Empirical and semiempirical interaction potentials for rare gas–rare gas and rare gas–halide systems

Abstract

The Tang–Toennies (TT) semiempirical model potentials for ion–atom systems is applied to the rare gas–halide negative ion exciplexes. The coefficients defining the repulsive Born–Mayer term in the TT semiempirical potentials are determined from the equilibrium bond length Re and dissociation energy De taken from ab initio calculations and from transport studies of these molecular ions. The damped dispersion and induction energy terms in the TT potentials are obtained from coupled Hartree–Fock calculations for the neutral rare gas atoms and F− and Cl− ions. The multipole polarizabilities for the heavier halogen atomic negative ions are estimated from a knowledge of polarizability ratios across isoelectronic sequences. The resultant semiempirical ionic potentials are compared to available ab initio calculations and the results of inversion of transport theory. To facilitate the comparison of the (sparse) ab initio data with the semiempirical potentials, a simple fitting procedure is presented for determining empirical potentials for diatomic molecules from a set of three constraint equations. The fitting procedure is applied to a total of 22 rare gas excimers and rare gas–halide exciplexes (both neutral and ionic) of interest to a variety of applications in gaseous discharges and excimer lasers. A three-term representation of the empirical potentials generated is accomplished with the use of a minimal data set which include the ‘‘geometric’’ parameters {R0,Re,De} and the additional parameters {αd, I.P., E.A.} needed for the dispersion and induction energy terms. A novel feature of the empirical procedure is the formulation of the constraint equations at two nuclear displacements (one constraint at R0, wherein the potential passes through zero, and two constraints at Re the equilibrium separation) which yields an accurate fit to available ab initio data and greatly extends the range of internuclear separations R for which an accurate piecewise analytical empirical potential can be generated. To test the relative importance of the different terms in the fitted three-term empirical representations, the classical orbiting cross section Qorbit(E) is computed using the full empirical potential and compared against the standard Langevin orbiting cross section Qpol(E) for a pure polarization interaction.