C. Roetti

CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals

Abstract 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].

Crystal field effects on the topological properties of the electron density in molecular crystals: The case of urea

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.

Calculation of the vibration frequencies of α-quartz: The effect of Hamiltonian and basis set

The central‐zone vibrational spectrum of α‐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.

On the elastic properties of lithium, sodium and potassium oxide. An ab initio study

Abstract The binding energy, equilibrium lattice parameter, elastic constants and central zone phonon frequencies of Li2O, Na2O and K2O have been calculated at an ab initio level with CRYSTAL, a Hartree-Fock linear combination of atomic orbitals (LCAO) program for periodic compounds. The variational basis set has been optimized for each compound, and is reported for future reference and work. A quite satisfactory agreement with very recent experimental data is obtained for Li2O. With regard to Na2O and K2O no experimental data exist, to our knowledge, for the elastic constants and the central zone phonon frequencies, so that the present data represent the first determination of these quantities.

Abinitio approach to molecular crystals: A periodic Hartree–Fock study of crystalline urea

The electronic structure of crystalline urea (two molecules, 16 atoms per unit cell) is investigated at an ab initio level with CRYSTAL, a Hartree–Fock linear combination of atomic orbitals (LCAO) program for periodic systems. The influence of the basis set and of the computational parameters which control the treatment of the Coulomb and exchange series and the reciprocal space integration is documented; results include total and interaction energy, Mulliken analysis data and interaction (solid minus molecules) density maps, band structure, and density of states. The crystal field modifies the electronic structure of the isolated molecule, the main effect being an increase in the ionicity of bonds. The interaction energy obtained with a 6‐21** basis set is 28 kcal/mol, (16 kcal/mol after a correction of the basis set superposition error by using the counterpoise method) to be compared with 21±0.5 kcal/mol from experiment. This preliminary application shows that accurate ab initio calculations of hydrogen...

AB initio hartree-fock study of the MgO(001) surface

Abstract The MgO(001) surface has been studied with an ab initio Hartree-Fock crystalline orbital LCAO program. An optimized basis set containing nine atomic orbitals (three s and six p) per atom has been used. The semi-infinite crystal has been simulated by a slab containing three planes (six atoms per cell). In agreement with the most recent LEED experiments, no relaxation is found and the “rumpling” is very small (1% of the nearest neighbour separation in the bulk). The analysis of the electron charge distribution and of the ion multipoles shows that the fully ionic character found for the bulk is maintained at the surface, and that the anion deformation is very small. A surface energy of 1.43 J/m 2 was obtained.

Ab-initio prediction of materials properties with CRYSTAL: MOF-5 as a case study

MOF-5 is by far the most relevant member of the new class of metal–organic framework materials and has been adopted as a case study to show that reliable ab initio prediction of materials properties of complex systems can be obtained by means of a solid state computational tool like the CRYSTAL code. Structure, electronic properties and vibrational frequencies of MOF-5 computed at the B3LYP level of theory are reported and discussed. Animations representing MOF-5 vibrations are available at the web site: http://www.crystal.unito.it/vibs/mof5

On the electrostatic potential in crystalline systems where the charge density is expanded in Gaussian functions

Methods for the evaluation of the electrostatic potential in systems which are periodic in three dimensions, where the electronic charge distribution is expanded as a linear combination of Gaussian functions of arbitrary quantum number, are described. An ‘exact’ method based on the Ewald potential function is derived, and an approximate scheme using a distributed point multipole representation of the charge distribution is then presented. Recursion formulae enable Cartesian and thence spherical derivatives (of any order) of the potential to be computed. Related procedures for the evaluation of the Fock matrix elements and the coulombic contribution to the total energy per unit cell are described. Tests of the exact and approximate procedures establish their relative accuracy and cost in the MgO, Si and Si12O24 systems in the rock-salt, diamond and chabazite structures, respectively. Applications include a study of the electric field gradient at the C, N and O sites in urea (crystalline and molecular), and...

Ab initio characterization of the (0001) and (101̄0) crystal faces of α-alumina

Abstract Ab initio Hartree-Fock calculations of the (0001) and (1010) crystal faces of α-alumina have been performed using a slab model and taking full account of two-dimensional periodicity. Surface relaxation, surface formation energy, Mulliken populations, charge density maps, and densities of states are obtained and discussed. The validity of the slab model is discussed by analyzing the dependence of results on slab thickness.

The Periodic Hartree‐Fock Method and Its Implementation in the Crystal Code

The present chapter discusses the Hartree-Fock (HF) method for periodic systems with reference to its implementation in the Crystal program. The HF theory is shortly recalled in its Closed Shell (CS), Unrestricted (UHF) and Restricted open shell (RHF) variants; its extension to periodic systems is illustrated. The general features of Crystal, the periodic ab initio linear combination of atomic orbitals (LCAO) program, able to solve the CS, RHF and UHF, as well as Kohn-Sham equations, are presented. Three examples illustrate the capabilities of the Crystal code and the quality of the HF results in comparison with those obtained with the Local Density Approximation using the same code and basis set: NiO in its ferro-magnetic and anti-ferromagnetic structure, trapped electron holes in doped alkaline earth oxides, and F-centres in LiF.