A new method for determining semiclassical tunneling probabilities in atom–diatom reactions

We present an approximate semiclassical method for determining state to state transition probabilities for reactions which proceed via tunneling which uses a trajectory integrated along purely real and purely imaginary time contours from reagents through the barrier to products. The real and imaginary time portions of the trajectory are connected by introducing separable approximations to the potential near certain translational turning points in the trajectory. For atom–diatom collinear reactions, the use of a vibrationally adiabatic approximation from these turning points to the asymptotic region leads to a very simple expression for the imaginary part of the action involving a nonseparable contribution from a purely real valued portion of the trajectory passing through the barrier along an imaginary time contour, and a separable contribution from a path which follows part of the locus of outer vibrational turning points. At very low translational energies E0, we find that the nonseparable contribution ...

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

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

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

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

[5]  R. Wyatt,et al.  History of H3 Kinetics , 1976 .

[6]  G. Schatz,et al.  Dynamical resonances in collinear, coplanar, and three-dimensional quantum mechanical reactive scattering , 1975 .

[7]  William H. Miller,et al.  Semiclassical transition state theory for nonseparable systems: Application to the collinear H+H2 reaction , 1975 .

[8]  W. Miller,et al.  Modified classical S matrix for tunneling in the collinear H + H2 reaction , 1974 .

[9]  J. Bowman,et al.  Comparison of semiclassical, quasiclassical, and exact quantum transition probabilities for the collinear H + H2 exchange reaction , 1973 .

[10]  R. Marcus.  Semiclassical S‐matrix theory. VI. Integral expression and transformation of conventional coordinates , 1973 .

[11]  G. Schatz,et al.  Role of direct and resonant (compound state) processes and of their interferences in the quantum dynamics of the collinear H + H2 exchange reaction , 1973 .

[12]  J. Ross,et al.  Quantum Dynamical Theory of Molecular Collisions , 1973 .

[13]  D. Truhlar.  Test of Bond-Order Methods for Predicting the Position of the Minimum-Energy Path for Hydrogen Atom Transfer Reactions , 1972 .

[14]  C. Rankin,et al.  The Classical S-Matrix: Linear Reactive Collisions of H + Cl2 , 1971 .

[15]  D. J. Diestler.  Close‐Coupling Technique for Chemical Exchange Reaction of the Type A+BC→AB+C. H+H2→H2+H , 1971 .

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

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

[18]  Martin Karplus,et al.  Exchange Reactions with Activation Energy. I. Simple Barrier Potential for (H, H2) , 1965 .

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

[20]  M. Karplus,et al.  Potential Energy Surface for H3 , 1964 .

[21]  F. T. Wall,et al.  General Potential‐Energy Function for Exchange Reactions , 1962 .

[22]  R. Bell.  The tunnel effect correction for parabolic potential barriers , 1959 .