Local Second-Order Møller–Plesset Theory with a Single Threshold Using Orthogonal Virtual Orbitals: Theory, Implementation, and Assessment

It has long been clear that electron correlation methods
exhibit
unphysical compute scalings with molecular size, which has motivated
the development of local correlation methods to discard effectively
zero contributions in a controlled way to yield an approximate correlation
energy. The ideal local correlation method should have a single numerical
threshold that controls the dropping of terms with the ability to
have that threshold set small enough so that the correlation energy
is reproduced to enough significant figures such that the result is
chemically identical. This work reports such a method for the second-order
Møller–Plesset (MP2) theory. The theory, implementation,
and testing of this local MP2 theory are reported. Thresholds ranging
from 10–5 to 10–8 and basis sets
ranging from split valence plus polarization through to quadruple-ζ
are assessed for local MP2 calculations on a range of molecules, including
linear chains and molecules with two- and three-dimensional character.
The implementation is shared memory parallel via OpenMP and yields
roughly 50% parallel efficiency with 16 cores for a large job. Considerable
efforts were made to minimize memory demands, which increased as thresholds
were tightened. A variety of relative energy calculations are presented
as a function of threshold to provide some guidance to users on how
to obtain adequate precision at a low compute cost. It is particularly
clear that derivative properties require tighter thresholds in order
to achieve an adequate precision.