Calculation of the electron density distribution in silicon by the density-functional method. Comparison with X-ray results

Velders, G. J. M.; Feil, D.

doi:10.1107/s0108768189003782

Cited by 8 publications

(6 citation statements)

References 13 publications

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“…19,20 Here, R j = |r − r j |, and the sum is taken over ion coordinates r j within a cluster of 4 × 4 × 4 unit cells. The charges q j and the ionic radii R Fig.…”

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confidence: 99%

μSR investigation of magnetism and magnetoelectric coupling in Cu2OSeO3

et al. 2011

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A detailed zero-and transverse-field muon spin rotation investigation of magnetism and the magnetoelectric coupling in Cu 2 OSeO 3 is reported. An internal magnetic field B int (T = 0) = 85.37(25) mT was found, in agreement with a ferrimagnetic state below T c = 57.0(1) K. The temperature dependence of the magnetic order parameter is well described by the relation2 )β with an effective exponentβ 0.39(1), which is close to the critical exponent β 1/3 for a three-dimensional (3D) magnetic system. Just above T c the muon relaxation rate follows the power law λ(T ) ∝ (T /T c − 1) −ω withω = 1.06(9), which is characteristic for 3D ferromagnets. Measurements of B int (T ) with and without an applied electrostatic field E = 1.66 × 10 5 V/m suggest a possible electric-field effect of magnitude B V = B V (0 V) − B V (500 V) = −0.4(4) mT.

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“…19,20 Here, R j = |r − r j |, and the sum is taken over ion coordinates r j within a cluster of 4 × 4 × 4 unit cells. The charges q j and the ionic radii R Fig.…”

mentioning

confidence: 99%

μSR investigation of magnetism and magnetoelectric coupling in Cu2OSeO3

et al. 2011

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“…Their strategy consists of numerically partitioning the theoretical electron density into atomic fragments (Hirshfeld, 1977), fitting these fragments with a finite expansion of nuclear-centred spherical harmonics with Laguerre polynomials and analytically Fourier transforming these expansions. The method has been applied to oxalic acid dihydrate (Krijn et al, 1988), crystalline Si (Velders & Feil, 1989), water and its dimer (Bruning & Feil, 1992;De Vries et al, 1994;Poorthuis & Feil, 1994) and, most recently, a series of nucleic acid components (Klooster, 1992). To our knowledge there has been no attempt made to compare the structure factors produced by these different procedures, although clearly that would be of some interest.…”

Section: Compute Molecular Propertiesmentioning

confidence: 99%

“…Model data sets were also computed in a similar manner for methylamine and formamide in a study of a density matrix refinement technique (Howard, Huke, Mallinson & Frampton, 1994) and for phosphoric acid in a test of the multipole procedure for phosphorus-containing systems (Moss, Souhassou, Blessing, Espinosa & Lecomte, 1995). Feil and co-workers have developed quite a different strategy, partly dictated by their choice of an STO basis set for the computation of molecular wave functions via the DVM-Xc~ method (Krijn, Graafsma & Feil, 1988;Velders & Feil, 1989;Bruning & Feil, 1992;De Vries, Briels & Feil, 1994;Poorthuis & Feil, 1994). Their strategy consists of numerically partitioning the theoretical electron density into atomic fragments (Hirshfeld, 1977), fitting these fragments with a finite expansion of nuclear-centred spherical harmonics with Laguerre polynomials and analytically Fourier transforming these expansions.…”

Section: Compute Molecular Propertiesmentioning

confidence: 99%

Molecular electric moments and electric field gradients from X-ray diffraction data: model studies

Spackman¹,

Byrom²

1996

Acta Crystallogr Sect B

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Model X-ray data sets, with and without the inclusion of experimental thermal motion parameters, have been computed via Fourier transformation of ab initio molecular electron densities for 12 different molecular crystals. These datasets were then analysed with three different multipole models of varying sophistication and, from the multipole functions, molecular dipole and second moments, as well as electric field gradients (EFG's), at each nuclear site were computed and compared with results obtained from the original ab initio wavefunctions. The results provide valuable insight into the reliability of these properties, extracted in the same way from experimental X-ray data. Not all molecular systems display identical trends, but a general pattern is discernible. Specifically, dipole moments are typically underestimated by a small but significant amount (~ 10-15%), the trace of the second moment tensor is well determined but overestimated by a few per cent and electric field gradients at protons are confirmed to be well within reach of a careful charge density analysis of X-ray diffraction data.

