Applications Of Variational Algebraic Energy Consistent Method In The Quantum Structures Of Diatomic Molecular Electronic States

This paper briefly describes the research background and status of the microscopic vibrational spectra and potential energy functions of the diatomic electronic states;reviews the important basic theories for studying the quantum spectra and the potential energy functions of the diatomic electronic states;and summarizes some important mathematics methods,physical models and the difficulties in solving scientific problems that still exist in this field.Based on mathematical theories of the variation and perturbation,Sun et al.have established the variational algebraic method?VAM?to calculate the vibrational quantum spectra and the variational algebraic energy consistent method?VAECM?to construct the analytical potential energy functions of diatomic electronic states.In this paper,the VAM method was used to numerically calculate theB¹?_u,C ¹?_u,?1?¹?_g and 3³?_g⁺ electronic states of the alkali metal Cs₂ molecule,and obtained the VAM vibrational spectral constants,the full VAM vibrational energies;the VAECM was used for constructing the analytical potential energy functions of the NaH-X¹?⁺,CsH-X¹?⁺ electronic states and the ClF-A'2?³??,ICl-X¹?⁺,IBr-X¹?⁺,IF-X¹?⁺electronic states,the vibrational spectral constants,the full vibrational energies,the potential energy expansion coefficients_naand the vibrational forced constantsf_nof each electronic state are obtained.In this paper,some new mathematical criteria are proposed by analyzing the error ranges of the global solutions of these systems under the constraints of convergence limit uncertainty.The research results show that the VAM and VAECM methods have very good convergency and applicability in dealing with the correct physical behavior of these high-excited states,especially in the dissociation region.This mathematical method is established by the combination of rigorous mathematical deduction and physical thinking not only solves the high-excited quantum vibrational structures which is difficult to obtain from the experiment,but also provides valuable reference data and method support for other related frontier research fields.