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Results for DC.creator="Z." AND DC.creator="Su" in section 8.7.3 of volume C page 1 of 3 pages. |
Charge densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3, pp. 714-725 [ doi:10.1107/97809553602060000615 ]
... function R(r) = N exp (-[zeta]r), (8.7.3.13) gives , where Z is the nuclear charge, and is the Bohr unit. Thus ... yz, (x2 - y2)/2, and xy, where x, y and z are the components of a unit vector from the origin ... a shift of origin by R[alpha], or X, Y, Z in the original coordinate system. In three dimensions, we ...
Uncertainties in experimental electron densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.8, pp. 724-725 [ doi:10.1107/97809553602060000615 ]
Uncertainties in experimental electron densities 8.7.3.8. Uncertainties in experimental electron densities It is often important to obtain an estimate of the uncertainty in the deformation densities in Table 8.7.3.1. If it is assumed that the density of the static atoms or fragments that are subtracted out are precisely known, three sources ...
Reciprocal-space averaging over external vibrations
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7.2, pp. 723-724 [ doi:10.1107/97809553602060000615 ]
Reciprocal-space averaging over external vibrations 8.7.3.7.2. Reciprocal-space averaging over external vibrations Thermal averaging of the electron density is considerably simplified for modes in which adjacent atoms move in phase. In molecular crystals, such modes correspond to rigid-body vibrations and librations of the molecule as a whole. Their frequencies ...
General considerations
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7.1, p. 723 [ doi:10.1107/97809553602060000615 ]
General considerations 8.7.3.7.1. General considerations In the Born-Oppenheimer approximation, the electrons rearrange instantaneously to the minimum-energy state for each nuclear configuration. This approximation is generally valid, except when very low lying excited electronic states exist. The thermally smeared electron density is then given bywhere R represents the 3N nuclear ...
Thermal smearing of theoretical densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7, pp. 723-724 [ doi:10.1107/97809553602060000615 ]
Thermal smearing of theoretical densities 8.7.3.7. Thermal smearing of theoretical densities 8.7.3.7.1. General considerations | | In the Born-Oppenheimer approximation, the electrons rearrange instantaneously to the minimum-energy state for each nuclear configuration. This approximation is generally valid, except when very low lying excited electronic states exist. The thermally smeared electron density ...
Occupancies of transition-metal valence orbitals from multipole coefficients
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.6, pp. 722-723 [ doi:10.1107/97809553602060000615 ]
Occupancies of transition-metal valence orbitals from multipole coefficients 8.7.3.6. Occupancies of transition-metal valence orbitals from multipole coefficients In general, the atom-centred density model functions describe both the valence and the two-centre overlap density. In the case of transition metals, the latter is often small, so that to ...
Quantitative comparison with theory
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.5, pp. 721-722 [ doi:10.1107/97809553602060000615 ]
Quantitative comparison with theory 8.7.3.5. Quantitative comparison with theory Frequently, the purpose of a charge density analysis is comparison with theory at various levels of sophistication. Though the charge density is a detailed function, the features of which can be compared at several points of interest in space, it is by ...
The total energy of a crystal as a function of the electron density
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.4.4, p. 721 [ doi:10.1107/97809553602060000615 ]
The total energy of a crystal as a function of the electron density 8.7.3.4.4. The total energy of a crystal as a function of the electron density One can write the total energy of a system as where T is the kinetic energy, represents the exchange and electron correlation contributions, and ...
Electrostatic functions of crystals by modified Fourier summation
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.4.3, pp. 720-721 [ doi:10.1107/97809553602060000615 ]
Electrostatic functions of crystals by modified Fourier summation 8.7.3.4.3. Electrostatic functions of crystals by modified Fourier summation Expression (8.7.3.49) is an example of derivation of electrostatic properties by direct Fourier summations of the structure factors. The electrostatic potential and its derivatives may be obtained in an analogous manner. In order to ...
Evaluation of the electrostatic functions in direct space
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.4.2.3, p. 720 [ doi:10.1107/97809553602060000615 ]
... density parameters of the multipole expansion have been given by Su & Coppens (1992). They employ the Fourier convolution theorem, used ... from X-ray diffraction. J. Chem. Phys. 77, 1048-1060. Su, Z. & Coppens, P. (1992). On the mapping of electrostatic ...
