More Numerical Precision for Less Compute Cost: Optimizing a Local Correlation Algorithm for Second Order Møller–Plesset Theory and Comparing against Pair Natural Orbital Methods

Correlations associated with dynamical
fluctuations of electrons
in molecules can be spatially localized, which offers the promise
of reducing the compute complexity of many-body quantum chemical methods
such as second-order Møller–Plesset (MP2) theory. This
work reports efforts to significantly improve a recent approach to
local MP2 that is based on a single numerical threshold to control
accuracy versus compute cost, and the use of localized orthogonal
orbitals for both occupied and virtual spaces. The most important
improvement is a novel embedding correction to the right-hand-side
of the linear equations for the retained MP2 amplitudes, which includes
the effect of integrals that are evaluated but discarded as below
threshold. Together with a modified set of occupied orbitals that
increases diagonal dominance in the occupied-occupied Fock operator,
and an on-the-fly block Kapuy solver for below-threshold amplitudes,
this scheme provides roughly an order of magnitude improvement in
accuracy. Other algorithm optimizations include nonrobust local fitting,
sharper occupied/virtual sparse maps, and on-the-fly selection of
locally BLAS-2 and BLAS-3 evaluation of matrix-vector products in
the conjugate gradient iterations. These advances have been shown
to significantly reduce memory and improve compute efficiency, without
affecting accuracy control by ϵ. Detailed comparisons against
the domain-localized pair natural orbital, DLPNO-MP2, algorithm in
the ORCA 6.0.1 package demonstrate significant improvements in accuracy
for given time-to-solution. Reported benchmarks include ACONF20 conformational
energies, L7, S12L, and ExL8 noncovalent interactions, C60 isomerization energies, and selected MME55 transition metal complex
energetics.