Application of electrostatic and multi-layer embedding in Hirshfeld atom refinements: a cost-effective approach for approximating bulk effects in crystalline environments

One of the main advantages of Hirshfeld atom refinement (HAR), besides improved refinement statistics and reduced uncertainties of all derived parameters, is the possibility of refining anisotropic hydrogen atoms without any type of restriction to a correct distance. Notwithstanding this, there are still some problems that need attention for an accurate refinement of H atoms. For instance, X —H bond distances ( X = N, O) are typically underestimated when they participate in a strong hydrogen bond and the crystallographic environment is not accounted for in the refinement model. In this work, we propose the use of an embedding scheme to model bulk effects approximately, where a molecule or group of molecules is polarized by electrostatic potential (ESP)-derived charges. Quantum mechanics/molecular mechanics methods based on ESP-derived charges have been used successfully to reproduce band gaps or optical and electronic properties of crystalline systems. It is demonstrated that the H-atom refinement parameters obtained with this approach are comparable to those obtained from pure quantum mechanical models, but with a significantly lower computational cost. Thus, this embedded HAR method is suitable for performing refinements in reasonable time frames for large systems in which strong intermolecular interactions, such as hydrogen bonds, exist.