A Linear-scaling AO-based MP2 Method for Large Molecules by Rigorous Integral Estimates

Thursday, August 2, 2007 - 3:00pm - 3:30pm
EE/CS 3-180
Christian Ochsenfeld (Eberhard-Karls-Universität Tübingen)
Describing electron correlation effects for large molecules
is a major challenge for quantum chemistry due to the
strong increase of the computational effort with molecular
size. In order to overcome this limitation,
we present a rigorous method based on an AO-formulation of MP2
theory, which allows to avoid the conventional fifth-power scaling
of MO-MP2 theory and to reduce the scaling to linear without
sacrificing accuracy. The key feature of our method are
multipole-based integral estimates (MBIE),
which account for the 1/R coupling in two-electron integrals and
allow to rigorously preselect integral products in AO-MP2 theory.
Here, the magnitude of products decays at least with 1/R**4, so that a
linear-scaling behavior can be achieved by numerical thresholding without
sacrificing any accuracy. The linear-scaling increase of the computational effort is reached
much earlier than for HF or DFT approaches: e.g. the exact behavior of products
indicates a scaling of N**1.0 from one to two DNA base-pairs for a 6-31G* basis.
The number of significant elements in the pseudo-density matrices and of shell pairs
hints to a very similar linear-scaling behavior for larger basis sets studied
up to cc-pVQZ. First results of a preliminary implementation show
that an early crossover to conventional MP2 schemes below two DNA base pairs
is observed, while already for a system with four DNA base pairs wins
are at least a factor of 16.