# Ectrostatic Potentials in Crystals

## Abstract

In an X-ray diffraction experiment, the integrated Bragg intensities can be reduced to structure factor amplitudes, \(\left| {{F_{\vec H}}} \right|\), which may be accurate to a few percent. Data reduction models include deviations from kinematic scattering conditions (extinction models), inelastic scattering due to phonons in the crystal (thermal diffuse scattering) and current density contributions (anomalous scattering). The relative success of the correction terms can be improved on occasion with controlled experimental parameters such as reduced crystal size, reduced temperatures or higher-frequency X-rays. The phases of \(\left| {{F_{\vec H}}} \right|\) are determined exclusively by model calculations and are generally more reliable for centric crystal structures than acentric ones. If the crystallographer has pursued these sundry steps from the measured, scattered X-ray photons to a set of \({F_{\vec H}}\) with success, then these data may be used to map out a crystal structure at atomic resolution. The \({F_{\vec H}}\), in principle, are the Fourier components of the thermal average electron density in the crystallographic unit cell. If, in addition, the mean thermal nuclear distribution is known (as from a neutron diffraction experiment) then the total charge density distribution can be determined to within the resolution of the experiment, which is restricted to the finite size of the Ewald sphere with radius 1/λ where λ is the wavelength of the X-ray.

## Keywords

Electrostatic Potential Nuclear Site Thermal Diffuse Scattering Equipotential Contour Structure Factor Amplitude## Preview

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## References

- 1.R. F. Stewart and D. Feil, A theoretical study of elastic X-ray scattering, Acta Cryst. A36: 503 (1980).CrossRefGoogle Scholar
- 2.R. F. Stewart, On the mapping of electrostatic properties from Bragg diffraction data, Chem. Phys. Lett. 65: 335 (1979).CrossRefGoogle Scholar
- 3.F. E. Harris, Hartree-Fock studies of electronic structures of crystalline solids, in: “Theoretical Chemistry, Advances and Perspectives,” Vol. 1, H. Eyring and D. Henderson, eds., Academic Press, New York (1975), p. 147.CrossRefGoogle Scholar
- 4.R. F. Stewart, Electron population analysis with rigid pseudo-atoms, Acta Cryst. A32: 565 (1976).CrossRefGoogle Scholar
- 5.C. K. Johnson, Addition of higher cumulants to the crystallographic structure factor equation: a generalized treatment for thermal-motion effects, Acta Cryst. A25: 187 (1969).CrossRefGoogle Scholar
- 6.B. R. A. Nijboer and F. W. De Wette, On the calculation of lattice sums, Physica 23: 309 (1957).CrossRefGoogle Scholar
- 7.P. J. Brown, A study of charge density in beryllium, Phil. Mag. 26: 1377 (1972).Google Scholar
- 8.R. F. Stewart, A charge-density study of crystalline beryllium, Acta Cryst. A33: 33 (1977).CrossRefGoogle Scholar
- 9.E. Clementi, Tables of atomic functions, Supplement to IBM J. Res. Dev. 9: 2 (1965).Google Scholar
- 10.F. K. Larsen, M. S. Lehmann and M. Merisalo, Mean-square atomic displacement and antisymmetric atomic vibrations in beryllium at room temperature determined from short-wavelength neutron data, Acta Cryst. A36: 159 (1980).Google Scholar
- 11.Y. W. Yang and P. Coppens, On the experimental electron distribution in silicon, Solid State Comm. 15: 1555 (1974).CrossRefGoogle Scholar
- 12.Y. Le Page and G. Donnay, Refinement of the crystal structure of low-quartz, Acta Cryst. B32: 2456 (1976).CrossRefGoogle Scholar
- 13.Y. Le Page, private communication (1978).Google Scholar
- 14.J. Epstein, Model studies for the analysis of scattered intensities from X-ray and high energy electron diffraction, Ph.D. Thesis, Carnegie-Mellon University (1978).Google Scholar
- 15.J. Epstein, J. R. Ruble and B. M. Craven, unpublished (1978).Google Scholar
- 16.R. K. McMullan, J. Epstein, J. R. Ruble and D. M. Craven, The crystal structure of imidazole at 103 K by neutron diffraction, Acta Cryst. B35: 688 (1979).CrossRefGoogle Scholar
- 17.B. M. Craven, P. Benci, J. Epstein, R. O. Fox, R. K. McMullan, J. R. Ruble, R. F. Stewart and H. P. Weber, X-ray and neutron diffraction studies of charge density in small molecules of biological interest, ACA Program and Abstracts Ser. 2, 7:No. 1, 42 (1979).Google Scholar
- 18.E. Scrocco and J. Tomasi, The electrostatic molecular potential as a tool for the interpretation of molecular properties, Fortschr. Chem. Forsch. 42: 95 (1973).Google Scholar