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Calculation of the vibration frequencies of α‐quartz: The effect of Hamiltonian and basis set
Author(s) -
ZicovichWilson C. M.,
Pascale F.,
Roetti C.,
Saunders V. R.,
Orlando R.,
Dovesi R.
Publication year - 2004
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20120
Subject(s) - basis set , wannier function , hamiltonian (control theory) , hessian matrix , basis function , mathematical analysis , vibration , plane wave , mathematics , quantum mechanics , chemistry , physics , atomic physics , density functional theory , mathematical optimization
The central‐zone vibrational spectrum of α‐quartz (SiO 2 ) 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 . © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1873–1881, 2004