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.