UC Berkeley

In this dissertation, we will investigate two different areas of electronic structure theory.

In the first portion, we shall focus on the study of molecular transition metal systems.

Specifically, we will be modeling oxidation and reduction catalysts, which are potentially useful in creating new clean energy sources.

Secondly, we will develop a wave-function based method for computing electronic excited states, with a focus on multielectron excitations.

These excitations play an important role in many areas of physics and chemistry, including photosynthesis, vision, and organic solar cells.

Quantum mechanics tells one how to compute all the properties of a system which correspond to operators, but what if a property of a given system has no corresponding operator and what if this property provides synthetic chemists a collectively obtained historical intuition about reactivity?

This set of questions exactly applies to the case of oxidation state, a property which represents the hypothetical charge on a given atom.

This makes calculating oxidation states from electronic structure a matter of creating a recipe which respects both the physics of the system and matches "known'' values.

We develop one such recipe which we call the localized orbital bonding analysis (LOBA).

This method is based on two standard electronic structure methods: localization of molecular orbitals and population analysis.

We show that LOBA matches "known'' oxidation states of a large set of transition metal systems, we compare it with other recipes for calculating oxidation states, and use it to show a ligand reduction in a proposed transition-metal water-oxidation catalyst.

Now that we have a method which allows us to present computational results in a chemically intuitive framework, we applied LOBA and Kohn-Sham Density Functional Theory (KS-DFT) to study the electro-catalytic generation of hydrogen from protons in an aqueous solution by a molecular molybdenum-oxo complex.

We mapped out the thermodynamics of the catalytic cycle including both the reduction steps, which by comparison with experimental evidence were found to be coupled with a proton transfer.

We also evaluated the kinetics of the release of hydrogen gas, using transition state theory.

It was found experimentally that the reduction overpotential would be the limiting factor in using this catalyst for real world applications

By analyzing the LOBA results across this cycle, we found that one of the reductions partially occurred on the ligand, because of this we supposed that substitutions on the ligand could provide changes in the reduction potentials.

With this evidence we calculated the same path for the complex with electron withdrawing (fluorides) and electron donating (methyl-) groups located on the ligand and found that the fluorides reduced the potential making the catalyst theoretically more efficient.

Additionally, we present an alternative mechanism for H₂ release which has a lower energy barrier by the inclusion of a bridging water, propose a mechanism for the stoichiometric reaction which produces the catalyst, and discuss alternative catalytic cycles.

Our second major advance was the development of an excited state method, Non-orthogonal Configuration Interaction (NOCI).

This method has many advantages including the ability to treat double excitations at the same level as single excitations and low computational scaling when compared with other methods.

NOCI is a configuration interaction method where the basis in which one diagonalizes the Hamiltonian can be any Slater determinant, each of which may be non-orthogonal with the rest of the basis.

To provide proof of concept, we choose systems for which the character of the wavefunctions of excited states are known; the linear polyenes and β-carotene.

This also showed that NOCI is able to treat double excitations which are important for these systems.

We demonstrate that NOCI, when applied to systems with extended conjugation, provides a feasible way to obtain a qualitatively correct wavefunction.

We also present a new extension to this method allowing for purification of higher-order spin states by utilizing Generalized Hartree--Fock (GHF) Slater determinants and the details for computing < S² > for the ground and excited states.

In order to apply NOCI more straightforwardly to other systems, we develop a procedure for automatically generating the Slater determinants used in the expansion of the wavefunction.

This method utilizes information from the Hartree--Fock Hessian to generate the basis for diagonalizing the Hamiltonian.

We validate this method by considering a subset of the systems studied in the previous section, showing that the method performs almost the same as when prior knowledge of the system is used to choose the basis.

We also corroborate this success by applying the method to a wide range of well-characterized chromophores, resulting in errors very similar to CIS for single excitations and much improved for double excitations.