Correlation and prediction of dispersion coefficients for isoelectronic systems

Combination rules for dispersion coefficients are greatly extended by way of a parameter corresponding to an effective number of equivalent electrons, the same parameter N that appears in the Slater–Kirkwood formula for the dipole–dipole coefficient. The same N can be used for all members of an isoelectronic sequence, and new formulas are given for higher-order two-body dispersion coefficients and three-body nonadditive coefficients, in which the same N can also be used. The only additional input data needed are static multipole polarizabilities. A theoretical justification is given using screening-constant wave functions. Extensive empirical testing suggests that the results are usually accurate within about 5% for dipole coefficients and about 5%–10% for higher coefficients. The results apply only to S-state atoms and ions, but should be capable of extension to other systems.