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“…We calculated the EDD of silicon with the density functional program ADF-BAND [21]. Structure factors were calculated from this static density, and isotropic thermal vibration was introduced via a Debye-Waller factor (B 0.4642 Å 22 , taken from [22]) [23]. The resulting EDD, calculated by means of a Fourier transformation of a full set of structure factors, did not show any non-nuclear maximum in the Si-Si bond; see Fig.…”

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Critical Analysis of Non-Nuclear Electron-Density Maxima and the Maximum Entropy Method

1996

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Experimental evidence for the existence of non-nuclear maxima in charge densities is questioned. It is shown that the non-nuclear maxima reported for silicon are artifacts of the maximum entropy method that was used to analyze the x-ray diffraction data. This method can be improved by the use of appropriate prior information. We report systematic tests of the improved method leading to the absence of non-nuclear maxima in Si. Likewise, the non-nuclear maxima reported earlier in beryllium are not substantiated. [S0031-9007(96) [4] recently reported that the presence of the non-nuclear maxima in the Na clusters appears to be a basis-set or method-dependent effect. Unfortunately, no experimental methods exist to confirm or invalidate these theoretical results.We now turn to crystals. Periodicity allows accurate studies of the EDD by x-ray diffraction. In reality, perturbation of the periodicity by the presence either of a surface or of impurities cause oscillations in the EDD, the so-called Friedel oscillations. In the present paper, however, we refer to non-nuclear maxima with the periodicity of the lattice, such as found by Mei et al. [5] in the bcc lattices of lithium and sodium, using the HartreeFock program CRYSTAL [6]. In 1990 Sakata and Sato [7] analyzed the highly accurate x-ray Pendellösung data on Si measured by Saka and Kato [8] with the maximum entropy method (MEM). They found maxima in the electron density in the Si-Si bond. Recently, non-nuclear maxima were also found in Be by Iversen et al. [9], applying the MEM to structure factors that were measured by Larsen and Hansen [10]. These two findings are the first and only experimental support for the rather elusive non-nuclear maxima. They constitute a considerable challenge to theoretical solid state physics, since the many present wave-function calculations on Si, including our own [11], do not corroborate the result. Since we do not doubt the quality of the primary data in the MEM analysis, we decided to reassess the MEM procedure itself and test its ability to bring to light subtle features in electron density maps. In the course of the work we discovered the essential role of the prior assumptions in the analysis, a role that has not yet received the attention it deserves.Structure factors, obtained from a single crystal x-ray experiment, are directly related to the EDD by means of a Fourier transform. The problems one is facing when performing the inverse Fourier transformation are that (i) the experiment provides us with a limited number of structure factors, (ii) all structure factors are determined within a certain experimental error, and (iii) the phase of the structure factors is unknown. In case the crystal is centrosymmetric the phases can usually be derived without any ambiguity and only the first two problems remain.The traditional way to extract the EDD from a limited set of noisy data is to fit the structure factors by a model. The drawback of this method is that features which are not allowed by the model will never show up in the ED...

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Calculation of the electron density distribution in silicon by the density-functional method. Comparison with X-ray results

Cited by 8 publications

References 13 publications

μSR investigation of magnetism and magnetoelectric coupling in Cu2OSeO3

μSR investigation of magnetism and magnetoelectric coupling in Cu2OSeO3

Molecular electric moments and electric field gradients from X-ray diffraction data: model studies

Critical Analysis of Non-Nuclear Electron-Density Maxima and the Maximum Entropy Method

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