Plane waves versus correlation-consistent basis sets: A comparison of MP2 non-covalent interaction energies in the complete basis set limit

Second-order Møller Plesset perturbation theory (MP2) is the most expedient wavefunction-based method for considering electron correlation in quantum chemical calculations and as such provides a cost-effective framework to assess the effects of basis sets on correlation energies, for which the complete basis set (CBS) limit can commonly only be obtained via extrapolation techniques. Software packages providing MP2 energies are commonly based on atom-centered bases with innate issues related to possible basis set superposition errors (BSSE), especially in the case of weakly-bonded systems. Here, we present non-covalent interaction energies in the CBS limit, free of BSSE, for 20 dimer systems of the S22 dataset obtained via a highly-parallelized MP2 implementation in the plane-wave pseudopotential molecular dynamics package CPMD. The specificities related to plane waves for accurate and efficient calculations of gas-phase energies are discussed, and results compared to the localized (aug-)cc-pV[D,T,Q,5]Z correlation-consistent bases as well as their extrapolated CBS estimates. We find that the BSSE-corrected aug-cc-pV5Z basis can provide MP2 energies highly consistent with the CBS plane wave values with a minimum mean absolute deviation of ~0.05 kcal/mol without the application of any extrapolation scheme. In addition, we tested the performance of 13 different extrapolation schemes and found that the $X^{-3}$ expression applied to the (aug-)cc-pVXZ bases provides the smallest deviations against CBS plane wave values if the extrapolation sequence is composed of points D and T, while $(X + \frac{1}{2})^{-4}$ performs slightly better for TQ and Q5 extrapolations. Also, we propose $A (X-\frac{1}{2})^{-3} + B (X+\frac{1}{2})^{-4}$ as a reliable alternative to extrapolate total energies from the DTQ, TQ5 or DTQ5 data points. In spite of the general good agreement between the values obtained from the two types of basis set, it is noticed that differences between plane waves and (aug-)cc-pVXZ basis sets, extrapolated or not, tend to increase with the number of electrons, thus raising the question whether these discrepancies could indeed limit the attainable accuracy for localized bases in the limit of large systems.