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Spooky correlations and unusual van der Waals forces between gapless and near-gapless molecules

We consider the zero-temperature van der Waals interaction between two molecules, each of which has a zero or near-zero electronic gap between a groundstate and the first excited state, using a toy model molecule ( equilateral H3) as an example. We show that the van der Waals energy between two groundstate molecules falls off as D^(-3) instead of the usual D^(-6) dependence, when the molecules are separated by distance D: We show that this is caused by perfect "spooky" correlation between the two fluctuating electric dipoles. The phenomenon is related to, but not the same as, the "resonant" interaction between an electronically excited and a groundstate molecule introduced by Eisenschitz and London in 1930. It is also an example of "type C van der Waals non- additivity" recently introduced by one of us ( Int. J. Quantum Chem. 114, 1157 (2014)). Our toy molecule H3 is not stable, but symmetry considerations suggest that a similar vdW phenomenon may be observable, despite Jahn-Teller effects, in molecules with discrete rotational symmetry and broken inversion symmetry, such as certain metal atom clusters. The motion of the nuclei will need to be included for a definitive analysis of such cases, however.