Systematic Approach to Multideterminant Wavefunction Development

Abstract

Electronic structure methods aim to accurately describe the behaviour of the electrons in molecules and materials. To be applicable to arbitrary systems, these methods cannot depend on observations of specific chemical phenomena and must be derived solely from the fundamental physical constants and laws that govern all electrons. Such methods are called ab initio methods. Ab initio methods directly solve the electronic Schrödinger equation to obtain the electronic energy and wavefunction. For more than one electron, solving the electronic Schrödinger equation is impossible, so it is imperative to develop approximate methods that cater to the needs of their users, which can vary depending on the chemical systems under study, the available computational resources and time, and the desired level of accuracy. The most accessible ab initio approaches, including Hartree-Fock methods and Kohn-Sham density functional theory methods, assume that only one electronic configuration is needed to describe the system. While these single-reference methods are successful when describing systems where a single electron configuration dominates, like most closed-shell ground-state organic molecules in their equilibrium geometries, single-reference methods are unreliable for molecules in nonequilibrium geometries (e.g., transition states) and molecules containing unpaired electrons (e.g., transition metal complexes and radicals). For these types of multireference systems, accurate results can only be obtained if multiple electronic configurations are accounted for. Wavefunctions that incorporate many electronic configurations are called multideterminant wavefunctions. This thesis presents a systematic approach to developing multideterminant wavefunctions. First, we establish a framework that outlines the structural components of a multideterminant wavefunction and propose several novel wavefunction ansätze. Then, we present a software package that is designed to aid the development of new wavefunctions and algorithms. Using this approach, we develop an algorithm for evaluating the geminal wavefunctions, a class of multideterminant wavefunctions that are expressed with respect to electron pairs. Finally, we explore using machine learning to solve the Schrödinger equation by presenting a neural network wavefunction ansatz and optimizing its parameters using stochastic gradient descent.