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Two alternative approaches for the quantum-mechanical calculation of the nuclear-relaxation term of elastic and piezoelectric tensors of crystalline materials are illustrated and their computational aspects discussed: (i) a numerical approach based on the geometry optimization of atomic positions at strained lattice configurations and (ii) a quasi-analytical approach based on the evaluation of the force- and displacement-response internal-strain tensors as combined with the interatomic force-constant matrix. The two schemes are compared both as regards their computational accuracy and performance. The latter approach, not being affected by the many numerical parameters and procedures of a typical quasi-Newton geometry optimizer, constitutes a more reliable and robust mean to the evaluation of such properties, at a reduced computational cost for most crystalline systems. © 2016 Wiley Periodicals, Inc.

A fully ab initio technique is discussed for the determination of dynamical X-ray structure factors (XSFs) of crystalline materials, which is based on a standard Debye–Waller (DW) harmonic lattice dynamical approach with all-electron atom-centered basis sets, periodic boundary conditions, and one-electron Hamiltonians. This technique requires an accurate description of the lattice dynamics and the electron charge distribution of the system. The main theoretical parameters involved and final accuracy of the technique are discussed with respect to the experimental determinations of the XSFs at 298 K of crystalline silicon. An overall agreement factor of 0.47% between the ab initio predicted values and the experimental determinations is found. The best theoretical determination of the anisotropic displacement parameter, of silicon is here 60.55 × 10−4 A2, corresponding to a DW factor B = 0.4781 A2. © 2012 Wiley Periodicals, Inc.

Alternative techniques are presented for the evaluation of the electron momentum density (EMD) of crystalline systems from ab initio linear combination of atomic-orbitals calculations performed in the frame of one-electron self-consistent-field Hamiltonians. Their respective merits and drawbacks are analyzed with reference to two periodic systems with very different electronic features: the fully covalent crystalline silicon and the ionic lithium fluoride. Beyond one-electron Hamiltonians, a post-Hartree–Fock correction to the EMD of crystalline materials is also illustrated in the case of lithium fluoride. © 2012 Wiley Periodicals, Inc.