Defense Date

2024

Document Type

Thesis

Degree Name

Master of Science

Department

Chemistry

First Advisor

Ka Un Lao

Abstract

Vibrational frequencies are crucial for accurately characterizing molecular systems, particularly in molecular dynamics and spectroscopy where these frequencies are used to analyze and predict the structure and proper ties of a given system. Typically, analytical second derivatives are used to generate the Hessian matrix, but this process can be resource intensive and time consuming due to solving coupled-perturbed equations. In this study, we adopted an energy-based approach to numerically calculate the Hessian matrix using the finite difference method at step sizes 0.01˚ A, 0.001˚ A, and 0.0001˚ A . To mitigate inaccuracies inherent in the standard three-point finite difference method, we applied Grassmann interpolation to generate additional sampling points in the five-point stencil. Additionally, we examined the influence of diffuse functions across different systems to determine the reliability of the five-point finite difference method across various basis sets.

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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