits us to compute cross-section functions, a(T), for the differently excited categories of product molecules.This is made possible by the fact that the k(T') in fig. 3 is the result of a batch of trajectories Monte Carlo selected from a 300 K reagent translational distribu- tion. The individual trajectories can be totalled within successive intervals of reagent translation, T, to yield the cross-section functions recorded in fig. 12. Fig. 12 indicates once again (see the previous section) that the type of dynamics f : I. a Y 0 E 3 0.5 L \ * C 1 I 1 2 3 4 5 6 7 0 9 V'82 DISTRIBUTION OF REACTION PRODUCTS f : V' FIG. 10.-Relative distribution among vibrational states, of products of H + ICl with 2685 K thermal initial conditions: (a) HCI product, (b) HI product. associated with low Eint is becoming more probable as 7' increases, and that the contrary is the case for high Eint dynamics; we surmise from this that the low El,, reaction mode involves the crossing of a potential barrier, whereas the high E;,, does not.Experimental evidence for a declining cross-section in reactions H + X2 pro- ceeding across a negligible barrier has been obtained recently ; 37 theoretical evidence has been available for some time p a ~ t . ~ ~ . ~ ' Table 2 lists activation energies for the low Eint and high Eint components of the HC1 product; they are 1.36 and 0.10 kcal mol-', respectively. Hudgens and Mc- Donald4 compared their experimentally determined yields of low Eint and high Eint HCl for the reaction H + IC1 at high temperature with Polanyi and Skrlac's relative yields at room temperat~re,~ and concluded that the difference in activation energies must be at least 1.1 kcal mol-l, which is in agreement with the results on surface D.The existence of a higher energy barrier for the formation of the low Eint HCl product than the high Elnt component, is in accord with the model proposed in earlier communications from this The model is summarised in the Intro- duction. The low Eint product is formed as the outcome of direct reaction at the C1 end of ClI. Approach from this end of IC1 requires that the system surmount a bar- rier. The high E;,, product is formed by migration from the I end of IC1 to the C1. There is no barrier to approach at the I end, hence there is an energetic advantage to forming HCI by migration from the I end. By contrast it is energetically disadvan-J .C . P O L A N Y I , J . L . SCHREIBER A N D W . J . SKRLAC 1.2 I I I I I 1 I I 4 0 . 4 c IL 4 b 3 ul N \ - u u IN - 1.6 Ol t T 83 FIG. 1 1 .-Product differential cross-sections for products of H + ICI with T;,,, 2685 K therma initial conditions, (a) HCI product, (6) HI product. tageous to form the alternate product, HI, by migration from the C1 end of the molecule, since the C1 end is blocked by an energy barrier. Fig. 13(a) shows equipotential contours for H approaching ICl when the molecule is fixed at its equilibrium bond length, 2.321 A. Approach of H toward C1 requires a minimum of 1.0 kcal mol-l to surmount the barrier. This barrier is only slightly higher for direct collinear approach than for approach from the side; i.e., the cone-of- approach is broad.It is evident that H experiences an attractive force towards the84 DISTRIBUTION OF REACTION PRODUCTS I end of ICI (once again with a wide cone of approach). This is consistent with the proposed model, which describes the second route to HC1 as passing through an inter- mediate in which H is bound to I, but is transferred to Cl before the heavy particles C1 and I separate to such an extent that " migration " is precluded. We have examined bond and force plots of randomly selected trajectories in both groups of HCl products. The following conclusions may be drawn. For the low TABLE 2.-RESULTS OF TRAJECTORY CALCULATIONS ON SURFACE D HI overall <f$> 0.59 <fRI> 0.13 <fi) 0.28 @/A' 3.10 Eac/kcal mol-l 0.63 no. of react. trajectories 356 <e>,,a/o 93 low EI,, 0.48 0.07 0.45 1.30 1.36 87 152 high Eint 0.67 0.34 0.1 8 0.26 0.15 0.40 97 87 1.80 10.36 0.10 0.01 204 1160 <f;> 0.37 < f R > 0.18 <fi> 0.45 <e>,x"l" 93 Bb/& 7.5 Eat/ kcal mol - 1.99 no. of react.trajectories 446 ~ ~~ 0.22 0.32 0.46 1.49 - 1.99 93 89 a Atomic scattering angle, 8 = 0" for backward molecular scattering, 8 = 180" for forward mole- cular scattering, relative to the incoming atomic beam direction. ii is the thermal-average cross- section, which is proportional to the thermal rate constant k; k = (v>3, where ( v > is the average relative velocity, given by (3RT0/2p)''' (To is the translational temperature and p is the reduced mass of the H + ICl system). The translational activation energy is the difference between the mean collision energy for reactive collisions, and the overall mean collision energy; E, = (T')rx - ($)k T L N S .Eint group, the majority of reactions occur by a process in which HCl is formed by direct approach of H toward C1. The newly-formed HC1 leaves with sufficient trans- lational energy to prevent any further interaction of HC1 with I. This kind of dynamics is normal for surfaces with repulsive energy release such as H + Clz. Inspection of trajectories belonging to the high Eint category revealed, as antici- pated, that reaction took place by way of an initial interaction with the I end of the molecule followed by migration to the C1. The migration was observed to occur after the I and the C1 had begun to separate. This is illustrated in the " bond plot " and " force plot " of a typical complex trajec- tory, shown in fig.14. In this encounter migration did not occur until the I-Cl distance had increased from equilibrium (2.321 A) to nearly 4 A. The H atom had undergone several rotations about the I atom, and has oscillated 20 times against the I. The migration of the H atom did not take place until quite late in the encounter. It involved passage through a linear ClHI configuration, since the H passed betweenJ . C . POLANYI, J . L . SCHREIBER AND W . J . SKRLAC 85 the C1 and the I. We refer to this as " insertion " of H into the extended I-Cl bond.14 Insertion was a feature common to almost all of the complex trajectories examined. It is shown clearly, for the sample trajectory on surface D, in fig.15. When the I-C1 distance has increased to 3.75 A, the equipotential contours can be ' \T T / kcal mol -' FIG. 12.-Reactive cross-sections for the low Eint (- - - -) and high EinC (- -) fractions of the HCl product of H + ICl(300 K thermal initial conditions). seen to have altered dramatically [fig. 13(b)] There is no longer a barrier preventing the passage of H through the intermediate configuration IHCl en route to migration; for the configuration with the H between I and C1 there is a marked potential-well. This helps explain the pattern of motion in fig. 15. While Cl and I are still close to one another the motion of H toward C1, as it rotates and vibrates about I (close examination reveals some 5 vibrations) fails to give rise to migration.Instead H rebounds off C1, and the direction of rotation about I reverses (first at position 7, and then once more at position 27). Finally (at position 40) the H is subjected to a strong attraction toward Cl and is drawn into the region between the separating atoms, Cl and I. Insertion has occurred. The acceleration of the H becomes high Eint (vibration and rotation) in an incipient HC1 molecule. The rotation of H around C1 brings the H atom between C1 and I for a second time, at position 57. By this time the I-Cl distance is > 5.5 A, and there is little likelihood of back-migration to the HI. Bond plots computed for trajectories on the other trial surfaces showed similar36 DISTRIBUTION OF REACTION PRODUCTS I CI FIG. 13.-(a) Potential contours for H approaching ICI from arbitrary directions. The molecule is fixed at its equilibrium bond length.The barrier to approach of H toward the C1 end of ICI is seen to decrease as H approaches from more lateral directions. The approach of H toward I is attractive out to large bending angles of the HICl intermediate. (b) Potential contours for H approaching IC 1 from arbitrary directions, when rIC1 = 3.75 A. The zero of energy is the potential of the stretched ICI (zk., the H-ICI interaction potential is plotted, not the full three atom potential). behaviour, namely direct reaction and migratory reaction with insertion, the former leading to low Eint and the latter to high It is evident from an analysis of the dynamics exemplified in fig. 15 that migration, without back-migration, requires a degree of synchronisation between the angular motion of the attacking atom and the linear rate of separation of the particles under attack.The pattern of motion cannot be quite so simply described if the three par- ticles are of more-nearly comparable mass. Nonetheless, the importance of a high degree of rotation of A about B if a " clutching " secondary encounter of A with the departing atom C is to lead to migration + AC, has been noted earlier for reactions of metals with halogen^.'^^^^ This early work showed the importance of attractiveJ. c . POLANYI, J. L . SCHREIBER AND W . J . SKRLAC 87 5 8 I I I I I I I I I I I I I I - - ?.=.a c 0 a J \ U - - 4 - n - I I I I I I I I I I I I I I I I I 1 I - c x . -2001 1 I I I I I I I I I I 0 2 4 6 8 10 12 14 time / 1 0 ~ ~ FIG.14.