# A MODIFIED LENNARD-JONES OSCILLATOR MODEL FOR DIATOMIC POTENTIALS

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 Title: A MODIFIED LENNARD-JONES OSCILLATOR MODEL FOR DIATOMIC POTENTIALS Creators: Hajigeorgiou, P. G.; Le Roy, Robert J. Issue Date: 1994 Publisher: Ohio State University Abstract: Recent years have seen remarkable success in the development of flexible few-parameter model potentials able to accurately represent very large amounts of high quality data to spectroscopic accuracy, while simultaneously accounting for isotope end Born-Oppenheimer breakdown effects. However, even the best of these functions, the generalized Morse oscillator $model,^{1,2}$ fails to take account of the theoretically known inverse-power long-range behaviour of internuclear potentials, and this limits the utility of such models for extrapolation or for determining dissociation energies. This paper addresses this question by proposing a new analytical representation for the internuclear potential energy of a diatomic molecule, which may be thought of as a generalization of the Lennard-Jones (2n,n) function. $U(R) = D_{e} \left[1 - \left(\frac{R_{e}}{R}\right)^{n} e^{-\beta(x)z}\right]$ 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, and n is the power of the leading term in the long-range inverse-power expansion for {U(R)}. As in any direct-fit method, the potential parameters can be determined in nonlinear least-squares fit to spectroscopic line positions. The modified Lennard-Jones (MLJ) potential is compared with other functions for a variety of diatomic electronic states. Description: $^{1}$J.A. Coxon and P.G. Hajigerorgion, {J. Mol. Spectrosc}. \textbf{150}, 1 (1991). $^{2}$H.G. Hedderich, M. Dulick, and P.F. Bernath, {J. Chem. Phys}. \textbf{99}, 8363 (1994). Author Institution: Guelph-Waterloo Centre for Graduate Work in Chemistry, University of Waterloo URI: http://hdl.handle.net/1811/13324 Other Identifiers: 1994-WE-04