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 non-robust 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 non-covalent interactions, C60 isomerization energies, and selected MME55 transition metal complex energetics.