MULTIPOLE ELECTRON DENSITY MODELING IN ACENTRIC SPACE GROUPS? PERIODIC AB INITIO CALCULATIONS ON HEXAMETHYLENETETRAMINE. Henrik Birkedal and Sine Larsen, Centre for Crystallographic Studies, University of Copenhagen, Denmark
The multipole formalism for modeling of experimental electron densities is a well established method, but problems are encountered in acentric space groups due to the lack of general phase restrictions. To obtain a quantitative measure of the quality of phase reconstruction in acentric space groups periodic ab initio Hartree-Fock calculations on hexamethylenetetramine (HMT) have been performed making use of the CRYSTAL 92 package1. The atomic parameters were taken from a 15 K neutron diffraction study2. X-ray structure factors were calculated from the HF electron density. From the experimental atomic displacement parameters an overall displacement parameter was estimated, which was used to calculate pseudo-dynamic structure factors, that display the decrease of the intensities with sin [[theta]]/[[lambda]] due to the effects of thermal motion.
The static and pseudo-dynamic structure factors are used as observations in a least squares refinement with the generalized structure factor (gsf) formalism3. Three different sets of static and pseudo-dynamic structure factors were used. They correspond to the maximum resolution with the wavelengths 0.71073 Å (MoK[[alpha]]), 0.56087 Å (AgK[[alpha]]), and 0.24 Å (synchrotron radiation). The resulting gsf phases are compared to the original ab initio phases.
The quality of the total multipole modeled electron density has been examined by mapping of the difference density (ab initio - multipole model) and by comparing its characteristic topological features with those found with the TOPOND program4 from the ab initio electron density.
1R. Dovesi, V.R. Saunders, and C. Roetti Crystal 92 An Ab initio HartreeFock LCAO program for periodic systems, User Manual, 1992
2Kampermann, Sabine, Craven, and McMullan. Acta Cryst. A51, 489-497
3R.F. Stewart, M.A. Spackman, and C. Flensburg. Valray Manual, 1995
4C. Gatti, V.R. Saunders, and C. Roetti. J. Chem. Phys. 101, 10686 (1994)