A step-by-step investigation of sodium chloride clusters: accurate references, assessment of low-cost methods, and convergence from molecule to salt

Abstract

In the present study, we use high-level coupled-cluster-based methods to obtain benchmark geometries and lattice energy for small sodium chloride clusters up to (NaCl)15. Reliable geometries can be obtained with the CCSD(T)-F12b method in conjunction with a small double-ζ basis set, while accurate energies can be obtained with relatively economical methods (e.g. DLPNO-CCSD(T1)-F12) by adjusting for systematic bias against higher-level methods (e.g. W2). For the calculation of larger clusters, we find PBE0-D3BJ and GFN1-XTB to be suitable for geometry optimisation, while B97M-V and GFN1-XTB provide an adequate means for energy calculations once they are calibrated against high-level references. For much larger systems, a Born–Landé-type model can be used to obtain fairly good lattice energies. The results show the progression from a single NaCl molecule to bulk salt, with full convergence expected for cluster sizes in the range of 5–10 nm. The protocol for obtaining highly accurate lattice energies and calculating large clusters may be used to examine the energetics of ionic clusters more generally.