Reduced Density Matrix Methods for the Resolution of Electron Correlation and Their Applications to Bimetallic Complexes

The most fundamental struggle of modern electronic structure theory is the accurate description of electron correlation, which is commonly divided into its dynamic and multireference or strong parts. The former is readily captured with various modern electronic structure methods at polynomial computational cost, while the latter exhibits exponential scaling in traditional wave function based theories. For the precise and tractable computation of molecular electronic properties and processes it is essential to develop methods that capture both dynamic and strong correlation effects at affordable computational cost. Reduced density matrix (RDM) based theories, which exploit the fact that fermions interact pairwise to express the electronic energy as a linear functional of the two electron RDM (2-RDM), provide a promising path towards achieving this goal. In the first part of this dissertation several theoretical developments based on the anti-Hermitian contracted Schrödinger equation are detailed, which enable the computation of all-electron correlation. This includes the introduction of a spin-averaging scheme allowing for the efficient calculation of non-singlet spin states, the elucidation of its orbital dependence, as well as the use of a hybrid quantum-classical algorithm to calculate the multi-reference correlation on a quantum computer. Additionally, it is demonstrated that pure N-representability conditions imposed on the 2-RDM may yield sparse non-orthogonal wave function expansions, which may serve as a sparse ansatz in the development of RDM functional theories. In the second part of this dissertation RDM methods are applied to resolve the electronic structures and properties of several bimetallic complexes. Binuclear transition metal complexes exhibit significant multi-reference character arising from the degenerate d-orbital manifolds and their complex and tunable electronic structures make them prime candidates in development of single molecule magnets (SMMs), molecular switches, molecular conductors, as well as in the fields of spintronics and quantum information storage. The magnetic exchange interaction in a cobalt quinoid dimer is investigated, as well as the biradical character and electronic properties, including the excited states and singlet-triplet gaps, of a series of tetrathiafulvalene-2,3,6,7-tetrathiolate bridged bimetallic complexes.