From Force Fields to Dynamics: Classical and Quantal Paths

Reaction path methods provide a powerful tool for bridging the gap between electronic structure and chemical dynamics. Classical mechanical reaction paths may usually be understood in terms of the force field in the vicinity of a minimum energy path (MEP). When there is a significant component of hydrogenic motion along the MEP and a barrier much higher than the average energy of reactants, quantal tunneling paths must be considered, and these tend to be located on the corner-cutting side of the MEP. As the curvature of the MEP in mass-scaled coordinates is increased, the quantal reaction paths may deviate considerably from the classical ones, and the force field must be mapped out over a wider region, called the reaction swath. The required force fields may be represented by global or semiglobal analytic functions, or the dynamics may be computed "directly" from the electronic structure results without the intermediacy of potential energy functions. Applications to atom and diatom reactions in the gas phase and at gas-solid interfaces and to reactions of polyatomic molecules in the gas phase, in clusters, and in aqueous solution are discussed as examples

[1]  B. C. Garrett,et al.  Test of variational transition state theory and the least-action approximation for multidimensional tunneling probabilities against accurate quantal rate constants for a collinear reaction involving tunneling into an excited state , 1985 .

[2]  Imre G. Csizmadia,et al.  New theoretical concepts for understanding organic reactions , 1989 .

[3]  D. Truhlar,et al.  Erratum: Monte Carlo trajectories: The reaction H+Br2→HBr+Br , 1976 .

[4]  R. Marcus Chemical‐Reaction Cross Sections, Quasiequilibrium, and Generalized Activated Complexes , 1966 .

[5]  Scott G. Wierschke,et al.  Variational transition state for the reaction of Cl2C: with ethylene and the thermodynamics of carbene additions , 1989 .

[6]  B. C. Garrett,et al.  Variational transition state theory and tunneling for a heavy–light–heavy reaction using an ab initio potential energy surface. 37Cl+H(D) 35Cl→H(D) 37Cl+35Cl , 1983 .

[7]  D. Kouri,et al.  ℒ2 Solution of the quantum mechanical reactive scattering problem. The threshold energy for D + H2(v = 1) → HD + H , 1986 .

[8]  Donald G. Truhlar,et al.  Polyatomic canonical variational theory for chemical reaction rates. Separable‐mode formalism with application to OH+H2→H2O+H , 1982 .

[9]  H. Bernhard Schlegel,et al.  An improved algorithm for reaction path following , 1989 .

[10]  E. Kraka,et al.  Insights into the mechanisms of chemical reactions. Reaction paths for chemical reactions , 1987 .

[11]  C. Horowitz,et al.  Functional representation of Liu and Siegbahn’s accurate ab initio potential energy calculations for H+H2 , 1978 .

[12]  B. C. Garrett,et al.  A least‐action variational method for calculating multidimensional tunneling probabilities for chemical reactions , 1983 .

[13]  G. L. Hofacker,et al.  Model Approach to Nonadiabatic Reaction Processes , 1969 .

[14]  K. Laidler,et al.  Vibrationally Adiabatic Model for the Dynamics of H+H2 Systems , 1970 .

[15]  D. Truhlar,et al.  Effect of curvature of the reaction path on dynamic effects in endothermic chemical reactions and product energies in exothermic reactions , 1975 .

[16]  J. McIver,et al.  Singlet biradicals as intermediates. Canonical variational transition-state theory results for trimethylene , 1988 .

[17]  B. C. Garrett,et al.  WKB approximation for the reaction‐path Hamiltonian: Application to variational transition state theory, vibrationally adiabatic excited‐state barrier heights, and resonance calculations , 1984 .

[18]  B. C. Garrett,et al.  Reliable ab initio calculation of a chemical reaction rate and a kinetic isotope effect: H + H(2) and H + H(2). , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Paul F. Barbara,et al.  A theoretical study of multidimensional nuclear tunneling in malonaldehyde , 1989 .

[20]  R. E. Weston H3 Activated Complex and the Rate of Reaction of Hydrogen Atoms with Hydrogen Molecules , 1959 .

[21]  D. Truhlar Adiabatic Theory of Chemical Reactions , 1970 .

[22]  Michael E. Coltrin,et al.  A new tunneling path for reactions such as H+H2→H2+H , 1977 .

[23]  S. Goursaud,et al.  Effect of curvature of the minimum energy path upon reaction dynamics: the H2O−(2B1)→H−(1S) + OH(2Π) dissociation , 1981 .

[24]  Scott F. Smith,et al.  SN2 reaction profiles in the gas phase and aqueous solution , 1984 .

[25]  D. Truhlar,et al.  Potential energy surfaces for atom transfer reactions involving hydrogens and halogens , 1971 .

