Premium
VII. Vibrational Averaging of X‐Ray Scattering Intensities
Author(s) -
Stewart Robert F.
Publication year - 1977
Publication title -
israel journal of chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.908
H-Index - 54
eISSN - 1869-5868
pISSN - 0021-2148
DOI - 10.1002/ijch.197700023
Subject(s) - diatomic molecule , chemistry , harmonic oscillator , scattering , wave function , adiabatic process , charge (physics) , atomic physics , matrix (chemical analysis) , quantum mechanics , physics , molecule , organic chemistry , chromatography
The adiabatic potential for vibrational wavefunctions is given in a Preface. The vibrational average of ℐ XR el ( 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 sin θ/Λ dependence of ℐ Bragg and ℐ TDS . The averaged X‐ray intensity, ℐ av , 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 from F OBS Bragg . 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 on charge‐density models.