On the Construction of a Novel Mean Field Platform and Broadly Applicable Variational Principle Methods for Electronically Excited States

Electronic structure theory is an evolving field with abounding potential applications to a multitude of interesting systems, including atoms and molecules in electronically excited states. Central to this dissertation are two critical components of excited state electronic structure methods – the ansatzes that describe a system’s electronic configuration and the algorithms used to optimize them. In this thesis, advancements on both fronts are presented. To contextualize this new work, several prominent excited state ansatzes and optimization methods are reviewed, and their performances in applications to DNA photophysics and organic photovoltaics are examined. The strengths and weakness of the existing ansatzes inspired the construction of a flexible, computationally affordable excited state mean field wave function that is analogous to ground state mean field theory. This qualitatively accurate, state-specific ansatz provides the foundation upon which higher accuracy correlation methods are built that rival the accuracy of existing excited state theories at lower overall cost scaling. Further developments detailed in this thesis occur on the optimization side of electronic structure methods and relate to excited state variational principles. First, a novel analysis on the lack of size consistency within a class of excited state variational principles widely used in stochastic quantum chemistry methods is presented. A unique algorithm that transforms between variational principles on the fly while rigorously maintaining size consistency and state specificity is shown to eliminate this optimization-induced source of error. Finally, a generalized variational principle that guarantees state specificity via a unique global minimum and identifies electronic states based on a list of user-specified properties is defined, and its ability to resolve even energetically degenerate states in dense excitation manifolds is realized. From the construction of a novel mean field excited state wave function, to the analysis and restoration of size consistency in a class of excited state variational principles, to the development of a generalized variational principle, the research herein constitutes significant steps towards more robust, efficient, and accurate modelling of electronically excited states