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

Abstract

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 H 3 ) 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 nonadditivity" recently introduced by one of us ( Int. J. Quantum Chem. 114, 1157Chem. 114, (2014). Our toy molecule H 3 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.

Faraday cage screening reveals intrinsic aspects of the van der Waals attraction

“…As a result, a wide range of empirical correction schemes are commonly added to GGA calculations so as to produce a realistic description of the critical interactions ( 24 , 25 ). The vdW dispersion interactions described by these schemes typically involve sums over interatomic interactions, each described by the London force ( 21 , 26 – 28 ), with only small corrections. Related variants include replacing the atomic sums by electron-density integrals.…”

MBD + C: How to Incorporate Metallic Character into Atom-Based Dispersion Energy Schemes

“…Comparing eqs 13 and 9, we find that we can make our Ansatz give the correct long-wavelength response provided that we choose the constant B in χ 0 Ansatz such that (14) The factor of 1/R on the right side of eq 14 comes from the conversion between continuous "()" and discrete "[ ]" Fourier transforms. Putting eqs 9 and 13 into eq 14 gives (15) So, eq 16 becomes (16) This agrees with the known 1D metallic response when q → 0 but is not necessarily correct for larger q. However, the principal "Type-C" effects of metallicity on dispersion interactions come from the long-wavelength metallic response, and so, the present model should be appropriate.…”

“…In low-dimensional metals, this gives rise to gapless plasmon excitations that are not captured by the MBD theory. Coupling between these plasmons results in unusual power law decays of the dispersion interaction between low-dimensional metals, sometimes termed “Type-C” dispersion interactions. − Similar anomalous dispersion interactions have been proposed in a variety of other cases with a small or zero electronic energy gap. − The Type-C interactions are not captured by standard MBD calculations. ,, …”

The significance of fluctuating charges for molecular polarizability and dispersion coefficients

“…Recent studies have suggested that Type-B non-additivity can also be interpreted as a manifestation of electric many-body effects. 17 Type-C non-additivity is observed in low-dimensional nanostructures or metallic systems, where long-range charge ŕuctuations result in dispersion interactions with non-standard power laws, with a smaller magnitude of the exponent of R. 18 Semiclassical models with pairwise expressions, such as Eq. ( 1), including Grimme's DFT+Dn (n = 1, 2, 3, 4) schemes, [19][20][21][22][23] Tkatchenko and Scheffler (TS) method, 13 the exchange-hole dipole moment (XDM) method by Becke and Johnson, 12,24,25 and the localresponse dispersion (LRD) model by Sato and Nakai, [26][27][28] consider type-A non-additive dispersion interactions.…”