Linearized Pair-Density Functional Theory

Photophysical and photochemical processes are ubiquitous throughout chemistry, biology, and nature. Advanced multireference electronic-structure methods are necessary to accurately model the electronically-excited states of molecular systems and provide potential energy surfaces for the nuclei to evolve along during semi-classical, ab initio molecule dynamics. Multiconfiguration pair-density functional theory (MC-PDFT) is a post-self-consistent field, multireference electronic-structure method that has been successful at computing both ground- and excited-state electronic energies. However, MC-PDFT is a single-state method in which the MC-PDFT energies come from an energy functional that depends on the kinetic energy, electron density, and on-top pair density of a wave function, and they do not come from diagonalization of a model-space Hamiltonian matrix. This can lead to inaccurate topologies of potential energy surfaces near locally avoided crossings and conical intersections, which are common features of excited states. In order to perform physically correct ab initio molecular dynamics for electronically nonadiabatic processes with MC-PDFT, it is necessary to develop a method that recovers the correct potential energy surface topology throughout the entire nuclear configuration space. This thesis develops a computationally efficient multi-state extension of MC-PDFT that accurately treats the nuclear-electronic coupling near conical intersections and locally avoided crossings in order to model photochemical processes. Given a a pre-defined model space, I construct an effective Hamiltonian called the linearized pair-density functional theory (L-PDFT) Hamiltonian, that is a functional of the one- and two-electron reduced density matrices (RDM) of the states in that space. I construct the L-PDFT Hamiltonian by expanding the MC-PDFT energy functional in a power series of the one- and two-RDM about their state-averaged values within the model space and truncate this series at first order, such that for any state within this model space, the expectation value of the L-PDFT Hamiltonian is a linear approximation to its MC-PDFT energy. By construction, the L-PDFT Hamiltonian is a well-defined linear operator whose off-diagonal elements are generally nonzero, and diagonalization within a given subspace yields a set of potential energy surfaces with the correct topology near conical intersections and locally avoided crossings. In this thesis, I show that L-PDFT is able to correctly compute the potential energy surfaces near conical intersections and locally-avoided crossings for a variety of challenging cases including phenol, methylamine, and the spiro cation. Furthermore, I benchmark its accuracy on predicting vertical excitation energies and show that it performs similarly to multireference many-body perturbation theory, but at a reduced computational cost. I then derive and implement analytical nuclear gradients for L-PDFT to enable both molecular dynamics and geometry optimizations. Finally, I study the cis-to-trans photoisomeraization of azomethane using L-PDFT nonadiabatic molecular dynamics.