CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree–Fock (HF). The cost for HF or hybrids is only about 3–5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores.

The static and high frequency dielectric tensors, Born effective charges, vibrational spectrum at the Γ point, TO-LO splitting and IR intensities of calcite CaCO 3 have been calculated with the periodic ab initio CRYSTAL program, with five different basis sets of increasing size and four different Hamiltonians (HF, LDA, PBE, B3LYP). B3LYP is shown to perform better than the other options, in particular of LDA and PBE that are often used for the calculation of the vibrational spectrum of crystalline solids. When comparing B3LYP and experimental frequencies, the mean absolute difference is as small as 8.5 cm -1 ; this number reduces to 4.8 cm -1 if the two lowest experimental frequencies, that we suspect to be affected by a relatively large error, are excluded from statistics. Static and high frequency dielectric tensors, as well as IR intensities computed with the same hybrid scheme (B3LYP) compare quite favourably with experiment. The full set of modes is characterized by various tools including isotopic substitution, “freezing” one of the two subunits (Ca 2+ or CO 3 2- ) and graphical representations. A general tool has been implemented, that permits the automatic generation of the animation of the full set of modes starting from the CRYSTAL output (available at www.crystal.unito.it/vibs/calcite).