Non-universality of the dispersion interaction:
analytic benchmarks for van der Waals
energy functionals in layered systems
John F. Dobson, Griffith University, Australie
e-mail:J.Dobson@griffith.edu.au
Lundi 24 janvier 2005, 11h00
We point out the non-universality of the asymptotic behavior of dispersion
forces, such that the usual sum of inverse sixth power atom-atom
contributions R-6 is often inadequate.
A technologically important case is the interaction between the
pi-conjugated electrons in graphitic structures such as intercalated
graphite and nanotube arrays. Starting from the standard tight-binding model
of the electron Bloch states in a graphene layer, we evaluate the mutual
electronic correlation energy between two layers separated by a large
distance D, within the nonlocal electromagnetically non-retarded Random
Phase Approximation.
For undoped layers at zero temperature we find that this attractive energy
falls off as D-3. The usual sum of R-6 contributions
predicts D-4, which is
appropriate for finite-gap 2D semiconductors but not for this zero-gap
system. Our result is closer to the D-5/2 attractive energy
applicable to 2D metals, than to the insulating result. Even more unusual
results are obtained for the attraction of metallic nanotubes.
These asymptotic results for "stretched" matter suggest that revisions are
required to several currently popular energy functionals for soft layered
matter. We also briefly discuss some evidence for the inadequacy of standard
theory for layered systems near to their equilibrium spacing.