[26]  Donald G. Truhlar,et al.  Criterion of minimum state density in the transition state theory of bimolecular reactions , 1979 .

[27]  B. C. Garrett,et al.  2?* Calculations of Accurate Quantal-dynamical Reactive Scattering Transition Probabilities and their Use to test Semiclassical Applications , 1987 .

[28]  B. C. Garrett,et al.  Vibrationally adiabatic models for reactive tunneling , 1982 .

[29]  Tunnelling and reaction path curvature effects in the isomerization of the methoxy radical , 1988 .

[30]  Xiche Hu,et al.  Properties of canonical variational transition state theory for association reactions without potential energy barriers , 1989 .

[31]  Y. Asai,et al.  Morphology of dynamic electron transfer characteristic of chemical reaction dynamics , 1985 .

[32]  B. C. Garrett,et al.  A general small-curvature approximation for transition-state-theory transmission coefficients , 1981 .

[33]  F. B. Brown,et al.  An improved potential energy surface for F+H2→HF+H and H+H′F→HF+H′ , 1985 .

[34]  R. Levine Radiationless transitions and population inversions: Two examples of internal conversion , 1971 .

[35]  B. C. Garrett,et al.  Reaction-path hamiltonian model of partial widths for vibrationally elastic and inelastic decay of adiabatically trapped reactive resonances , 1984 .

[36]  M. A. Collins,et al.  Determination of the intrinsic reaction coordinate: Comparison of gradient and local quadratic approximation methods , 1988 .

[37]  Akitomo Tachibana,et al.  Stability of the reaction coordinate in the unimolecular reaction of thioformaldehyde , 1985 .

[38]  Donald G. Truhlar,et al.  A double many‐body expansion of the two lowest‐energy potential surfaces and nonadiabatic coupling for H3 , 1987 .

[39]  Bin Liu,et al.  An accurate three‐dimensional potential energy surface for H3 , 1978 .

[40]  B. C. Garrett,et al.  Generalized transition state theory and least-action tunneling calculations for the reaction rates of atomic hydrogen(deuterium) + molecular hydrogen(n = 1) .fwdarw. molecular hydrogen(hydrogen deuteride) + atomic hydrogen , 1985 .

[41]  R. Marcus On the Theory of Chemical‐Reaction Cross Sections. II. Application to the H + H2 Reaction , 1967 .

[42]  Mark S. Gordon,et al.  Potential energy surfaces for polyatomic reaction dynamics , 1987 .

[43]  B. C. Garrett,et al.  Tests of the extension of variational transition state theory to calculate reaction rates for molecules in selected excited vibrational states , 1986 .

[44]  J. Dodd,et al.  Dipole moments of highly excited vibrational states of HCN , 1988 .

[45]  J. Tully,et al.  Effects of surface crossing in chemical reactions - The H3 system , 1971 .

[46]  Donald G. Truhlar,et al.  Generalized transition state theory. Bond energy-bond order method for canonical variational calculations with application to hydrogen atom transfer reactions , 1979 .

[47]  W. Hase Variational unimolecular rate theory , 1983 .

[48]  B. C. Garrett,et al.  Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules and isotopically substituted hydrogen molecules , 1979 .

[49]  B. C. Garrett,et al.  Evaluation of dynamical approximations for calculating the effect of vibrational excitation on reaction rates. O+H2(n=0,1)↔OH(n=0,1)+H , 1986 .

[50]  D. Truhlar,et al.  A multiproperty empirical potential energy surface for the reaction H+Br2→HBr+Br , 1985 .

[51]  J. Hirschfelder,et al.  General Collision Theory Treatment for the Rate of Bimolecular, Gas Phase Reactions , 1959 .

[52]  R. T. Skodje,et al.  Localized Gaussian wave packet methods for inelastic collisions involving anharmonic oscillators , 1984 .

[53]  M. Gordon,et al.  Theoretical studies of the reactions XHn→XHn−1−+H+ and XHn−1−+SiH4→[SiH4XHn−1]− , 1986 .

[54]  Local Approximation of Potential‐Energy Surfaces by Surfaces Permitting Separation of Variables , 1964 .

[55]  B. C. Garrett,et al.  Thermal and state‐selected rate constant calculations for O(3p) + H2 → OH + H and isotopic analogs , 1986 .

[56]  Thom H. Dunning,et al.  A theoretical study of the potential energy surface for OH+H2 , 1980 .

[57]  M. Blomberg,et al.  The H3 potential surface revisited , 1985 .

[58]  W. Hase The criterion of minimum state density in unimolecular rate theory. An application to ethane dissociation , 1976 .

[59]  L. Raff,et al.  A valence-bond potential-energy surface for silylene dissociation , 1985 .

