Date on Master's Thesis/Doctoral Dissertation

12-2025

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Chemistry

Degree Program

Chemistry, PhD

Committee Chair

Thompson, Lee

Committee Member

Kozlowski, Pawel

Committee Member

Wilson, Andrew J.

Committee Member

Liu, Shudun

Author's Keywords

Nonorthogonal multiconfiguration self-consistent field; NOMCSCF; orbital robust optimization; multi-correlation mechanism; goldstone manifold; black-box

Abstract

The "different orbital different configuration" (DODC) framework is a general formulation of multireference wavefunctions that allows each configuration (determinant) to possess its own set of optimized molecular orbitals, rather than sharing a common orbital basis as in conventional orthogonal configuration interaction (CI) or Complete Active Space Self-Consistent Field (CASSCF) methods. One prominent example of the DODC framework is the Nonorthogonal Configuration Interaction (NOCI) method, which relaxes the orthogonality constraint between the orbitals of different configurations. This relaxation enables a compact yet flexible description of systems exhibiting strong correlation. By employing multiple nonorthogonal reference determinants, NOCI naturally incorporates orbital relaxation and captures essential multireference effects without requiring complex active-space selection. However, NOCI also demands significant chemical intuition and faces technical challenges in identifying the appropriate set of determinants to include in the expansion. To overcome the challenges associated with the NOCI approach and develop a more black-box protocol for obtaining the relevant set of nonorthogonal determinants, this dissertation advances the Nonorthogonal Multiconfiguration Self-Consistent Field (NOMCSCF) method, which simultaneously optimizes configuration interaction (CI) and molecular orbital (MO) coefficients within the DODC framework. Specifically, this work included several key developments and findings. First, the NOMCSCF electronic Hessian was derived and implemented, enabling systematic stability analysis of NOMCSCF wavefunctions and clear identification of symmetry breaking and symmetry-restoring solutions. The stability behavior was investigated for multiple-determinant descriptions of N2, revealing that although the orbital rotation landscape within NOMCSCF becomes more complicated, it still exhibits Goldstone-like manifold features, which represent modes of restoring the symmetries. This behavior is not limited to mean-field approximations but is also observed on the NOMCSCF energy surface. Second, robust orbital optimization algorithms were developed, including line-search based quasi-Newton and both CI–MO uncoupled (two-step) and coupled (one-step) trust region Newton–Raphson schemes, to improve convergence reliability across challenging potential energy surfaces. It was found that the trust-region technique generally outperformed the line-search method. Because the NOMCSCF wavefunction parameter space is highly nonlinear and contains multiple minima, different optimization strategies may converge to distinct solutions, even when starting from the same initial guess. Third, through analysis of spin and spatial symmetry constraints in orbital rotation optimization, this work demonstrated how controlled symmetry breaking enhances the treatment of static correlation while maintaining physical interpretability and spin quantum numbers in the nonrelativistic limit. The multi-correlation mechanism was further examined and revealed in several molecular systems, shedding light on the underlying nature of electron correlation in NOMCSCF. Finally, NOMCSCF was applied to optimize (quasi-)diabatic states, exploiting its intrinsic diabatic–adiabatic transformation to model nonadiabatic electron transfer processes and compute diabatic electronic coupling parameters. It was concluded that electronic couplings obtained from Boys-localized (quasi-)diabatic states coupling optimized through NOMCSCF serve as an effective and relatively black-box approach, reducing around 10% overestimation observed in NOCI when compared to the reference Multireference Configuration Interaction with Davidson correction (MRCI+Q) method. Overall, these developments establish NOMCSCF as a powerful and practical framework for studying strongly correlated, electronically coupled, and nonadiabatic molecular systems.

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