Marco De La Pierre

The vibrational spectrum of CaCO3 aragonite: A combined experimental and quantum-mechanical investigation

The vibrational properties of CaCO(3) aragonite have been investigated both theoretically, by using a quantum mechanical approach (all electron Gaussian type basis set and B3LYP HF-DFT hybrid functional, as implemented in the CRYSTAL code) and experimentally, by collecting polarized infrared (IR) reflectance and Raman spectra. The combined use of theory and experiment permits on the one hand to analyze the many subtle features of the measured spectra, on the other hand to evidentiate limits and deficiencies of both approaches. The full set of TO and LO IR active modes, their intensities, the dielectric tensor (in its static and high frequency components), and the optical indices have been determined, as well as the Raman frequencies. Tools such as isotopic substitution and graphical animation of the modes are available, that complement the analysis of the spectrum.

The IR vibrational properties of six members of the garnet family: A quantum mechanical ab initio study

Abstract The IR vibrational properties and the corresponding reflectance spectra of the six most common members of the garnet family (pyrope Mg3Al2Si3O12, almandine Fe3Al2Si3O12, spessartine Mn3Al2Si3O12, grossular Ca3Al2Si3O12, uvarovite Ca3Cr2Si3O12, and andradite Ca3Fe2Si3O12) were simulated at the ab initio level with the CRYSTAL09 code by using a large all-electron Gaussian-type basis set and the B3LYP hybrid functional. The 17 IR active F1u transverse optical (TO) and longitudinal optical (LO) frequencies, the oscillator strengths, the high frequency and static dielectric constants, and the reflectance spectrum were computed. The agreement with experiments for the TO and LO peaks is always excellent, the mean absolute difference for the whole set of data (overall 178 peaks) being 5 cm-1. Oscillator strengths, calculated from the mass-weighted effective Born charges, are found in semi-quantitative agreement with the experimental data. The reflectance spectra, simulated through the classical dispersion relation, reproduce the experimental curves extremely well. The availability of the full set of simulated frequencies and intensities, obtained by using uniform computational tools (computer code, variational basis sets, density functional), permits the establishment of correlations between IR wavenumbers and structural features suggested, but only partially documented, in the past

On the full exploitation of symmetry in periodic (as well as molecular) self-consistent-field ab initio calculations

Use of symmetry can dramatically reduce the computational cost (running time and memory allocation) of self-consistent-field ab initio calculations for molecular and crystalline systems. Crucial for running time is symmetry exploitation 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 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. Quantitative examples, referring to the implementation in the CRYSTAL code, are given for high symmetry families of compounds such as carbon fullerenes and nanotubes.

Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids

A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered crystalline systems or solid solutions is presented here. Starting from Pólyas formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compositions or for a chosen one, and symmetry constraints can be applied. The approach yields the multiplicity of the SICs and allows us to operate configurational statistics in the reduced space of the SICs. The present low-memory demanding implementation is briefly sketched. The probability of finding a given SIC or a subset of SICs is discussed as a function of the number of draws and their precise estimate is given. The method is illustrated by application to a binary series of carbonates and to the binary spinel solid solution Mg(Al,Fe)2O4.

Toward an accurate ab initio estimation of compressibility and thermal expansion of diamond in the [0, 3000 K] temperature and [0, 30 GPa] pressures ranges, at the hybrid HF/DFT theoretical level

Abstract The isothermal bulk modulus, together with its temperature dependence, and the thermal expansion of diamond at various pressures were calculated from first principles in the [0, 30 GPa] and [0, 3000 K] pressure and temperature ranges, within the limits of the quasi-harmonic approximation (QHA). The hybrid HF/DFT functional employed (WC1LYP) proved to be particularly effective in providing a very close agreement between the calculated and the available experimental data. In particular, the bulk modulus at 300 K was estimated to be 444.6 GPa (K′ = 3.60); at the same temperature, the (volume) thermal expansion coefficient was 3.19×10-6 K-1. To the authors’ knowledge, among the theoretical papers devoted to the subject, the present one provides the most accurate thermo-elastic data in high-pressure and temperature ranges. Such data can confidently be used in the determination of the pressure of formation using the “elastic method” for minerals found as inclusions in diamonds (recently applied on different minerals included in diamonds), thus shedding light upon the genesis of diamonds in the Earth’s upper mantle.

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.

Use of ab initio methods for the interpretation of the experimental IR reflectance spectra of crystalline compounds

It is shown that ab initio simulation can be used as a powerful complementary tool in the interpretation of the experimental reflectance spectra R(ν) of crystalline compounds. Experimental frequencies and intensities are obtained from a best fit of R(ν) with a set of damped harmonic oscillators, whose number and initial position in frequency can dramatically influence the final results, as the parameters are strongly correlated. Computed ab initio values for frequencies and intensities are accurate enough to represent an excellent starting point for the best fit process. Moreover, at variance with respect to experiment, simulation permits to identify all the symmetry allowed modes, also when characterized by low intensity or when close to a very intense peak. Overall, simulation‐aided analysis of experimental spectra prevents from classifying combination modes as fundamental modes and permits to discard artifacts due to superposition of bands, background, and noise. Finally, it allows to (almost) completely characterize the set of fundamental modes.

