Part i: Computational Methods for the Evaluation of the 1-2 Type Three Center Integral of 1/R(12) Over Slater - Orbitals. Part II: Studies in Rayleigh-Schroedinger Perturbation Theory.
The analytic expressions for the 1-2 type three center electron repulsion integral over Slater-type orbitals are cast into formulas which can be implemented into a computer program. These formulas involve a collection of special functions defined in terms of derivative operators acting on exponential integrals and related functions. Recurrence formulas for the special functions were developed and investigated in regard to numerical stability. A computational scheme to evaluate the special functions is developed based on the use of the recurrence relations. The schemes for the calculation of the special functions are incorporated along with the formulas into a system of computer programs to calculate the 1-2 type integral. Various alternative algorithms for implementing the formulas are studied in the development of the programs. The resulting system of programs are tested and compared with the results of other computational methods. The system of programs is included in Appendix B. Formulas are developed to solve recursively for the degenerate Rayleigh-Schrodinger perturbation theory wavefunctions and energy. The formulas for the case of a first order perturbation to the Hamiltonian and the degeneracy lifted in first order are used by a computer program to calculate the energy coefficients for the Zeeman effect in hydrogen. The energy coefficients are calculated up to 87('th) order in the perturbation series in 1/2b('2) for the 3s-3d(,0) states. A more general situation can be treated by adapting the recursive formulas for use in a computer program for the case with the degeneracy being lifted in second or lower order and with a second order perturbation to the Hamiltonian. The combined Stark-Zeeman effect along with various limiting conditions associated with it are treated as examples. In addition a computational method is developed for treating the ground state of hydrogen in a perturbation of the form. (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).
- Pub Date:
- June 1981
- Physics: Molecular