Towards efficient description of type-C London dispersion forces between low-dimensional metallic nanostructures

Abstract

Abstract This paper concerns one of the remaining difficulties encountered in efficient modelling schemes for dispersion forces between nanostructures. Dispersion (van der Waals, vdW) interactions between molecules and nanostructures can be reliably described in principle by computationally intensive high-level theory, but this is often not computationally feasible in practice, so more efficient methods are continually being developed. Progress has been made with nonlocal density functionals (vdW-DFs) and with atom-based schemes (D4, MBD, uMBD). In such efficient schemes, the effects beyond additive two-atom terms have been categorized as ‘type A’, ‘type B’ and ‘type C’ non-additivity (see Dobson (2014 Int. J. Quantum Chem. 114 1157)). Atom-based models using coupled-harmonic-oscillator theory (MBD) now deal adequately with type A and type B non-additivity, but type-C effects, related to gapless collective electronic excitations, can occur in low-dimensional metals, and these are not correctly described by the efficient schemes mentioned above. From analytic work within the direct random phase approximation (dRPA), type-C effects have long been known to cause the vdW interaction between well-separated low-d metals to fall off much more slowly with separation than is predicted by the above-mentioned efficient schemes. The slower decay means that type-C effects dominate in this asymptotic large-separation regime. It has not been clear, however, whether type-C physics contributes significantly to the vdW interaction of low-d metals near to contact, where the forces are much larger. The present work uses recent semi-analytic dRPA results to provide some evidence that type-C effects are indeed significant near to contact between metallic carbon nanotubes, and between doped graphene sheets. Some guidelines are therefore suggested for ways to combine the semi-analytic dRPA approach, here termed ‘SAM-dRPA’, with the existing efficient vdW algorithms described above.