Basis Set Convergence of the Post-CCSD(T) Contribution to Noncovalent Interaction Energies.

We investigated the basis set convergence of high-order coupled-cluster interaction energy contributions for 21 small weakly bound complexes. By performing CCSDT(Q) calculations in at least the aug-cc-pVTZ basis set, and CCSDT calculations in at least aug-cc-pVQZ (aug-cc-pVTZ for one system), we found the convergence to be quite slow. In particular, the 6-31G*(0.25) and 6-31G**(0.25,0.15) bases advocated by Hobza et al. (J. Chem. Theory Comput. 2013, 9, 2151; ibid. 2013, 9, 3420) are unsuitable for the post-CCSD(T) effects, with average errors for the CCSDT(Q)-CCSD(T) interaction energy contribution of about 80% for 6-31G**(0.25,0.15) and 110% for 6-31G*(0.25). Upgrading the basis set to aug-cc-pVDZ reduces the average error to about 35% and extremely demanding CCSDT(Q)/aug-cc-pVTZ calculations are necessary for further improvement in accuracy. An error cancellation between basis set incompleteness effects at the CCSDT-CCSD(T) and CCSDT(Q)-CCSDT levels occurs for most (but not all) complexes, making it unproductive to carry out CCSDT calculations in a larger basis set than the more demanding CCSDT(Q) calculations. We also found that the frozen natural orbital approximation at the CCSDT and CCSDT(Q) levels works well only if the thresholds for discarding least occupied natural orbitals are very tight (significantly tighter than the thresholds recommended for molecular correlation energies in the original work of Rolik and Kállay, J. Chem. Phys. 2011, 134, 124111), making the performance gains quite limited. The interaction energy contributions through CCSDT(Q) are both a necessity and a bottleneck in the construction of top-accuracy interaction potentials and further improvements in the efficiency of high-order coupled-cluster calculations will be of great help.