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CRYSTAL [1] computes the electronic structure and properties of periodic systems (crystals, surfaces, polymers) within Hartree-Fock [2], Density Functional and various hybrid approximations. CRYSTAL was developed during nearly 30 years (since 1976) [3] by researchers of the Theoretical Chemistry Group in Torino (Italy), and the Computational Materials Science group in CLRC (Daresbury, UK), with important contributions from visiting researchers, as documented by the main authors list and the bibliography.The basic features of the program CRYSTAL are presented, with two examples of application in the field of crystallography [4,5].

The Quantum Theory of Atoms in Molecules, due to Bader, is applied to periodic systems. Results for molecular and crystalline urea are presented. Changes in both bond critical points and atomic properties due to changes of chemical environment are described. A rationale for the different lengths of the in-plane and out-of-plane hydrogen bonds and for the lengthening of the CO bond in bulk urea is provided in terms of the properties of the Laplacian of the oxygen atom electron density distribution. An evaluation of molecular and atomic volume changes indicates that the decrease of molecular volume upon change of phase from gas to solid originates primarily from a contraction of the atomic basins directly involved in hydrogen bonds. Other atoms show a small expansion. The considerable decrease of oxygen and hydrogen atomic volumes is related to the mutual penetration of their van der Waals envelopes following hydrogen bond formation. The results confirm that urea is more polar in the solid phase.

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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).

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