Results for DC.creator="Z." AND DC.creator="Su" in section 8.7.3 of volume C   page 3 of 3 pages.
Hellmann-Feynman constraint
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.3.4, p. 715
Hellmann-Feynman constraint 8.7.3.3.4. Hellmann-Feynman constraint According to the electrostatic Hellmann-Feynman theorem, which follows from the Born-Oppenheimer approximation and the condition that the forces on the nuclei must vanish when the nuclear configuration is in equilibrium, the nuclear repulsions are balanced by the electron-nucleus attractions (Levine, 1983 ...

International Tables for Crystallography (2006). Vol. C, Section 8.7.3.3.3, p. 715
Radial constraint 8.7.3.3.3. Radial constraint Poisson's electrostatic equation gives a relation between the gradient of the electric field [nabla]2[Phi](r) and the electron density at r. As noted by Stewart (1977), this equation imposes a constraint on the radial functions R(r). For , the condition must be ...

Cusp constraint
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.3.2, p. 715
... function R(r) = N exp (-[zeta]r), (8.7.3.13) gives , where Z is the nuclear charge, and is the Bohr unit. Thus ...

Electroneutrality constraint
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.3.1, p. 715
Electroneutrality constraint 8.7.3.3.1. Electroneutrality constraint Since a crystal is neutral, the total electron population must equal the sum of the nuclear charges of the constituent atoms. A constraint procedure for linear least squares that does not increase the size of the least-squares matrix has been described by Hamilton (1964). ...

Physical constraints
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.3, p. 715
... function R(r) = N exp (-[zeta]r), (8.7.3.13) gives , where Z is the nuclear charge, and is the Bohr unit. Thus ...

Modelling of the charge density
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.2, pp. 714-715
Modelling of the charge density 8.7.3.2. Modelling of the charge density The electron density [rho](r) in the structure-factor expression can be approximated by a sum of non-normalized density functions with scattering factor centred at Substitution in (8.7.3.4a) gives When is the spherically averaged, free-atom density, (8.7.3.4b) represents ...

Introduction
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.1, p. 714
Introduction 8.7.3.1. Introduction The charge density is related to the elastic X-ray scattering amplitude F(S) by the expression or, for scattering by a periodic lattice, As F(h) is in general complex, the Fourier transform (8.7.3.1) requires calculation of the phases from a model for the charge distribution. In ...

Uncertainties in derived functions
International Tables for Crystallography (2006). Vol. C, Section 8.7.3.9, p. 725
... of the scale factor, the positional parameters x, y and z of the atoms, and their charge-density parameters [kappa] and ...

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