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