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The structure and stability of atomic and molecular systems with van der Waals (vdW) bonding are often determined by the interplay between attractive dispersion interactions and repulsive interactions caused by electron confinement. Arising due to different mechanisms --- electron correlation for dispersion and the Pauli exclusion principle for exchange-repulsion --- these interactions do not appear to have a straightforward connection. In this paper, we use a coarse-grained approach for evaluating the exchange energy for two coupled quantum Drude oscillators and investigate the mutual compensation of the attractive and repulsive forces at the equilibrium distance within the multipole expansion of the Coulomb potential. This compensation yields a compact formula relating the vdW radius of an atom to its multipole polarizabilities, $R_{rm vdW} = A_l^{,}, alpha_l^{{2}/{7(l+1)}}$, where $l$ is the multipole rank and $A_l$ is a conversion factor. Such a relation is compelling because it connects an electronic property of an isolated atom (atomic polarizability) with an equilibrium distance in a dimer composed of two closed-shell atoms. We assess the accuracy of the revealed formula for noble-gas, alkaline-earth, and alkali atoms and show that the $A_l$ can be assumed to be universal constants. Besides a seamless definition of vdW radii, the proposed relation can also be used for the efficient determination of atomic multipole polarizabilities solely based on the corresponding dipole polarizability and the vdW radius. Finally, our work provides a basis for the construction of efficient and minimally-empirical interatomic potentials by combining multipolar interatomic exchange and dispersion forces on an equal footing.
The atomic dipole polarizability, $alpha$, and the van der Waals (vdW) radius, $R_{rm vdW}$, are two key quantities to describe vdW interactions between atoms in molecules and materials. Until now, they have been determined independently and separate
A version of the Greens functions theory of the Van der Waals forces which can be conveniently used in the presence of spatial dispersion is presented. The theory is based on the fluctuation-dissipation theorem and is valid for interacting bodies, se
We analyse van der Waals interactions between a pair of dielectrically anisotropic plane-layered media interacting across a dielectrically isotropic solvent medium. We develop a general formalism based on transfer matrices to investigate the van der
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