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Results for DC.creator="P." AND DC.creator="Coppens" 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 ]
... electronic part of the charge distribution is defined by where p = ± when m is larger than 0, and is a radial ... described in International Tables for Crystallography, Volume B, Chapter 1.2 (Coppens, 2001). They differ from the functions by the normalization ... functions are the Cartesian representations of the real spherical harmonics (Coppens, 2001). More general models include non-atom centred ...
Uncertainties in experimental electron densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.8, pp. 724-725 [ doi:10.1107/97809553602060000615 ]
... scale factor and the other parameters (Rees, 1976, 1978; Stevens & Coppens, 1976). Similarly, for the covariance between the deformation densities ... factor contribution. Acta Cryst. A34, 254-256. Stevens, E. D. & Coppens, P. (1976). A priori estimates of the errors in ...
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 ]
... given by with [rho](r) defined by (8.7.3.81) (Stevens, Rees & Coppens, 1977). In the harmonic approximation, P(u) is a normalized three-dimensional Gaussian probability function, the ... omega] can be ignored (neglect of the screw tensor S), P(u, [omega]) = P(u)P([omega]), and both types ...
General considerations
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7.1, p. 723 [ doi:10.1107/97809553602060000615 ]
... given bywhere R represents the 3N nuclear space coordinates and P(R) is the probability of the configuration R. Evaluation of ... International Tables for Crystallography (2006). Vol. C, ch. 8.7, p. 723 © International Union of Crystallography 2006 | home | resources | advanced search ...
Thermal smearing of theoretical densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7, pp. 723-724 [ doi:10.1107/97809553602060000615 ]
... given bywhere R represents the 3N nuclear space coordinates and P(R) is the probability of the configuration R. Evaluation of ... given by with [rho](r) defined by (8.7.3.81) (Stevens, Rees & Coppens, 1977). In the harmonic approximation, P(u) is a normalized three-dimensional Gaussian probability function, ...
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 ]
... the experimental multipole populations by the inverse expression, (Holladay, Leung & Coppens, 1983). The matrix M-1 is given in Table ... orbital occupancies Pij to multipole populations Plm (from Holladay, Leung & Coppens, 1983) d-orbital populationsMultipole populations P00P20P22+P40P42+P44+ 0.200 1.039 ... to point towards a ligand atom. References Holladay, A., Leung, P. C. & Coppens, P. (1983). Generalized relation between d- ...
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 ]
... only on the charge density [rho]. References Dahl, J. P. & Avery, J. (1984). Local density approximations in quantum chemistry ... atoms and molecules. J. Chem. Phys. 56, 3122-3133. Hohenberg, P. & Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev. B ... International Tables for Crystallography (2006). Vol. C, ch. 8.7, p. 721 © International Union of Crystallography 2006 | home | resources | advanced ...
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 ]
... having a singularity at h = 0 (Dahl & Avery, 1984; Becker & Coppens, 1990). The contribution from this term to the potential ... as electron kinetic energy contributions must be added. References Becker, P. (1990). Electrostatic properties from X-ray structure factors. Unpublished results. Becker, P. & Coppens, P. (1990). About the Coulombic potential in ...
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 ]
... 8.7.3.51), (8.7.3.54) and (8.7.3.57) for the electrostatic properties at point P as a sum over atomic contributions. in which the exclusion of M = P only applies when the point P coincides with a nucleus, and therefore only occurs for ...
International Tables for Crystallography (2006). Vol. C, Section 8.7.3, pp. 714-725 [ doi:10.1107/97809553602060000615 ]
... electronic part of the charge distribution is defined by where p = ± when m is larger than 0, and is a radial ... described in International Tables for Crystallography, Volume B, Chapter 1.2 (Coppens, 2001). They differ from the functions by the normalization ... functions are the Cartesian representations of the real spherical harmonics (Coppens, 2001). More general models include non-atom centred ...
Uncertainties in experimental electron densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.8, pp. 724-725 [ doi:10.1107/97809553602060000615 ]
... scale factor and the other parameters (Rees, 1976, 1978; Stevens & Coppens, 1976). Similarly, for the covariance between the deformation densities ... factor contribution. Acta Cryst. A34, 254-256. Stevens, E. D. & Coppens, P. (1976). A priori estimates of the errors in ...
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 ]
... given by with [rho](r) defined by (8.7.3.81) (Stevens, Rees & Coppens, 1977). In the harmonic approximation, P(u) is a normalized three-dimensional Gaussian probability function, the ... omega] can be ignored (neglect of the screw tensor S), P(u, [omega]) = P(u)P([omega]), and both types ...
General considerations
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7.1, p. 723 [ doi:10.1107/97809553602060000615 ]
... given bywhere R represents the 3N nuclear space coordinates and P(R) is the probability of the configuration R. Evaluation of ... International Tables for Crystallography (2006). Vol. C, ch. 8.7, p. 723 © International Union of Crystallography 2006 | home | resources | advanced search ...
Thermal smearing of theoretical densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.7, pp. 723-724 [ doi:10.1107/97809553602060000615 ]
... given bywhere R represents the 3N nuclear space coordinates and P(R) is the probability of the configuration R. Evaluation of ... given by with [rho](r) defined by (8.7.3.81) (Stevens, Rees & Coppens, 1977). In the harmonic approximation, P(u) is a normalized three-dimensional Gaussian probability function, ...
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 ]
... the experimental multipole populations by the inverse expression, (Holladay, Leung & Coppens, 1983). The matrix M-1 is given in Table ... orbital occupancies Pij to multipole populations Plm (from Holladay, Leung & Coppens, 1983) d-orbital populationsMultipole populations P00P20P22+P40P42+P44+ 0.200 1.039 ... to point towards a ligand atom. References Holladay, A., Leung, P. C. & Coppens, P. (1983). Generalized relation between d- ...
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 ]
... only on the charge density [rho]. References Dahl, J. P. & Avery, J. (1984). Local density approximations in quantum chemistry ... atoms and molecules. J. Chem. Phys. 56, 3122-3133. Hohenberg, P. & Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev. B ... International Tables for Crystallography (2006). Vol. C, ch. 8.7, p. 721 © International Union of Crystallography 2006 | home | resources | advanced ...
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 ]
... having a singularity at h = 0 (Dahl & Avery, 1984; Becker & Coppens, 1990). The contribution from this term to the potential ... as electron kinetic energy contributions must be added. References Becker, P. (1990). Electrostatic properties from X-ray structure factors. Unpublished results. Becker, P. & Coppens, P. (1990). About the Coulombic potential in ...
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 ]
... 8.7.3.51), (8.7.3.54) and (8.7.3.57) for the electrostatic properties at point P as a sum over atomic contributions. in which the exclusion of M = P only applies when the point P coincides with a nucleus, and therefore only occurs for ...
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