Analytical stress tensor and pressure calculations with the CRYSTAL code

Phonon softening induced phase transition of CeSiO4: a density functional theory study

Density functional theory plus Hubbard U (DFT+U) methodology was used to calculate the structures and energetic landscapes of CeSiO4, including its stetindite and scheelite phases from ambient pressure to ∼24 GPa. To ensure accurate simulations of the high-pressure structures, assessments of strain-stress methods and stress-strain methods were conducted in prior, with the former found to have a better agreement with the experimental result. From DFT calculations the equation of states (EOS) of both stetindite and scheelite were further obtained, with the fitted bulk moduli being 182(2) GPa and 190.0(12) GPa, respectively. These results were found to be consistent with the experimental values of 177(5) GPa and 222(40) GPa. Furthermore, the calculated energetics suggest that the stetindite structure is more thermodynamically stable than the scheelite structure at a pressure lower than 8.35 GPa. However, the stetindite → scheelite phase transition was observed experimentally at a much higher pressure of ∼15 GPa. A further phonon spectra investigation by the density functional perturbation theory (DFPT) indicated the Eg1 mode is being softened with pressure and becomes imaginary after 12 GPa, which is a sign of the lattice instability. Consequently, it was concluded that the stetindite → scheelite transition is predominantly initiated by the lattice instability under high-pressure.

Efficient calculation of derivatives of integrals in a basis of non-separable Gaussians

A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations. The approach, based on symbolic computation with computer algebra systems and automated generation of optimized subroutines, takes full advantage of sparsity and is here applied to first energy derivatives with respect to nuclear displacements and lattice parameters of molecules and materials. The implementation in the Crystal code is presented, and the considerably improved computational efficiency over the previous implementation is illustrated. For this purpose, three different tasks involving the use of analytical forces are considered: (i) geometry optimization; (ii) harmonic frequency calculation; and (iii) elastic tensor calculation. Three test case materials are selected as representatives of different classes: (i) a metallic 2D model of the Cu(111) surface; (ii) a wide-gap semiconductor ZnO crystal, with a wurtzite-type structure; and (iii) a porous metal-organic crystal, namely the ZIF-8 zinc-imidazolate framework. Finally, it is argued that the present symbolic approach is particularly amenable to generalizations, and its potential application to other derivatives is sketched.

Predicting the structures and vibrational spectra of molecular crystals containing large molecules with the generalized energy-based fragmentation approach

The generalized energy-based fragmentation (GEBF) approach under periodic boundary conditions (PBCs) has been developed to facilitate calculations of molecular crystals containing large molecules. The PBC-GEBF approach can help predict structures and properties of molecular crystals at different theory levels by performing molecular quantum chemistry calculations on a series of non-periodic subsystems constructed from the studied systems. A more rigorous formula of the forces on translational vectors of molecular crystals was proposed and implemented, enabling more reliable predictions of crystal structures. Our benchmark results on several typical molecular crystals show that the PBC-GEBF approach could reproduce the forces on atoms and the translational vectors and the optimized crystal structures from the corresponding conventional periodic methods. The improved PBC-GEBF approach is then applied to predict the crystal structures and vibrational spectra of two molecular crystals containing large molecules. The PBC-GEBF approach can provide a satisfactory description on the crystal structure of a molecular crystal containing 312 atoms in a unit cell at density-fitting second-order Møller-Plesset perturbation theory and density functional theory (DFT) levels and the infrared vibrational spectra of another molecular crystal containing 864 atoms in a unit cell at the DFT level. The PBC-GEBF approach is expected to be a promising theoretical tool for electronic structure calculations on molecular crystals containing large molecules.

57Fe Mössbauer isomer shift of pure iron and iron oxides at high pressure-An experimental and theoretical study

The ⁵⁷Fe isomer shift (IS) of pure iron has been measured up to 100 GPa using synchrotron Mössbauer spectroscopy in the time domain. Apart from the expected discontinuity due to the α → ε structural and spin transitions, the IS decreases monotonically with increasing pressure. The absolute shifts were reproduced without semi-empirical calibrations by periodic density functional calculations employing extensive localized basis sets with several common density functionals. However, the best numerical agreement is obtained with the B1WC hybrid functional. Extension of the calculations to 350 GPa, a pressure corresponding to the Earth's inner core, predicted the IS range of 0.00 to -0.85 mm/s, covering the span from Fe(0) to Fe(VI) compounds measured at ambient pressure. The calculations also reproduced the pressure trend from polymorphs of prototypical iron oxide minerals, FeO and Fe₂O₃. Analysis of the electronic structure shows a strong donation of electrons from oxygen to iron at high pressure. The assignment of formal oxidation to the Fe atom becomes ambiguous under this condition.

The CRYSTAL code, 1976-2020 and beyond, a long story

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree-Fock (HF). The cost for HF or hybrids is only about 3-5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores.

Pressure-dependent X-ray diffraction of the multiferroics RMn2O5

The room-temperature structural properties of the RMn₂O₅ multiferroics have been investigated under pressure, using powder X-ray scattering and density functional theory (DFT) calculations. It was possible to determine the lattice parameters and the main atomic positions as a function of pressure. Good agreement was observed between the X-ray and DFT results for most of the determined crystallographic data. From the DFT calculations, it was possible to infer the pressure evolution of the exchange interactions, and this analysis led to the conclusion that the onset of the q = (½, 0, ½) magnetic structure under pressure is related to the increase in the J₁ super-exchange terms (due to the reduction in the Mn-O distances) compared with the Mn-R exchange interactions. In addition, the 1D antiferromagnetic character of the compounds should be reinforced under pressure.

