RESUMEN
The vibrational spectrum of Ca3Fe2Si3O12 andradite is calculated at the Gamma point by using the periodic ab initio CRYSTAL program that adopts an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. The full set of frequencies (17 IR active, 25 Raman active, and 55 inactive modes) is calculated. The effect of the basis set on the calculated frequencies is discussed. The modes are characterized by direct inspection of the eigenvectors and isotopic substitution. The present calculations permit us to clarify some of the assignment problems raised by experiments. The mean absolute differences of the various modes with respect to the available experimental IR and Raman data are as small as 9 and 5 cm(-1), respectively.
RESUMEN
The central-zone vibrational spectrum of alpha-quartz (SiO2) is calculated by building the Hessian matrix numerically from the analytical gradients of the energy with respect to the atomic coordinates. The nonanalytical part is obtained with a finite field supercell approach for the high-frequency dielectric constant and a Wannier function scheme for the evaluation of Born charges. The results obtained with four different Hamiltonians, namely Hartree-Fock, DFT in its local (LDA) and nonlocal gradient corrected (PBE) approximation, and hybrid B3LYP, are discussed, showing that B3LYP performs far better than LDA and PBE, which in turn provide better results than HF, as the mean absolute difference from experimental frequencies is 6, 18, 21, and 44 cm(-1), respectively, when a split valence basis set containing two sets of polarization functions is used. For the LDA results, comparison is possible with previous calculations based on the Density Functional Perturbation Theory and usage of a plane-wave basis set. The effects associated with the use of basis sets of increasing size are also investigated. It turns out that a split valence plus a single set of d polarization functions provides frequencies that differ from the ones obtained with a double set of d functions and a set of f functions on all atoms by on average less than 5 cm(-1).