Quantum scattering via the log derivative version of the Kohn variational principle

Abstract The log derivative version of Kohn's variational principle is used as a setting for a new numerical approach to quantum scattering problems. In particular, a new radial basis set is devised which is both (a) ideally suited to the log derivative boundary value problem, and (b) directly amenable to a discrete representation based on Gauss-Lobatto quadrature. This discrete representation greatly facilitates the evaluation of the exchange integrals which arise in Miller's formulation of chemical reactive scattering, and therefore significantly simplifies calculations which exploit this formulation. Applications to the 3-D H+H 2 reaction clearly demonstrate the practical utility of the method.

[1]  G. A. Parker,et al.  Discrete variable representations and sudden models in quantum scattering theory , 1982 .

[2]  W. Miller.  Coupled Equations and the Minimum Principle for Collisions of an Atom and a Diatomic Molecule, Including Rearrangements , 1969 .

[3]  William H. Miller,et al.  Accurate three‐dimensional quantum scattering calculations for F+H2→HF+H , 1988 .

[4]  William H. Miller,et al.  Quantum scattering via the S‐matrix version of the Kohn variational principle , 1988 .

[5]  Bernie D. Shizgal,et al.  A discrete ordinate method of solution of linear boundary value and eigenvalue problems , 1984 .

[6]  J. Light,et al.  On distributed Gaussian bases for simple model multidimensional vibrational problems , 1986 .

[7]  J. Light,et al.  Highly excited vibrational levels of "floppy" triatomic molecules: A discrete variable representation - Distributed Gaussian basis approach , 1986 .

[8]  Blackmore,et al.  Discrete-ordinate method of solution of Fokker-Planck equations with nonlinear coefficients. , 1985, Physical review. A, General physics.

[9]  Richard A. Friesner,et al.  Solution of the Hartree–Fock equations for polyatomic molecules by a pseudospectral method , 1987 .

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

[11]  B. R. Johnson,et al.  The multichannel log-derivative method for scattering calculations , 1973 .

[12]  William H. Miller,et al.  A new basis set method for quantum scattering calculations , 1987 .

[13]  W. Miller,et al.  New method for quantum reactive scattering, with applications to the 3-D H+H2 reaction , 1987 .

[14]  J. Light,et al.  Accurate localized and delocalized vibrational states of HCN/HNC , 1987 .

[15]  D. Secrest,et al.  The generalized log‐derivative method for inelastic and reactive collisionsa) , 1983 .

[16]  W. Miller,et al.  A pointwise representation of the s-matrix Kohn variational principle for quantum scattering , 1988 .

[17]  D. Kouri,et al.  Variational basis-set calculations of accurate quantum mechanical reaction probabilities , 1987 .

[18]  J. Light,et al.  Generalized discrete variable approximation in quantum mechanics , 1985 .

[19]  D. Kouri,et al.  Quantum mechanical algebraic variational methods for inelastic and reactive molecular collisions , 1988 .

[20]  Richard A. Friesner,et al.  Solution of the Hartree–Fock equations by a pseudospectral method: Application to diatomic molecules , 1986 .

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

[22]  G. A. Parker,et al.  Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory , 1987 .

[23]  Richard A. Friesner,et al.  Solution of self-consistent field electronic structure equations by a pseudospectral method , 1985 .

[24]  D. Kouri,et al.  L2 amplitude density method for multichannel inelastic and rearrangement collisions , 1988 .