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

The dispersion component of the van der Waals interaction in low-dimensional metals is known to exhibit anomalous "Type-C non-additivity" [Int. J. Quantum Chem. 2014, 114, 1157]. This causes dispersion energy behavior at asymptotically large separations that is missed by popular atom-based schemes for dispersion energy calculations. For example, the dispersion interaction energy between parallel metallic nanotubes at separation D falls off asymptotically as approximately D^-2, whereas current atom-based schemes predict D^-5 asymptotically. To date, it has not been clear whether current atom-based theories also give the dispersion interaction inaccurately at smaller separations for low-dimensional metals. Here, we introduce a new theory that we term "MBD + C". It permits inclusion of Type C effects efficiently within atom-based dispersion energy schemes such as many body dispersion (MBD) and universal MBD (uMBD). This allows us to investigate asymptotic, intermediate, and near-contact regimes with equal accuracy. (The large contact energy of intimate metallic bonding is not primarily governed by dispersion energy and is described well by the semi-local density functional theory.) Here, we apply a simplified version, "nn-MBD + C", of our new theory to calculate the dispersion interaction for three low-dimensional metallic systems: parallel metallic chains of gold atoms, parallel Li-doped graphene sheets, and parallel (4,4) armchair carbon nanotubes. In addition to giving the correct asymptotic behavior, the new theory seamlessly gives the dispersion energy down to near-contact geometry, where it is similar to MBD but can give up to 15% more dispersion energy than current MBD schemes, in the systems studied so far. This percentage increases with separation until nn-MBD + C dominates MBD at asymptotic separations.