Assessing the domain-based local pair natural orbital (DLPNO) approximation for non-covalent interactions in sizable supramolecular complexes

The titular DLPNO approximation has become a de facto standard for extending correlated wave function models to large molecular systems yet its fidelity for intermolecular interaction energies has not been thoroughly vetted. Non-covalent interaction energies are sensitive to tails of the electron density, involving parts of the wave function that are far from the nuclei and may be discarded in some local correlation treatments. Meanwhile, the accuracy of the DLPNO approximation is known to deteriorate as molecular size increases and questions have been raised regarding the accuracy of benchmark calculations for large van der Waals complexes. Here, we test the DLPNO approximation at the level of second-order Moller-Plesset perturbation theory (MP2) in systems with up to 240 atoms, for which canonical MP2 calculations can be performed for comparison. For small dimers, we find that DLPNO-MP2 interaction energies are within 3% of canonical values but the approximation is quite poor for larger systems, unless the results are extrapolated to to the limit where the threshold for discarding PNOs is taken to zero. For a sequence of nanoscale graphene dimers up to (C96H24)2, extrapolated DLPNO-MP2 interaction energies agree with canonical values to within 1%, independent of system size, provided that the basis set does not contain diffuse functions. The presence of diffuse basis functions causes oscillatory behavior as a function of the PNO threshold, making it impossible to extrapolate the results in a meaningful way.