Moderately Long-Range Interatomic Forces

TLDR: In this article, it has been shown that the van der Waals dispersion energy for the first-row atoms is of almost the same size as the quadrupole-quadrupole interaction energies at the separation of twice the sum of the atomic radii.

Abstract: The moderately long-range interaction energies of degenerate atoms for nonresonant cases have been studied throughout the moderately long-range region. Extensive tabulation of necessary parameters and atomic properties for the calculation of the first-order quadrupole-quadrupole interaction energies has been made. Higher multipole interactions also have been considered and it has been shown that the $\frac{1}{R}$ series of the first-order Coulombic interaction energies converges very fast throughout the long-range region for atoms in the ground configuration. The effects of atomic spin-orbit splitting have been considered explicitly. It has been shown that ($\ensuremath{\Delta}, S$) coupling and intermediate coupling may be important for the interactions between B, C, O, Al, Si, and Sc atoms in the relatively short internuclear separation range. For other atoms, the (${J}_{a}, {J}_{b}$) coupling scheme will give satisfactory results throughout the long-range region. The experimental determination of the moderately long-range interatomic forces from predissociation data also has been discussed.The estimated van der Waals dispersion energies for the first-row atoms are shown to be of almost the same size as the quadrupole-quadrupole interaction energies at the separation of twice the sum of the atomic radii. It has been also shown that the leading term [$\ensuremath{\theta}(\frac{{\ensuremath{\alpha}}^{2}}{{R}^{3}})$] of the magnetic interaction energy of two degenerate atoms is 10\ensuremath{\sim}20% of the quadrupole-quadrupole interaction energy at $R=30{a}_{0}$ through the third-row atoms.