An Integral-Direct Linear-Scaling Second-Order Møller–Plesset Approach

An integral-direct, iteration-free,
linear-scaling, local second-order
Møller–Plesset (MP2) approach is presented, which is also
useful for spin-scaled MP2 calculations as well as for the efficient
evaluation of the perturbative terms of double-hybrid density functionals.
The method is based on a fragmentation approximation: the correlation
contributions of the individual electron pairs are evaluated in domains
constructed for the corresponding localized orbitals, and the correlation
energies of distant electron pairs are computed with multipole expansions.
The required electron repulsion integrals are calculated directly
invoking the density fitting approximation; the storage of integrals
and intermediates is avoided. The approach also utilizes natural auxiliary
functions to reduce the size of the auxiliary basis of the domains
and thereby the operation count and memory requirement. Our test calculations
show that the approach recovers 99.9% of the canonical MP2 correlation
energy and reproduces reaction energies with an average (maximum)
error below 1 kJ/mol (4 kJ/mol). Our benchmark calculations demonstrate
that the new method enables MP2 calculations for molecules with more
than 2300 atoms and 26000 basis functions on a single processor.