The van der Waals potential of the magnesium dimer

The ground state van der Waals potential of the magnesium dimer is described by the Tang-Toennies potential model, which requires five essential parameters. Among them, the three dispersion coefficients C(6), C(8), and C(10) are available from accurate ab initio calculations. The other two are the Born-Mayer parameters in A exp(-bR). In this paper, we show that A and b can be determined from the self-consistent Hartree-Fock calculations and the experimental dissociation energy D(0). The predicted well depth D(e) and equilibrium distance R(e) are in nearly perfect agreement with the experiment. In fact, the entire potential energy curve, which is given by a single analytic function, is in excellent agreement with the pointwise potential energies constructed from the spectroscopic measurements in the interval of 6a(0)-14a(0) and in good agreement with the experimental repulsive potential determined from Franck-Condon factors of the bound-free transitions for R less than 6a(0). The reduced potential of Mg(2) is analyzed in terms of its components, and the number of terms in the dispersion series necessary for convergence is investigated.