[60]  Kazuhiro Ishida,et al.  The intrinsic reaction coordinate. An ab initio calculation for HNC→HCN and H−+CH4→CH4+H− , 1977 .

[61]  S. Sato,et al.  On a New Method of Drawing the Potential Energy Surface , 1955 .

[62]  I. Shavitt Correlation of Experimental Rate Constants of the Hydrogen Exchange Reactions with a Theoretical H3 Potential Surface, Using Transition‐State Theory , 1968 .

[63]  George C. Schatz,et al.  A quasi-classical trajectory study of product vibrational distributions in the OH + H2 → H2O + H reaction , 1980 .

[64]  D. Kouri,et al.  Accurate quantum mechanical reaction probabilities for the reaction O+H2→OH+H , 1987 .

[65]  George C. Schatz,et al.  The analytical representation of electronic potential-energy surfaces , 1989 .

[66]  M. Gordon,et al.  Intrinsic frequency analysis of the generalized normal-mode vibrations for the reaction H sub 2 + CH sub 3 yields H + CH sub 4 , 1989 .

[67]  William L. Jorgensen,et al.  Energy profile for a nonconcerted SN2 reaction in solution , 1985 .

[68]  J. Doll,et al.  The isotope and temperature dependence of self-diffusion for hydrogen, deuterium, and tritium on Cu(100) in the 100–1000 K range , 1985 .

[69]  Don L. Bunker,et al.  Trajectory Studies of Hot‐Atom Reactions. I. Tritium and Methane , 1970 .

[70]  B. C. Garrett,et al.  Phenomenological manifestations of large-curvature tunneling in hydride-transfer reactions , 1986 .

[71]  Donald L. Thompson,et al.  Ab initio dynamics: HeH+ + H2 → He + H3+ (C2ν) classical trajectories using a quantum mechanical potential‐energy surface , 1973 .

[72]  Eugene P. Wigner,et al.  Calculation of the Rate of Elementary Association Reactions , 1937 .

[73]  D. Truhlar,et al.  Variational transition state theory calculations for an atom--radical reaction with no saddle point: O+OH , 1983 .

[74]  B. C. Garrett,et al.  Application of the large-curvature tunneling approximation to polyatomic molecules: Abstraction of H or D by methyl radical , 1989 .

[75]  M. Gordon,et al.  Intrinsic reaction coordinate calculations for very flat potential energy surfaces: application to singlet disilenylidene isomerization , 1989 .

[76]  G. L. Hofacker,et al.  Diabatic transition state theory and the concept of temperature , 1972 .

[77]  Mark S. Gordon,et al.  Algorithms and accuracy requirements for computing reaction paths by the method of steepest descent , 1988 .

[78]  F. B. Brown,et al.  Global potential-energy surfaces for H2Cl , 1989 .

[79]  William A. Lester,et al.  Trajectory studies of O+H2 reactions on fitted abinitio surfaces. II. Singlet case , 1979 .

[80]  Tucker Carrington,et al.  Reaction surface description of intramolecular hydrogen atom transfer in malonaldehyde , 1986 .

[81]  William L. Jorgensen,et al.  Hydration and energetics for tert-butyl chloride ion pairs in aqueous solution , 1987 .

[82]  R. Boyd Macroscopic and microscopic restrictions on chemical kinetics , 1977 .

[83]  L. Raff Theoretical investigations of the reaction dynamics of polyatomic systems: Chemistry of the hot atom (T* + CH4) and (T* + CD4) systems , 1974 .

[84]  J. I. Brauman,et al.  Transesterification in the gas phase: transfer of a solvent molecule from reactant to product ions , 1989 .

[85]  R. Marcus,et al.  Dynamics of hydrogen atom and proton transfer reactions. Symmetric case , 1981 .

[86]  Lionel M. Raff,et al.  Quasiclassical trajectory studies using 3D spline interpolation of ab initio surfaces , 1975 .

[87]  M. Ovchinnikova The tunneling dynamics of the low temperature H exchange reactions , 1979 .

[88]  Rudolph A. Marcus,et al.  On the Analytical Mechanics of Chemical Reactions. Classical Mechanics of Linear Collisions , 1966 .

[89]  B. C. Garrett,et al.  Test of variational transition state theory with a large‐curvature tunneling approximation against accurate quantal reaction probabilities and rate coefficients for three collinear reactions with large reaction‐path curvature: Cl+HCl, Cl+DCl, and Cl+MuCl , 1983 .

[90]  J. Mareda,et al.  Theoretical studies of halocarbene cycloaddition selectivities: A new interpretation of negative activation energies and entropy control of selectivity , 1985 .

[91]  M. Gordon,et al.  Ab initio reaction paths and direct dynamics calculations , 1989 .

