On the information about deformations of the atoms in X-ray diffraction data

Kurki-Suonio, K.

doi:10.1107/s0567739468000744

Cited by 70 publications

(42 citation statements)

References 4 publications

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“…One such family of curves for a P atom was published by Stewart (1973a). This general feature by rather different radial scattering functions has been noted by Kurki-Suonio (1968). For valence-shell radial density functions of first-row atoms most of the radial scattering is within an Ewald sphere of 0"8 A_ -1 in sin 0/2 and the functions have maxima typically in the range 0.3-0.5 A -1 in sin 0/2.…”

Section: Least-squares Applicationsmentioning

confidence: 69%

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Electron population analysis with rigid pseudoatoms

Stewart¹

1976

Acta Cryst A

386

326

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The one-electron density function for a group of atoms within the asymmetric region of a unit cell is represented by a finite multipole expansion of the charge density about each atomic center. Each atomic expansion is called a pseudoatom. If the pseudoatom charge density is effectively rigid with nuclear motion, then the model may be used for a static charge density analysis of X-ray diffraction data. A valence density multipole model for pseudoatoms is restricted to single exponential radial functions. The representation is rotationally invariant. The model may be used for determination of static charge physical properties as well as aspects of chemical bonding. These results can be a critical test of the X-ray diffraction experiment for the determination of electron density distributions. The pseudoatoms discussed are primarily intended for crystals comprised of first and second-row atoms. The valence scattering model demands extensive data sets (probably at low temperatures) or an independent determination of atomic positions and mean square amplitudes of vibration.

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Section: Least-squares Applicationsmentioning

confidence: 69%

“…The valence scattering model is based on a multipole expansion similar to the proposal of Kurki-Suonio (1968). The radial functions, however, are restricted to single exponential functions.…”

Section: Resultsmentioning

confidence: 99%

Electron population analysis with rigid pseudoatoms

Stewart¹

1976

Acta Cryst A

386

326

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“…This approach resembles that of Dawson (1967), and is a further development beyond the extension to low site symmetry by Kurki-Suonio (1968). However STO (exponential) radial functions are preferred to Gaussian functions, and the orders of the functions are chosen so that the high-order gradients of the electric field remain finite.…”

Section: Multipole Expansionsmentioning

confidence: 99%

Electron-density studies. IV. A comparison of techniques for charge-density analysis and their application tos-triazine

Price¹,

Maslen²,

Delaney³

1978

Acta Cryst Sect A

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Some techniques for charge-density analysis proposed by R. F. Stewart have been compared by application to s-triazine, with X-ray data and neutron structural parameters. There is strong correlation between population coefficients for density basis functions which overlap heavily with each other, and in extreme cases individual populations are indeterminate. Multipole expansions centred on the nuclei are better defined than sets of orbital products which include two-centre terms. Trigonal octupole functions centred on the carbon and nitrogen nuclei give a marked improvement in the description of the scattering experiment provided the exponents which determine the radial variation of the density functions are optimized. The optimum exponent varies with the length of the multipole expansion. New algorithms developed for these studies give improved computational efficiency.

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“…In the earliest treatment the radial function of the valence shell is that of the isolated atom, but the Dawson formalism allows a modified Gaussian radial function for all but the leading spherical term, which is assumed to have the same radial dependence as the isolated atom. A more flexible radial function consisting of a set of harmonic-oscillator wave functions was used by Kurki-Suonio (1968) and applied in the analysis of bonding in diamond, silicon, NaCI, AgCI and CaF2 (Kurki-Suonio, 1971). Least-squares adjustment of the parameters in the Dawson model was carried out by McConnell & Sanger (1970), while Stewart (1969Stewart ( , 1973a) first introduced density basis functions which apply to the atoms at rest rather than the thermallysmeared atoms.…”

Section: Introductionmentioning

confidence: 99%

Testing aspherical atom refinements on small-molecule data sets

Hansen¹,

Coppens²

1978

Acta Cryst A

1,654

1,478

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X-ray data on silicon, tetracyanoethylene, p-nitropyridine N-oxide and ammonium thiocyanate are refined with a generalized aspherical-atom formalism as introduced by Stewart, but modified to have a spherical valence more similar to the unperturbed HF valence shell. Several types of radial dependences of the multipole functions are tested and criteria are developed for judging the adequacy of the aspherical-atom refinement. The aspherical-atom model leads to a significant decrease in the least-squares error function, a reduction of features in the residual map, and an improvement in thermal parameters when comparison is made with the neutron results or when the rigid-bond postulate proposed by Hirshfeld is applied. Positional parameters are often improved except in the case of terminal atoms for which discrepancies, attributed to correlation between dipole-population and positional parameters, are sometimes observed. Deformation maps based on the aspherical-atom least-squares parameters contain less noise than X --N maps and benefit from inclusion of calculated values of weak structure amplitudes in the summation. In the cases studied, deformation maps including terms beyond the experimental resolution do not yield additional information.

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On the information about deformations of the atoms in X-ray diffraction data

Cited by 70 publications

References 4 publications

Electron population analysis with rigid pseudoatoms

Electron population analysis with rigid pseudoatoms

Electron-density studies. IV. A comparison of techniques for charge-density analysis and their application tos-triazine

Testing aspherical atom refinements on small-molecule data sets

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