Computational and Theoretical Advances in Accurately Modeling Molecular Wave Functions

Abstract

Throughout the past few decades, the use of theoretical methods has become standard practice in the chemical disciplines. This thesis addresses developments in quantum chemical methods for studying challenging electronic structure problems. Background in quantum chemistry and various correlated methods are presented throughout the first chapter. The remaining chapters are described in the following.

Chapter 2 is based on an experimental collaboration studying a novel, open-shell coronoid system. Using the spin-flip (SF) method combined with restricted active space (RAS) configuration interaction, the ground state is predicted to be a singlet with significant hexaradicaloid character (γ0 = 0.826, γ1 = γ2 = 0.773). It has multiple high-spin, low-lying states (up to septet) that are found to be thermally accessible, with nearly uniform energy gaps between consecutive multiplicities. Using the results of RAS-SF, a spin-interaction Hamiltonian—generated to analyze the spin alignment of the molecule—finds predominantly antiferromagnetic coupling between radical site pairs.

In Chapter 3, computational advances in the heat-bath configuration interaction (HCI) method are presented. MPI+OpenMP are used to target improvements in speed, parallel efficiency, and memory requirements. The implementation introduces a hash function to distribute determinants in both the CI and perturbative spaces. These advances enable the study of the triplet-quintet gap in the [FeO(NH3)5]2+ molecule using a (22e,168o) active space, which explicitly included 2.39 × 107 variational determinants and 8.95 × 1010 perturbative determinants. Benchmarks show up to 86% parallel efficiency of the perturbative step on 32 nodes (4096 cores) and total efficiency of 75%. The chapter also includes benchmarks for accuracy against prior studies.

The complete active space self-consistent field (CASSCF) method holds a central place in conceptualizing and practicing quantum chemistry. For application to realistic molecules, however, CASSCF must be approximated to circumvent its exponentially scaling. Applying the many-body expansion—also known as the method of increments—to CASSCF (iCASSCF) has been shown to produce a polynomially scaling method retaining the accuracy of the parent theory while also being capable of treating substantially larger active spaces. However, the orbital parameters of the original iCASSCF implementation were not variationally optimized. Chapter 4 details the theoretical advances to iCASSCF making the method fully variational. These advances enable the method to produce accurate nuclear gradients and optimize stable geometries as well as transition states. Demonstrations on challenging test cases, such as the oxoMn(salen)Cl complex with an active space of (84e,84o) and the automerization of cyclobutadiene show the power of fully variational iCASSCF for describing challenging molecular systems.

Finally, Chapter 5 introduces SlaterGPU, a GPU accelerated library to numerically evaluate the Slater-type orbital (STO) integrals. The electron repulsion integrals (ERIs) are computed under the RI approximation using the analytic Coulomb potential of the Slater basis function. To fully realize the performance capabilities of modern GPUs, the Slater integrals are evaluated in mixed-precision, resulting in speedups for the ERIs of over 80×. Parallelization on multiple GPUs allows for integral throughput of over 3 million integrals per second, placing STO integration within reach of single-threadeed, conventional Gaussian integration schemes. Benchmarks highlighting the quality and speed of the integrals demonstrate the library’s ability to generate the full set of integrals necessary for configuration interaction with up to 6h functions in the auxiliary basis.