Ab initio investigation of majorite and pyrope garnets: Lattice dynamics and vibrational spectra

Abstract A detailed ab initio quantum-mechanical characterization is presented of the vibrational properties of pyrope and majorite garnets, using the hybrid B3LYP functional and large all electron Gaussian type basis sets. Discussed quantities include infrared (both TO and LO) and Raman frequencies, normal mode coordinates, spectroscopic intensities, mode Grüneisen parameters, isotopic substitution, and infrared and Raman spectra. Comparison with data available in the literature demonstrates the accuracy of the adopted method. Main spectral features of the two garnets are interpreted in terms of either symmetry analysis or structural contributions to the vibrational modes. Missing peaks in the experiments are discussed in light of the simulated spectra. The present high-quality vibrational data can be used to compute thermal expansivities at high-pressure and high-temperature conditions. Calculated values for majorite at the bottom of the mantle transition zone (αV = 2.2 × 10−5 K−1 at T = 1500 K and P = 20 GPa) turn out to be sensibly greater (up to three times) than those currently adopted in geophysical thermodynamic databases, thus calling for a careful revision of the numerical models for thermo-chemical convection of the Earths mantle.

Serpentine polymorphism: a quantitative insight from first-principles calculations

Single-walled chrysotile nanotubes [Mg3Si2O5(OH)4] of increasing size (up to 5004 atoms per unit cell, corresponding to a radius of 205 A) have been modelled at the Density Functional level of theory. For the first time, it is demonstrated that the (n, −n) and (n, n) series present a minimum energy structure at a specific radius (88.7 and 89.6 A, respectively, referring to the neutral surface), corresponding to a rolling vector of (60, −60) and (105, 105), respectively. The minima are nearly overlapped and are lower in energy than the corresponding slab of lizardite (the flat-layered polymorph of chrysotile) by about 3.5 kJ mol−1 per formula unit. In both cases, the energy profile presents a shallow minimum, where radii in the range of 63 to 139 A differ in energy by less than 0.5 kJ mol−1 per formula unit. The energy of larger nanotubes has a trend that slowly converges to the limit of the flat lizardite slab. Structural quantities such as bond distances and angles of nanotubes with increasing size asymptotically converge to the flat slab limit, with no discontinuities in the surrounding of the minimum energy structures. However, analysis of the elongation of a rectangular pseudo-unit cell along the nanotube circumference indicates that the main factor that leads lizardite to curl in tubes is the elastic strain caused by the mismatch between the lattice parameters of the two adjacent tetrahedral and octahedral sheets. It is also shown in this study that the curvature of the layers in one of the lately proposed models of antigorite, the “wavy-layered” polymorph of chrysotile, falls within the range of radii of minimum energy for the nanotubes. These findings provide quantitative insights into the peculiar polymorphism of these three phyllosilicates. They show also that chrysotile belongs to those families of inorganic nanotubes that present a minimum in their strain energy profile at a specific range of radii, which is lower in energy with respect to their flat equivalent.

First-principle modelling of forsterite surface properties: Accuracy of methods and basis sets

The seven main crystal surfaces of forsterite (Mg2SiO4) were modeled using various Gaussian‐type basis sets, and several formulations for the exchange‐correlation functional within the density functional theory (DFT). The recently developed pob‐TZVP basis set provides the best results for all properties that are strongly dependent on the accuracy of the wavefunction. Convergence on the structure and on the basis set superposition error‐corrected surface energy can be reached also with poorer basis sets. The effect of adopting different DFT functionals was assessed. All functionals give the same stability order for the various surfaces. Surfaces do not exhibit any major structural differences when optimized with different functionals, except for higher energy orientations where major rearrangements occur around the Mg sites at the surface or subsurface. When dispersions are not accounted for, all functionals provide similar surface energies. The inclusion of empirical dispersions raises the energy of all surfaces by a nearly systematic value proportional to the scaling factor s of the dispersion formulation. An estimation for the surface energy is provided through adopting C6 coefficients that are more suitable than the standard ones to describe OO interactions in minerals. A 2 × 2 supercell of the most stable surface (010) was optimized. No surface reconstruction was observed. The resulting structure and surface energy show no difference with respect to those obtained when using the primitive cell. This result validates the (010) surface model here adopted, that will serve as a reference for future studies on adsorption and reactivity of water and carbon dioxide at this interface.