Localized basis functions and other computational improvements in variational nonorthogonal basis function methods for quantum mechanical scattering problems involving chemical reactions
Abstract
The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.
 Publication:

Computing Methods in Applied Sciences and Engineering
 Pub Date:
 1990
 Bibcode:
 1990cmas.proc..291S
 Keywords:

 Chemical Reactions;
 Computer Techniques;
 Hamiltonian Functions;
 PredictorCorrector Methods;
 Quantum Mechanics;
 Schroedinger Equation;
 Variational Principles;
 Boundary Conditions;
 Electron Scattering;
 Finite Difference Theory;
 Green'S Functions;
 Thermodynamics and Statistical Physics