Periodic local MP2

Canonical periodic MP2 scales with the fifth power of system size, which prices it out of exactly the materials it would help most. Electron correlation is short-ranged, though, so most of that work goes into pairs that contribute almost nothing. lpno exploits the locality. It implements pair-natural-orbital and orbital-specific-virtual variants of MP2 (KPNOMP2, kdOSVMP2) with full k-point sampling, as an installable extension to PySCF.

The methods take localized occupied orbitals and build a compressed virtual space for each pair, dropping the fifth-power scaling to roughly cubic, about 90% lower cost in practice. The residual equations run through Cython kernels that call BLAS dgemm directly. Accuracy is controlled by a single threshold. As it tightens, KPNO-MP2 converges to canonical periodic MP2, and the correlation part of a cohesive energy extrapolates to the thermodynamic limit alongside the canonical k-point result.

The repository ships runnable examples, including one that goes from a small test cell to a KPNO-MP2 correlation energy in about a second on a laptop. A manuscript on the method is in preparation, and closely related local-correlation implementation work is published in J. Chem. Theory Comput. 21, 2918 (2025).