# Interatomic 'van der Waals' Forces and the Schroedinger equation

role for equilibrium structure and nonequilibrium behaviour of complex molecular

systems (carbon nanotubes, DNA, proteins, ...), but must at present be modelled

empirically: ab initio computation remains out of reach. The latter would be

particularly desirable because of the huge chemical specificity (i.e., atom

dependence) of the VdW force, e.g. for a pair of sodium atoms it is bigger by

a factor 1000 than for two Helium atoms.

The difficulty is that 'order N' computational quantum models

like Hartree-Fock theory and density functional theory (and their variants integrated

into molecular dynamics in the spirit of Car-Parinello) do not resolve VdW forces,

only short range covalent bonding. No model short of full all-N-body Schroedionger

is known which captures VdW - but that is order e^{N} (prohibitive).

Our main result is that the presence, magnitude and underlying

mechanism (quantum electron-electron correlations) of this attraction is in

fact a rigorous theorem about the many-body Schroedinger equation. This leads,

in particular, to an explicit expression at long range with greatly reduced

computational complexity: roughly speaking, e^{number of electrons in a single atom}.

In the talk, we will start by reviewing the interesting history

(starting from van der Waals 1873) and the well developed chemistry 'lore' (starting

with Eisenschitz and London 1927) of van der Waals forces.