Higher-order C_n dispersion coefficients for the alkali-metal atoms

The van der Waals coefficients, from C₁₁ through to C₁₆ resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the C_n∕rⁿ potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to C₁₀∕r¹⁰ results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than 20a₀. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive (C₁₁,C₁₃,C₁₅) and attractive (C₁₂,C₁₄,C₁₆) dispersion forces.