Density matrix theory of diatomic molecules

Abstract

The thesis introduces the concept of the adiabatic approximation in relation to the dynamics of the electrons and nuclei within a diatomic molecule. A complete mathematical formulation of molecular dynamics is included. This is shown to reduce to the adiabatic approximation if certain coupling terms are set to zero. The subtleties of how these terms relate to translation and distortion of the electronic part of the molecular wavefunction with internuclear separation, are discussed and shown to pose difficult problems which lead to the introduction of the term ' electron translation factor '. Reduced density matrices are introduced as an alternative to the wavefunction for the evaluation of physical observables of a quantum mechanical system. A summary of their properties clarifies their potential to describe concisely the dynamics of particles within an isolated system. The equations governing these density matrices for a general system are derived from the Schroedinger equation and then specialized to the case of a diatomic molecule. The density matrix equations for the simplest molecule, the HI ion, are examined. A Hartree self consistent field approximation between electronic and nuclear motion is invoked to solve the single particle density matrix equations. Details of the calcula tion are provided along with a presentation of the r esults. Also included is a description of the procedure for systematic improvements upon the Hartree approximation. It is shown that a low order solution of the many electron molecule density matrix equations may be obtained by implementing both a Hartree electron-nuclear interaction approximation and a Hartree-Fock electruu-elecLron interaction approximation. The procedure for obtaining a numerical solution within such approximations is outlined. Finally systematic improvements upon this low order method are investigated. It is shown that improvements may be made along various pathways depending upon how electron correlation is treated. Only further investigations will determine the optimum procedure.