Yves Noel

Ab-initio prediction of materials properties with CRYSTAL: MOF-5 as a case study

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

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials.

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two‐dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono‐ and bi‐electronic integrals that enter into the Fock (Kohn‐Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M × 2M matrix. The efficiency and accuracy of the computational scheme is documented.

The vibrational spectrum of lizardite-1T [Mg3Si2O5(OH)4] at the Γ point: A contribution from an ab initio periodic B3LYP calculation

Abstract The vibrational spectrum of lizardite at the Γ point has been calculated with ab initio methods, using a hybrid HF/DFT Hamiltonian (B3LYP). Apart from a few bending modes involving hydrogen motion, very good agreement has been found between calculated and experimental infrared and Raman spectra of the mineral. The anharmonic correction to the OH-stretching modes proved to be crucial for a correct evaluation of their frequencies and, on average, it amounts to a lowering of about 150 cm-1 with respect to the values computed within the harmonic approximation. LO-TO splitting effects had to be taken into account for a correct interpretation of the data obtained from infrared spectra on powder samples. The calculation can be used either to confidently identify which bands in the experimental spectra do correspond to fundamental vibrational transitions or to unequivocally assign them to specific normal modes.

Structure and energetics of imogolite: a quantum mechanical ab initio study with B3LYP hybrid functional

Imogolite (Al2(OH)3SiO3OH) single-walled nanotubes are simulated at the ab initio level by using an all electron Gaussian type basis set and the hybrid B3LYP functional. Full exploitation of the roto-translational symmetry drastically reduces the computational cost. Two kinds of tubes, (n, 0) and (n, n), are considered, resulting from rolling up a hypothetical structure containing a gibbsite-like hexagonal layer linked to a silanolic SiOH unit. In both cases a minimum is observed, corresponding to n = 10 for (n, 0) (the radius, taken as the distance between the tube axis and one of the basal SiO4 oxygen atoms, is 7.26 A) and n = 8 for (n, n) (10.3 A). Hydrogen bonds and orientation of the silanolic group inside the tube play an important role in stabilising the structures. The (10, 0) structure is 10.6 kJ mol−1 per formula unit more stable than the (8, 8) tube, the difference being due, at least partially, to the formation of hydrogen bonds in the inner wall of the tube (the shortest H⋯O distances are 2.14 and 3.01 A, respectively). Two curves are observed in the (n, 0) case, whose minima, both at n = 10, are separated by 2.0 kJ mol−1 per formula unit. These two structures are extremely similar, the main difference being the orientation of the OH unit pointing inside the tube.

Zinc oxide nanotubes: an ab initio investigation of their structural, vibrational, elastic, and dielectric properties.

Structural, vibrational, elastic, and dielectric properties of ZnO single-walled nanotubes are investigated theoretically. Calculations are carried out by using a Gaussian basis set and the B3LYP hybrid functional as implemented in the periodic ab initio CRYSTAL code. Nanotubes with increasing radius display asymptotic limits to the infinite monolayer. One soft phonon mode is recognized, whose vibration frequency is shown to be connected to the elastic constant C11 of the monolayer as the 1D → 2D transition is approached. The value of Youngs elastic modulus of the nanotubes denotes a remarkable flexibility. Electronic and ionic contributions to the polarizability turn out to be comparable in magnitude. In particular, geometry relaxations at increasing radii show large influence on the transverse vibrational polarizability.

Structural, electronic, and vibrational properties of solid Sr(OH)2, calculated with different Hamiltonians

The structural equilibrium parameters, the energetic of formation and hydration processes, and the O–H vibrational frequencies of crystalline Sr(OH)2 have been investigated at the ab initio level using the periodic CRYSTAL package. Both Hartree–Fock (HF) and density functional theory (DFT) Hamiltonians have been used, the latter in its local density (LV), gradient-corrected (PP), and hybrid (B3LYP) versions. The computed Sr(OH)2 structural parameters are in reasonable agreement with experiment, the largest deviation being for the a cell parameter, which is overestimated by all the adopted methods. With respect to experiment, DFT Hamiltonians give errors of the order of 13% for the formation energies, whereas errors for the heats of hydration from the corresponding oxide are as large as 27% for the LV functional. Two families of OH groups occur in the structure, in which one acts as a weak hydrogen bond donor. The fundamental ω01(OH) stretching frequency has been computed for the two OH groups, and their d...

