Ab initio simulation of the IR spectra of pyrope, grossular, and andradite

Abstract

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

“…As in previous works by some of the present authors 24-29 the B3LYP Hamiltonian 30 was employed, that contains a hybrid Hartree-Fock/density-functional exchangecorrelation term, and is widely and successfully used in molecular quantum chemistry 31 as well as in solid state calculations, where it has been shown to reproduce vibrational frequencies in general good agreement with experiment. [32][33][34][35] The adopted basis set has already been used in a previous investigation of calcite (BSD in Ref. 36).…”

Theoretical and Experimental Study of LiBH4-LiCl Solid Solution

“…For hydrogen, a 31G(p) (α sp = 0.1613 bohr −2 for the most diffuse shell exponent and α pol = 1.1 bohr −2 for polarization) was considered; for chlorine, a 86-311G basis set was used (α sp = 0.125 bohr −2 for the most diffuse shell exponent). Phonons at Γ point in the harmonic approximation were computed to derive the thermodynamic functions by diagonalizing the associated mass-weighted Hessian matrix (for details on the computational procedure see references [31,32]). Grimme's correction to the electronic energy was computed to take dispersion forces into account for all calculations, following the D* approach described in the literature [33,34].…”

First-principles calculation of the structure and dielectric properties ofBi2Ti2O7

“…20,21 The phonon contribution to the dielectric function was calculated using Born charges derived from changes induced in Wannier orbitals by atomic displacements along phonon normal coordinates. 20,22 The methods used are briefly outlined below. It is well known that the polarization in systems with periodic boundary conditions is ill defined.…”