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

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-<i>ζ</i> 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.

本研究采用基于耦合簇（coupled-cluster）的高精度量子化学方法，针对尺寸不超过(NaCl)₁₅的小型氯化钠团簇，获取其基准几何构型与晶格能。结合小型双ζ基组的CCSD(T)-F12b方法，可获得可靠的团簇几何构型；而通过针对高阶参考方法（如W2）的系统偏差进行校正后，使用相对经济的计算方法（如DLPNO-CCSD(T1)-F12）即可得到精准的能量结果。针对更大尺寸的团簇计算，本研究发现PBE0-D3BJ与GFN1-XTB适用于几何优化；而B97M-V与GFN1-XTB在以高精度参考值完成校准后，可用于可靠的能量计算。针对超大型体系，则可采用玻恩-兰德（Born–Landé）型模型以获取精度较为可观的晶格能。研究结果呈现了从单个NaCl分子到块体盐的结构演化规律，当团簇尺寸处于5–10 nm范围时，其性质预计将完全收敛至块体体系。本研究建立的高精度晶格能获取方案与大尺寸团簇计算流程，可推广用于更广泛的离子团簇能量学研究。