title: Hirshfeld atom refinement.
abstract: Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly-l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree-Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints - even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu's), all other structural parameters agree within less than 2 csu's. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Å for temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å(2) as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements - an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.
authors.affiliation: Department of Chemistry, University of Milan, Via Golgi 19, 20133 Milan, Italy.
authors.forename: Silvia C
authors.initials: SC
authors.lastname: Capelli
authors.affiliation: Department of Chemistry and Biochemistry, Universität Bern, Freiestrasse 3, 3012 Bern, Switzerland ; Department of Chemistry, Universität Zürich, Winterthurstrasse 190, 8057 Zürich, Switzerland.
authors.forename: Hans-Beat
authors.initials: HB
authors.lastname: Bürgi
authors.affiliation: Institut für Anorganische und Angewandte Chemie, Universität Hamburg, Martin-Luther-King-Platz 6, 20146 Hamburg, Germany ; Institut für Anorganische Chemie, Georg-August-Universität Göttingen, Tammannstr. 4, 37077 Göttingen, Germany.
authors.forename: Birger
authors.initials: B
authors.lastname: Dittrich
authors.affiliation: School of Chemistry and Biochemistry, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia.
authors.forename: Simon
authors.initials: S
authors.lastname: Grabowsky
authors.affiliation: School of Chemistry and Biochemistry, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia.
authors.forename: Dylan
authors.initials: D
authors.lastname: Jayatilaka
keywords: X-ray structure refinement; anisotropic displacement parameters; aspherical atom partitioning; hydrogen atom modelling; quantum mechanical molecular electron densities