MOF-5 is by far the most relevant member of the new class of metal–organic framework materials and has been adopted as a case study to show that reliable ab initio prediction of materials properties of complex systems can be obtained by means of a solid state computational tool like the CRYSTAL code. Structure, electronic properties and vibrational frequencies of MOF-5 computed at the B3LYP level of theory are reported and discussed. Animations representing MOF-5 vibrations are available at the web site: http://www.crystal.unito.it/vibs/mof5
A computational strategy is devised for the accurate ab initio simulation of elastic properties of crystalline materials under pressure. The proposed scheme, based on the evaluation of the analytical stress tensor and on the automated computation of pressure-dependent elastic stiffness constants, is implemented in the CRYSTAL solid state quantum-chemical program. Elastic constants and related properties (bulk, shear and Young moduli, directional seismic wave velocities, elastic anisotropy index, Poisson's ratio, etc.) can be computed for crystals of any space group of symmetry. We apply such a technique to the study of high-pressure elastic properties of three silicate garnet end-members (namely, pyrope, grossular, and andradite) which are of great geophysical interest, being among the most important rock-forming minerals. The reliability of this theoretical approach is proved by comparing with available experimental measurements. The description of high-pressure properties provided by several equations of state is also critically discussed.
Grossular and andradite are garnet end-members stable under upper mantle conditions. We perform ab initio simulations to investigate the dependence of the bulk modulus on chemical composition of the grossular-andradite solid solution, Ca3Fe(2-2x)Al(2x)(SiO4)3. All-electron local basis sets of Gaussian-type orbitals and the hybrid B3LYP density functional are used. Our calculations predict a linear modulus-composition trend, in contrast to previous conjectures based on "heterogeneous" experimental measurements. We estimate the largest deviation from linearity to be about 0.5 GPa under ambient conditions, and to progressively reduce to less than 0.2 GPa at pressure P = 20 GPa. The bulk modulus is computed over the whole composition range 0 ≤x≤ 1 following two independent approaches: fitting energy-volume data to an equation-of-state and calculating elastic tensors. Results from the two methods are in perfect agreement, assuring consistency and high numerical accuracy of the adopted algorithms.
Abstract The "supercell" scheme is applied to the study of local defects in MgO (Ca substitution, cation and anion vacancies) and bulk silicon (carbon substitution). The trend of the quantities of interest (defect formation energy, geometrical relaxation, charge distribution around the defect) as a function of the supercell size is explored; when neutral defects are considered, supercells containing 50 to 100 atoms are large enough to allow for most of the nuclear and electronic relaxation and to produce a negligible interaction between defects in different cells. These conclusions apply both to ionic and covalent host crystals. Present day ab initio quantum mechanical periodic computer programs can handle cells of such a size at a relatively low cost and high numerical accuracy. When charged defects are considered (vacancies in MgO), the supercell scheme must be modified in order to avoid Coulomb divergencies, but the usually adopted correction, which consists in introducing a compensating uniform background of charge, generates spurious higher order electrostatic interactions, which are far from being negligible. The resulting defect formation energies show very slow, if any, convergence trends and "a posteriori" semiclassical corrections proposed in the literature do not represent a general solution to the problem. On the other hand, other properties, such as atom relaxation and charge distribution, show a much faster convergence than energy with respect to the cell size. Key Words: Local defectscrystalssupercell
