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Self Consistent Excited State Mean Field Theory: Development and Applications

Abstract

In the wide spectrum of excited state quantum chemistry methods, there is no direct analogue to Hartree-Fock theory. This dissertation presents the theory and initial applications for a self consistent framework for Excited State Mean Field (ESMF) theory. This method presents a self consistent equation analogous to the Roothaan-Hall equation, that is constructed with mean-field one-electron operators. The convergence criteria is described by a commutator condition between Fock-type operators and density operators, just like in Hartree-Fock theory. Finally, this method is accelerated via direct inversion of the iterative subspace (DIIS), akin to acceleration in the ground state theory. Futhermore, this work discusses applications of ESMF to larger solvated systems, afforded by ESMF's scaling -- the method costs roughly twice the cost of a Hartree-Fock calculation. Getting an accurate physical picture of excited states in solvated systems is challenging, and the second half of this dissertation focuses on a comparative analysis of various methods, their degree of correlation, and their ability to qualitatively describe donor and acceptor regions for a charge transfer excitation. This comparison shows that ESMF can accurately describe the degree of participation of solvent water molecules in the excitation, unlike Density Functional Theory (DFT) based methods. However, when there is minimal participation from the solvent, Restricted Open-shell Kohn Sham methods fare better, indicating that the lack of correlation in ESMF prevents the method from providing a more quantitatively accurate picture. Using ESMF as a stepping rung for developing a hierarchy of excited state specific methods is a promising platform to achieve affordable excited state specific calculations.

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