Multipole refinement

Spackman, M.A. and Byrom, P.G. (1997) Retrieval of structure factor phases in acentric space groups. Model studies using multipole refinements, Acta Cryst., B53, 553-564. 

Destro,R., Bianchi,R., Gatti,C. andMerati,F. (1991)TotalelectronicchargedensityofL-alaninefrom X-ray diffraction at 23 K, Chem. Phys. Lett., 186, 47-52 Iversen, B.B., Larsen, F.K., Souhassou, M. and Takata, M. (1995) Experimental for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method, Acta Cryst., B51, 580-591 and references therein. 

Thermal parameters of conventional independent-atom refinements using BLFLS [8] were applied as starting values for full multipole refinements, which were performed with VALRAY [10]. Both data sets were successfully refined. The results were compared to those published by Kirfel and Eichhom [7], and good agreement was found. 

Figure 1. Difference map after high order refinement - data cutoff at sin 0/k = 0.9A1 for reflections with F2 > (a) this work (b) SC. Model map after multipole refinement - data cutoff at... 

Figure 1. Residual density in Si,—O - Al and Sii-Oi0-Si3 planes of scolecite after the multipole refinement 4 in Table 2. Contour interval 0.1 e A 3 negative contours are dashed, zero contour omitted.

The discussions of the structure and the electron density are based on the structure found by a full multipole refinement of the X-ray data with the hydrogen positions fixed at the neutron values and the hydrogen thermal parameters fixed at scaled neutron values (Figure 5).1 The interatomic distances and intramolecular bond angles are given in Table 2. 

Koritzansky, T., Howard, S., Mallison, P.R., Su, Z., Richter, T. and Hansen, N.K. (1995) XD, a computer program package for multipole refinement and analysis of charge densities from diffraction data, Institute for Crystallography, Berlin. 

There are two approaches to map crystal charge density from the measured structure factors by inverse Fourier transform or by the multipole method [32]. Direct Fourier transform of experimental structure factors was not useful due to the missing reflections in the collected data set, so a multipole refinement is a better approach to map charge density from the measured structure factors. In the multipole method, the crystal charge density is expanded as a sum of non-spherical pseudo-atomic densities. These consist of a spherical-atom (or ion) charge density obtained from multi-configuration Dirac-Fock (MCDF) calculations [33] with variable orbital occupation factors to allow for charge transfer, and a small non-spherical part in which local symmetry-adapted spherical harmonic functions were used. 

The static model deformation density corresponding to the multipole refinement results is given by... 

In the application of the two-channel method to a-glycine, use of a uniform prior density sharpens and enhances the bond peaks relative to the observed deformation density, but suppresses the lone-pair peaks to much lower levels. The use of the multipole refinement deformation density as a nonuniform prior gives better results and some increase in detail. 

Acknowledgments. This work was supported by the United States Public Health Service (National Institutes of Health grants HL-19481 and GM-50694), and utilized computational facilities made available by the National Center for Supercomputing Applications (supported by NSF grant CHE97-0020N). We are grateful to Professor P. Coppens for assistance with multipole refinement of our x-ray data. 

Fig. 4. Residual map in the plane of a nitro group in HMX after the final multipole refinement. Solid contours are positive, dotted contours are negative, and dashed contours are zero. Contour interval is 0.05 eA 3.

T. Koritsanszky, S. Howard, P.R. Mallison, Z. Su, T. Ritcher and N.K. Hansen, XD, A computer Program Package for Multipole Refinement and Analysis of Electron Densities from Diffraction Data, User s Manual, University of Berlin, Germany (1995). 

In the multipole refinement of TPPFe(THF)2, a D4h local symmetry was imposed on the iron atom which explains that only four dt population parameters were derived inspection of Table 4 leads to the same conclusion derived qualitatively from the examination of the deformation maps i.e., the 5 2g state is the main contributor to the ground state of the complex. This interesting calculation of d electron population calculations was also performed on other coordination compounds like metal carbonyls [38] and metal carbynes [39]. 

The most likely cause of such discrepancy is an unsuitable atomic scattering factor. That means, some factor that affects the chemical behaviour of an atom may, for instance, not be properly accounted for in the calculated electronic structure from which scattering factors are derived. The use of oriented non-spherical atomic ground-states has been proposed [182] as a possible remedy. On this basis theoretically acceptable chemical deformation densities have been obtained. Such usage has led to the development of aspherical-atom, or multipole refinement of crystallographic structures in charge-density studies. 

Deformation densities based on multipole refinements do not include the effects of thermal smearing and hence represent static densities, with a high degree of dependence on the basis sets used in generating the aspherical functions. 

Such observations immediately raise the question how reliable are projections of crystal-field effects onto multipoles The analyses of wavefunction-simulated X-ray data of small model compounds have revealed that the interaction density (8p = p(crystal) — p(isolated molecule)) manifests itself in low-order structure factors, and only to an extent that is comparable with the experimental noise [80]. Nevertheless, the multipole refinement was shown to retrieve this low signal (about 1% in F) successfully. A related study on urea, however, demonstrated that this is not the case if random errors of magnitude comparable with the effect of interaction density are added to the theoretical data [81]. The result also implies that indeterminacies associated with the interpretation of non-centrosymmetric structures can severely limit the pseudoatom model in distinguishing between noise and physical effects [82, 83]. 

A thorough investigation of simulated structure factor data of ammonia provides us with quantitative figures for the accuracy of BCP properties achievable with the pseudoatom projection [72]. The Pbcp> Pbcp> tBCp(H) indices of the static model density obtained by the multipole refinement of HF/6-31IG static structure factors deviate from the correct values (derived... 

M. A. Spackman, P. G. Byrom, M. Alfredsson and K. Hermansson, Influence of intermolecular interactions on multipole refined electron densities, Acta Cryst. ASS, 30-47 (1999). 

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