On the use of symmetry in configurational analysis for the simulation of disordered solids

The starting point for a quantum mechanical investigation of disordered systems usually implies calculations on a limited subset of configurations, generated by defining either the composition of interest or a set of compositions ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compound. The way in which symmetry can be used in the identification of symmetry independent configurations (SICs) is discussed here. First, Pólya's enumeration theory is adopted to determine the number of SICs, in the case of both varying and fixed composition, for colors numbering two or higher. Then, De Bruijn's generalization is presented, which allows analysis of the case where the colors are symmetry related, e.g. spin up and down in magnetic systems. In spite of their efficiency in counting SICs, neither Pólya's nor De Bruijn's theory helps in solving the difficult problem of identifying the complete list of SICs. Representative SICs are obtained by adopting an orderly generation approach, based on lexicographic ordering, which offers the advantage of avoiding the (computationally expensive) analysis and storage of all the possible configurations. When the number of colors increases, this strategy can be combined with the surjective resolution principle, which permits the efficient generation of SICs of a problem in |R| colors starting from the ones obtained for the (|R| − 1)-colors case. The whole scheme is documented by means of three examples: the abstract case of a square with C4v symmetry and the real cases of the garnet and olivine mineral families

Structural, electronic and energetic properties of giant icosahedral fullerenes up to C6000: insights from an ab initio hybrid DFT study

The properties of the (n,n) icosahedral family of carbon fullerenes up to n = 10 (6000 atoms) have been investigated through ab initio quantum-mechanical simulation by using a Gaussian type basis set of double zeta quality with polarization functions (84 000 atomic orbitals for the largest case), the hybrid B3LYP functional and the CRYSTAL14 code featuring generalization of symmetry treatment. The geometry of giant fullerenes shows hybrid features, between a polyhedron and a sphere; as n increases, it approaches the former. Hexagon rings at face centres take a planar, graphene-like configuration; the 12 pentagon rings at vertices impose, however, a severe structural constraint to which hexagon rings at the edges must adapt smoothly, adopting a bent (rather than sharp) transversal profile and an inward longitudinal curvature. The HOMO and LUMO electronic levels, as well as the band gap, are well described using power laws. The gap is predicted to become zero for n ≥ 34 (69 360 atoms). The atomic excess energy with respect to the ideal graphene sheet goes to zero following the log(Nat)/Nat law, which is well described through the continuum elastic theory applied to graphene; the limits for the adopted model are briefly outlined. Compared to larger fullerenes of the series, C60 shows unique features with respect to all the considered properties; C240 presents minor structural and energetic peculiarities, too

Exploitation of symmetry in periodic Self-Consistent-Field ab initio calculations: application to large three-dimensional compounds

Symmetry can dramatically reduce the computational cost (running time and memory allocation) of Self-Consistent-Field ab initio calculations for crystalline systems. Crucial for running time is use of symmetry in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices (overlap, Fock and density) in the Atomic Orbital (AO) basis are avoided and a direct transformation from the packed AO to the SACO (Symmetry Adapted Crystalline Orbital) basis is performed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. We here illustrate the effectiveness of this scheme, following recent advancements in the CRYSTAL code, concerning memory allocation and direct basis set transformation. Quantitative examples are given for large unit cell systems, such as zeolites (all-silica faujasite and silicalite MFI) and garnets (pyrope). It is shown that the full SCF of 3D systems containing up to 576 atoms and 11136 Atomic Orbitals in the cell can be run with a hybrid functional on a single core PC with 500 MB RAM in about 8 h. © 2014 Science China Press and Springer-Verlag Berlin Heidelberg