[92]  Donald G. Truhlar,et al.  A new potential energy surface for the CH3+H2↔CH4+H reaction: Calibration and calculations of rate constants and kinetic isotope effects by variational transition state theory and semiclassical tunneling calculations , 1987 .

[93]  Rudolph A. Marcus,et al.  Analytical Mechanics of Chemical Reactions. III. Natural Collision Coordinates , 1968 .

[94]  B. C. Garrett,et al.  Test of Variational Transition State Theory and Multidimensional Semiclassical Transmission Coefficient Methods against Accurate Quantal Rate Constants for H + H2/HD, D + H2, and O + H2/D2/HD, Including Intra- and Intermolecular Kinetic Isotope Effects , 1986 .

[95]  H. Schaefer,et al.  Tunneling in the unimolecular decomposition of formaldehyde: a more quantitative study , 1981 .

[96]  D. Clary Close‐coupling calculations on the H+BrH→HBr+H reaction in three dimensions , 1985 .

[97]  D. Truhlar,et al.  Surface diffusion of hydrogen on copper: the effect of phonon-adsorbate coupling on the diffusion rate , 1987 .

[98]  C. W. Eaker,et al.  Optimization of diatomic state mixing in diatomics‐in‐molecules theory: The CHn potential‐energy surfaces , 1976 .

[99]  William L. Jorgensen,et al.  Ab initio and Monte Carlo calculations for a nucleophilic addition reaction in the gas phase and in aqueous solution , 1986 .

[100]  G. Schatz,et al.  The centrifugal sudden distorted wave method for calculating cross sections for chemical reactions: Angular distributions for Cl + HCl → ClH + Cl , 1987 .

[101]  D. Truhlar,et al.  Statistical‐diabatic model for state‐selected reaction rates. Theory and application of vibrational‐mode correlation analysis to OH(nOH)+H2(nHH)→H2O+H , 1982 .

[102]  L. Raff,et al.  Theoretical investigations of elementary processes in the chemical vapor deposition of silicon from silane. Unimolecular decomposition of SiH4 , 1984 .

[103]  Mark S. Gordon,et al.  Decomposition of Normal-Coordinate Vibrational Frequencies , 1989 .

[104]  Donald G. Truhlar,et al.  Improved treatment of threshold contributions in variational transition-state theory , 1980 .

[105]  D. Truhlar,et al.  Calculation of reaction rates and kinetic isotope effects for dissociative chemisorption of H2 and D2 on Ni(100), Ni(110), and Ni(111) surfaces , 1989 .

[106]  Scott F. Smith,et al.  Theoretical examination of the SN2 reaction involving chloride ion and methyl chloride in the gas phase and aqueous solution , 1985 .

[107]  P. Rossky,et al.  Hydration effects on SN2 reactions: an integral equation study of free energy surfaces and corrections to transition-state theory , 1989 .

[108]  B. C. Garrett,et al.  Test of the accuracy of small‐curvature and minimum‐energy reference paths for parametrizing the search for least‐action tunneling paths: (H,D)+H’Br→(H,D)Br+H’ , 1989 .

[109]  D. Truhlar,et al.  Monte Carlo trajectories: The reaction H + Br2 → HBr + Br , 1974 .

[110]  D. Truhlar,et al.  Effect of nonequilibrium solvation on chemical reaction rates. Variational transition-state-theory studies of the microsolvated reaction Cl-(H2O)n + CH3Cl , 1990 .

[111]  John E. Adams,et al.  Reaction path Hamiltonian for polyatomic molecules , 1980 .

[112]  K. Houk,et al.  Origin of negative activation energies and entropy control of halocarbene cycloadditions and related fast reactions , 1984 .

[113]  Mark S. Gordon,et al.  The Intrinsic Reaction Coordinate and the Rotational Barrier in Silaethylene , 1985 .

[114]  D. Truhlar,et al.  Diffusion of hydrogen, deuterium, and tritium on the (100) plane of copper: Reaction-path formulation, variational transition state theory, and tunneling calculations , 1985 .

[115]  H. Schaefer,et al.  Reaction path Hamiltonian: Tunneling effects in the unimolecular isomerization HNC→HCN , 1980 .

[116]  Donald G. Truhlar,et al.  Generalized transition state theory. Classical mechanical theory and applications to collinear reactions of hydrogen molecules , 1979 .

[117]  Bowen Liu,et al.  Ab initio potential energy surface for linear H3 , 1973 .

[118]  Donald G. Truhlar,et al.  Generalized born fragment charge model for solvation effects as a function of reaction coordinate , 1989 .

[119]  Donald G. Truhlar,et al.  POLYRATE: A general computer program for variational transition state theory and semiclassical tunneling calculations of chemical reaction rates , 1987 .