Date on Master's Thesis/Doctoral Dissertation

12-2023

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Chemistry

Degree Program

Chemistry, PhD

Committee Chair

Thompson, Lee

Committee Co-Chair (if applicable)

Kozlowski. Pawel

Committee Member

Kozlowski. Pawel

Committee Member

Jayanthi, Chakram

Committee Member

Zhang, Xiang

Author's Keywords

Metropolis–Hastings criteria; energy landscape; single orbital entropy; polarizability; second-order hyperpolarizability; HHG spectra

Abstract

Global elucidation of SCF (self-consistent-field) solutions is an extension of global optimization in which the goal is the identification of all solutions, which can be defined as a NP (nonpolynomial)-hard problem. The value of identifying multiple SCF solutions is to use as reference wavefunctions, such as NOCI (nonorthogonal configuration interactions), NOMCSCF (nonorthogonal multiconfigurational SCF), etc. However, the high-dimensional space over which to search and the relatively high cost of local optimization in Hartree-Fock (HF) models cause difficulty in efficiently searching over the full SCF space. In order to address the technical issues of high-dimensionality and nonlinearity, a Lie algebraic description of electronic structure combined with a stochastic basin hopping approach have been used. Besides, the correlation mechanism is interpreted using the disconectivity graph of nearby SCF solutions found based on the stability test among the high-dimensional space. The proposed method helps to better select determinants for NOCI or NOMCSCF with knowing whether solutions have same correlation or not. Solutions which are close in energy but connect to the different ‘node’ are further differentiate using the mutual information from the orbital levels. In addition, developments in laser technology have enabled the study of processes at increasingly fast time-scales, including the ability to directly study electron dynamics. Interpretation of experimental results, as well as gaining additional understanding of electronic dynamics, has motivated corresponding development of real-time time-dependent theoretical methods. Several electronic response properties of nonorthogonal determinants are evaluated inside RT-TDCI (real time time-dependent configuration interactions) expansions relative to the orthogonal expansions.

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