Numerical Hartree–Fock and Many-Body Calculations for Diatomic Molecules

Abstract

The Hartree–Fock theory for diatomic molecules and a theoretical approach for performing many-body calculations are described. Using single-electron wave functions and energies produced by a numerical Hartree–Fock program, the Goldstone diagrams that arise in a perturbation expansion of the energy are evaluated by expressing the Goldstone diagrams in terms of pair functions that are the solution of first-order pair equations. The relevant pair equations are discretized and solved using the spline collocation method with a basis of third-order Hermite splines. Both the Hartree–Fock theory and many-body theory are more complex for diatomic molecules than they are for atoms. While the Hartree–Fock equations for atoms involve a single radial variable and the two-electron pair equation for atoms involve two radial variables, the Hartree–Fock equations for diatomic molecules involve two independent variables and the pair equation for diatomic molecules involves five independent variables. To deal with these problems of higher-dimensionality, we have developed numerical methods for dividing the variable space into smaller subregions in which the equations can be solved independently. This domain decomposition theory is described and numerical results are given for a single-electron model problem and for many-body calculations for diatomic molecules. Because the long-range goal of our work is to develop an extensive program for doing numerical coupled-cluster calculations on molecules, we will take special care to show how each part of our numerical approach is tested.