Analysis of Vibrational–Rotational Spectra with Optimal Fitting Parameters for Born–Oppenheimer Corrections to Dunham’s Yij: An Application to Spectral Data of HCl

Abstract

Analytic expressions for Born–Oppenheimer corrections to Dunham’s Yij with optimal fitting parameters, i.e., determinable clusters of expansion coefficients, are applied in analysis of data of reported vibrational–rotational and rotational transitions of HCl. In this method of analysis the choices of a set of fitting parameters and also a corresponding set of Yij that connects the fitting parameters with the term values are unique. A layered structure for empirical parameters Δij is revealed. All spectral lines of four isotopomers of HCl are simultaneously fitted to a single set of molecular constants well within the experimental errors. The approach thus provides a better fit of smaller standard deviations with fewer number of adjustable parameters than from other methods of analysis. The determined values for the coefficients of adiabatic effects s1H and s1Cl reveal the wobble-stretch term to be unimportant in the adiabatic correction for HCl.

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

“…The level of correction of a set of eleven Y* ij (0) and the Dunham potential constants up to a 9 are found to be sufficient for the present analysis, i.e., a set of 41 Y ij that connected the fitting parameters with the energy levels is that of Y* ij (0) + Y ij (2) for ij ) 01, 02, 03, 04, 05, 10, 11, 12, 13, 20, and 21 and Y ij (0) for ij ) 06, 07, 08, 09, 010, 011, 14,15,16,17,18,19,22,23,24,25,26,27,30,31,32,33,34,35,40,41,42,43,50, and 51. The spectral uncertainties, δ obs , are those given in each paper.…”

“…22 One redundancy exists among eight Y ij * (0) . 15 In the next level set of eleven Y ij * (0) , i.e., the set of eight Y ij * (0) plus Y 05 * (0) , Y 13 * (0) , and Y 21 * (0) , nine correction parameters, δ∆ B , δ∆ ω , δ∆ a1q , δ∆ a2q , δ∆ a3q , δr 1q , δr 2q , δr 3q , and δr 4q , are included.…”

“…The corresponding Dunham correction Y ij (2) has to be added to each of the eleven Y ij * (0) when expressions of Y ij * (0) are applied to a spectral analysis. Although expressions of Y 01 (2) , Y 02 (2) , Y 03 (2) , Y 04 (2) , Y 10 (2) , Y 11 (2) , Y 12 (2) , Y 20 (2) , and Y 21 (2) , have been reported in references, as indicated by superscripts for the reference numbers, no expressions for Y 05 (2) and Y 13 (2) have yet been registered. The calculated values with Maple in this work are given as Supporting Information.…”

“…An analytical approach to obtain the eigenvalues of the Schrödinger equation given by the effective non-Born−Oppenheimer Hamiltonian generated expressions of Y ij * in terms of the determinable parameters Δ B , r iq , Δ ω , and Δ aiq . This line of approach has been applied to analyses of reported spectral data sets of LiH and HCl. , …”

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

“…, dr 1q , dr 2q }, and {dD x , dD B , dD a1q , dD a2q , dr 1q , dr 2q , dr 3q }, respectively [25]. We fitted the molecular parameters to the data set on changing stepwise the level of correction.…”