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Chemistry is teeming with light-driven processes such as photosynthesis and molecular switches, where electronically excited states are paramount to understanding the underlying mechanisms at play. Nevertheless, the appropriate treatment of effects such as strong electron correlation and orbital relaxations are beyond the simplifying assumptions of linear response theory and remains a challenge for theoretical modeling, consequently hampering the theory’s ability to provide meaningful predictions and inform experiment. In this thesis, we present a novel approach with the flexibility and precision to overcome these obstacles.To contextualize this work, we first discuss current excited state ansatzes and optimization methods, demonstrating their strengths and weaknesses in handling the challenges of modeling multi-reference systems like excited states. Using a generalized variational principle, we construct a fully excited-state-specific wave function optimization algorithm and demonstrate both its resilience to common optimization problems such as root flipping and its ability to locate and tightly converge excited state stationary points. Exhibiting both accuracy and reliability in calculating states with strongly correlated character and strong orbital relaxations, this approach is capable of providing state-specific insight in scenarios which elude existing methods, including some core, charge transfer and double excitations. We expand our study to explore the effect of these methodological improvements in comparison to a prominent traditional approach for geometry relaxations and potential energy surfaces for a photochemically relevant system, helping to elucidate the complexity of excited state energetics. The realization of this novel method constitutes significant steps forward for state-specific multi-reference approaches for the precise, accurate and robust modeling of 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.

This thesis is concerned with the development of minimally-parameterized and highly-transferable density functionals. A methodology for searching a given functional space is developed and used to parameterize three novel functionals: ωB97X-V -- a 10-parameter, range-separated hybrid, generalized gradient approximation density functional with VV10 nonlocal correlation, B97M-V -- a 12-parameter, local meta-generalized gradient approximation density funcitonal with VV10 nonlocal correlation, and ωB97M-V -- a 12-parameter, range-separated hybrid, meta-generalized gradient approximation density functional with VV10 nonlocal correlation. These three functionals are validated by comparisons to the best existing density functionals in their class, and their proper usage (with respect to basis sets and integration grids) is documented to facilitate use in chemical applications.

Due to the unfavorable scaling of quantum chemical methods one usually has to compromise between accuracy and computational effort with growing system size. Finding approximations that overcome this constraint sparked the interest of researchers which eventually led to the development of so-called multiscale methods. This thesis pertains to a multiscale method called Frozen-Density Embedding theory (FDET), in which the system is described by means of two independent quantum mechanical descriptors, the wavefunction of the embedded species and the charge density of the environment. This work examined the effect of the non-linearity of FDET equations. The second topic of this thesis was the development and implementation of FDET-based methods for ground and excited states. For this purpose the fdeman module, which manages all steps of an FDET calculation, was implemented into the quantum chemistry software package Q-Chem.

A reduction of the molecular “communication channel” in atomic resolution, which generates the entropy/information indices of the system chemical bonds, is performed by combining several atomic inputs and/or outputs into a single unit representing a collection of bonded atoms. The implications of such fragment-reduced communication channels for gaining both the internal (intra-subsystem) and external (inter-subsystem) bond-indices are examined. The entropy/information quantities of the reduced channels of molecular subsystems are proposed as descriptors of their information bond “order” and its covalent/ionic composition. These predictions are compared with the bond indices resulting from the molecular orbital (MO) theory. The rules for combining the subsystem entropy/information data into the corresponding global quantities describing the system as a whole are derived and tested. The so-called complementary reductions are used to formulate the exact combination rules for the molecular entropy/information bond indices. Applications to the three-orbital model and π-bond systems (butadiene and benzene) in the Huckel theory approximation are reported and used to illustrate the proposed concepts and techniques. The subsystem bond-order conservation and a competition between its ionic and covalent contributions are discussed. In contrast to the familiar MO bond indices, the entropic descriptors of molecular fragments are shown to exhibit a remarkable degree of equalization, thus emphasizing the information equilibrium of the ground-state distributions of electrons.

Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure–property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating inex nihilocrystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program.

Metal-organic frameworks (MOFs) are appealing candidates for use in energy harvesting and concentrating because of their high chromophore density and structural tunability. The ability to engineer electronic excitation energy transport pathways is of particular interest for designing energy harvesting materials. In this study, theoretical analysis was performed on energy transfer in MOFs that contain light absorbing ruthenium complexes that serve as hopping intermediates for energy transfer kinetics and energy trapping osmium complexes. We find that the excitation transport kinetics is well described by a Dexter (exchange) triplet-to-triplet energy transfer mechanism with multistep incoherent exciton hopping. The modeling combines ab initio electronic structure theory with kinetic network analysis. The sensitivity of Dexter mechanism energy transfer to framework structure establishes different kinds of energy transport paths in the different structures. For example, the mixed Ru/Os MOF structures described here establish one or three-dimensional hopping networks. As such, Dexter mechanism energy harvesting materials may be amenable to designing structures that can spatially direct exciton energy along specific pathways for energy delivery to reaction centers. © 2013 American Chemical Society. 117 43 22250 22259 Cited By :15

Recent studies on applications of the information theoretic concepts to molecular systems are reviewed. This survey covers the information theory basis of the Hirshfeld partitioning of molecular electron densities, its generalization to many electron probabilities, the local information distance analysis of molecular charge distributions, the charge transfer descriptors of the donor-acceptor reactive systems, the elements of a “thermodynamic†description of molecular charge displacements, both “vertical†(between molecular fragments for the fixed overall density) and “horizontal†(involving different molecular densities), with the entropic representation description provided by the information theory. The average uncertainty measures of bond multiplicities in molecular “communication†systems are also briefly summarized. After an overview of alternative indicators of the information distance (entropy deficiency, missing information) between probability distributions the properties of the “stockholder†densities, which minimize the entropy deficiency relative to the promolecule reference, are summarized. In particular, the surprisal analysis of molecular densities is advocated as an attractive information-theoretic tool in the electronic structure theory, supplementary to the familiar density difference diagrams. The subsystem information density equalization rules satisfied by the Hirshfeld molecular fragments are emphasized: the local values of alternative information distance densities of subsystems are equal to the corresponding global value, characterizing the molecule as a whole. These local measures of the information content are semi-quantitatively related to the molecular density difference function. In the density functional theory the effective external potentials of molecular fragments are defined, for which the subsystem densities are the ground-state densities. The nature of the energetic and “entropic†equilibrium conditions is reexamined and the entropy representation forces driving the charge transfer in molecular systems are introduced. The latter combine the familiar Fukui functions of subsystems with the information densities, the entropy representation “intensive†conjugates of the subsystem electron densities, and are shown to exactly vanish for the “stockholder†charge distribution. The proportionality relations between charge response characteristics of reactants, e.g., the Fukui functions, are derived. They are shown to follow from the minimum entropy deficiency principles formulated in terms of both the subsystems electron densities and Fukui functions, respectively.