The Many-Body Expansion of Electron Interactions for Transition Metal Complexes

Abstract

Transition metals complexes (TMCs) express a variety of interesting physical properties brought about by varying geometry, electronic state, and orbital interactions. In principle, the electronic structure of TMCs can be approached through first principles theories, giving a complete description of the energy, electron density, and other physical properties. For realistic models of TMCs with relevance to chemical experiment, however, the complicated metal-metal, metal-ligand, and ligand-ligand interactions stretch the ability of conventional electronic structure tools to provide consistent accuracy.

Many computational methods have been developed to address challenges with TMCs, but these have been limited in accuracy or unfavorable scaling with system size. The method of increments, or the many-body expansion (MBE), has shown promise to alleviate these difficulties, by approaching exacting, high-cost wave function results with tractable computational cost. This expansion also expresses a beneficial framework that is conducive to deeper revelations of the electronic state. Herein, this dissertation is focused on developing methodologies to evaluate the electronic structure of TMCs tractably and systematically via incremental methods.

The utility and convergence of the MBE is first demonstrated with small molecules, methane dissociation, and conjugated polyenes with 100+ electrons. The last of these test cases is computationally impossible to assess without truncation of the orbital space through other electronic structure paradigms. Construction of incremental expectation values is illustrated, and the accuracy of resulting energies and optimized geometries suggests that the incremental approach has potential for treating more complex systems. Additionally, the scaffolded structure of the MBE lends itself to a deeper analysis of orbital interactions via visualization schemes, presenting a means of understanding the underlying properties that can be understood via these methods, rather than just the total energy.

The first study of TMCs via the MBE includes accurate and tractable computations for four diradical species with near-degenerate singlet-triplet spin gaps and up to 142 valence electrons, a first for electronic structure methods. Given their larger size and inclusion of metal centers, a new tailorable screening technique is introduced to increase the efficiency without sacrificing accuracy, the versatility of which can also be used to gain insight into the overall electronic structure. Using this method, convergence patterns of the MBE are revealed, and key metal-ligand interactions are shown to be responsible for measurable portions of the spin gap.

Application of these methods are extended to a strongly correlated iron−porphyrin complex, where newly developed visualization techniques are utilized to perform a thorough investigation of interactions of up to four orbitals at a time. Strong correlations between the metal d and porphyrin’s π orbitals are identified to be pivotal in accurately determining the spin gap, with distinct d-d, d-π, and π-π orbital interactions being key influencers of the triplet-triplet manifold. These techniques are used to analyze an iron−oxo complex as well, where the presence of numerous metal-ligand interactions poses a computational and investigative challenge. Spatial locality of electrons is found to be a significant factor in deciding electronic features, a factor that is capitalized upon with a new orbital grouping procedure that strategically captures all interactions among the strongly correlating metal-centered orbitals. Overall, the many-body expansion provides accurate, tractable, and improvable computations on transition metal complexes, with valuable insight into the electronic structure granted by novel correlation visualization methods.