-Bond and force plot of a reactive H + C11 trajectory showing migration. In the upper panel, r1 = rHI (-), r2 = rlcl (- - - -), r3 = rHCl (- + - a ) and S (. . . . .) = the sum of the shorter two bond lengths. Note that when S is equal to the longest bond length (as occurs at the position marked with *, shortly after t = 12 x In the lower panel, force components along the three bcnds (using the same legend for associating the lines with bonds as in the upper panel) are shown. Initially a highly-vibrating incipient HI molecule is formed while the three atoms are in the HICl arrangement. This complex undergoes several bends, indicated by oscillations of the r3 distance between equality with S (linear), and equality with r2 (bent).Finally, at the asterisk, the ICl distance has increased sufficiently to allow this bend to become an insertion following which an HCl molecule is formed. s), the three-atom system is linear. - 3 .Ol 1 I I I I I J -6.0 -4.5 -3.0 -1. 5 0 1,5 3 .O A FIG. 15.-Atomic coordinates in the x-y plane for an H + ICI trajectory showing insertion. Here the initial conditions were chosen for simplicity to produce a trajectory which remained in a plane. The initial bond formation of H to I and the bending of the HICl complex are clear in steps 1 to 30. At step 30 the ICI relative motion suddenly shows evidence of a mutual repulsion which determines what follows. At step 36, the H, rather than being repelled by lateral approach to the CI, is able to insert between C1 and I.The ClHI complex makes one full asymmetric vibration before falling apart to HCI + I.88 DISTRIBUTION OF REACTION PRODUCTS energy-release at the B end of the molecule permitting reaction out to high impact parameter with consequent angular motion of A about B, and lingering encounters of A with B.13v39 The ranges of reagent parameters that led to migration depended on the potential energy surface and mass combination. A batch of 64 reactive trajectories on surface D using a 300 K reagent energy and equal masses, L + LL, gave z 25 % migration, indicating that on this type of energy surface dualityof reaction path (" microscopic branching ") is not restricted to the extreme L + HH mass combination. Inspection of o v e r 0 0 bond-and-force plots for the 300 K H + ICl reaction on surface D indicated that the alternate product HI was formed exclusively by direct ( i e ., non-migratory) reaction. The attacking H could form HI by approach from the I end of ICl, or as a consequence of a grazing collision from the C1 end. The latter cases did not constitute " migration ", since the atomic separations and forces showed no evidence of incipient formation of an HC1 bond, which would be characterised by an oscillation of the H against the C1. Instead the H passed by C1 at large im- pact parameter b, and subsequently was drawn in to the I. If the line-of-centres momentum between H and C1 was sufficient to carry H over the barrier, so that it became subject to H-Cl attraction, then it remained attached to the C1. Not only is C1 the more electronegative of the two halogen atoms under attack, but it is (for closely related reasons) the atom that binds more strongly to H.In fig. 13(b) it is evident that when the I-C1 bond is stretched (so that I and C1 appear to H akin to isolated atoms) the attraction operating on H, as it inserts, is greater at the C1 end. This is an important additional reason that, at normal collision energies, migration takes place toward the more electronegative atom (+HX) but not away from it (-+HY; in this case HI). A more general statement of the present ob- servations would be that migration is an important route for the formation of the product that bonds more strongly with the attacking atom. Hence microscopic branching occurs in the more exoergic of the macroscopic branches.Microscopic branching would be expected to have the most conspicuous consequences if the alternative dynamics (direct reaction --+HX, and migratory reaction -+HX) occur in different ranges of impact parameter; the presence of a barrier to direct reaction and not to migratory reaction ensures this. The general form of potential-energy surface used in the present work (attracting the attacking atom, A, at the B end of the molecule under attack and repelling it at the C end) is in accord with proposals made by H e r ~ c h b a c h ~ ~ on the basis of simple molecular orbital argument^,^^'^^ and recently documented in the work of Lee and ~ o - w o r k e r s ~ ~ who have been able to observe stable species HYX (xx > xy) in crossed molecular beam studies.For HIF they obtain a figure of 30 kcal mol-' for the stability relative to H + IF.42 The adduct HICl should be stable by a few kcal mol-I, but has not yet been reported. We are indebted to Prof. C. A. Parr for his contribution to the present study at its inception (see section on potential energy surface above). Mr. David Messersmith and the Computer Facility of Armstrong Cork Co., Lancaster, Pa., U.S.A., kindly assisted in the preparation of fig. 13. The research was made possible by a grant from the National Research Council of Canada. K. G. Anlauf, P. E. Charters, D. S. Horne, R. G. Macdonald, D. H. Maylotte, J. C. Polanyi, W. J. Skrlac, D. C. Tardy and K. B. Woodall, J . Chem. Phys., 1970,53,4091. M. A. Nazar, J. C. Polanyi and W. J. Skrlac, Chern.Phys. Letters, 1974, 29,473. J. C. Polanyi and W. J. Skrlac, Chem. Phys., 1977, 23, 167. J. W. Hudgens and J. D. McDonald, J . Chem. Phys., 1977, 67, 3401.J . C . P O L A N Y I , J . L . SCHREIBER A N D W. J . SKRLAC 89 J. Grosser and H. Haberland, Chem. Phys., 1973, 2, 342. J. D. McDonald, P. R. LeBreton, Y. T. Lee and D. R. Herschbach, J . Chem. Phys., 1972,56, 769. D. Brandt and J. C. Polanyi, Chem. Phys., in press. A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi and J. L. Schreiber, Faraday Disc. Chem. SOC., 1973, 55, 252. C. A. Parr, J. C. Polanyi, W. H. Wong and D. C. Tardy, Faruduy Disc. Chem. SOC., 1973, 55, 308. L. T. Cowley, D. S. Horne and J. C. Polanyi, Chem. Phys. Letters, 1971, 12, 144. H. Heydtman and J. C . Polanyi, J . Appl. Optics, 1971, 10, 1738; J.P. Sung and D. W. Setser, Chem. Phys. Letters 1978, 58, 98. l 3 (a) P. J. Kuntz, E. M. Nemeth and J. C. Polanyi, J . Chem. Phys., 1969, 50, 4607; (b) P. J. Kuntz, M. H. Mok and J. C . Polanyi, J . Chem. Phys., 1969,50,4623. l4 J. C. Polanyi, J. L. Schreiber and W. J. Skrlac, Furaday Disc. Chem. SOC., 1977, 62, 319. ” For recent reviews see R. B. Bernstein and R. D. Levine, Adv. Atom Mol. Phys., 1975,11, 215; R. D. Levine and R. B. Bernstein, in Modern Theoretical Chemistry, ed. W. H. Miller (Plenum Press, N.Y., 1976), vol. 3, pp. 323-364. lo J. C. Polanyi, J. L. Schreiber and J. J. Sloan, Chem. Phys., 1975, 9,403. l6 J. C. Polanyi and J. L. Schreiber, Chem. Phys., 1978, 31, 113. l 7 G. P. Smith, J. C. Whitehead and R. N. Zare, J. Chem. Phys., 1977,67,4912. J. C . Polanyi, Faradny Disc. Chem. SOC., 1973, 55, 389. l9 D. R. Herschbach, G. H. Kwei and J. A. Norris, J . Chem. Phys., 1961,34,1842; D. R. Hersch- bach, Disc. Faraduy SOC., I962,33, 149 ; R. B. Bernstein and A. M. Rulis, Furaday Disc. Chem. SOC., 1973, 55, 293. ’ O P. R. Brooks, J. Chem. Phys., 1969,50,503 1 ; Furaday Disc. Chem SOC., 1973,55,299. ’l C . C. Mei and C . Bradley Moore, J . Chem. Phys., 1977, 67, 3936. 22 R. G. Macdonald and J. J. Sloan, Chem. Phys., 1978, 31, 165. 23 M. D. Pattengill, J. C. Polanyi and J. L. Schreiber, J.C.S. Faraday ZZ, 1976, 72, 897, and refer- 24 J. C. Polanyi and J. L. Schreiber, Faraduy Disc. Chem. SOC., 1977,62,267. 25 C. A. Parr, J. C . Polanyi and W. H. Wong, J. Chem. Phys., 1973,58, 5 . ences therein. R. N. Porter and L. M. Raff in Dynamics of Molecular Collisions, ed. W. H. Miller (Plenum Press, N.Y., 1976), part B, chap. 1, p. 1 . 27 K. G. Anlauf, D. S. Horne, R. G. Macdonald, J. C . Polanyi and K. B. Woodall, J. Chem. Phys., 1972,57, 1561. J. C. Polanyi and J. J. Sloan, J . Chem. Phys., 1972, 57, 4988. 29 J. D. McDonald, J . Chem. Phys., 1974, 60, 2040. 30 N. C. Blais and D. G. Truhlar, J . Chem. Phys., 1974, 61, 4186. 31 Part of this series, J. C . Polanyi, J. L. Schreiber and J. J. Sloan, Chem. Phys., 1975,9, 403. 32 D. H. Maylotte, J. C. Polanyi and K. B. Woodall, J . Chem. Phys., 1972,57, 1547. 33 J. Grosser and H. Haberland, Chem. Phys., 1973, 2, 342. 34 D. R. Herschbach, Conference on Potential Energy Surfaces in Chemistry, ed. W. A. Lester, Jr. 35 J. D. McDonald, Faraday Disc. Chem. SOC., 1973, 55, 372. 36 J. C. Polanyi and J. L. Schreiber, Faraduy Disc. Chem. SOC., 1973, 55, 372. (IBM Research Laboratory, San Jose, Calif,; Publication RA 18, 1971) p. 44. 37 J. W. Hepburn, D. Klinek, K. Liu, J. C. Polanyi and S . C.-Wallace,J. Chem. Phys., 1978, 69, 4311. 38 J. M. White, J . Chem. Phys., 1973, 58, 4482. 39 J. C. Polanyi and J. L. Schreiber in Physical Chemistry, An Advanced Treatise, ed. H. Eyring, D. Henderson and W. Jost (Academic Press, New York, 1974), vol. VIA; Kinetics of Gas Reac- tions, chap. 6, p. 383. 40 G. C. Pimentel, J . Chem. Phys., 1951, 19, 446. 41 A. D. Walsh, J. Chem. SOC., 1953, 2266. 42 J. J. Valentini, M. J. Coggiola and Y . T. Lee, J. Amer. Chem. SOC., 1976,98,853; Faraday Disc. Chem. SOC., 1977, 62,232.

