Campuses:

Interatomic 'van der Waals' Forces and the Schroedinger equation

Thursday, April 14, 2005 - 9:30am - 10:30am
EE/CS 3-180
Gero Friesecke (Technical University of Munich )
Long range interatomic 'Van der Waals' forces play an important
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 eN (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, enumber 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.