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518-2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097-3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn-Sham matrix formation. © 2019 Wiley Periodicals, Inc.

Effects of temperature and pressure on the optical and vibrational properties of thermoelectric SnSe

We have conducted a comprehensive investigation of the optical and vibrational properties of the binary semiconductor SnSe as a function of temperature and pressure by means of experimental and ab initio probes. Our high-temperature investigations at ambient pressure have successfully reproduced the progressive enhancement of the free carrier concentration upon approaching the Pnma → Bbmm transition, whereas the pressure-induced Pnma → Bbmm transformation at ambient temperature, accompanied by an electronic semiconductor → semi-metal transition, has been identified for bulk SnSe close to 10 GPa. Modeling of the Raman-active vibrations revealed that three-phonon anharmonic processes dominate the temperature-induced mode frequency evolution. In addition, SnSe was found to exhibit a pressure-induced enhancement of the Born effective charge. Such behavior is quite unique and cannot be rationalized within the proposed effective charge trends of binary materials under pressure.

Thermo-Elasticity of Materials from Quasi-Harmonic Calculations

An effective algorithm for the quasi-harmonic calculation of thermo-elastic stiffness constants of materials is discussed and implemented into the Crystal program for quantum-mechanical simulations of extended systems. Two different approaches of increasing complexity and accuracy are presented. The first one is a quasi-static approximation where the thermal dependence of elastic constants is assumed to be due only to the thermal expansion of the system. The second one is fully quasi-harmonic, takes into account thermal expansion, and explicitly computes Helmholtz free energy derivatives with respect to strain. The conversion of isothermal into adiabatic thermo-elastic constants is also addressed. The algorithm is formally presented and applied to the description of the thermo-elastic response of the forsterite mineral.

Barium Sulfide under Pressure: Discovery of Metastable Polymorphs and Investigation of Electronic Properties on ab Initio Level

Barium sulfide (BaS) is an important precursor to other barium compounds with applications from ceramics and flame retardants to luminous paints and additives, and recent research shows potential technological applications in electrical and optical devices. Under normal conditions, BaS crystallizes in the NaCl type of structure, and with the increase in pressure BaS undergoes a structural phase transition to a CsCl type modification. This study presents modeling of barium sulfide under pressure with special focus on structural aspects and electronic properties. We predict metastable BaS polymorphs which have not yet been observed in the experiment or in previous calculations, and we investigated their vibrational and thermodynamical properties. Furthermore, we investigate the electronic properties of experimentally known structures as well as novel predicted modifications of BaS on ab initio level using Hartree-Fock, GGA-PBE, and the hybrid B3LYP functional. In this way, we address new possibilities of synthesizing BaS and possible band gap tuning which can have great applications in optoelectrical technologies.

Structure prediction of aluminum nitride combining data mining and quantum mechanics

This study covers the experimentally observed modifications of AlN, investigates their relations and searches for new possible modifications combining data mining and ab initio methods.

On combining temperature and pressure effects on structural properties of crystals with standard ab initio techniques

A general-purpose, fully automated, computationally efficient implementation is presented of a series of techniques for the simultaneous description of pressure and temperature effects on structural properties of materials, by means of standard ab initio simulations. Equilibrium volume, bulk modulus, thermal expansion coefficient, equation-of-state, Grüneisen parameter, constant-pressure and constant-volume specific heats are computed as a function of temperature and pressure for the simple crystal of diamond and compared with accurate experimental data. Convergence of computed properties with respect to super-cell size is critically discussed. The effect on such properties of the adopted exchange-correlation functional of the density-functional-theory is discussed by considering three different levels of approximation (including hybrids): it is found to be rather small for the temperature dependence of equilibrium volume and bulk modulus, whereas it is quite large as regards their absolute values.

Katoite under pressure: an ab initio investigation of its structural, elastic and vibrational properties sheds light on the phase transition

Structural, elastic and vibrational properties of the katoite hydrogarnet are investigated as a function of pressure, up to 65 GPa, with an ab initio simulation. A group-subgroup phase transition is found to occur in the 5–15 GPa range of pressure.

High pressure elastic properties of minerals from ab initio simulations: the case of pyrope, grossular and andradite silicate garnets

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.

The effects of stoichiometry on the mechanical properties of icosahedral boron carbide under loading

The effects of stoichiometry on the atomic structure and the related mechanical properties of boron carbide (B(4)C) have been studied using density functional theory and quantum molecular dynamics simulations. Computational cells of boron carbide containing up to 960 atoms and spanning compositions ranging from 6.7% to 26.7% carbon were used to determine the effects of stoichiometry on the atomic structure, elastic properties, and stress-strain response as a function of hydrostatic, uniaxial, and shear loading paths. It was found that different stoichiometries, as well as variable atomic arrangements within a fixed stoichiometry, can have a significant impact on the yield stress of boron carbide when compressed uniaxially (by as much as 70% in some cases); the significantly reduced strength of boron carbide under shear loading is also demonstrated.

Sterically active electron pairs in lead sulfide? An investigation of the electronic and vibrational properties of PbS in the transition region between the rock salt and the α-GeTe-type modifications

Recently, we have investigated the energy landscape of PbS for many different pressures on the ab initio level by using Hartree-Fock and density functional theory to globally search for possible thermodynamically stable and metastable structures. The perhaps most fascinating observation was that besides the experimentally known modification exhibiting the rock salt structure a second minimum exists close-by on the landscape showing the low-temperature α-GeTe-type structure. In the present study, we investigate the possible reasons for the existence of this metastable modification; in particular we address the question, whether the α-GeTe-type modification might be stabilized (and conversely the rock salt modification destabilized) by steric effects of the non-bonding electron pair.