ISSN:0301-7249    

DOI:10.1039/DC9796700066

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

F + H, Collisions in the Presence of Intense Laser Radiation: Reactive and Nonreactive Processes BY PAUL L. DEVRIES AND THOMAS F. GEORGE* Department of Chemistry, University of Rochester, Rochester, New York 14627, U.S.A. AND JIAN-MIN YUAN Department of Physics and Atmospheric Science, Drexel University, Philadelphia, Pennsylvania 19 104, U.S.A. Received 5th December, 1978 Two sets of calculations are discussed for F + H2 collisions occurring in the presence of intense laser radiation. The first set, based on a semiclassical theory whereby nuclear degrees of freedom are treated classically, considers collinear reactive collisions in the presence of the 1.06 pm line of a Nd- glass laser. For a high enough intensity the laser alters the vibrational distribution of the HF product.The second set, where all degrees of freedom are treated quantum mechanically, considers the quench- ing of fluorine in its excited spin-orbit state by three-dimensional (nonreactive) collisions with H2 in the presence of a laser whose photon frequency is ~4408 cm-'. For high enough intensity the laser substantially enhances the quenching cross-section. 1. INTRODUCTION There has been considerable interest in the theory of the interaction of intense laser radiation with molecular collision systems [see review of work done at Rochester in ref. (l)]. With high enough intensity, the laser radiation can actually interact with the collision dynamics, even if the frequency of the laser photon is not in resonance with energy levels of the asymptotic collision species. Recently we have obtained some results for both reactive2 and nonreactive3 processes in the F + Hz collision system, which we summarize in this paper.For the reactive processes, discussed in section 2, we restrict ourselves to collinear collisions and consider the case where the fluorine atom is initially in its ground spin- orbit state. We further restrict ourselves to two (semiempirical) potential energy surfaces, where one correlates to fluorine in its ground spin-orbit state and the other to fluorine in its excited spin-orbit state. By integrating classical trajectories for the nuclear degrees of freedom, we investigate how the reaction dynamics is affected by the 1.06 pm line of a Nd-glass laser. For the nonreactive processes, discussed in section 3, we represent the electronic degrees of freedom by a 6 x 6 diatomics-in-molecules Hamiltonian matrix.This problem is simplified by ignoring reactive channels, in which case we are able to con- sider three-dimensional collisions, where all degrees of freedom are treated quantum mechanically. We consider how a laser with photon frequency of ~ 4 0 8 cm-' affects the quenching of fluorine in its excited spin-orbit state to its ground spin-orbit * Camille and Henry Dreyfus Teacher-Scholar ; Alfred P. Sloan Research Fellow.P . L . DEVRIES, T . F . GEORGE AND J . - M . YUAN 91 state. This frequency is sufficiently different from the spin-orbit splitting in fluorine (404 cm-') that radiative transitions cannot occur without the aid of the H2 collision partner. 2.REACTIVE PROCESSES In this section we shall study how the reaction dynamics of the F + H2 collision system can be affected by shining an intense laser field on the collision region. The F + H2 reactive system is especially interesting for this study for several reasons. First, this is a reaction which produces laser emission, namely, the HF-laser. If a second laser shining through the laser cavity could change the branching ratios of the HF vibration states, one would then be able to change the characteristics of the H F laser. Secondly, this is one of the rare systems for which we have ab initio information for ground- and excited-state potential energy surfaces and transition dipole moments as functions of internuclear distances. All our calculations were performed with an initial collision energy of 0.049 eV, relative to the F + H2 (u = 0) state, which is insufficient to access the excited spin- orbit state (which lies at ~ 0 .0 5 eV). Thus, in terms of the electronic-field surfaces employed in this work, reaction can only occur through nonadiabatic transitions between the electronic-field surfaces. Semiclassical trajectory methods developed for electronic transitions in field-free cases can be applied here. We have used the decoupling approximation developed for the Miller-George theory ' in our calcula- tiorx2 The field-free ground electronically diabatic surface is the semiempirical Muckerman V surface.6 The field-free excited electronic surface is obtained by fitting parameters to data based on GRHF-CI calculation^.^ Field-free adiabatic surfaces, W, and W2, are then calculated by coupling adiabatic surfaces through a constant spin-orbit interaction term.W, and W2 plotted against a reaction coordinate s are shown schematically in fig. 1. The transition dipole moment between the 'C and Ill states of HF as a function of interatomic distance has been calculated by Bender and Davidson.' The overall transition dipole coupling is taken to be proportional \ +-S FIG. 1 .--Scheme of the field-free adiabatic surfaces, W, and W,, including spin-orbit interaction, for the reactive F + H, system along a reaction coordinate s. The vertical line indicates the photon energy from a Nd-glass laser, which comes into resonance with W, and W2 along s.92 F + H, COLLISIONS I N LASER FIELDS to the moment they have calculated, so that the coupling is a function of just the H-F distance.The electronic-field surfaces, E- and E,, can then be constructed from W,, W, and the radiative coupling d12 according to the relation where E , = *(W1 + W2 + hm [ W2 - W1 - hw)’ + 4d12]1/2} (1) 4 2 = P12% (2) p12 is the overall transition dipole coupling, E is the field strength and co is the laser photon frequency. The reaction we have studied is hw (1.06 pm) F(2P3/2) + H ~ ( u = 0) - HF(u’) + H (3) in the presence of a Nd-glass laser, which involves no net absorption or emission of photons. We are especially interested in the change in the reaction probability and the final vibrational distribution of the HF molecule induced by the laser field. We have also calculated inelastic transition probabilities for the process (4) which does involve absorption of a photon.In the reactant asymptotic region, E,, on which we start all the trajectories, be- comes Wl + hm, and Wl itself becomes a Morse potential of a hydrogen molecule plus a free fluorine atom. To select initial conditions for a grid of trajectories, we transform the coordinates of the Morse oscillator of the reactant diatomic molecule into action-angle variables.’ The vibrational quantum number and the phase of the oscillator are the corresponding action and angle variables, respectively. All trajec- tories start in the asymptotic region with H2 in the ground vibrational state, and we have selected the initial vibrational phase with a uniform grid of one hundred values between 0 and 27t.Let rl be the H2 internuclear distance and r3 the distance between F and the closer H atom. Associated with rl and r3 are the translational coordinates R1 and &, where R1 is the separation between F and the centre of mass of H2, and, denoting H, (H,) as the H atom further from (closer to) F, R3 is the separation between H, and the centre of mass of H,F. To apply the Miller-George theory we need to locate complex branch points (ix., intersection points) between the electronic-field surfaces. For each field strength of the laser field we have a different set of electronic-field surfaces, and therefore a different set of branch points. The way we find the proper set of branch points is that for a fixed real rl we change r3 iteratively in the complex plane until the equation E, = E- holds to a high degree of accuracy a.u.).The curve formed by projecting the set of branch points onto the real plane will be called a “ seam ”. In the decoupling approximation one needs to integrate the trajec- tory perpendicularly to the “ seam ” into the complex space to find the transition probability. To separate effectively the nuclear kinetic energy term into two com- ponents, one containing the perpendicular momentum and the other the parallel one, we project the set of branch points onto the (r3, R3) plane. The seam lies approximately on a straight line, which defines an axis called RII with a unit vector $11. The axis perpendicular to the seam is labelled as RI, with unit vector ii;, PI and PI, are momen- tum components along RL and R;I, respectively.The separable approximation, namely, F(2P3/2) + H2(u = 0) + hw(1.06 pm) + F*(2P1,2) + H2(u’), u’ = 0, 1 We shall study the reaction only in a collinear configuration.P . L . DEVRIES, T . F . GEORGE A N D J . - M . YUAN 93 holds to a high degree of accuracy in the (r3, R3) coordinate system. In eqn ( 5 ) E is the total energy of the system, El is E- or E+, and MI and M ~ I are defined by MI' = M-l AI and Mi1 = All M-I ill, with the inverse mass tensor M-I given as where p is the reduced mass between H and HF and m is the reduced mass of HF. When a trajectory is propagated to a seam, the representative particle may either switch surfaces or stay on the original surface. The probability of switching surfaces is equal to the local nonadiabatic transition probability p t , which can be calculated by integrating PI, as defined in eqn (9, around the branch point and taking the expo- nential of the imaginary part of the action integral.The probability of staying on the original surface is then 1 - p t . For reaction (3), at all field intensities studied (109-1013 W cmM-2) only vibra- tional states u = 2 and 3 of HF are populated, which is also true for the field-free case. The population ratio of u = 3 to u = 2 for field intensities below 1 TW cm-, is almost a constant and is -0.75. However, as the field intensity increases to 10 TW cm-, the ratio increases to 1.64. The total reaction probability decreases slightly from 0.63 to 0.60 as the field intensity increases from 0 to 1 TW cm-2, which can be explained by the fact that as the separation of the electronic-field surfaces increases at the seam, pt becomes smaller.However, as the field intensity further increases to 10 TW cm-2, the total reaction probability jumps to 0.74. These results are interesting, because they suggest that laser emission from u = 3 to u = 2 is possible without con- sidering the rotational manifold, as is necessary for an ordinary HF laser. Our preliminary study then points out the possibility that laser characteristics can be affected by shining another laser through the laser cavity. The threshold field in- tensity (% 10 TW cm-2) predicted may be too high for any practical USC, but since this is the result of a collinear system, the threshold field intensity for a realistic three- dimensional system could be lower.Inelastic scattering probabilities for the u = 0 and 1 states in process (4), which is not energetically accessible in the corresponding field-free case, increase from the order of to the order of 0.01 as the field intensity increases from 1 GW cm-2 to 10 TW cm-2. It is worth noting that H, can be vi- brationally excited to u = 1 while the ground-state F(2P3/2) atom is a t the same time electronically excited to F(,P1,,), even though no vibrational transition moment has been included in our calculation. 