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Quantum‐mechanical condensed matter simulations with CRYSTAL

Software Focus

Roberto Dovesi, Alessandro Erba, Roberto Orlando, Claudio M. Zicovich‐Wilson, Bartolomeo Civalleri, Lorenzo Maschio, Michel Rérat, Silvia Casassa, Jacopo Baima, Simone Salustro, Bernard Kirtman

Published Online: Mar 04 2018

DOI: 10.1002/wcms.1360

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The latest release of the Crystal program for solid‐state quantum‐mechanical ab initio simulations is presented. The program adopts atom‐centered Gaussian‐type functions as a basis set, which makes it possible to perform all‐electron as well as pseudopotential calculations. Systems of any periodicity can be treated at the same level of accuracy (from 0D molecules, clusters and nanocrystals, to 1D polymers, helices, nanorods, and nanotubes, to 2D monolayers and slab models for surfaces, to actual 3D bulk crystals), without any artificial repetition along nonperiodic directions for 0–2D systems. Density functional theory calculations can be performed with a variety of functionals belonging to several classes: local‐density (LDA), generalized‐gradient (GGA), meta‐GGA, global hybrid, range‐separated hybrid, and self‐consistent system‐specific hybrid. In particular, hybrid functionals can be used at a modest computational cost, comparable to that of pure LDA and GGA formulations, because of the efficient implementation of exact nonlocal Fock exchange. Both translational and point‐symmetry features are fully exploited at all steps of the calculation, thus drastically reducing the corresponding computational cost. The various properties computed encompass electronic structure (including magnetic spin‐polarized open‐shell systems, electron density analysis), geometry (including full or constrained optimization, transition‐state search), vibrational properties (frequencies, infrared and Raman intensities, phonon density of states), thermal properties (quasi‐harmonic approximation), linear and nonlinear optical properties (static and dynamic [hyper]polarizabilities), strain properties (elasticity, piezoelectricity, photoelasticity), electron transport properties (Boltzmann, transport across nanojunctions), as well as X‐ray and inelastic neutron spectra. The program is distributed in serial, parallel, and massively parallel versions. In this paper, the original developments that have been devised and implemented in the last 4 years (since the distribution of the previous public version, Crystal14, occurred in December 2013) are described. This article is categorized under: Software > Quantum Chemistry Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Density Functional Theory

Detailed list of features of the Crystal program. For each topic, the new developments made in the Crystal17 major release are highlighted in the darker boxes at the bottom

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Schematic representation of a lead‐conductor‐lead nano‐junction, where the conductor layer (of thickness L) is constituted by organic molecules

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Transport properties of cubic CoSb₃ skutterodite crystal evaluated at the PBE0 level at three different temperatures as a function of chemical potential. Plotted values are tensor elements along principal direction xx ≡ yy ≡ zz; others are null. The zero of the potential is set at the Fermi level, defined as the top of conduction bands. For other details see text

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XRD spectrum of Al₂O₃ corundum as computed within the density functional theory with the PBE functional (upper panel), as corrected for Lorentz‐polarization factors (middle panel) and as experimentally recorded (lower panel)

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Upper panel: Total (black continuous line) and atomic (dashed green line for O, blue dotted for Al, dark red dot‐dashed for Si and continuous red for either Mg or Ca) phonon density‐of‐states (PDOS) of the grossular silicate garnet, computed on a supercell containing 2,160 atoms, with additional k points obtained by Fourier interpolation (for a overall sampling of phonon dispersion over 13,824 k points in the First Brillouin Zone). Lower panel: Calculated incoherent (blue thin line) and coherent (thick orange line) neutron‐weighted phonon density‐of‐states (NW‐PDOS) for grossular. The experimental coherent inelastic neutron scattering spectrum is reported in red (Zhao, Gaskell, Cormier, & Bennington, )

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Graphical representation of four point‐defects in diamond: (a) the 〈100〉 split self‐interstitial (in red); (b) the VI₁ defect where a vacancy and a self‐interstitial are first neighbors; (c) the VI defect where a vacancy is a second‐neighbor of a self‐interstitial with all C–C single bonds, and (d) the VI defect where a vacancy is a second‐neighbor of a self‐interstitial with one C–C double bond (in green)

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Selected large‐scale systems studied with the parallel versions of the Crystal program in recent years. See text for the size of the basis set adopted for each system

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Wall‐clock time speedup of MPPcrystal as a function of the number of cores used for the X8 (upper panel) and X24 (lower panel) supercells of the MCM‐41 model of amorphous mesoporous silica (solution of the SCF procedure). The baseline used in the definition of the speedup is 512 and 4,096 cores for X8 and X24, respectively. The dashed line shows the fit of the speedup values to Amdahl’s law. At each point, the scaling efficiency is reported (in %), where the diagonal of the plot corresponds to the ideal scaling

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SHG d_xyz tensor component of bulk urea as a function of wavelength λ = 2π/ω, as obtained with various functionals. The computed data are fit to the three parameter function: d(λ) = a + b(1/(ω₀ − 2ω)(ω₀ − ω) + 1/(ω₀ + ω)(ω₀ − ω) + 1/(ω₀ + ω)(ω₀ + 2ω))

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Left panel: The crystal structure of tetragonal PbMoO₄. Right panel: Indicative surfaces of the piezo‐optic effect (in Brewster) of PbMoO₄ when a uniaxial pressure is applied parallel to the X₃ principal optical axis (a) and parallel to the X₁ principal optical axis (b) (Mytsyk et al., )

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Upper panels: Elastic wave phase velocities as a function of propagation direction; lower panels: The corresponding power flow angles as a function of propagation direction. Data refer to the simple cubic crystal of MgO

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Thermal expansion coefficient of MgO periclase as determined experimentally (Anderson, Isaak, & Oda, ; Ganesan, ; White & Anderson, ) (black symbols) and through quasi‐harmonic lattice dynamical simulations (Erba, Shahrokhi, Moradian, & Dovesi, ) (black line). The quasi‐harmonic approximation is expected to be valid only up to the temperature (marked by a vertical red dashed line) above which the computed thermal expansion coefficient starts deviating from linearity (the linear region is marked by a blue line)

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Average Coupled‐Perturbed‐Hartree‐Fock (CPHF) and CPHF2 cycles needed to reach convergence with (black bars) and without (red bars) DIIS convergence accelerator, as benchmarked on a test set of 25 periodic systems. White numbers reported on the bars indicate the number of calculations which reached convergence over the total of 25

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Average self‐consistent field (SCF) cycles needed to reach convergence with (green bars) and without (blue bars) DIIS convergence accelerator, as benchmarked on a test set of 42 periodic systems, grouped in seven categories. MOF stands for metal–organic frameworks and M/O for metal/oxide interfaces. The rightmost column reports the global average. For more details see text

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