Accurate Born-Oppenheimer Molecular Calculation with Explicitly Correlated Gaussian Function

Abstract

The research over-viewed in this dissertation concerns very accurate variational calculations of the molecular systems with more than two electrons under the assumption of the Born-Oppenheimer (BO) approximation. The centerpiece of this research is the use of explicitly correlated Gaussian (ECG) basis functions with floating centers to generate the potential energy curve (PEC) and potential energy surface (PES) of the considered molecular systems. One challenge of such calculations is the occurrence of the linear dependency between basis functions in the process of basis set optimization. The BO PECs generated with ECG basis sets were limited to two-electron molecular systems for a few decades prior to the implementation of the author's approaches to this issue. These approaches include methods for a partial remedy to linear dependence, better guessing of initial basis functions, permanently removing the restriction of memory usage in parallel computer systems, and efficiently paralleling the calculations. The approach effectively utilizing the super computer systems yields benefits not only to the ECG calculations but could also be useful in the fields that require the significant amount of the computational resources. These procedures were implemented in computer codes that were run quite extensively on several parallel computer systems during the period of the author's Ph.D study. The calculated adiabatic PECs and the rovibrational energy levels are proven to be the most accurate ones to date. The dissertation is primarily based on the content of the papers that were published in co-authorship with my scientific advisor and other collaborators in several scientific journals. It also includes some details that were not considered in the publications but are essential for the completeness and good understanding of the presented work. In order to provide readers an insight into the development of the ECG based BO molecular calculation, the published results of many calculations are classified and presented in a comprehensive way.