3. NONREACTIVE PROCESSES In this section, we shall investigate the effect of intense radiation on nonreactive processes in the F + H, collision system. Specifically, we are interested in the quenching of fluorine in this situation. The potential surface correlating to the ground spin-orbit state of F leads to formation of HF, whereas the surface correlating to the excited spin-orbit state does not lead to reaction.Thus the quenching of the excited state can lead directly to an enhanced reaction cross section. This quenching does occur in the absence of a radiation field and, in fact, the asymptotic level of F* + H2(j = 0) is nearly resonant with F + H,(j = 2), leading to substantial quenching. (In this section H2 is treated as a rigid rotor.) The purpose of the present work is to determine to what extent the quenching can be enhanced by the presence of an intense radiation field. T!ic use of a nonreactive formalism to treat this quenching problem is justifiable only if the region of importance to the quenching process is far removed from the94 F + H2 COLLISIONS I N LASER FIELDS reaction region.This condition is satisfied in the absence of the field, where the " quenching region " occurs at an F-H2 separation of ~5 bohr. We have met this requirement in the presence of the radiation field by choosing a radiation field which is nearly resonant with the asymptotic state; the spin-orbit splitting of fluorine is z 404 cm-', and we chose the radiation field to be ~ 4 0 8 cm-'. This ensures that the region of significant interaction occurs far from the reaction region. However, the electric dipole moment of the system becomes vanishingly small for F-H, separations > ~3 bohr. Thus, unlike the usual physical situation, in the region of significant quenching the magnetic dipole is the dominant factor in the radiative process.The calculations were performed within a three-dimensional quantum mechanical close-coupled formalism in the body-fixed coordinate system, as described e1sewhere.l' Matrix elements of the hamiltonian were evaluated by the diatomics-in-molecules method." The presence of the radiative interaction introduces several complexities to the problem, including the fact that the total molecular angular momentum is not conserved (since photons have an intrinsic angular momentum) and that the total hamiltonian is not rotationally invariant." The first difficulty was minimized by truncating the basis-set expansion to include only those states coupled to the F* + H2 states by single photon transitions, and the second overcome by employing the orienta- tional average appr~ximation.'~*'~ In all, 48 channels were included in the calcu- lating, correlating to the states F + H2(j = 0, 2) + nhco, F* + H2(j = 0, 2) + nhco, and F + H2(j = 0) + (n + 1)hw.In the body-fixed system, the hamiltonian matrix is (approximately) block-diagonal so that a maximum of 14 states were considered simultaneously. The close-coupled equations were then solvedby the R-matrix method of Light and Walker." There are at least two very interesting intermediate results of this calculation. The first is that the transitions F* + H2(j = 0) + nhco -+ F + H2(j = 0, 2) + nhco are (within the accuracy of our calculation) independent of n (i.e., the intensity of the radiation field) for intensities as high as lot2 W cm-2.The effect of the radiation field in transitions of this sort is to distort the shape of the potential surfaces, and hence to effect the process indirectly, e.g., without net absorption or emission of photons. The fact that the cross-sections are not altered indicates that this distortion is small, which is easily confirmed. An order of magnitude estimate of the distortion can be obtained by considering two crossing surfaces W, + hw and W,, and computing the amount of splitting in the corresponding surfaces E, and E-. For our situation, in which only the magnetic dipole component of the radiation field interacts with the molecular system, it is found that the splitting at the avoided crossing is only z 2.5 cm-' for a field of 10l2 W ern-,.(This should be compared with the situation of the previ- ous section, in which the electric dipole interaction induced a splitting of z 260 cm-' in a field of lo1, W cm-2.) Thus it is understandable that the intensity of the radia- tion field plays an insignificant role in those processes not involving net absorption or emission of photons. The second result of some interest is the behaviour of the cross-section for the resonant quenching transition F* + H2(j = 0) + nhco -+ F + H2(j = 2) + nhco as a function of J , the initial total molecular angular momentum. (As discussed in the preceding paragraph, these results are found to be independent of the intensity of the radiation field.) Since states of different parity do not couple, the cross-sections for the even and odd parity states are computed separately from one another.These J- dependent cross-sections (for a collision energy of 0.03 eV) are exhibited in fig. 2, the even parity results indicated by the solid line and the odd parity results by the dashed line. As seen from the figure, the even and odd parity cross-sections alternate in magnitude as a function of J. This behaviour has been observed in previous (field-P . L . DEVRIES, T . F . GEORGE AND J . - M . YUAN 0.01 0.02 0.03 0.04 95 4.15 4.21 4.80 10.6 3.41 3.44 3.75 6.79 3.14 3.17 3.37 5.43 2.83 2.85 3.01 4.56 I i J I J FIG. 2.-Cross sections as a function of the total (initial) molecular angular momentum J for the process F* + Hz ( j = 0) + nho -+ F + Hz ( j = 2 ) + nho at a collision energy of 0.03 eV ( h o z 408 cm-I).The even parity results are indicated by the solid line and the odd parity results by the dashed line. free) calculations, for C + + Hz by Chu and Dalgarno,16 and F + H2 by Wyatt and Walker," who explained it in terms of the interweaving of avoided crossings. An- other feature of this figure is the presence of two distinct regions of J values where the cross-section is significant. Calculations at other collision energies indicate that as the energy increases, the second region moves to higher J values, and the contribution to the total cross section decreases. Note that our calculation differs from that of Wyatt and Walker in several respects, not the least of which is the use of different electronic surfaces; and it is well known that cross sections at low collision energies can be extremely sensitive to the shapes of the electronic surfaces.The major results of this investigation are presented in table 1. The cross sections TABLE TOTAL CROSS SECTIONS (A') FOR QUENCHING OF F* BY &(j = 0) IN PRESENCE OF A LASER FIELD (ko Z 408 Cm-') reported are the total degeneracy-averaged cross-sections for the quenching of F* by H2(j = 0), summed over final H, rotational states and over the final states of the radiation field. As indicated in table 1, the presence of the radiation field can sub- stantially alter the quenching cross section for a radiation field intensity as low as 10" W cm-'. Furthermore, the effect of the field is stronger at the lower collision energies. This is easily understandable since, at the lower energies, the system remains in the interaction region for a longer amount of time.(Similar behaviour has been observed in an atom-atom collision system in which the radiative process was dominated by the Liectric dipole interaction.)" These results clearly indicate that the quenching process can be considerably enhanced by the radiation field, even though the transition96 F + Hz COLLISIONS IN LASER FIELDS must proceed through the magnetic dipole interaction rather than the (typically larger) electric dipole interaction. 4. CONCLUSION The calculations reported in sections 2 and 3 by no means represent a complete description of the F + H2 collision system in the presence of intense laser radiation. In fact, these calculations mark the first time, for an atom-diatom collision system in a laser field, that reactive channels and rotational degrees of freedom have explicitly been treated.Nevertheless, the results should help maintain the interest among experimentalists to continue to explore the effects of intense laser radiation on the dynamics of molecular rate processes. Due to the various approximations employed, we do not want to state absolutely that field intensities must be in a range as high as 1011-1013 W cm-2 in order to observe effects as suggested by our calculations. We hope that interesting effects might be observable with lower field intensities. One of us (P. L. D.) thanks Prof. C. Moser and CECAM for their hospitality at the Workshop on Selective Excitation of Atoms and Molecules (University of Paris at Orsay, Summer, 1978), where part of this work was carried out.The research was financed by U.S. Government Agencies, including NASA, the U.S. Air Force and the National Science Foundation. * T. F. George, I. H. Zimmerman, P. L. DeVries, J.-M. Yuan, K. S. Lam, J. C. Bellum, H. W. Lee, M. S. Slutsky and J. T. Lin, in Chemical and Biochemical Applications of Lasers, ed. C. B. Moore (Academic Press, New York, 1979), vol. IV, pp. 253-354. P. L. DeVries and T. F. George, J. Chem. Phys., in press. A. Komornicki, T. F. George and K. Morokuma, J . Chem. Phys., 1976, 65, 48. W. H. Miller and T. F. George, J . Chem. Phys., 1972, 56, 5637. ' J. T. Muckerman, J. Chern. Phys., 1972, 56, 2997, and personal communication. ' R. L. Jaffe, K. Morokuma and T. F. George, J . Chem. Phys., 1975,63, 3417. * C. F. Bender and E. R. Davidson, J . Chem. Phys., 1968, 49,4989. C. C. Rankin and W. H. Miller, J . Chem. Phys., 1971, 55, 3150. lo P. L. DeVries and T. F. George, J . Chem. Phys., 1977, 67, 1293. J. C. Tully, J . Chem. Phys., 1973, 58, 1396. P. L. DeVries and T. F. George, Mu/. Phys., 1978, 36, 151. l3 P. L. DeVries and T. F. George, Phys. Reu. A, 1979, 18, 1751. l4 P. L. DeVries and T. F. George, Mu/. Phys., 1979, in press. J. C. Light and R. B. Walker, J. Chem. Phys., 1976, 65, 4272. S. I. Chu and A. Dalgarno, J. Chem. Phys., 1975, 62,4009. l7 R. E. Wyatt and R. B. Walker, J. Chem. Phys., 1979, 70, 1501. l8 P. L. DeVries, M. S. Mahlab, and T. F. George, Phys. Rev. A, 1978, 17, 546. * J.-M. Yuan and T. F. George, J. Chem. Phys., 1979, 70,990.

