A SIMPLIFIED ANALYSIS OF FUNDAMENTAL BANDS IN SPHERICAL-TOP SPECTRA: A NEW FORMALISM FOR PERTURBATIONS TO DOMINANT APPROXIMATION
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Date
1981
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Ohio State University
Abstract
Significant shifts of lines away from their dominant-approximation positions in the high-J rotational manifolds have forced many workers to analyze the fundamental-band spectra of such heavy spherical tops as $SF_{6}, CF_{6}, OsO_{4}$, and $SiF_{4}$ by incorporating a full diagonalization of Hecht’s Hamiltonian for each value of J and each symmetry species. This method is very accurate, but the large-core computer calculations are expensive. Approximate algorithms were developed based on standard perturbation theory (which is fairly accurate but still somewhat cumbersome) and on the clustered-eigenvalue $approximation^{2}$ (which is simple and accurate at the ends of a high-J manifold but breaks down in the middle). We have developed the perturbative approach further. The perturbation expansion can be written in the form $$ W_{J,R,P}(pert,) \gamma (g^{2}/Br,) (F_{2} +n _{3} F_{3} +n _{4} F_{4} +\cdots),$$ where $F_{2}$ and $F_{3}$ are functions only of J, R, and diagonal $F^{(4)}$ - and $F^{(6)}$ - coefficients. Here $n_{3}, n_{4}$, etc. are dimensionless molecular parameters with $1>>|n_{3}|>>|n_{4}|$, and the explicit forms for $F_{2}$ are particularly simple. The formalism and its practical applications will be illustrated with computer fits to the $v_{3}$ band of $SiF_{4}$.
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$^{1}$B. J. Krohn, J. Mol. Spectrosc. 73, 462--474 (1978). $^{2}$H. W. Galbraith, C. W. Patterson, B. J. Krohn, and W. G. Harter, J. Mol. Spectrosc. 73, 475-493 (1978).
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