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

The titular DLPNO approximation is the most widely used method for extending correlated wave function models to large molecular systems, yet its fidelity for intermolecular interaction energies in large supramolecular complexes has not been thoroughly vetted. Non-covalent interactions are sensitive to tails of the electron density and involve nonlocal dispersion that is discarded or approximated if the screening of pair natural orbitals (PNOs) is too aggressive. Meanwhile, the accuracy of the DLPNO approximation is known to deteriorate as molecular size increases. Here, we test the DLPNO approximation at the level of second-order Moeller-Plesset perturbation theory (MP2) and coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)], for a variety of large supramolecular complexes. DLPNO-MP2 interaction energies are within 3% of canonical values for small dimers with $\lesssim 10$ heavy atoms, but for larger systems the DLPNO approximation is often quite poor unless the results are extrapolated to the canonical limit, where the threshold for discarding PNOs is taken to zero. Counterpoise correction proves to be essential in reducing errors with respect to canonical results. 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, as these cause the DLPNO approximation to behave erratically, such that results cannot be extrapolated in a meaningful way. DLPNO-CCSD(T) calculations are typically performed using looser PNO thresholds as compared to DLPNO-MP2, but this significantly impacts the accuracy for large supramolecular complexes. Standard DLPNO-CCSD(T) settings afford errors of 2-6 kcal/mol for dimers involving coronene (C24H12) and circumcoronene (C54H18), even at the DLPNO-CCSD(T1) level.