Numerically Exact Configuration Interaction at Quadrillion-Determinant Scale

Abstract

Quantum chemistry is the field of study that uses quantum mechanics to make chemical predictions. The chemistry of the systems of interest (atoms and molecules) is faithfully described by the electronic Dirac equation. The equation describes the relativistic dynamics of the electrons in a molecule subject to electric forces from the nuclei and other electrons. For virtually all systems of practical interest, the equation is impossible to solve by means of exact analytical techniques. Thus, the use of numerical methods becomes inevitable. The most accurate such method is configuration interaction (CI), which yields the exact formal solution of the Dirac equation in the complete-basis-set limit. Due to the factorial growth in the resource requirements of CI calculations, they have historically been applied to the smallest of chemical systems. In this dissertation, we introduce categorical compression of CI vectors within the small tensor product distributed active space (STP-DAS) CI framework. We demonstrate its capabilities by conducting a CI calculation consisting of over one quadrillion determinants, the largest CI calculation to date. We then explore strategies to accelerate STP-DAS CI calculations by adapting the STP-DAS σ-build step to graphics-processing units (GPUs). Finally, we use the developed framework to conduct previously untenable benchmark studies of two state-of-the-art quantum chemical methods, namely coupled cluster (CC) and density matrix renormalization group (DMRG).