ISSN:0301-7249    

DOI:10.1039/DC9796700090

出版商:RSC    

年代:1979

数据来源: RSC

摘要:

Vibrational-mode-specific Energy Consumption Translational and Vibrational State Dependence of the Ba + N20 (vl, v2, u,) -+ BaO* + N2 Reaction BY DAVID J. WREN AND MICHAEL MENZINGER Lash Miller Chemical Laboratories, University of Toronto, Toronto, Ontario M5S 1A1, Canada Received 2 1 st December, 1978 The excitation functions eCL(E, T,) for forming chemiluminescent (CL) products in the (Ba + N20) reaction is found to depend sensitively on N20 vibrational temperature T,. In a second experiment thermal rate constants for CL production kcL, and for Ba beam attenuation kT, were measured as functions of N20 temperature, and activation energies were obtained. Analysis shows that u2- bending acts as promoting mode, and participation by uI (N-0 stretch) is highly likely. Promotion by v2 is consistent with the initial formation of an ion pair Ba+N20-.Rearrangement of this inter- mediate to BaO*(A' 'n) products, believed to be the CL emitter, is adiabatically allowed. Specificity of energy consumption is traditionally discussed in the context of vib- rot-el-trans reactant excitation in direct A + BC reactions.' A further aspect enters the picture with polyatomic molecules: The 3N - 6(5) vibrational degrees of freedom will generally show mode-specificity. Although little is known at present about these matters, simple symmetry considerations alone, i.e., the degree to which a given normal vibration projects onto the reaction coordinate, provide a starting point for predicting the efficacy of that mode. The present chemiluminescent (CL) atom-triatom reaction Ba + N20: --+ BaO* + N2 (1) will be shown to differ in an interesting way from such a naive expectation.This sheds a new light on its reaction dynamics. The Ba + N20 system has been studied extensively in recent years, with particular emphasis on problems of energy disposal and the nature and effects of the so-called " reservoir states ".2 In this paper we report energy consumption measurements by two complementary methods : (1) A crossed supersonic/thermal beam experiment alllows us to measure the CL excitation function eCL(j?, T,) over a range of vibrational temperatures T,. Super- sonic beams of a constant nominal energy3 are generated by changing the He/N20 seeding ratio as well as the nozzle temperature To. Since the vibrational distri- bution remains essentially unrelaxed at To, this allows one to vary T, N To independ- ently from J?.A pronounced vibrational enhancement of ecL(E7 T,) was found, in agreement with an early report on this The lowest collision energy achieved in this experiment was 9 kJ mol-'. (2) In order to cover the low energy region, thermal rate constants kcL(TN20) and kT(TN20) were measured as a function of TNz0, and activation energies were derived (kcL refers to total CL production and k, to attenuation of the Ba beam). The goal of the analysis was (a) to determine the vibrational mode(s) responsible for the enhancement and (b) to reconstruct (effective) state-specific excitation functions98 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION cTi(E) that are consistent with both measurements and extend over the whole energy range.This requirement turns out to be very stringent since it allows us to eliminate the u1 (N-0 stretch) mode as the only promoting mode (N-N stretch u3 is easily disqualified) while definitely requiring the v 2 bending mode to be active, possibly in conjunction with vl. This is explained, as b e f ~ r e , ~ by the initial formation of an ion- pair (Ba+N,O-) in a hard collision, followed by its rearrangement to observed products. This ion pair intermediate also resolves some difficulties in previous interpretation^,^ since it correlates adiabatically with several BaO* states, amongst others the A' Ill state believed6 to be the CL emitter. EXPERIMENTAL The molecular beam apparatus in which two types of measurement were performed has been described elsewhere.7 A.ENERGY CONSUMPTION: CL CROSS -SECTIONS rFCL(E, T,) as independent functions of (nominal c.m.) collision energy E and of N20 vibrational temperature T, were obtained by crossing a collimated effusive Ba beam with a chopped and collimated, (He-seeded) supersonic N20 beam. Dimensions and operating parameters are given in table 1. E and T.. were varied TABLE 1 ,-CROSSED-BEAM GEOMETRY AND OPERATING PARAMETERS N20/He beam: nozzle diameter nozzle temperature nozzle pressure skimmer diameter nozzle-skimmer nozzle-collimator nozzle-scattg. centre beam divergence Ba beam: oven temperature oven orifice diam. oven-scattg. centre beam divergence dN = 0.1 mm Po = 5.33 x lo4 Pa (400 Torr) 0.36 mm 12 mm 45 mm 95 mm 2.1" To = 280 - 869 K 973 K 3.1 mm 64 mm 7.1" by the N,O/He-seeding ratio (mole fraction) XNtO and by the nozzle temperature TO(=Tv, see below).The intersection volume was viewed by a bare E.M.I. 9558 QB photomultiplier coupled to a lock-in amplifier. Low resolution (10 nm spectral slitwidth) beam-beam spectra, recorded by using a multiple reflection White-Welsh cell9 and a + m monochromator, were, within the experimental noise, independent of E and T,. This dispenses with E, Tv-dependent correction factors in further analysis. The observed CL signal &b is related to the CL cross-section by: Here nBa, nNZO are the reactant number densities at the scattering centre and UR is the average relative velocity. The beam geometries were chosen to assure a constant collision volume V .The number density nBa was determined by monitoring the Ba flux on a quartz crystal micro- balance located 25 mm above the scattering centre. N20 densities were measured concur- rently with the light signals by a quadrupole mass spectrometer located in a differentially pumped chamber. The ionizer was 494 mm downstream of the nozzle. ComplementaryD . J . W R E N A N D M . M E N Z I N G E R 99 flux measurements using a closed ionization gauge operated in the phase sensitive mode’” agreed with the mass spectrometric results. The nominal collision energy I? is given by I? = &/2 = p(Uia + fikao) where CBa is the average velocity of the Maxwellian Ba beam and & is the measured streaming velocity of the supersonic beam. The results l i c ~ (fig.1) represent relative values since all measurements were uncalibrated. The N20 velocity distributions were measured in a separate experiment by time-of-flight as described else~here.’~~ B. THERMAL RATE CONSTANTS kCL(TNe0), kT(TNzO) for CL production and Ba beam attenu- ation were obtained in a thermal beam-gas experiment by measuring the pressure and temperature dependence of the CL intensity. An effusive Ba beam (x 1000 K, x 9 x lo9 atoms cm-3) was collimated and chopped at 50 Hz before entering a resistively heatable A1 scattering chamber (SC) through a 1.6 mm diameter orifice. The temperature of the SC(T,,, -- 298-591 K) was taken as the arithmetic mean (f5 % variance) of the readings from 3 thermocouples buried in the chamber walls. Pure N20 (Matheson >99.99 %) was admitted from a reservoir to the SC through a calibrated leak.The absolute SC pressure was computed by gas flow continuity from the flow rate into the chamber (= backing pres- sure, measured on a capacitance manometer, times conductance of leak) and the conductance of the scatterbox orifices towards the high vacuum chamber. The N20 gas density deter- mined in this fashion covered the nNxO = (3.6 x 1010)-(1.9 x 1014) C M - ~ range [correspond- ing to pNfO = 10-6-(5 x Torr at 298 K]. The Ba flux was monitored by a quartz crystal microbalance” located on the far end of the reaction chamber. A bare photomulti- plier (E.M.I. 9558 QB, cooled to 190 K) viewed a 6.2 mm long section of the Ba beam, 22.2 mm downstream of the SC entrance hole. This makes the scattering path length 1 = 22.2 i- 3.1 mm.The CL signal follows the relation: 12,13 Sbg(nN,O TNaO) = kCL( TN,0)nBanN20 exp [-lnN,OoT( TNIO)I (3) where V is the volume of the observation region (assumed constant) and oT is the effective Ba beam attenuation (=total scattering) cross-section. The latter represents an upper limit to the total reactive cross-section oR < oT. A corresponding limit to the reactive rate constant is given by kT(TNz0) = UoT(TNaO), where z7 = ( 8 R T e f f / 7 ~ ~ ) ” ~ , the reduced mass is p and Teff is the effective translational temperature characteristic of a thermal beam-gas experiment : l4 Teff = (MBaTNaO + MN,OTBa)/(MBa + MNaO). (4) Relative CL rate constants kCL(Terf) were obtained as a function of temperature as the limit- ing low pressure slope of &g(nNIO) determined by linear least square fits. oT(Teff) was obtained from linear least square fits to plots of h[&g(t?NzO, Tcff)/f?N,@Ba V] for data at higher nN20, where attentuation is appreciable. C.CHARACTERIZATION OF THE SUPERSONIC N20 BEAMS with respect to translational and internal energy distributions is crucial to our data analysis. The velocity distributions measured by time-of-flight and analysed as described elsewhere7 were used to (a) calibrate the collision energy scale and (b) to deconvolute the data. The N20 internal state distributions were inferred from the following considerations : As the local translational temperature decreases in the course of the adiabatic expansion, internal degrees of freedom will also tend to relax.The extent of this relaxation is characterized by the ratio Z / Z , of the average number 2 of collisions which one molecule suffers during the expansion (typically 2 x 10’- lo3) ‘’*16 to the number Z1 of (gas kinetic) collisions required to relax the internal mode i. Electronic degrees of freedom are unimportant since the lowest excited state lies 28 000 cm-’ above the groundstate and is negligibly p0pu1ated.l~ Molecules with small rotational spac- ings are known to relax rotationally with near gas-kinetic as experiments with N2 and CsF beams20p3 show. Accordingly we assume that N,O is rotationally relaxed and is100 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION characterized by a rotational temperature TR nearly equal to the local translational tempera- ture Tt w TR - AT.This assumption is also required by energy balance considerations in order to account for the measured beam energy. Vibrational distributions, on the other hand, are assumed to remain frozen at the nozzle temperature To N T,. Ample experimental 21,22 and theoretical evidence23 supports this assumption for the relatively stiff N20 modes (1288, 588, 2237 cm-l). The linear relation (Lambert-Salter plot),24 between log Z,,, and vmin, the frequency of the lowest energy mode that limits the rate of the overall relaxation (i.e., the v 2 = 588 cm-' bending mode), yields an estimate Z,,, z lo4 (at 300 K) in agreement with measured relaxation Another well established corollary of the vibrational cooling is the formation of clusters. Our source conditions do not favour dimerization 30331 and comparison with experiments performed under source conditions comparable to ours32 lead us to expect a cluster content of <1 % for our beams.We assume that this small contamination has no noticeable effect on the CL rate. RESULTS Our primary data, the CL excitation functions dCL(l?, To) == 6cL(E, T,), measured at different nozzle (=vibrational) temperatures are shown in fig. 1. The most strik- ing result is the strong enhancement of cross-sections with To. The solid curves E/kJ mol-' FIG. 1 .-Chemiluminescence cross-sections b,,(E, To) as functions of nominal collision energy I? for a series of nozzle temperatures To: 0 , 2 8 1 ; A, 389; 0 , 4 7 0 ; 0 , 5 4 8 ; V, 599; a, 716; A , 793 and y , 869 K. represent least square fits of the data points by two-parameter curvesb,, = CE-" except for the lowest temperature To = 281 K where below 19 kJ mol-I the flattening curve was drawn by hand. One is tempted to extrapolate this portion to a threshold below the energetically accessible region.The reproducibility of the To = T, = const. curves is &lo % from run to run due to systematic errors (gas mixtures XNz0, beam densities nNz0; To), but the experimental scatter of individual data points on these curves is only &6%.D. J . WREN A N D M. M E N Z I N G E R 101 BEAM-GAS EXPERIMENTS The relative rate constant for CL production kcL, and beam attenuation kT, as functions of Teff, are given as Arrhenius plots in fig. 2. The kT plot appears linear, and a linear least squares fit yields E: = 12.1 & 1 kJ mol-l.The k,, plot, however, is distinctly non-linear. The activation energy EaCL decreases with T,,, from EaCL (475 K) = 10.0 A linear fit gives EzL = 8.4 & 1.5 kJ mo1-l. 1.7 kJ mol-1 to EaCL (675 K) = 5.9 & 2.0 kJ mol-’. 1 . 2 - cn c .- ?I 0.8 n 0 L \ -L, 0.4 1.4 1.6 1.8 2.0 lo3 K / Teff FIG. 2.-Arrhenius plots for CL production ( OkcL) and Ba beam attenuation (Ok,). Solid lines are linear least square fits. The dashed line drawn freehand follows the curvature of the kcL data. An estimate of the T‘,,-dependence of the (relative) quantum yield @(Teff) = kCL/kT oc exp (+3.5/RTe,,) is obtained from these numbers by approximating the total reactive rate constant by k,. Our total attenuation cross-section at TNzo = 300 K is uT = 27 5 6 8L2, in agree- ment with earlier measurements12 and in contrast to a more recent value.13 The small value of the total reaction cross-section oR < uT confirms the earlier that one is dealing with “ hard ”, repulsive wall collisions.The experimental data are now analysed in the light of the following two ques- tions : (1) Which degree of freedom (trans, rot, vib, electron, excitation; clustering) is primarily responsible for the To effect? A translational effect is readily excluded by deconvoluting the measured 6,L33 and by observing that the resulting cross-sections oCL differ only insignificantly from the primary data. This also justifies the use of the primary data GCL in the subsequent analysis, and eliminates the need of using the de- convoluted ucL.The lowest electronically excited state of N20 (3Cf, To = 28 000 cm-’) l7 lies too high to contribute significantly. As shown above, rotation is relaxed to the translational (streaming) temperatures T’ = T R E 20-210 K [for pure N20 (To = 281 K) and 98% He-seeded N20 (To = 840 K), respectively]. Several other studies have revealed relatively weak dependences of reactivity on r o t a t i ~ n . ~ ” - ~ ~ Rotational enhancements of the reported magnitudes prove insufficient to account for our observations. N20 rotation can thus be eliminated as the dominant cause of the To effect. The cluster content has been shown above to be < z 1 %, eliminating (N20) clusters as a possible cause. This completes the proof, by successive elimina- tion, that N20 vibration is the source of CL enhancement at elevated To = T,.See text for activation energies.102 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION (2) Which of the three vibrational modes (ul, u,, u,) = (1288, 588, 2237 cm-1)41 is primarily responsible for the effect? This is now examined by decomposing the observed oCL into specific CL cross-sections bi of reactant state i: ocL(E, T v ) = 2 xi(Tv)bi(E)- ( 5 ) The weighting factors are the equilibrium populations xi(Tv) = gi exp (-Ei/krv)/C gi exp (-&i/kTv), (6) 1 where the degeneracies for g i = 1 for ul, u3 and gi = u, + 1 for 0,. The solution of the N linear equations (N = 8 in our case, see fig. 1) provides in principle N detailed cross-sections, provided the data were of high precision. We have restricted ourselves to N = 2 and 3 state analyses, since N 3 3 already yields unphysical 6, [i.e., a(,??) < O for some El.Excitation of a single mode at a time, rather than combination vibrxtions, is assumed to promote the reaction: model 1 (u, = 0, 1 . . .). The u, mode is assumed " active " in the states 2 (i, j , k), i 3 1 while 2 ( O , j , k ) forms the less reactive " ground " state. The u, (bending) mode was considered threefold: model 2a(u, = 0, 1 . . .) assumes 2 (i, 0, k ) the " ground" and 2 (i, j , k ) , j 1 the " active " state, model 26 (u2 = 0 I , 2 . . .) 