Ab-initio quantum mechanical study of akdalaite (5Al2O3· H2O): structure and vibrational spectrum

The structure and the vibrational spectrum of akdalaite (5Al2O3·H2O, also known as tohdite) have been investigated at the periodic ab-initio quantum-mechanical level by using a high quality Gaussian type basis set and the hybrid B3LYP Hamiltonian with the CRYSTAL06 code. Three space groups proposed in the literature, namely P63mc and its two P31c and Cmc21 subgroups, have been considered, obtaining essentially the same energy (the largest total energy difference is 0.2 kJ/mol per cell) and geometry. The harmonic frequencies at the τ point have been computed. Isotopic substitution and graphical representation permit a complete classification of normal modes in terms of simple models (octahedra and tetrahedra modes, hydrogen stretching and bending). The Al-O octahedra and tetrahedra modes appear below 880 cm−1, Al-OH bending modes are located in the range 870-900 cm−1, and OH stretching modes are at 3330-3400 cm-1.

The infrared vibrational spectrum of andradite-grossular solid solutions: A quantum mechanical simulation

Abstract Infrared spectroscopy is a powerful technique for the characterization of minerals, permitting insights into their structural and thermodynamic properties. The intrinsic complexity of mineral solid solutions makes the interpretation of their spectroscopic data a challenging task. In this work, the IR vibrational spectra of andradite-grossular (Ca3Fe2Si3O12-Ca3Al2Si3O12) solid solutions were simulated at the ab initio level with the CRYSTAL09 code by using a large allelectron Gaussian-type basis set and the B3LYP hybrid functional. All the 23 symmetry-independent configurations resulting from the substitution of 1 to 8 Fe atoms with Al atoms in the 16a octahedral site of the andradite primitive cell were considered. The IR active transverse optical frequencies and their intensities were computed. Graphical representation of the spectra, animation of the modes and isotopic substitution of the cations were used as additional interpretation tools. The dominant highfrequency modes, corresponding to Si-O stretching motions, show a simple linear behavior of both frequencies and intensities with respect to the binary composition; this trend is related to the linear behavior of the mean lattice parameter. Also the frequencies of the low-energy bands show, roughly speaking, a linear dependence on composition; however, the behavior of the dominant intensities is more complicated and strongly connected to the Al and Fe atomic fraction. When considering different possible structures at fixed composition, some spectral features display a dependence upon short-range Y cation ordering. Overall, we show how ab initio calculations permit to analyze complex systems such as solid solutions, establishing relations among structure and properties and providing critical and robust interpretations to the experimental findings.

DFT modeling of anatase nanotubes

TiO2 nanotubes constructed from anatase TiO2 layers were investigated with DFT methods employing the periodic CRYSTAL code. Films of thickness from one to three TiO2 layers (1–3 ml) have been considered. The dependence of strain energies, structural and electron properties on the tube diameter was investigated in the 10–70 A range. Relative stabilities have also been considered. We found that the most stable nanotubes are in the region of D > 50 A: lepidocrocite, fluorite–1 ml and 001–3 ml nanotubes differ in energy by less than 0.1 eV/TiO2. This is in agreement with experimental observations of tubes that have a size that range between 50 and 100 A. At D < 20 A, nanotubes with a 1 ml thickness (fluorite and 101 nanotubes) show higher stability. In addition, present calculations indicate that anatase films with a thickness of 1 to 3 ml only single walled nanotubes can be constructed. All investigated nanotubes possess a high (∼5–5.5eV) band gap compared to bulk TiO2 phases (4.3 eV for anatase calculated with the same functional and basis set) that differs by less than 0.1–0.3 eV from the corresponding flat slab and approaches smoothly this reference value.

On the use of symmetry in SCF calculations. The case of fullerenes and nanotubes

The way point symmetry can be exploited to reduce the computational cost (CPU time and memory allocation) in SCF ab initio calculations is discussed. Crucial for the CPU time are the calculation of the mono-and bi-electronic integrals and the diagonalization of the Fock matrix at selected points in reciprocal space; as regards memory allocation, the full square density and Fock matrices must be avoided. Quantitative examples are given in the case of high symmetry compounds such as carbon fullerenes and nanotubes.