# ANALYTICAL RADIAL HAMILTONIANS FOR THE $X^{1}\Sigma^{+}$ STATES OF HF AND HCl

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 Title: ANALYTICAL RADIAL HAMILTONIANS FOR THE $X^{1}\Sigma^{+}$ STATES OF HF AND HCl Creators: Coxon, John A.; Hajigeorgiou, P. G. Issue Date: 1994 Abstract: Over three years ago, we presented radial Hamiltonians for the $X^{1}\Sigma^{+}$ electronic states of hydrogen $fluoride^{1,2}$ and hydrogen $chloride^{3}$ which represented very accurately the wide range of spectroscopic data available on these important molecules. However, those functions were determined in numerical form on a radial grid, and despite their overall success in representing spectroscopic information, the Hamiltonians lacked compactness. In the present work, this problem is addressed by reducing the several thousand line measurements for HF, HCl and related isotopomers, to Born-Oppenheimer potential functions which are modeled as modified Leannard-Jones (MLJ) $oscillators^{4}$ $U^{BO}(R) = D_{e} \left[1- \left(\frac{R_{e}}{R}\right)^{e} e^{-\beta(x)x} \right]^{2}$ where $\beta(z) = \beta_{0} + \beta_{1}z + \beta_{2}z^{2} + \ldots + \beta_{m} z^{m} z = 2(R - R_{e})/(R+ R_{e})$ is the Ogilvie-Tipping expansion parameter. The analysis also furnishes analytical functions which collectively describe adiabatic, homogeneous and heterogeneous non-adiabatic, relativistic, and quantum-electrodynamic effects. In addition to the significant improvement in compactness, improved representations for the radial functions which describe the aforementioned effects have been developed, and fits using the new model yield direct estimates of the dissociation energies, $D_{e}$. URI: http://hdl.handle.net/1811/13325 Other Identifiers: 1994-WE-05