Quantum model of coherent X‐ray diffraction: Extension to Bloch orbitals

Abstract

The description of electron density in solids by quantum theory and by x-ray diffraction experiments should closely coincide. A formalism for describing the electronic structure of single crystals in terms of a density matrix is presented. Iterative equations for calculating the density matrix in a basis of Bloch orbitals using measured crystallographic intensity data are derived. Numerical results are presented. The Bloch orbital formalism explicitly accounts for the mutual interaction of atoms in different unit cells, and is useful for insulators, semiconductors, and metals.

Quantum crystallography

“…Massa and coworkers extended the original approach (i) to the case of open-shell systems 19 and (ii) to extended systems using Bloch and Wannier functions. 29 The latter extension takes into account the interaction among unit cells and allows to study insulators, semiconductors and metals, at least in principle. The most important step forward for this family of techniques is probably the one proposed by Pecora.…”

Reconstruction techniques in angular correlation of positron annihilation experiments

“…It is possible to take another step in the reconstruction process, namely to obtain information on the quantum density matrix of the bands contibuting to p ( p ) . The possibility of extracting quantum density matrices from experimental data has been under investigation for some time by many workers investigating x-ray scattering in solids (Goldberg and Massa 1983, Clinton and Massa 1972, Pecora 1986. A complete review of this topic is beyond the scope of this paper, but it is an appropriate area of investigation for anyone doing reconstruction of 2 ~-A C P A R data, since it might allow the possibility of obtaining information about wave functions from reconstructions.…”

The Advent of Quantum Crystallography: Form and Structure Factors from Quantum Mechanics for Advanced Structure Refinement and Wavefunction Fitting

“…The pioneering studies in this field date back to the 1960s when Clinton, Massa and collaborators proposed strategies to extract N-representable one-electron density matrices from X-ray diffraction data [96][97][98][99][100]. These studies were the starting points for the development of other techniques to obtain "experimental" wavefunctions and density matrices, such as Tanaka's X-ray Atomic Orbital [40] (XAO) and X-ray Molecular Orbital [101] (XMO) strategies, the Molecular Orbital Occupation Number [102, 103] (MOON) method and all the approaches aiming at reconstructing the diagonal and the off-diagonal parts of the one-electron density matrices by simultaneously exploiting X-ray diffraction data, magnetic structure factors and inelastic…”