John C Morrison
University of Louisville, USA
Title: Numerical Hartree-Fock and correlation calculations of the properties of diatomic molecules
Biography
Biography: John C Morrison
Abstract
A summary will be given of various approaches that can be used for doing first-principle calculations on atoms and molecules. The theoretical approaches considered include the multi-configuration Hartee-Fock method and many-body perturbation theory. Because molecules lack spherical symmetry, the orbital equations for molecules typically involve many more independent variables. 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 involves two independent variables and the pair equation for diatomic molecules involve five independent variables. To deal with these problems of higher-dimensionality, our mathematical collaborators have developed numerical methods for dividing the variable space into smaller sub-regions in which the equations can be solved independently. This domain decomposition theory is described and numerical results are given for Hartree-Fock calculations for diatomic molecules and for numerical solutions of the first-order pair equation, which can be used to evaluate the goldstone diagrams that arise in many-body calculations of molecular spectra. The goal of our calculations is to describe the energy levels and transition probabilities of diatomic molecules to a high level of accuracy. In our contributed paper in this conference, we will show how such methods can be used to calculate the energy of two helium atoms approaching each other in cold atomic collisions and to obtain the spectral fingerprints of CO and OH molecules in planetary atmospheres.