A “modified Lennard-Jones oscillator” model for diatom potential functions

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Abstract
A flexible new analytical representation for the internuclear potential energy of a diatomic molecule is proposed and tested. The new model may be thought of as a generalization of the prototypical Lennard-Jones (2n,n) function, with the form V(R)=De[1−(Re/R)ne−β(z)z]2, where z=(R−Re)/(R+Re) is a dimensionless radial distance variable which approaches 1 as R→∞. This form explicitly incorporates the theoretically predicted attractive inverse-power asymptotic behavior V(R)=D−Cn/Rn associated with most potential energy curves. This “modified Lennard-Jones” (MLJ) function is tested against other flexible forms for the potential energy by performing nonlinear least-squares fits both to known numerical potential curves and to spectroscopic line positions.

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