Eric Timian

Date of Award

January 2018

Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Mark Hoffmann


Electronic structure theory programs strive to be as widely applicable as possible. In order to account for effects exhibited by heavier elements, relativistic considerations must be incorporated into these programs. The methods developed in recent years generally succeed in describing the relativistic nature of systems containing heavier elements with reasonable accuracy, but have limited application due to their complexity and computational demand. Highly correlated systems exhibiting significant relativistic effects remain as a challenge to quantum chemical methods.

In this thesis, I present the application of a well-defined relativistic Hamiltonian to a high-level electronic structure theory to generate a relativistic variant of a high-level multireference electronic structure theory capable of obtaining accurate results for highly correlated relativistic systems. This theory applies the exact two-component (X2C) relativistic Hamiltonian and a third-order Douglass-Kroll-Hess (DKH3) transformation for the spin-free and spin-orbit terms, respectively. The spin-orbit integrals are contracted into an effective one-electron Hamiltonian using the atomic mean field (AMFI) approximation, which increases computational efficiency with little loss in accuracy. By applying this scheme to the second-order generalized van Vleck perturbation theory (GVVPT2), which offers appropriate treatment of electron correlation, a theory providing an accurate analysis of chemical systems with strong relativistic effects is obtained.

The method developed in this work is used to explore ground and low-lying excited states of the lanthanide dimer systems Gd2 and Dy2. Results from scalar relativistic studies show that GVVPT2 can accurately characterize these systems. The ground electronic states obtained (Gd2: 19Σg- ; Dy2: 11Πg) match literature and theoretical results. The spectroscopic data obtained for the ground state of Gd2 (Re = 2.826 Å; De = 2.48 eV; ωe = 153.0 cm-1) are in excellent agreement with literature values (Re = 2.877 Å; D0 = 2.1 ± 0.7 eV; ωe = 138-149 cm-1). Inclusion of spin-orbit coupling in these studies is expected to improve the results to agree with literature values to within chemical accuracy. Future work is planned to extend this method to transition metal trimers.