IMPROVED PARAMETERIZATION FOR DIATOMIC BORN-OPPENHEIMER BREAKDOWN EFFECTS, AND A NEW COMBINED-ISOTOPES ANALYSIS FOR HD AND DF
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Date
1997
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Ohio State University
Abstract
Although the Ross {et al.}$^{m}$-$Bunker^{n}$-$Watson^{o}$ expression for the vibration-rotation levels of isotopomers-$\alpha$ of diatomic molecule A-B, $E^{o}(\nu, J) =\sum_{l, m}\frac{V_{l,m}}{U_{a} ^{l,m1/2}}\left(1+ \frac{m_{a}}{m^{a}_{A}}\Delta^{A}_{l,m}+ \frac{m_{a}}{m^{a}_{B}}\Delta^{B}_{l,m}\right)(\nu + 1/2)^{l} [J(J+1)]^{m}$ is fairly widely used, it has a number of deficiencies. In particular: (i) It is nor dear how to treat the (l, m) = (0,0) term, (ii) The $U_{l,m}$ constants have inconveniently varying units depending on fractional powers of the mass (iii) fits to data for only two isotomers cannot yield ``true” mass-independent $U_{i,m}$ values, (iv) for non-hydrides, the magnimdes of the $U_{l,m}$ constants are not even qualitatively similar to those of the analogous familiar Dunham $Y_{l,m}$ constants, and (v) direct fits to this expression are impossible, so non linear fits or indirect methods must be used to determine the $\Delta^{a}_{l,m}$ values and their uncertainties. Moreover, this formulation incompatible with the use of non-Dunham expressions (such as near-dissociation expansions) for the vibrational energies and rotational and centrifugal distortion consults. The present paper presents an alternate description of the Born-Oppenheimer and JWKB breakdown corrections which resolves all of these difficulties, and illustrates its use by a combined- isotopes analysis of the best available microwave, infrared and electronic data for the ground electronic states of HF and DF.
Description
$^{m}$A.H.M. Ross, R.S. Eng and H. Kildal. {Opt. Commun}. \textbf{12}, 433 (1974). $^{n}$P.R. Bunker, {J. Mol. Spectrosc}. \textbf{68}, 367 (1977). $^{o}$J.K.G. Watson, {J. Mol. Spectrosc}. \textbf{68}, 367 (1977).
Author Institution: Guelph-Waterloo Centre for Graduate Work in Chemistry, University of Waterloo
Author Institution: Guelph-Waterloo Centre for Graduate Work in Chemistry, University of Waterloo