Vibrations / Calcite / IR Intensities / Ab Initio SimulationThe static and high frequency dielectric tensors, Born effective charges, vibrational spectrum at the Γ point, TO-LO splitting and IR intensities of calcite CaCO 3 have been calculated with the periodic ab initio CRYSTAL program, with five different basis sets of increasing size and four different Hamiltonians (HF, LDA, PBE, B3LYP). B3LYP is shown to perform better than the other options, in particular of LDA and PBE that are often used for the calculation of the vibrational spectrum of crystalline solids. When comparing B3LYP and experimental frequencies, the mean absolute difference is as small as 8.5 cm −1 ; this number reduces to 4.8 cm −1 if the two lowest experimental frequencies, that we suspect to be affected by a relatively large error, are excluded from statistics. Static and high frequency dielectric tensors, as well as IR intensities computed with the same hybrid scheme (B3LYP) compare quite favourably with experiment. The full set of modes is characterized by various tools including isotopic substitution, "freezing" one of the two subunits (Ca 2+ or CO 3 2− ) and graphical representations. A general tool has been implemented, that permits the automatic generation of the animation of the full set of modes starting from the CRYSTAL output (available at www.crystal.unito.it/vibs/ calcite).

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IR spectra of pyrope Mg(3)Al(2)Si(3)O(12), grossular Ca(3)Al(2)Si(3)O(12) and andradite Ca(3)Fe(2)Si(3)O(12) garnets were simulated with the periodic ab initio CRYSTAL code by adopting an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. Two sets of 17 F(1u) Transverse Optical (TO) and Longitudinal Optical (LO) frequencies were generated, together with their intensities. Because the generation of LO modes requires knowledge of the high frequency dielectric constant epsilon(infinity) and Born effective charges, they were preliminary evaluated by using a finite field saw-tooth model and well localized Wannier functions, respectively. As a by-product, the static dielectric constant epsilon(0) was also obtained. The agreement of the present calculated wavenumbers (i.e. peak positions) with the available experimental data is excellent, in that the mean absolute difference for the full set of data smaller than 8 cm(-1). Missing peaks in experimental spectra were found to correspond to modes with low calculated intensities. Correspondence between TO and LO modes was established on the basis of the overlap between the eigenvectors of the two sets and similarity of isotopic shifts; as result, the so called LO-TO splitting could be determined. Animation of the normal modes was employed to support the proposed pairing.

The full vibrational spectra of the gamma, delta, and epsilon crystalline phases of syndiotactic polystyrene (sPS), i.e., phases presenting the s(2/1)2 helical conformation, have been experimentally determined and compared with that calculated at the B3LYP/6-31G(d,p) level of theory for an infinite helix. The assignment of the different modes was highly facilitated and validated by the experimental evaluation of the direction of the transition moment vector of most IR peaks, which was made possible for the first time by measurements on sPS films with different uniplanar orientations of the crystalline phase. The normal vibration analysis of most representative modes of the periodic model allowed for a general description of each one to be obtained, which was further confirmed by the direct inspection of mode animations.

Recently, zeolites have been proposed as media for hydrogen by means of molecular adsorption. The interaction of a dihydrogen molecule on alkali metal ions in high-silica zeolites has been theoretically studied in cluster and periodic models at the B3-LYP level of theory. The cluster models have been obtained by embedding Li + , Na + , and K + in aluminosilicate rings of different sizes (Si n-1 AlO n H 2n , 4 e n e 6). The structure of Li, Na, and K-exchanged chabazite with Si/Al ) 11:1 has been adopted as the periodic model. In both cases, the hydrogen molecule interacts side-on with the cations, forming T-shaped complexes. The results have been compared with similar data obtained for bare cations and previous experimental studies. Furthermore, the necessity of employing correlated methods for a proper description of the interaction has been verified at the MP2 level.

The full vibrational spectra of alpha and beta crystalline phases of syndiotactic polystyrene (sPS), that is, phases presenting the trans-planar conformation, have been experimentally determined and compared with that calculated at the B3LYP/6-31G(d,p) level of theory for an infinite trans-planar chain. The normal vibrational analysis of most representative modes of the periodic model allowed us to give a general description of each one, which was further confirmed by the direct inspection of mode animations. An assignment of the different modes was performed in terms of frequency, relative intensity, and direction of the transition-moment vector of the observed IR peaks as well as Raman vibrational frequencies.

The vibrational spectrum of the Si-free katoite hydrogarnet (116 atoms in the unit cell) has been calculated at the periodic ab initio quantum mechanical level with the CRYSTAL program, by using a Gaussian type basis set and the hybrid B3LYP Hamiltonian. The harmonic frequencies at the Gamma point have been obtained by diagonalizing the mass-weighted Hessian matrix, that is evaluated by numerical differentiation of the analytical first derivatives of the energy with respect to the atomic Cartesian coordinates. The parameters controlling the numerical differentiation, as well as the numerical integration of the exchange-correlation functional for the self-consistent field (SCF) calculation, are shown to affect the obtained frequencies by less than 3 cm-1. Before diagonalization, the dynamical matrix is transformed to a block diagonal form according to the irreducible representations of the point group, so that the 345 vibrational modes are automatically classified by symmetry. Various tools are adopted (graphical representation, isotopic substitution, "freezing" part of the unit cell) that permit a complete classification of normal modes and, in particular, an analysis of the modes in terms of simple models (octahedra modes, Ca modes, H stretching, bending, rotations). The harmonic OH stretching band (48 modes) is quite narrow (20 cm-1), indicating that the interaction among OH groups is very weak. As the OH stretching modes are known to be totally separable from the other modes and strongly anharmonic, the one-dimensional Schroedinger equation for the anharmonic oscillator is solved numerically for the two extreme situations, corresponding to the vibration of one decoupled OH and of all 48 OH groups moving in phase. The anharmonic frequencies are 3682 and 3673 cm-1, respectively, in good agreement with IR experiments (a single band at 3661 cm-1 with a width at half band height of 33 cm-1) and confirming that the interaction between OH groups is extremely weak.

An enthalpy of adsorption of ca. −10 kJ/mol was theoretically predicted for the interaction of molecular hydrogen with Mg-exchanged low silica chabazite (Si/Al = 5/1), which is significantly higher than the theoretical prediction for alkali-metal-exchanged chabazites (−3.0/−7.0 kJ/mol) and in acceptable agreement with a recent experimental finding of −17.5 kJ/mol obtained for a different zeolite, that is, (Mg,Na)−Y.