Quantum Crystallography: Features and Application

Abstract

Quantum crystallography (QCr) is an area of research that arises from the fact that experimental X-ray diffraction data obtained from crystals can also be readily described theoretically by the use of quantum mechanical modeling. The intimate connection between experiment and theory arises from the fact that X-rays are scattered by electrons whose distributions are represented in the experimental data and models of electron density distributions are given by quantum mechanics (Q.M.). An objective of this type of research is to obtain a quantum mechanical model that is consistent with the crystallographic data, thus affording the opportunity to calculate numerous properties of interest, for example, various energies, electron distributions, atomic charges and electrostatic potentials. Our approach to quantum crystallography is based on the use of a single, idempotent density matrix (a projector matrix) [1]. In the initial stages of the process of optimizing the fit of a quantum mechanical model to X-ray diffraction data, it is valuable to have a projector matrix that is as close as possible to the one that results from the fitting process. Such a matrix is obtainable from ab initio calculations. The fitting process involves the adjustment of the values of the elements in the projector matrix and certain other parameters while preserving the idempotency of the matrix and its normalized trace. These properties will be described later on.