Abstract

The objective of this thesis is to compare the upper bound of the ground state energy of doubly ionized carbon (C⁺⁺) to the lower bound obtained by reduced density matrices.

To make a fair comparison, the number of orbitals used in both is the same, namely ten. The upper bound is obtained by use of the standard Rayleigh-Ritz Variational Principle which states ⟨Ψ|H|Ψ⟩ ≥ Eo(H) were Eo(H) is the exact ground state energy, H is the Hamiltonian, and Ψ is the trial wave function.

Abstract The objective of this paper is to demonstrate the usefulness of density matrix techniques in the determination of the ground state energy of certain atomic systems. Use of the method, currently under development, results in a lower energy bound in contrast with the Rayleigh-Ritz method which yields an upper bound. The former technique is illustrated for the C⁺⁺ atomic system. It was found that the Pauli Principle was being violated even when the 2-particle density matrix is expanded in...