Diatomic Molecules Vibrational Energy Spectra And Dissociation Energies Accurate Research

There are two parts in this dissertation. In part one, an algebraic method (AM) used to study the full vibrational energy spectra of diatomic molecular electronic states is outlined. An algebraic energy method (AEM) is proposed to study the molecular dissociation energies. A new analytical formula is also established to calculate accurate molecular dissociation energies based on the AM vibrational spectrum. In part two, relationship between rovibrational energies of diatomic molecules and thermodynamic functions are analyzed, and the accurate AM vibrational spectrum is recommended to be used in calculating the thermodynamics functions of diatomic molecules.The AM described in the first part generates accurate full vibrational spectra by solving an correct algebraic equation of vibrational energies using limited experimental energies without adopting any mathematical approximations and physical models. Molecular dissociation energies are evaluated using the AEM which is a method based on the AM vibrational spectrum and the energy bounds analyzed in the content. Starting from LeRoy and Bernstein's potential expression which is based on the WKB theory, a new analytical formula is proposed to obtain accurate diatomic molecular dissociation energies using accurate high-lying vibrational energies near dissociation limit.Studies show that: (1) the AM is a reliable and economical method to obtain accurate full vibrational spectrum{Ev} and generates important physical data for the studies that need accurate high-lying vibrational energies which may be difficult to obtain experimentally. (2) the proposed analytical formula and the AM vibrational spectrum provide a new physical route to obtain accurate molecular dissociation energies De for many diatomic molecular states whose accurate values of experimental De may not be available.The second part discusses statistical partition functions and thermodynamical functions using the AM rovibrational energies for the diatomic molecular systems, and provides a good computational basis for accurate studyies of thermodynamical functions.