# 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.

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.