Vibrational Structure Analysis Of The Absorption Spectra Between Several Low-lying Electronic Excited States Of PN Molecule

Molecular spectroscopy is the study of the interaction between molecules and light,and is one of the most important methods for understanding the structure,internal motion,and physical and chemical properties of molecules themselves.As the earliest phosphorus-containing(P)molecule found in interstellar observation,the related research of PN molecule is of great significance to interstellar exploration.In this paper,the potential energy curves of each electron state are calculated based on quantum chemistry,and nuclear dynamics is studied.The initial wave function of the system is solved by finite difference method and propagated by split-operator method.The absorption spectra generated by transitions between five low-lying electronic excited states(X1∑+、A1∏、C1∑-、D1A、21∏)of PN molecules are calculated and the vibrational structures are analyzed.According to the calculated results,we can see that the displacement of the equilibrium interatomic distance and the difference between the initial and final state dissociation limits significantly affect the distribution of vibrational structures in the absorption spectra.When the displacement of the minima of the potential energy curve before and after the transition is very small or the dissociation limits of two electronic states are very close,the vibrational quantum number changes little during the transition and the vibrational structure collapses into a few isolated peaks.On the contrary,when the displacement of the minima of the potential energy curve before and after the transition is large or the dissociation energy of two electronic states differ greatly,the vibrational quantum number changes obviously during the transition,which makes the vibrational structure have a high density of states and a wider range of spectra distribution.In the Frank-Condon factors,the transition dipole moment is approximately equal to a constant,but in the actual transition process,the transition dipole moment is a function of nuclear coordinates,so it is necessary to consider the influence of the transition dipole moment on the spectral line with the distribution of the interatomic distance R.In order to analyze the influence of transition dipole moment distribution on spectral lines,the transition dipole moment is directly applied to the vibrational wave function of ground state,and its distribution is corrected.The change of wave function before and after correction is directly related to the change of spectral line distribution.When the change amplitude of the transition dipole moment with the interatomic distance R is small,the distribution of the vibrational wave function after the correction of the transition dipole moment is basically unchanged compared with the initial vibrational wave function,and the corresponding absorption spectra distribution does not change significantly.When the change amplitude of the transition dipole moment is large,the vibrational wave function after the correction of the transition dipole moment shifts to the left and the distribution changes significantly compared with the initial vibrational wave function,and the range of spectra distribution is wider.