Multi-state density functional theory (MS-DFT) and multi-state energy decomposition analysis (MS-EDA)

Abstract

This work presents the theory and application of a multistate energy decomposition analysis (MS-EDA), making use of multistate density functional theory (MSDFT). Through this research, a method has been developed that can be conveniently used to elucidate the energy terms contributing to intermolecular interactions of molecular complexes in electronically excited states. Multistate density functional theory is a novel quantum theory that employs matrix density as the fundamental variable both for the ground state and for excited states. The method goes beyond the Hohenberg-Kohn theorems for one electronic state and treats all electronic states on an equal footing. Chapter 1 reviews the fundamental principles and theorems of MSDFT and introduces the concepts of minimal active space (MAS) and matrix correlation functional. In addition, the computational procedure and approximations of non-orthogonal state interaction (NOSI) are presented, upon which the remainder of the research and calculation is built. Chapter 2 summarizes the development of a block-localized excitation (BLE) approach for self-consistent-field (SCF) optimization of excited state (non-aufbau) configurations. The BLE method is a form of delta SCF (∆SCF) procedure using a projection scheme in molecular orbital basis that matches the order and occupation of the initial, predefined electronic configuration. The main novelty of the BLE method is to allow block localization of molecular orbitals on individual molecules in a molecular complex or a subset of atomic orbitals belonging to a given symmetry. Consequently, it is possible to optimize a set of non-orthogonal block-localized molecular orbitals for a system in which one molecule is excited to an excited configuration in the presence of other molecules in the ground state. The individually optimized excited configurations are used to form a minimal active space for subsequent MSDFT-NOSI calculations to determine the energies of the adiabatic ground and excited state as well as their densities. The BLE method is illustrated in the study of excimer formation for a naphthalene dimer and a preliminary analysis of energy terms of binding interactions was presented. The BLE method was further applied in Chapter 3 to a group of bi-molecular complexes that have low-lying charge transfer states. It was shown that both local covalent and intermolecular charge-transfer excited states can be adequately treated by using MSDFT-NOSI along with MAS in which individual configurations are optimized by the BLE method.The computed excitation energies, including charge-transfer states, from NOSI calculations employing the M06-2X functional to approximate the diagonal terms of the matrix correlation functional along with the cc-pVDZ basis functions are in good accord with results from EOM-CCSDT benchmarks.Chapters 4 and 5 rigorously formulate the theory, define energy terms for intermolecular interactions in excited states, and present findings from applications of energy decomposition analyses on a range of molecular complexes in excited states. In the present MS-EDA approach, energy terms associated with interactions in the ground state are grouped into a single term called local interaction energy and the focus of the energy decomposition analysis is placed on energy terms unique to excited states. These include the exciton resonance energy due to the electronic coupling interactions among locally excited states of individual monomers, the super-exchange stabilization energy due to forward and backward charge transfer states between two monomers, and orbital and configuration delocalization energy as a result of expanding the molecular orbitals from block-localized states to full molecular orbitals over the entire molecular complex and determinant configurations that specifically included in the MAS. A key feature in the MS-EDA method is that all intermediate states are variationally optimized using the BLE technique. It was found that molecular complexes in excited states can be categorized into three types: (1) encounter excited-state complex, (2) charge-transfer exciplex, and (3) intimate excimer or exciplex. For all examples, MS-EDA’s decomposition of the binding energy allows for an unambiguous identification of the excitation character. Finally, in Chapter A, the bond dissociation process of methyl radical in excited states is summarized, providing insights into the interplay of diabatic states corresponding to different electronic states of the dissociated species. The active space in this chapter has one noteworthy difference from the examples in all other chapters. In all of those examples, the off-diagonal elements of the Hamilton matrix functional have generally small contributions from their WFT-style terms. In this methyl dissociation example however, the NOSI-MSDFT procedures and TDFs that we developed are applied to valence-bond style determinants. This demonstrates that these procedures and TDFs are also applicable to such an active space, which is characterized by strong WFT-style contributions to the interactions between determinants (and by a large overlap between determinants). In summary, this work illustrates the computational method, accuracy and the wide range of applications of nonorthogonal state interaction in multistate density functional theory. It is hoped that the MS-EDA method will be a useful tool for understanding the nature of intermolecular interactions of excimers and exciplexes.