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Manuale del programma di calcolo Crystal98 www.crystal.unito.it

Manuale di del programma di calcolo Crystal95 www.crystal.unito.it

A periodic ab initio Hartree-Fock method (the program CRYSTAL) has been used to evaluate the total-electron-energy surface of MgF2 (rutile-type tetragonal structure) as a function of crystal strain. Mg and F atoms are represented by 13 atomic orbitals in the form of contracted Gaussian-type functions. The equilibrium unit-cell edges and fluorine coordinates, the binding energy, and the six elastic constants C-11, C-12, C-13, C33, C44, and C66 have been calculated. Inner strain was accounted for by relaxing the F-atom position for each lattice deformation applied, and contributed significantly to the C44, C66, and C33 components. An average deviation of 8.0% is observed with respect to experimental elastic data Classical two-body empirical calculations have been performed for the purpose of comparison. Energy bands, Mulliken electron populations, and charge-density maps are analyzed, and the chemical bonding is discussed, showing significant deviations from ionicity (z(Mg) = 1.80(e)).

The binding energy (BE), the equilibrium lattice parameter (alpha-0), the bulk modulus (B), and the central-zone transverse-optical phonon frequency (v) of seventeen diamond- and zinc-blende-type-structure semiconductors involving atoms belonging to the second to fifth periods have been evaluated. The periodic ab initio Hartree-Fock linear-combination-of-atomic-orbitals program CRYSTAL has been used. Core pseudopotentials have been adopted in order to limit the calculation to valence electrons. Thirteen atomic orbitals (2s, 6p, 5d) per atom have been used. The quality of the pseudo-potential results is checked by comparison with all-electron calculations performed on six light-atom systems (diamond, silicon, BN, BP, AlP, SiC). The mean errors of the pseudopotential calculations with respect to experimental data are -38%, +1.2%, +6.5%, and +7.8% for BE, alpha-0, B, and v, respectively. A correlation-only density-functional alpha-posteriori correction to the Hartree-Fock total energy is performed, which reduces the absolute BE mean error to 2.6%.

We have investigated various electronic band structures for different graphite modifications using the extended tight binding method. The specific crystal structures studied are the two naturally occurring graphite modifications (Bernal and rhombohedral), and a hypothetical configuration where the carbon atoms in consecutive layers are directly above each other. The latter structure has not been observed in pure graphite, but it is the backbone structure for different stages of intercalated graphite, e.g. Li-graphite compounds LiC n . On comparing band structures for various graphite modifications we find important differences in the π-bands close to the Fermi energy, the region dominating transport and low energy excitation properties.

The regular adsorption of CO on a MgO(001) monolayer has been investigated at an “ab initio Hartree-Fock crystalline-orbital level, with a basis set containing 9 atomic orbitals per atom. Both vertical bindings to Mg (through oxygen and carbon) have been considered and the C-O as well as the Mg-CO or Mg-OC distances have been optimized. At the 1/2 surface coverage (one CO molecule every two surface Mg ions) adsorption energies of 4.13 (carbon binding) and 3.29 (oxygen binding) kcal/mol were obtained, to be compared with an experimental adsorption heat of 3.6 kcal/mol. Similar energies were obtained for the 1/4 coverage, whereas the 1/1 adsorption is less favoured, due to the repulsion between the CO molecules. The charge redistributions in the CO molecule and in the substrate are considered, as well as the changes occurring in the density of states for the interacting systems.

The hydrate crystal lithium hydroxide monohydrate LiOH.H2O has been studied by ab initio periodic Hartree-Fock calculations. The influence of the crystalline environment on the local molecular properties (molecular geometry, atomic charges, electron density, molecular vibrations and deuterium quadrupole coupling constants) of the water molecule, the lithium and hydroxide ions has been calculated. A number of crystalline bulk properties are also presented, optimized crystalline structure, lattice energy and electronic band structure. The optimized cell parameters from calculations with a large basis set of triple-zeta quality differ by only 1-3% from the experimental neutron-determined cell, whereas the STO-3g basis set performs poorly (differences of 5-10%). With the triple-zeta basis also the atomic positions and intermolecular distances agree very well with the experiment. The lattice energy differs by approximately 8% from the experimental value, and by at most 3% when a density-functional electron correlation correction is applied. Large electron-density rearrangements occur in the water molecule and in the hydrogen bond and are in qualitative and quantitative agreement with experimental X-ray diffraction results. The quadrupole-coupling constants of the water and hydroxide deuterium atoms are found to be very sensitive to the O-H bond length and are in good agreement with experimental values when the calculation is based on the experimental structure. The anharmonic O-H stretching vibrations in the crystal are presented and found to be very close to results from calculations on molecular clusters. The electronic band and density-of-states spectra are discussed. Model calculations on a hydrogen fluoride chain were used to rationalize the results.

The layered mineral brucite Mg(OH${)}_{2}$ is investigated theoretically using an ab initio all-electron linear combination of atomic orbitals Hartree-Fock (HF) approximation. At the HF level, the interlayer interaction is weak and the interlayer distance is larger than the experimental one. Bonding is discussed on the basis of density of states and charge-density maps. No hydrogen bond is characterized. A posteriori correction of the energy for the correlation error is performed by use of the functional approach. The three semilocal functional formulas used yield similar results. This brings in extra interlayer bonding interaction, and yields a calculated geometry in agreement with experiments. The analysis of the interlayer bondings shows that it is mainly of dispersion type, and that the used functionals account for dispersion, in particular at short interatomic distances.

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...

Three different crystal phases of magnesium oxide [B1 (NaCl), B2 (CsCl), and B${8}_{1}$ (inverse NiAs)] are investigated theoretically. An ab initio all-electron linear combination of atomic orbitals Hartree-Fock approximation is adopted; extended basis sets are used which have been variationally optimized in each case. In ordinary conditions, the B${8}_{1}$ and B2 structures result less stable with respect to the rocksalt structure by 0.44 and 1.77 eV, respectively. With increasing pressure, the transition B1\ensuremath{\rightarrow}B2 is estimated to occur around 2.2 Mbar, while it is not excluded that a pressure interval exists around 2 Mbar where the B${8}_{1}$ phase is the most stable of the three structures. Data on the electronic properties of the three phases are provided and discussed: Mulliken populations, charge-density distribution, electron momentum distribution and anisotropy, magnesium core deformation, and band structure.

The electronic structure of corundum (α-Al 2 O 3 ) is calculated at the ab initio Hartree-Fock level. Cohesive energy, total and projected densities of states, atomic multipoles, bond populations and electron charge density distribution maps are given. The oxygen-aluminium bond is found to be partially covalent in nature; the atomic charges are −0.73 e and +1.09 e for O and Al respectively.

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.

The core pseudopotentials of Durand and Barthelat have been introduced in the periodic Hartree-Fock program CRYSTAL. This new option allows the treatment of crystals involving heavy atoms and therefore extends the applicability of the method. A comparison between all-electron and pseudopotential results is presented. Binding energies, optimized cell parameters, bulk moduli, band structures and electron density curves calculated with the two methods are presented for covalent (diamond and silicon), metallic (lithium) and ionic (MgO) systems. As expected the pseudopotential results for covalent compounds are in good agreement with those obtained from all-electron calculations; for MgO larger discrepancies are observed, possibly due to core polarization effects.

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.