International Tables for Crystallography (2006). Vol. C, Section 8.7.3, pp. 714-725 [ doi:10.1107/97809553602060000615 ]
... function R(r) = N exp (-[zeta]r), (8.7.3.13) gives , where Z is the nuclear charge, and is the Bohr unit. Thus ... yz, (x2 - y2)/2, and xy, where x, y and z are the components of a unit vector from the origin ... a shift of origin by R[alpha], or X, Y, Z in the original coordinate system. In three dimensions, we ...
Uncertainties in experimental electron densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.8, pp. 724-725 [ doi:10.1107/97809553602060000615 ]
Uncertainties in experimental electron densities 8.7.3.8. Uncertainties in experimental electron densities It is often important to obtain an estimate of the uncertainty in the deformation densities in Table 8.7.3.1. If it is assumed that the density of the static atoms or fragments that are subtracted out are precisely known, three sources ...
Reciprocal-space averaging over external vibrations
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7.2, pp. 723-724 [ doi:10.1107/97809553602060000615 ]
Reciprocal-space averaging over external vibrations 8.7.3.7.2. Reciprocal-space averaging over external vibrations Thermal averaging of the electron density is considerably simplified for modes in which adjacent atoms move in phase. In molecular crystals, such modes correspond to rigid-body vibrations and librations of the molecule as a whole. Their frequencies ...
General considerations
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7.1, p. 723 [ doi:10.1107/97809553602060000615 ]
General considerations 8.7.3.7.1. General considerations In the Born-Oppenheimer approximation, the electrons rearrange instantaneously to the minimum-energy state for each nuclear configuration. This approximation is generally valid, except when very low lying excited electronic states exist. The thermally smeared electron density is then given bywhere R represents the 3N nuclear ...
Thermal smearing of theoretical densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7, pp. 723-724 [ doi:10.1107/97809553602060000615 ]
Thermal smearing of theoretical densities 8.7.3.7. Thermal smearing of theoretical densities 8.7.3.7.1. General considerations | | In the Born-Oppenheimer approximation, the electrons rearrange instantaneously to the minimum-energy state for each nuclear configuration. This approximation is generally valid, except when very low lying excited electronic states exist. The thermally smeared electron density ...
Occupancies of transition-metal valence orbitals from multipole coefficients
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.6, pp. 722-723 [ doi:10.1107/97809553602060000615 ]
Occupancies of transition-metal valence orbitals from multipole coefficients 8.7.3.6. Occupancies of transition-metal valence orbitals from multipole coefficients In general, the atom-centred density model functions describe both the valence and the two-centre overlap density. In the case of transition metals, the latter is often small, so that to ...
Quantitative comparison with theory
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.5, pp. 721-722 [ doi:10.1107/97809553602060000615 ]
Quantitative comparison with theory 8.7.3.5. Quantitative comparison with theory Frequently, the purpose of a charge density analysis is comparison with theory at various levels of sophistication. Though the charge density is a detailed function, the features of which can be compared at several points of interest in space, it is by ...
The total energy of a crystal as a function of the electron density
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.4.4, p. 721 [ doi:10.1107/97809553602060000615 ]
The total energy of a crystal as a function of the electron density 8.7.3.4.4. The total energy of a crystal as a function of the electron density One can write the total energy of a system as where T is the kinetic energy, represents the exchange and electron correlation contributions, and ...
Electrostatic functions of crystals by modified Fourier summation
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.4.3, pp. 720-721 [ doi:10.1107/97809553602060000615 ]
Electrostatic functions of crystals by modified Fourier summation 8.7.3.4.3. Electrostatic functions of crystals by modified Fourier summation Expression (8.7.3.49) is an example of derivation of electrostatic properties by direct Fourier summations of the structure factors. The electrostatic potential and its derivatives may be obtained in an analogous manner. In order to ...
Evaluation of the electrostatic functions in direct space
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.4.2.3, p. 720 [ doi:10.1107/97809553602060000615 ]
... density parameters of the multipole expansion have been given by Su & Coppens (1992). They employ the Fourier convolution theorem, used ... from X-ray diffraction. J. Chem. Phys. 77, 1048-1060. Su, Z. & Coppens, P. (1992). On the mapping of electrostatic ...
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