Evaluation of Expansion Coefficients from Optimal Fitting Parameters for the Analysis of Spectra of Diatomic Molecules and an Application to LiH

Abstract

To evaluate individual expansion coefficients composing fitting parameters of the Born–Oppenheimer corrections to Dunham's coefficients Yij that have been given analytically with the ΔB and Δω formalism, we examined the consistency of analytic expressions for those corrections with Watson's assertion of the experimental inseparability of nonadiabatic corrections Qa, b(r) for a molecule AB. Derived analytic expressions in terms of optimal fitting parameters for the corrections are essential to evaluate individual expansion coefficients. These expressions also reveal redundancies between empirical correction parameters Δij. A method of evaluating nonadiabatic vibrational corrections Qa, b(r) and adiabatic corrections Sa, b(r) separately consistent with Watson's assertion of inseparability is presented and is applied to an analysis of spectral data of LiH. Functions Qa, b and Sa, b for LiH are thus successfully evaluated; SH, Li(r) values agree well with those predicted simply by wobble-stretch theory. Experimental values for optimal fitting parameters rH1q and rH2q are nearly equal to those of rLi1q and rLi2q, respectively, in agreement with a theoretical relation raiq=rbiq.