Calculation of NMR parameters in ionic solids by an improved self-consistent embedded cluster method

Abstract

A new embedded cluster method (extended embedded ion method = EEIM) for the calculation of NMR properties in non-conducting crystals is presented. It is similar to the Embedded Ion Method (EIM) (ref. 1) in the way of embedding the quantum chemically treated part in an exact, self-consistent Madelung potential, but requires no empirical parameters. The method is put in relation to already existing cluster models which are classified in a brief review. The influence of the cluster boundary and the cluster charge is investigated, which leads to a better understanding of deficiencies in EIM. A recipe for an improved semi-automated cluster setup is proposed which allows the treatment of crystals composed of highly charged ions and covalent networks. EIM and EEIM results for ¹⁹F and ³¹P shielding tensors in NaF and in four different magnesium phosphates are compared with experimental values from solid state MAS NMR, some of which are measured here for the first time. The quantum part of the clusters is treated at hybrid DFT level (mPW1PW) with atomic basis sets up to 6-311G(3df,3pd). The improved agreement of EEIM allows new signal assignments for the different P-sites in Mg₂P₄O₁₂, α-Mg₂P₂O₇ and MgP₄O₁₁. Conversion equations of the type σ = A + Bδ between calculated absolute magnetic shieldings σ and the corresponding experimental chemical shifts δ are obtained independently from linear regressions of plots of isotropically averaged σ versus δ values on 19 ³¹P signals of small molecules.