摘要:

AbstractA systematic treatment of those concepts of quantum chemistry relevant to electron‐density studies is given. The discussion is at an elementary level and encompasses not only the familiar concepts but more modern developments as wel

ISSN:0021-2148    

DOI:10.1002/ijch.197700017

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractStarting from the Schrödinger equation, the basic theory of scattering of X‐rays by electrons is given. The kinematic scattering, based on the first Born approximation, is treated in detail. The theory of phenomena, corresponding to a breakdown of this approximation, such as multiple and anomalous scattering, is given in outline. Kinematic scattering by a finite crystal is treated by using the convolution method. The consequences of finiteness of the crystal and of a series in a Fourier synthesis of the electron density are indicat

ISSN:0021-2148    

DOI:10.1002/ijch.197700018

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractWithin the Waller–Hartree theory it is possible to map out the interelectron density function (the diagonal elements of the intracule matrix) from an analysis of total X‐ray scattering intensities. Theoretical studies of He and H2show that electron correlation effects substantially influence total X‐ray scattering intensities, but do not appreciably alter the elastic X‐ray scattering intensity. On the other hand, theoretical studies of Be(1S), Ne(1S) and CO(1Σ*) indicate that electron correlation influences both total and elastic X‐ray scattering intensities by comparable amounts (∼ 1–2%), but at differing regions of the scattering v

ISSN:0021-2148    

DOI:10.1002/ijch.197700019

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractSignificance of symmetry in representing real‐ and reciprocal‐space properties of a crystal and of its constituents is discussed in terms of symmetry eigenfunctions. The formation of the site‐symmetrized multipole expansion for the 32 crystal point symmetries is shown, and the mutual relations between the real‐ and reciprocal‐space expansions are discussed. The origin of the symmetry‐based phase relations, equivalences and extinction rules of structure amplitudes is pointed out. Distinction is made between the accurate and approximate ones arising from the true space‐group symmetry and from the approximate free‐particle symmetry of the constituents, respectively. Finally, the symmetry imposed by reality of charge density and its violation through anomalous dispersion are discussed in terms of symmetric and antisymmetric contributions of atomic c

ISSN:0021-2148    

DOI:10.1002/ijch.197700020

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractThe one‐electron density function, ρ(r), (in principle deduced from elastically scattered X‐ray intensities) is the probability distribution function of an electron, averaged over the positions of all other electrons. A partitioning of ρ(r) into constituent parts is an intellectual exercise that does not lend itself to unique measurement from elastic X‐ray scattering experiments. It is shown that in the limit of perfect data and an infinite Ewald sphere, a least‐squares fit with a many‐centered finite multipole expansion of the charge density about theNnuclei will necessarily satisfy theq‐centered multipoles of the molecule forq= 1, 2,…,N. This means that a large number of static‐charge physical properties (averages over ρ(r)) are correctly given. Several expressions for averages of ρ(r) or overFHare given. It is shown that outer moments, such as atomic charges, dipole moments and quadrupole moments, always depend on a shape function. On the other hand, inner moments such as potentials, electric forces, and electric field gradients, may be represented by direct Fourier analysis ofFH(obs) (suitably phased, of course). Nuclear vibrations have been neglected throug

ISSN:0021-2148    

DOI:10.1002/ijch.197700021

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractBasic construction principles of charge‐density models based on independent deformed atoms are presented. The asymptotic validity of the rigid free‐atom model in reciprocal space; mathematical properties of possible radial bases of multipole expansions; requirements put by symmetry, by regularity, by approximate free‐atom nature, by approximate harmonicity of motion and byN‐representability on the deformation models; and the connection between orthogonality and independence of model parameters are discussed together with consequent conclusions about the analysis of diffraction data in terms of deformation

ISSN:0021-2148    

DOI:10.1002/ijch.197700022

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractThe adiabatic potential for vibrational wavefunctions is given in a Preface. The vibrational average of ℐXRel(K;Q) is studied by taking a canonical‐ensemble average of the states of motion for the nuclei. A simple example for an oriented diatomic molecule (one vibration) is used to illustrate the sinθ/Λdependence of ℐBraggand ℐTDS. The averaged X‐ray intensity, ℐav, is then fully developed (as done by Born) within the harmonic‐oscillator and rigid‐pseudoatom approximations for molecules and a crystal lattice. It is shown that generalized X‐ray scattering factors, characteristic of static charge properties, cannot in general be extracted fromFOBSBragg. With the rigid‐pseudoatom model, relationships betweeen the dynamical matrix and electric‐field gradients and charge densities are given. In this way self‐consistency between Born's scattering matrix and pseudoatoms can be imposed

ISSN:0021-2148    

DOI:10.1002/ijch.197700023

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractThe status of charge density studies is reviewed with special emphasis on factors limiting its potential, on a priori estimates of position‐dependent standard deviations and on present and possible future applications of the metho

ISSN:0021-2148    

DOI:10.1002/ijch.197700024

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractExperimental problems encountered in accurate electron density studies are discussed: choice of crystal, temperature effects, scanning mode, multiple scattering, accuracy. The effects of inelastic scattering (TDS) are indicated.

ISSN:0021-2148    

DOI:10.1002/ijch.197700025

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY

摘要:

AbstractThe different steps in the determination of precise X‐ray or neutron structure factors are reviewed. Items discussed are: absorption, extinction, X‐ray polarization, scale factor, Λ/2 contamination, long‐range intensity variations, anomalous dispersion, averaging of equivalent reflections, magnitude and phase of the structure

ISSN:0021-2148    

DOI:10.1002/ijch.197700026

出版商:WILEY‐VCH Verlag    

年代:1977

数据来源: WILEY