2 (i, j , k), The following models were explored. i,k i , k i,k i,k i,k TABLE 2.-FITTING PARAMETERS [EQN (9)-( lo)] OF 6i(E) model C1" Eob n mc ~2~ p 02' C3a q 0 3 ' u1 = 0, l/u 2.28 2.5 0.82 0.030 8.64 1.27 u1 = 0, l/t 2.28 1.9 0.82 0.030 8.64 1.27 9.5 u2 = 01, 2/u 2.31 3.1 0.81 0.033 3.41 1.27 u2 = 01, 2/t 2.31 0 0.81 0.033 3.41 1.27 4.5 u 2 = 0, 1, 2/t 4.32 1.9 0.50 0.019 3.63 2.65 10.3 220 1.15 17.8 (4.22) (1.9) (0.050) (0.019) (5.74) (2.65) (3.2) (220) (1.15) (10.3) Units are C,/A' kJ'-" mol"-', C,/Az kJ-P molp and C3/Az kJ-4 mol-4.Units are kJ mol-'. Units are mol kJ-'. j = 0, 1 " ground state " and 2 (i, j , k ) ; j 2 2 " active " and model 2c (21, = 0, 1, 2 . . .), a three state model with 2 (i, j , k ) ; j = 0 and j = 1 and j 2 2; finally model 3 (v, = 0, 1 . . .) in which v3 was considered by taking the two 2 (i, j , k ) ; k = 0 and k > 1 states. For the analysis, the populations Xi* of the effective states i' were obtained by summing over the true molecular states i contributing to i', Xi* = 2 X i i , .The N linear eqn (5) were then solved successively at constant ,!? by a least squares optimiza- tion routine. The quality of the fits by the 5 models described above are illustrated in fig. 3. Synthetic " experimental " cross-sections ecalc(E, To) obtained from eqn (5) are plotted as a func- tion of To at l? = const. for comparison with the measured eCL(,??, To). It is evident i , k i,k i, i 1 The resulting effective state cross-sections ai(E) are summarized in table 2.D. J . WREN A N D M. MENZINGER 103 T I K FIG. 3.-Comparison of experimental acL (open circles) at ,!? = 48 kJ mol-' with CL cross-sections calculated from best fit effective state cross-sections a&??) for different models [eqn (8), (90) and (10a); parameters are given in table 21.(a) v1 active: (ul = 0, 1 . . . ; solid line), (ul = 01, 2 . . . ; dashed curve) (b) uz active: both the two and the three state models (u2 = 01,2 . . .) and (u2 = 0, 1,2 . . .) give good fits as shown by the solid line. (u2 = 0 , l . . . ; dashed line): (c) v3 active: (u3 = 0, 1 . . . ; solid curve). The (ul = 0, 1 . . .), (u2 = 01,2 . . .) and (u2 = 0, 1, 2 . . .) models yield acceptable fits. that models 1 (v, = 0, 1 . . .), 2b (0, = 01, 2 . . .) and2c (u, = 0, 1 , 2 . . .) alone provide acceptable fits to the data, eliminating model 3 (u3 = 0, 1 . . .), i.e., the u3 mode and model 2a (u, = 0, 1 . . .), from consideration. The same holds at other collision energies, I?. So far there is little to choose between models 1, 2b and 2c from the quality of the fits (fig.3) alone. To make further progress in deciding between these possibilities we now examine which model is capable of yielding thermal activation energies that agree with the measured EZL. RECONSTRUCTION OF di(E) AT LOW I? FROM EaCL The thermal rate constants (fig. 2) and the excitation functions (fig. 1) carry rate information from two mutually exclusive but overlapping energy ranges. We use the E,CL(Teff) information to reconstruct consistent cross-sections in the experiment- ally inaccessible low energy range. The activation energy Ea3 f RT; aln k/ aT3 appropriate to a three temperature beam-gas experiment, characterized by T,, T2 the (internal and translational) tem- peratures of gases 1 (internal states i) and 2 (internal states j ) and T, the (effective) translational temperature [eqn ( 4 ) ] , is given by : Ea3V'3) = 2 Cfij [(Elf) - $ RT3I i j + J13 2 Cfij [Ei - (&i)TII + J23 Z: I f i j [ ~ i - (&i)T21 (7) i i i j Here Jnl are the Jacobians (aT; '/8Tl-') and f i j ( T l , T,) = (XiXikii/k) are the relative contributions of states i, j to the overall rate, where the XiX, are the (Boltzmann)104 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION fractions of reactants in the molecular states i and j , ki, is the detailed rate constant of states Ij.and k = 2 2.hjkij is the total rate constant. (~5;~) is the average transla- tional energy of the i + j reaction.42 The effective state i' cross sections 6,. (I?) (fig. 4) were extrapolated below 12 kJ mol-I in an attempt to bring agreement between calculated and observed E t L .This agreement was iteratively improved by (1) imposing the physical constraint that cross-sections cannot diverge [reflected by the adjustable cutoff parameters D,, D, in TABLE 3.-cOMPARISON OF MEASURED AND CALCULATED ACTIVATION ENERGIES (FIVE MODELS FOR PROMOTING MODE) experiment calculated: Eacalc/kJ mol-' for models: TN,o/K Teff = Tz/K EaCL/kJ mol-l (ul = 0, Ilu) ( u , = 0, lit) (un = 01, 21u) (u2 = 01, 21t) (08 = 0, 1, 211) 300 470 9.8 f 0.8 18.9 7.3 24.6 8.7 9.9 (11.1) 600 697 6.4 & 2.1 20.4 19.3 16.8 15.8 9.1 (10.7) 1000 1000 - 13.1 16.7 8.0 10.0 7.6 (8.2) eqn (9b) and (lob)] and (2) by iteratively advancing from model 1 (v, = 0, 1 . . .) to 2b (u, = 01, 2 . . .) to model 2c (0, = 0, 1, 2 .. .). The stages of the calculation, whose results are summarized in table 3, are: (1) Excitation of Ba, i.e., the third term in eqn (7) was neglected. (2) The molecular excitation energies c1 were replaced by the internal reactive energies averaged over those molecular states i that contribute to the " effective " states i' in the finite models: ( ~ f ) ~ ' = 2 cii*Xiit/2 X i i f where, e.g., i = 0, 1 and 2, 3 . . . for model 2a. (3) The cross-sections a,.(,!?) for models 1, 2a, b, c were least square fitted by functions (the parameters D2, 0, are introduced later) : 1 1 a,(E) = CIE-'(E - Eo>" exp [-m(E - EO)] E 2 Eo (8) = o E < Eo 62(E) = C2E-' E > 0 2 ( 9 4 = a,@,> E < 0 2 (9b) a3(E) = C3E-' E > 0 3 (104 = @,(DJ E<D3 (lob) The fitting parameters are given in table 2.(4) Using the analytical expressions for ki and ((ET) - 3 RT,) given by LeRoy4, and extensions thereof to deal with the forms of eqn (9) and (lo), E,(T3) EE EZL(Teff) was calculated at several temperatures for several a,@) models (table 3). Models 1 (u, = 0, 1 . . . lu) and 2b (u2 = 01, 2 . . . lu) employ un-truncated (" u ") 6,@) functions (D2 = 0.0) that non-physically go to infinity as E+ 0. This over- emphasizes the contribution of the upper state to the overall rate and yields corre- spondingly high activation energies. In addition (v, = 0, 1 . . . lu) introduces a EzL temperature dependence contrary to that observed (fig. 2). The physically more reasonable truncated (" t ") models l(u, = 0, 1 . . . It) and 2b(v2 = O , l , 2 .. . It) assume constant 6, below the adjustable cutoff energy D2. However, Ea values are still too high since the energy ( E ; ) ~ ' of the upper effective state i' is too high. The results recorded in table 3 are those closest to the experimental Ea from among a series of el and b2 that employed (D2, Eo) combinations other than those given in tableD . J . WREN AND M . MENZINGER 105 f / k J mol" FIG. 4.