Quantum crystallographic charge density of urea.

Michael E Wall

doi:10.1107/s2052252516006242

Abstract

Standard X-ray crystallography methods use free-atom models to calculate mean unit-cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a charge density model of crystalline urea was calculated using high-level quantum theory and was refined against publicly available ultra-high-resolution experimental Bragg data, including the effects of atomic displacement parameters. The resulting quantum crystallographic model was compared with models obtained using spherical atom or multipole methods. Despite using only the same number of free parameters as the spherical atom model, the agreement of the quantum model with the data is comparable to the multipole model. The static, theoretical crystalline charge density of the quantum model is distinct from the multipole model, indicating the quantum model provides substantially new information. Hydrogen thermal ellipsoids in the quantum model were very similar to those obtained using neutron crystallography, indicating that quantum crystallography can increase the accuracy of the X-ray crystallographic atomic displacement parameters. The results demonstrate the feasibility and benefits of integrating fully periodic quantum charge density calculations into ultra-high-resolution X-ray crystallographic model building and refinement.

Highlights

Efforts to increase the accuracy of charge density models from X-ray crystallography have mainly focused on fitting the Bragg data using functions that are more expressive than the usual free-atom spherical distributions. Stewart (1969) proposed using general scattering factors that are the products of atom-centered orbital wavefunctions, and restrictions to better match the number of free parameters to the number of reflections in fitting (Stewart, 1970). Coppens et al (1971) separated the free atom charge density into core and valence components, and allowed them to be centered on different positions
The results indicate that Hirshfeld Atom Refinement (HAR) can yield molecular geometries and atomic displacement parameters (ADPs) that are similar to the neutron crystal structure, and both 2Fo À Fc maps and static charge densities that are distinct from the multipole model, but that agree comparably with the experimental data
The agreement of the quantum crystallographic models of urea with ultra-high-resolution data compares favorably to the multipole model. Both the 2Fo À Fc map and the total static charge density are substantially different between the quantum and multipole models

Summary

Introduction

Efforts to increase the accuracy of charge density models from X-ray crystallography have mainly focused on fitting the Bragg data using functions that are more expressive than the usual free-atom spherical distributions. Stewart (1969) proposed using general scattering factors that are the products of atom-centered orbital wavefunctions, and restrictions to better match the number of free parameters to the number of reflections in fitting (Stewart, 1970). Coppens et al (1971) separated the free atom charge density into core and valence components, and allowed them to be centered on different positions. Efforts to increase the accuracy of charge density models from X-ray crystallography have mainly focused on fitting the Bragg data using functions that are more expressive than the usual free-atom spherical distributions. Coppens et al (1971) separated the free atom charge density into core and valence components, and allowed them to be centered on different positions. Hirshfeld developed a least-squares method that models aspherical atomic charge densities using basis functions related to spherical harmonics, but with alternative symmetry properties (Hirshfeld, 1971). Spherical harmonic-related methods were integrated into multipole refinement computer programs that are used when charge density models are desired (Hansen & Coppens, 1978; Hirshfeld, 1977a; Craven & Weber, 1977; Stewart & Spackman, 1983; Jelsch et al, 2005; Volkov et al, 2006)

Methods

Results

Conclusion