Combining High- and Low-Level Electronic Structure Theories for the Efficient Exploration of Potential Energy Surfaces

Abstract

The efficient exploration and characterization of potential energy surfaces paves the way for the theoretical elucidation of complex chemical processes. A potential energy surface arises from the application of the Born-Oppenheimer approximation when solving the Schrodinger equation for a molecular system. The extraction of energies and nuclear gradients from the Schrodinger equation is typically cost-prohibitive, which has inspired a plethora of approximations. In this thesis, we present the development of embedding and machine learning methodologies that provide fast and accurate energies and nuclear gradients for different chemical classes by combining high- and low-level electronic structure theories. If a chemical change occurs in a spatially localized region, embedding strategies offer an effective approach for balancing accuracy and computational cost. We first consider embedded mean-field theory (EMFT), which seamlessly combines different mean-field theories for different subsystems to describe the whole molecular system. We analyze the errors in EMFT calculations that occur when subsystems employ different atomic-orbital basis sets. These errors can be alleviated by a Fock-matrix correction scheme or by following general basis set recommendations. Systems exhibiting a more complicated electronic structure require a systematically improvable level of theory for the subsystems, which can be realized by projection-based embedding. Projection-based embedding enables the description of a small part of a molecular system at the level of a correlated wavefunction method while the remainder of the system is described at the mean-field level. We go on to derive and numerically demonstrate the analytical nuclear gradients for projection-based embedding. If description of the entire system at the high level of theory is deemed necessary, molecular-orbital-based machine learning (MOB-ML) calculations offers a framework to predict accurate correlation energies at the cost of obtaining molecular orbitals. We go on to present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients. We demonstrate the developed methodologies by exploring potential energy surfaces of organic and transition-metal containing molecules.