Tang-Toennies Model Revisited: Toward the General van der Waals Potential

Noncovalent van der Waals (vdW) interactions play an essential role in a wide range of systems throughout physics, chemistry, and biology. Noble-gas dimers serve as natural benchmark systems to develop models for vdW interactions. The potential energy curves of noble-gas dimers are well-described by the analytical Tang-Toennies (TT) model, which was recently improved by exploiting the fact that these potential curves are conformal [Sheng et al., PRL 125, 253402 (2020)]. However, this model requires ab initio data to set the values to its many parameters. Here, based on the ab initio data analysis and simple physical models (hydrogen atom, Quantum Drude Oscillator), we derive the scaling law for the potential well depths and use it to reduce the number of parameters in the TT model. Moreover, we derive the empirical relation which allows us to calculate the dispersion coefficients from static atomic polarizabilities with remarkable accuracy for all s- and p-elements in the Periodic Table. Together with the recently established scaling relation between vdW radius and polarizability [Fedorov et al., PRL 121, 183401 (2018)], our results represent an important step toward the self-consistent pairwise vdW potential which can be further generalized onto more complex systems.