Analysis of Rotational and Vibrational−Rotational Spectra of HF Based on the Non-Born−Oppenheimer Effective Hamiltonian

Abstract

Rotational transitions of HF that are important as a wavenumber standard have been analyzed by simultaneous fitting of the reported rotational and vibrational-rotational transitions plus rotational measurements of the present study with the non-Born-Oppenheimer effective Hamiltonian expressed with the optimal parameters, i.e., the determinable clusters of the expansion coefficients of the correction functions for the breakdown of the Born-Oppenheimer approximation. Since the spectral fit is made with the analytical solution of the Schrödinger equation, one can easily reproduce the fitting procedure. This is the first example of the non-Born-Oppenheimer analysis of a single isotopologue with physically meaningful parameters based on the traditional concept of the molecular constants. Fitting of a data set for HF has generated 15 independent parameter values that include 4 determinable clusters of the expansion coefficients. These 15 parameters are sufficient to generate 41 Yij coefficients and 72 rotational constants, which provide comprehensive sets of molecular constants of HF.

Vibrational–rotational spectra of 13CS and global multi-isotopologue analysis

“…in terms of the non-Born-Oppenheimer correction parameters, dD B , dD x , dD a1q , dD a2q , dD a3q , dr 1q , dr 2q , dr 3q and dr 4q , are given for eleven Y ij *(0) [19], i.e., Y 01…”

“…(13)-(15) of Refs. [22,19], respectively. The correction terms in Y ij *(0) are quantities of order Y ij (2) , i.e., the Dunham correction [24].…”

“…We fitted the molecular parameters to the data set on changing stepwise the level of correction. When all correction parameters were set adjustable for each level of the Y ⁄ ij (0) set, the level of an eight Y ⁄ ij (0) set [19] gave a smaller standard deviation of the fit. An analysis was made connecting these 22 parameters with the vibrational-rotational term values through Y ⁄ ij (0) + Y ij (2) and Y ij…”

“…As our measured vibrational-rotational wavenumbers for 12 C 32 S are slightly more accurate than those of Ram et al [17], both sets of values were included in the data set that was subjected to a global multi-isotopologue spectral analysis. The global analysis employed here, which was comprehensively reviewed [18], is based on a non-Born-Oppenheimer effective Hamiltonian expressed with determinable molecular parameters in a set [19][20][21] as follows:…”

“…The Dunham-like treatment of the Schrödinger equation of the Hamiltonian (1) generates analytical expressions for the vibrational-rotational term values [19,20,22], which enable an analysis of a spectral data set of CS with a single set of Born-Oppenheimer fitting parameters, U x (=l 1 Tables 1 and 2 of Ref. [20], respectively.…”