-Effective state cross-sections 8,(g) based on three state model 2c (u2 = 0, 1,2 . . .). Solid lines: derived direktly from primary data fig. 1. Dashed curves : (decreased Eo in el and truncated d2 and &) give optimal simultaneous fit of dCL and E,CL (table 3, last column; parameters given in table 2 last line). Dot-dashed curves: a new form of e2 avoids the non-physical intersection with cfl (as in previous model).Bracketed parameters in table 2 were used. Bracketed E,Ca" in table 3, last column were obtained. (a) f i 3 , (b) and (c) e2, ( d ) el. 3. Therefore, to decrease EaCalC to the measured values 8-10 kJ mol-1 while obtaining the observed T-dependence, it is necessary to introduce a lower-lying, internally excited state, the only candidate being v2 = 1. The three-state model 2c(u2 = 0, 1,2(t) alone yields a gratifying fit to the experimental E,CL-values. This is taken as proof that v, alone as promoting mode is inconsistent with the experiments and v2 is required as promoting mode, either alone or in combination with ul. The qualitative content of this analysis is clear and significant despite the fact that its quantitative details are less satisfactory. We have no explanation for the fact that the unbiased 3 state analysis of ecL yields a e2 (solid curves in fig.4) which drops below 8, at high energies while approaching e3 at low energies. It may be an artefact that reflects the limited precision of the raw data and the inflexibility of the analytical expressions @)-(lo). Yet this model, after incorporating D2, D3 and Eo as adjust- able parameters (E,, has to be made to float in order to reproduce E,CL; yielding the dashed curves in fig. 4), is remarkably successful in reproducing both experimental data. An ad hoc cross-section dZ for the intermediate state that is physically more plausible (dash-dotted curve in fig. 4, bracketed values in tables 2 and 3) yields slightly worse data fits.New beam-beam experiments will be required, with better energy resolu- tion, a wider energy range that covers in particular the low energy regime and106 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION preferably state selection, to determine the detailed state cross-sections with higher precision than that achieved in the present work. DISCUSSION MODE SPECIFIC DYNAMICS The foregoing analysis shows that: (1) the gCL raw data (fig. 1) are consistent (fig. 3) with both u, and/or u, as the " promoting " modes while definitely excluding u3. (2) The values and the temperature dependence of the activation energy EaCL, however, can only be reproduced by a much more specific model (v, = 0, 1,21t) requiring the bent molecule u2 = 1 to be among the promoting states.This establishes u2 as active mode without excluding, however, a possible contribution from u,. This conclusion becomes physically plausible as follows : A vibrational analysis of N,044 shows that u1 and v3 represent essentially N-0 stretch and N-N stretch modes, respectively, while v2 designates the bending mode, as usual. Elementary considerations predict u, to be active, and u3 to be inactive in promoting molecular dissociation N,O+ N2 + 0 as well as reaction. The causes for the involvement of u2 are less obvious. Previously4 u2 has been suggested by us as promoting mode. This is based on the increase of the N 2 0 electron affinity with bending angle (fig. 5 ) , arising from the fact that in this 22 electron system an extra electron will enter the lowest unoccupied 374 1Oa) orbital, whose energy drops sharply with bending angle of the originally linear N,0.45 A striking demonstration of this fact was given by C h a n t r ~ ~ ~ who observed a z lo3 fold increase of the dissociative attachment rate of thermal electrons (e + N,O+ N, + 0-) upon raising the vibrational temperature from 350 to 1000 K.120 150 180 +O/deg FIG. 5.-Potential energies of N,O and N20- as functions of N-N-0 bond angle. (a) NzO- 'A", The CL rate can be enhanced by N 2 0 bending ( i e . , by the electron affinity) if a close-range electron transfer, reminiscent of harpooning (1 1) initiates the reaction, followed by rearrangement of the intermediate ion pair. The valence orbital structure of the BaO(XIX +) groundstate resembles the doubly ionic configuration Ba2+ (6so)O2-(2p6), or 0202~4, where all orbitals written are centred (6) N2O 'A', (c) N20- 'A'.Ba('S) + N,O('X+) -3 Ba+(,S) + N20-(2A') +- (Ba+O-)* + N2('C;)D . J . WREN AND M. MENZINGER 107 primarily on the oxygen atom. The low lying excited states which may act as reser- voirs or as emitters all resemble the singly ionic configuration Ba+(6s1)0-(2p5) where one electron has been transferred to an orbital centred on Ba (underlined): BaO*(a311, A”n) arise from 0~0~71~0, and BaO*(3Z+, A1n+) from 0207140. This is confirmed by orbital population The reaction must therefore-be accom- panied by charge separation. Our v,-promoting model merely suggests that this event is the initial and rate determining step. N-0 stretch versus N-N-0 bend? There is good reason for v1 = 1 and v, = 2 to be about equally reactive, as the two-state analysis suggests.The (100) and (02OO) states (the superscript “ 0 ” refers to the state with 1 = 0 vibrational angular momentum) have both the same C+ symmetry and similar energy, and are known to be moderately strongly mixed by Fermi ~esonance.~~ Thus, even in isolated mole- cules, the assignments v, = N-0 stretch and 221, = bend break down. In addition collisions with Ba are expected to randomize the phases of the bending motion and thereby increase the coupling. The A(02,0), 1 = 2 state may also be coupled to (100) in this fashion. In effect, the (100) and (020) states become dynamically indistin- guishable and the combination of EA enhancement and N-0 stretch is expected to be particularly effective.Since the (0, 1,0) state is not mixed with v, it is very significant that this state is required by the foregoing EaCL analysis. Within the credi- bility limits of the rather indirect analysis, this shows that the bending mode is indeed one promoting mode as suggested earlier. If in a hypothetical molecule an “ inactive ” mode (in zeroth order) is coupled to an “ active ” mode by Fermi resonance, then the former would also become dynamically active. In this sense one might consider the activity of v, secondary to that of the u2 bending mode. A direct test of the present conclusions by the use of state selected is desirable as well as feasible. The adiabatic correlations between reactants and p r o d u c t ~ ’ ~ ~ ~ ~ appear in a new light through the inclusion of the intermediate ion pair.The neutral reactants corre- late directly only with BaO(X’C+), and ad hoc assumptions were made5 to invoke the possible adiabatic formation of excited BaO* products. In the present picture, the ion pair Ba+(’S) + N20-[211(2A’ in C,)] with its open shell electron configuration correlates formally (spin disregarded) with several energetically accessible excited product states: with BaO(A’ Ill and a”) in Cz,, and with [XIC+ and 3C+ (unobserved)] in C, symmetry. The formation of triplet products (a”, 3C+), requires a spin-flip in the ion pair, a process that would be favoured by a long lived c ~ m p l e x . ~ ~ * ~ ’ A long lived complex, however, appears to be in discord5’ with the highly non-statistical nature of the excitation functions, to be discussed presently.The correlation with A’ ‘II is particularly gratifying since this state has recently been identified as a CL emitter.6 The question of the dynamical content of ai(E) is answered straightforwardly by separating the excitation functions into a dynamical B and a statistical p(E’) factor: 53*54 di(E) = &@)/I@’) where Bi is termed “ average state-to-state cross-section ”, E’ is the (average) product energy exclusive of electronic excitation. The rot-vib-translational product state density is given in the rigid-rotor-harmonic-oscillator approximation 55 as log p(f?’> = (s + r/2 + n/2 - 1) log I?’, where s = number of oscillators, r = Edi (di is the dimensionality of the rotors) and n = number of translational degrees of freedom.The state-to-state cross-section Bi is plotted for the (u, = 0, 1,2ln) model (dash-dot bi in fig. 4). in fig. 6. The pronounced translational energy dependence of the dynamical factors demonstrates the highly non-statistical nature of the title reaction. The in- ternal state dependence of ai confirms again the mode-specificity discussed above.108 VIBRATIONAL-MODE-SPECIFIC ENERGY CONSUMPTION 10 vr C 3 Y .- J i L d $ 1 \ b' 10 30 50 E / k J rnol-' FIG. 6.-State-to-state cross-sections ai(E) derived from effective state cross-sections bi(E) for (u2 = 0, 1, 2 . . .) model. The dash-pointed curve of fig. 3 (bracketed values in table 2) was used. (a) 33, (b) Z1 and (c) Zo. 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ISSN:0301-7249    

DOI:10.1039/DC9796700097

出版商:RSC    

年代:1979

数据来源: RSC