A Data Driven Method To Study The Vibrational Spectra Of Diatomic Molecules

Molecular spectra and the corresponding energy level structure(energy spectra)play an important role in the study of physical and chemical phenomena at the atomic level,so they occupy an important position in the field of atomic and molecular physics.Diatomic molecular systems have become the touchstone of various theoretical models of quantum mechanics and the basic research tools of various derived application disciplines because of their simple structure and rich energy spectra characteristics.Although the basic composition and the basic interaction(nucleus-extranuclear electron model)of diatomic moleculars are clear,but often involving as many as hundreds of quantum objects,causing the details of quantum multi-body interaction to become very complicated and subtle,which makes it difficult to accurately predict the long-range vibrational behavior of diatomic molecules based on their basic structures and interactions.In recent years,data-driven machine learning method has made remarkable progress in capturing complex and subtle mapping relationships.Therefore,combining the advantages of this method with the characteristics of molecular spectroscopy,a data-driven spectral learning method is proposed in this paper,which can obtain high precision vibrational spectra including dissociation energy by using the information of low vibrational levels and heat capacity of diatomic molecules.The reliability of this method is guaranteed in two aspects:1)A quantum model is used to provide a flexible parameter form to cover any subtle physical effects in the long-range vibration and solve the under-fitting problem;2)Using experimental evidence such as low energy levels,dissociation energy and heat capacity,combined with machine learning strategy to solve the over-fitting problem.The proposed method was applied to the ground state of CO and Br₂ molecular system,based on some experimental data of vibrational levels and heat capacity,the entire vibrational spectra of the corresponding systems is reconstructed and the dissociation energy is predicted.Compared with the experimental values,the calculation accuracy of CO and Br₂molecular vibrational levels reaches 0.13cm^-1 and 0.36cm^-1,and the calculation accuracy of dissociation energy also reaches 500cm^-1 and 108cm^-1,respectively.This paper consists of five chapters.The first chapter is the introduction,including the research significance of molecular spectroscopy,research status and research content of this paper.The second chapter is the theoretical basis,which introduces the theoretical knowledge of diatomic molecular spectroscopy,expounds the algebraic and variational algebraic methods for studying spectra,and further,proposes a data-driven machine learning method that suitable for molecular spectroscopy.The third chapter is the introduction to spectral learning method,in which applies the data-driven machine learning method to practical problems,proposes the spectral learning method,and introduces the process preparation and calculation details of this method.The fourth chapter is the result analysis,including the energy spectra prediction analysis of the CO molecule and Br₂ molecule for their ground state.The fifth chapter is the conclusion of this paper.