The CRYSTAL code, 1976-2020 and beyond, a long story.

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions).

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: where it is shown how finite oligomer chains tend to the infinite periodic polymer.

The longitudinal polarizability, α(xx), and second hyperpolarizability, γ(xxxx), of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γ(xxxx), that is, very sensitive to the number of k(->) points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids).

The calculation of the static first and second susceptibilities of crystalline urea: A comparison of Hartree-Fock and density functional theory results obtained with the periodic coupled perturbed Hartree-Fock/Kohn-Sham scheme.

The static polarizability alpha and first hyperpolarizability beta tensors of crystalline urea and the corresponding first-(chi((1))) and second-(chi((2))) susceptibilities are calculated and compared to the same quantities obtained for the molecule by using the same code (a development version of CRYSTAL), basis set, and level of theory. In order to separate geometrical and solid state effects, two geometries are considered for the molecule in its planar conformation: (i) as cut out from the bulk structure and (ii) fully optimized. First, the effect of basis sets on computed properties is explored at the B3LYP level by employing basis sets of increasing complexity, from 6-31G(d,p) to 6-311G(2df,2pd) (Pople's family) and from DZP to QZVPPP (Thakkar/Ahlrichs/Dunning's family) on alpha and beta for both the molecule and the bulk.

Calculation of the dielectric constant epsilon and first nonlinear susceptibility chi((2)) of crystalline potassium dihydrogen phosphate by the coupled perturbed Hartree-Fock and coupled perturbed Kohn-Sham schemes as implemented in the CRYSTAL code.

The high-frequency dielectric varepsilon and the first nonlinear electric susceptibility chi((2)) tensors of crystalline potassium dihydrogen phosphate (KH(2)PO(4)) are calculated by using the coupled perturbed Hartree-Fock and Kohn-Sham methods as implemented in the CRYSTAL code. The effect of basis sets of increasing size on varepsilon and chi((2)) is explored. Five different levels of theory, namely, local-density approximation, generalized gradient approximation (PBE), hybrids (B3LYP and PBE0), and HF are compared using the experimental and theoretical structures corresponding not only to the tetragonal geometry I4d2 at room temperature but also to the orthorhombic phase Fdd2 at low temperature.

Calculation of the static electronic second hyperpolarizability or chi(3) tensor of three-dimensional periodic compounds with a local basis set.

The coupled perturbed Hartree-Fock (CPHF) method for evaluating static first (beta) and second (gamma) hyperpolarizability tensors of periodic systems has recently been implemented in the CRYSTAL code [Bishop et al., J. Chem.

Polarization of one-dimensional periodic systems in a static electric field: sawtooth potential treatment revisited.

Various periodic piecewise linear potentials for extracting the electronic response of an infinite periodic system to a uniform electrostatic field are examined. It is shown that discontinuous potentials, such as the sawtooth, cannot be used for this purpose. Continuous triangular potentials can be successfully employed to determine both even- and odd-order (hyper)polarizabilities, as demonstrated here for the first time, although the permanent dipole moment of the corresponding long finite chain remains out of reach.

Calculation of first and second static hyperpolarizabilities of one- to three-dimensional periodic compounds. Implementation in the CRYSTAL code.

A computational scheme for the evaluation of the static first (beta) and second (gamma) hyperpolarizability tensors of systems periodic in 1D (polymers), 2D (slabs), 3D (crystals), and, as a limiting case, 0D (molecules) has been implemented, within the coupled perturbed Hartree-Fock framework (CPHF), in the CRYSTAL code, which uses a Gaussian type basis set. This generalizes to 2D and 3D the work by Bishop et al. (J.

The calculation of static polarizabilities of 1-3D periodic compounds. the implementation in the crystal code.

The Coupled Perturbed Hartree-Fock (CPHF) scheme has been implemented in the CRYSTAL06 program, that uses a gaussian type basis set, for systems periodic in 1D (polymers), 2D (slabs), 3D (crystals) and, as a limiting case, 0D (molecules), which enables comparison with molecular codes. CPHF is applied to the calculation of the polarizability alpha of LiF in different aggregation states: finite and infinite chains, slabs, and cubic crystal. Correctness of the computational scheme for the various dimensionalities and its numerical efficiency are confirmed by the correct trend of alpha: alpha for a finite linear chain containing N LiF units with large N tends to the value for the infinite chain, N parallel chains give the slab value when N is sufficiently large, and N superimposed slabs tend to the bulk value.

Coupled perturbed Hartree-Fock for periodic systems: the role of symmetry and related computational aspects.

A general and efficient implementation of the coupled perturbed Hartree-Fock (CPHF) scheme in the CRYSTAL06 code that applies to systems periodic in one dimension (polymers), two dimensions (slabs), three dimensions (crystals) and, as a limiting case, zero dimension (molecules) is presented. The dielectric tensor of large unit cell systems such as boehmite (gamma-AlOOH, 8 atoms/cell), calcite (CaCO3, 10 atoms/cell), and pyrope (Mg3Al2Si3O12, 80 atoms/cell) has been computed. Results are well converged with respect to the computational parameters, in particular, to the number of k points in the reciprocal space and tolerances used in the truncation of the Coulomb and exchange series, showing that the same standard computational conditions used for the self-consistent-field (SCF) step can also be used safely in a CPHF calculation.

An ab initio periodic study of NiO supported at the Pd(100) surface. Part 2: The nonstoichiometric Ni3O4 phase.

The present computational study describes the structure and properties of a substoichiometric 2D monatomic in the height phase of nickel oxide, c(4 x 2)-Ni(3)O(4), which has been newly found to epitaxially grow under special deposition conditions on the (100) face of palladium. A slab model is adopted where palladium is simulated by a thin film covered on both sides by epilayers, in combination with a DFT hybrid-exchange Hamiltonian; to make convergence of the SCF procedure easier, a thermal smearing technique is used, whose consequences on the results are critically analyzed. Three adsorbed systems are considered and characterized: (i) RH, that is, the c(4 x 2)-Ni(3)O(4) phase with a rhombic distribution of Ni vacancies, as is experimentally observed; SQ, or p(2 x 2)-Ni(3)O(4), which differs from the previous one for a square, instead of a rhombic distribution of vacancies; (iii) OX, or p(2 x 2)-O, that is, a surface oxidized phase of Pd(100) which is believed to be the precursor for the formation of RH.