Incrementally Corrected Periodic Local MP2 Calculations: I. The Cohesive Energy of Molecular Crystals

A method for accurate calculations of the cohesive energy of molecular crystals is presented. The cohesive energy is evaluated as a sum of several components. The major contribution is captured by periodic Hartree–Fock (HF) coupled with the local Møller–Plesset perturbation theory of second order (LMP2) with a triple-ζ basis set. Post-MP2 corrections and corrections for the basis set incompleteness are calculated from inexpensive incremental calculations with finite clusters. This is an essential improvement with respect to the periodic LMP2 method and allows for results of benchmark quality for crystalline systems. The proposed technique is superior to the standard incremental scheme as concerns the cluster size and basis set convergence of the results. In contrast to the total energy or electron correlation energy, which are evaluated in standard incremental calculations, post-MP2 and basis set corrections are rather insensitive to approximations and converge quickly both in terms of the order of the increments and the number of terms at a given order. Evaluation of the incremental corrections within the sub-kJ/mol precision requires computing very few of the most compact two-center and three-center non-embedded clusters, making the whole correction scheme computationally inexpensive. This method as well as alternative routes to compute the cohesive energy via the incremental scheme are tested on two molecular crystals: carbon dioxide (CO₂) and hydrogen cyanide (HCN).