 
Summary: Stochastic Perturbation Theory: A LowScaling Approach to Correlated Electronic Energies
Alex J. W. Thom* and Ali Alavi
University of Cambridge, Chemistry Department, Lensfield Road, Cambridge CB2 1EW, United Kingdom
(Received 20 April 2007; published 4 October 2007)
We discuss a stochastic implementation of MøllerPlesset (MP) theory based upon the concept of a
``graph,'' a set of connected Slater determinants. We show how contributions from an arbitrary level, MPn,
of perturbation theory can be expressed diagrammatically in terms of graphs, and that these may be
stochastically sampled to give a good estimate of the energy. We show this to be the case for Ne, Ar, N2,
and H2O molecules. Nmolecule chains of He atoms and H2 molecules at equilibrium and stretched
geometries show an effective scaling of ON2:6 and ON5:6 for MP2 and MP3 theories.
DOI: 10.1103/PhysRevLett.99.143001 PACS numbers: 31.15.Md, 02.70.Ss
Wavefunctionbased methods such as MøllerPlesset
(MP) perturbation theory [1,2], can provide high accuracy
for calculating the energy of electronic systems and are
capable, for example, of describing longrange dispersion
interactions between closedshell molecules. However,
they are limited in their application to large systems by
prohibitive scaling with system size: MP2 and MP3 scale,
respectively, as ON4
and ON6
