Solid-state calculations for iterative refinement in quantum crystallography using the multipole model

Abstract

This work presents a new iterative refinement method, comparable to Hirshfeld atom refinement, using the Hansen–Coppens multipole model charge density description to obtain accurate atomic coordinates and atomic displacements based on CRYSTAL17 periodic boundary calculations. The refinement, performed using the Python code ReCrystal, allows the user to explore the full periodic charge density in the crystalline solid state for charge density analysis of weak interactions.

A quantum crystallographic refinement methodology has been developed using theoretical multipole parameters generated directly from solid-state calculations using the CRYSTAL17 program. This refinement method is comparable to other transferable form factor approaches, such as the Invariom model, but in contrast to the Hirshfeld atom refinement, it uses theoretical multipole parameters to describe the electron density from a solid-state calculation performed with CRYSTAL17 in an iterative refinement procedure. For this purpose, a Python3 code named ReCrystal has been developed. To start ReCrystal, a CIF, a Gaussian basis set, a DFT functional and the number of CPUs must be defined. The Pack–Monkhorst and Gilat shrinking factors, which define a lattice in the first Brillouin zone, must also be specified. After k-point sampling, CRYSTAL17 calculates structure factors directly from the static electron density. Multipole parameters are generated from these structure factors using the XD program and are fixed during least-squares refinement. The refinement of the xylitol molecular crystal has shown that the hydrogen atom positions can be determined with reasonable agreement to those obtained in the neutron diffraction experiment. This indicates that the periodic boundary condition in ReCrystal is an improvement over gas phase refinement with HAR. The multipole parameters obtained from ReCrystal can be used for further charge density studies especially if weak interactions are the focus. In this work, we demonstrate the performance of ReCrystal on molecular crystals of the small molecules d/l-serine and xylitol with weak hydrogen-bonding motifs using multipole refinement. The advantage of this approach is that multipole parameters can be obtained from high-resolution calculated diffraction data, no database is required, and errors due to the model and errors resulting from the experiment are clearly separated.