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The problem of numerical accuracy in the calculation of vibrational frequencies of crystalline compounds from the hessian matrix is discussed with reference to alpha-quartz (SiO(2)) as a case study and to the specific implementation in the CRYSTAL code. The Hessian matrix is obtained by numerical differentiation of the analytical gradient of the energy with… (More)

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio… (More)

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,… (More)

Two alternative approaches for the quantum-mechanical calculation of the nuclear-relaxation term of elastic and piezoelectric tensors of crystalline materials are illustrated and their computational aspects discussed: (i) a numerical approach based on the geometry optimization of atomic positions at strained lattice configurations and (ii) a… (More)

The use of symmetry-adapted crystalline orbitals SACOs in self-Ž. consistent-field SCF schemes for infinite periodic systems is discussed and documented with reference to many examples. The symmetry information generated during the SACOs construction is used to illustrate some particular features of the computational Ž. procedure at special points in the… (More)

A computational procedure for generating space-symmetry-adapted Ž. Bloch functions BF is presented. The case is discussed when BF are built from a basis of Ž wx. local functions atomic orbitals AOs. The method, which is completely general in the sense that it applies to any space group and AOs of any quantum number, is based on the diagonalization of Dirac… (More)

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