Molecular Vibration-Rotation Theory Based Calculations of Spectra for Water, Formaldehyde, Mercury (II) Chloride, and Mercury (I) Chloride

This theoretical study is an example of how symbolic computation can be used in the context of computer-generated algebra addressing intramolecular nuclear motion. The perturbation potential is defined as an analytical representation of molecular potential energy surfaces (PESs). This study examines the ease of evaluating algebraic formulas given only the isotopic masses of the atoms which make up the polyatomic system and expansion coefficients that define the analytical form representing the polyatomic PES. This project provides results for low-lying vibrational energy levels using symbolic computation and computational chemistry software developed in this laboratory. The prediction and analysis of spectra of heavy-element-containing molecules is conducted using ab initio quantum mechanical methods. These methods include applying a post-Hartree Fock method CCSD(T) applying the aug-cc-pVDZ-PP basis set. The methodology used H2O, H2CO and its isotopes along with HgCl2 (mercury (II) chloride), and Hg2Cl2 (mercury (I) chloride) to showcase the theoretical generation of vibrational-rotational spectra and molecular properties. Through the completion of this study, a new method for generating geometric distortions that define PESs was accomplished along with calculations of vibrational-rotational spectra for H2O and H2CO with errors less than 0.09% and 0.84%, respectively. Additionally, novel values were calculated for HgCl2 and Hg2Cl2. The study ultimately demonstrates how errors can typically be reduced to less than 1% using accurate analytical representations of PESs and property surfaces in the context of a Rayleigh-Schrodinger perturbation theory method that scales linearly with molecule size.