Author ORCID Identifier

https://orcid.org/0000-0003-2573-2307

Defense Date

2024

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Chemistry

First Advisor

Ka Un Lao

Second Advisor

Katharine Tibbetts

Third Advisor

Shiv Khanna

Fourth Advisor

Brian Fuglestad

Abstract

Since its original formulation, quantum effects have been implicated as the central argument underpinning many fundamental theories and concepts across virtually all domains of science. Despite this fundamental nature, quantum effects and the extent to which they contribute to overall system properties, in many relevant cases, remains to be determined due to limitations in computing power. Fragmentation provides a simple and efficient means by which a given chemical system can be “divided and conquered” as a direct consequence of mutual orthogonality. The Many-Body Expansion (MBE) and its generalized variant, the Generalized Many-Body Expansion (GMBE), allow for combinatorial bound set theoretic representations of the full system’s density matrix, at a fraction of the apparent cost, devoid of substantial loss in quality. Further still, the completeness of these methods is compared to a linearly scaling alternative density matrix construction algorithms, the Adjustable Density Matrix Assembler (ADMA), with great success. For covalently-bound systems, the recovery of both through-bond and through-space interactions has been a consistent problem for many fragmentation schemes. Nevertheless, the GMBE can be applied to many covalent systems of varying size and recover both critical concepts using the expansion. Although the GMBE has been shown to be generally invariant with respect to basis set selection or level of theory, additional techniques have been developed to not only increase the quality of the full system density further, but also efficiency in the derivation of its subsets.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

5-8-2024

Available for download on Monday, May 07, 2029

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