The Crystal Electron Energy and Compton Profile Calculations from X‐Ray Diffraction Data

Abstract

The met,hod of the one-electron density matrix determination from X-ray diffraction data is developed. It takes into account the translational symmetry and is applicable to covalent crystals. The crystal energies and directed Compton profiles are calculated in impulse approximation for silicon and diamond. The agreement with the experiments is rather good.Die Methode der Ein-Elektronen-Dichtematrixbestimmung aus Rontgenbeugungsdaten wird entwickclt. Sie beriicksichtigt die Translationssymmetrie und ist auf kovalente Kristalle anwcndbar. Die Kristallenergien und gerichteten Compton-Profile werden in Impulsnaherung fur Silizium und Diamant berechnet. Die Ubereinstimmung mit den Experimenten ist recht gut.

Quantum crystallography

“…The first density matrix determined from experimental X-ray structure factors was that of beryllium in 1985. 27 In a later study by Aleksandrov et al 28 one-electron density matrices for silicon and diamond were successfully fitted to experimental structure factors. Electronic kinetic energies and Compton profiles derived from them were in good agreement with corresponding experiments.…”

On the Possibility of Kinetic Energy Density Evaluation from the Experimental Electron-Density Distribution

“…Thus, K(r) and G(r) integrate to yield the same value of the total kinetic energy, T. In this sense, the local kinetic energy yielding the correct value of the total kinetic energy is only defined up to C * V2p(r), where C is an arbitrary constant. Although the problem of the reconstruction of the one-electron-density matrix p(r, r') from p(r) obtained from the diffraction experiment has been considered before (Aleksandrov, Tsirelson, Reznik & Ozerov, 1989;Tanaka, 1988;Schmider, Smith & Weyrich, 1992;Howard, Huke, Mallinson & Frampton, 1994), we are going to propose here an alternative less accurate but easier approach for the evaluation of the local kinetic energy density at the bond critical point of the multipolefitted electron density. A simple approximate way of directly relating the kinetic energy density to the electron density was introduced by the semiclassical Thomas-Fermi equation (March, 1957) with gradient quantum corrections (von Weizsacker, 1935;Kirzhnitz, 1957).…”

The mapping of electronic energy distributions using experimental electron density

“…The local energy functions can also be calculated using the one-electron density matrix reconstructed from the electron density (Tsirelson et al, 1977;Tsirelson & Ozerov, 1979, 1996Clinton et al, 1983;Gritsenko & Zhidomirov, 1987;Levy & Goldstein, 1987;Aleksandrov et al, 1989;Schwarz & Mueller, 1990;Schmider et al, 1992;Zhao & Parr, 1993;Jayatilaka, 1998). This approach is not discussed here.…”