Polarizability and hyperpolarizability of BN zigzag nanotubes calculated by the coupled perturbed Kohn-Sham scheme

cited By 16International audienceLinear and nonlinear electric dipole susceptibilities are evaluated for infinite periodic zigzag BN nanotubes utilizing primarily the coupled perturbed Kohn-Sham scheme recently implemented in the crystal code. The effect of different functionals, basis set, and computational parameters is examined. Most of the calculations are done at the B3LYP/6-31G* level. For electronic linear polarizabilities, substantial differences compared to the uncoupled sum-over-states scheme are found. Much larger radii were considered than in earlier studies, thereby permitting accurate comparison with corresponding properties of the hexagonal monolayer. In addition, we confirmed the dielectric shell model for the linear polarizability, but with a significantly different shell thickness than previously thought. Vibrational (ionic) contributions to the nonlinear susceptibilities are calculated. In doing so, the finite-field-nuclear-relaxation (FF-NR) method was employed for the transverse components of the (6,0), (9,0), and (12,0) nanotubes. Aside from being computationally more efficient than other procedures, this method includes anharmonicity effects through first order and, as shown, is readily applied to key dynamic as well as static properties (and yields the static linear polarizability as well). Our calculated nonlinear vibrational susceptibilities sometimes exceed, or even greatly exceed, the corresponding static electronic susceptibility. In such cases, the relative magnitude of the vibrational contribution grows substantially with tube radius over the range considered. Future plans include extending these FF-NR calculations to large nanotubes and to the longitudinal (periodic) direction as well. © 2011 American Physical Society

Elucidating the Interaction of CO<inf>2</inf> in the Giant Metal-Organic Framework MIL-100 through Large-Scale Periodic Ab Initio Modeling

In this work, we have tackled the challenging task of the ab initio modeling of a gigantic metal–organic framework (MOF). The structural features of MIL-100(MIII) with different metals (i.e., MIII = Al, Sc, Cr, Fe) and the interaction of CO2 with the unsaturated coordination metal sites were investigated by means of large-scale quantum mechanical calculations with hybrid Hartree–Fock/density functional theory methods augmented with an atom–atom pairwise dispersion correction in a fully periodic approach. In doing this, we took advantage of the high scalability of the massively parallel version of the CRYSTAL code. Overall results are in good agreement with the experiment, in particular for the predicted structures, whereas some discrepancies have been found for adsorption energies in the case of MIL-100(Cr) and MIL-100(Sc). We argue that this is due to a deviation of the ideal model structure of MIL-100 adopted in this work from the actual synthesized material. This is also supported by additional calculations on a MOF with similar adsorption sites and computed data from the literature. Above all, we demonstrate that ab initio modeling of the structure and properties of MOFs can now be performed on very large and complex frameworks

A new massively parallel version of CRYSTAL for large systems on high performance computing architectures

Fully ab initio treatment of complex solid systems needs computational software which is able to efficiently take advantage of the growing power of high performance computing (HPC) architectures. Recent improvements in CRYSTAL, a periodic ab initio code that uses a Gaussian basis set, allows treatment of very large unit cells for crystalline systems on HPC architectures with high parallel efficiency in terms of running time and memory requirements. The latter is a crucial point, due to the trend toward architectures relying on a very high number of cores with associated relatively low memory availability. An exhaustive performance analysis shows that density functional calculations, based on a hybrid functional, of low-symmetry systems containing up to 100,000 atomic orbitals and 8000 atoms are feasible on the most advanced HPC architectures available to European researchers today, using thousands of processors. © 2012 Wiley Periodicals, Inc

Ab Initio Periodic Simulation of the Spectroscopic and Optical Properties of Novel Porous Graphene Phases

We present a detailed periodic ab initio quantum-mechanical simulation of two recently proposed systems, namely hydrogenated porous graphene (HPG) and biphenyl carbon (BPC), using hybrid HF-DFT functionals and all-electron Gaussian-type basis sets. The equilibrium geometry, the vibrational spectrum (including IR intensities), the full set of components of the polarizability and hyperpolarizability tensors are provided, the latter evaluated through a coupled-perturbed KS/HF scheme. IR and Raman spectra for the two systems are quite different, and differ also from graphene, thus permitting their experimental identification. It is then shown that small defects inserted into the graphene sheet lead to finite values for the in-plane components of the static (hyper) polarizability tensors, spanning a relatively large range of values. By dehydrogenation of porous graphene into biphenyl carbon, a noteworthy enhancement of the nonlinear optical properties through the static second dipole hyperpolarizability can be achieved. Vibrational contributions to the polarizability are negligible for both systems