Periodic Hartree-Fock Research Articles

Approximations of the Mulliken charges for the oxygen and silicon atoms of zeolite frameworks calculated with a periodic Hartree–Fock scheme

Approximations of the Mulliken charges for the oxygen and silicon atoms of zeolite frameworks calculated with a periodic Hartree–Fock scheme

Electronic structure of alumina surface

The electronic structure of the (001) and (110) α-alumina surfaces was determined by periodic Hartree–Fock method in statically relaxed geometries. Both (001) and (110) surfaces generate specific surface states into the energy gap. Significant influence of charge-transfer effect on the surface–adsorbate potential is possible in both cases studied. The inclusion of the exponential part to the standard potential forms was suggested for the description of the interaction potential in such cases. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 341–350, 1998

Approximations of the Mulliken charges for the oxygen and silicon atoms of zeolite frameworks calculated with a periodic Hartree-Fock scheme

Distributed multipole analysis DMA on the basis of periodic . Hartree)Fock PHF calculations, using the CRYSTAL code, is applied to five different all-siliceous zeolite models: chabazite, gmelinite, merlinoite, montesommaite, and RHO. Mulliken charges of the framework atoms were calculated with a pseudopotential ps-21G* basis set for silicon and a 6-21G* basis for oxygen. The charge values of the silicon atoms were approximated by a simple one-dimensional function with respect to the average Si—O distance within the respective SiO tetrahedra, whereas a two- 4 dimensional function with respect to the average Si—O distance and the Si—O—Si angle was used for the oxygen atoms. Both dependences were then utilized to evaluate the Mulliken atomic charges of 10 other frameworks with a larger number of atoms per unit cell. The validity of such application is confirmed by comparison with results obtained through direct PHF calculation for all-siliceous mordenite. Q 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 993)1001, 1998

Periodic Hartree-Fock calculation of the A1 g (T z) and Eg (T x, T y) phonon modes in ice VIII

The raman active phonon modes A 1 g ( T z ) and E g ( T x , T y ) of ice VIII have been calculated at the periodic Hartree-Fock level for a selection of cell volumes covering the 0–30 GPa pressure range. The calculation correctly reproduces the frequencies as well as their pressure derivatives. These phonon modes correspond to the relative displacement of the two hydrogen bonded sublattices of ice VIII and are therefore a reliable probe to investigate the part of the intermolecular potential which does not depend upon the hydrogen bond formation. These results which complement those of previous calculations on ice VIII, bring additional support for the reliability of the Hartree-Fock scheme in the study of ice modifications.

Atomic and molecular photostimulated desorption from complex ionic crystals

Calcium carbonate and sodium nitrate are isostructural crystals in which the covalently bonded polyatomic anions are also isoelectronic, however, the chemical properties of these crystals are distinctly different. In this study, we report results involving the photostimulated desorption (PSD) of neutral CO and O(3P) products from geologic calcite (CaCO3) using low laser fluence at 193 nm. Product states are probed using (2+1) resonance enhanced multiphoton ionization for both neutrals. The CO products display a narrow angular distribution normal to the surface and a translational energy characterized, by a temperature (T=110K) significantly lower than that of the substrate (T=295K).1 Atomic oxygen products display both broader angular and kinetic energy distributions than that of the CO fragments. Emission of O(3P) is seen at angles greater than 30° with respect to the surface normal. In contrast, recent PSD studies of product NO from single crystal sodium nitrate (NaNO3) show product distributions with both thermal and hyper-thermal components.2 Projected density of state plots computed using periodic Hartree-Fock theory indicate a strong overlap in the metal and carbonate bands of the low lying excited states in CaCO3, while NaNO3 was found to have a well-separated nitrate band in the excited state below the mixed metal/nitrate bands. The differences in the electronic structure of these materials may account for differences in the observed product distributions in the PSD of calcite and sodium nitrate.

Chemisorption of H 2 and H 2S on the (100) surface of RuS 2: an ab initio theoretical study

The chemisorption of H 2 and H 2S molecules on the (100) surface of RuS 2 is studied with a periodic Hartree-Fock approach completed by density functional correlation energy corrections. The stable (100) surface is modeled by a slab for which both molecular and dissociative chemisorptions are considered. For H 2, as well as for H 2S, the best optimized situations are for the molecular adsorptions, even if dissociated forms are found to be more favorable than the free gas molecules. The H 2 molecule is chemisorbed on the surface Ru atom in an η 2 lateral coordination with a strongly weakened HH bond, whereas the H 2S molecule is interacting by the S lone pairs with the Ru completing around it the bulk-like environment. The electronic structures for both molecular and dissociated optima are discussed in terms of orbital analysis with the help of projected density-of-states and crystal orbitals overlap populations. The crucial role of the S 2 pairs at the surface on the chemisorption properties is underlined.

On the structure and stability ofTi-zeolites. A comparison of cluster and periodicab initio calculations

A periodic Hartree-Fock study of Ti-containing zeolites was performed. The zeolitic framework was modeled by means of the chabazite structure. Two framework compositions were considered (TiO( Si1Ti )40 and 0.5) and the corresponding periodic structures were optimized in order to estimate the geometric and energetic features of the Ti sites. Cluster models were also considered for comparison. It arises that the main structural distortion of the zeolite lattice upon SiOTi substitution comes from the increment of the T-site volume. From the obtained results, the limitations of the different models are discussed.

Theoretical study of the adsorption of acids and bases on TiO2 and MgO surfaces

The adsorption of small molecules on TiO2 and MgO is investigated byab initio periodic Hartree-Fock calculations. The adsorption may be molecular or dissociative. This depends on their acidic and basic properties in gas phase. For the molecular adsorption, the molecules are adsorbed as bases on the metal sites and the adsorption energies correlate with the proton affinities. This also true on MgO, even if CO2 is ordinary considered as an acidic probe molecule. HSBA theory allows to compare the relative adsorption of molecules on TiO2 and MgO. The dissociations on the surface correlate with the gas phase cleavages: basic cleavage for MeOH and acidic cleavage for MeSH. Another important factor is the adsorbate-adsorbate interaction: at high coverage, stabilization through H-bonds favors the vicinity of adsorbates on the surface (islands of adsorbates and coadsorption effects). Electrostatic interactions explain the change of orientation (CO2 ) with the coverage.

The stability of polymorphs of MgCl 2 — an ab initio study

Periodic Hartree-Fock calculations show that the layered structures of α- and β-MgCl 2 are stable at the HF level; earlier work has suggested this was not so for β-MgCl 2. The neglect of correlation leads to a large overestimate of the ClCl interlayer separation and hence of the c lattice parameter. Structures optimised using density functional theory and the same basis set are in better agreement with experiment. α- and β-MgCl 2 are close in energy at HF and DFT levels, and vibrational effects are likely to be important in determining their relative stability. Neglecting possible distorted variants of the more ionic rutile and fluorite structures, we estimate transition pressures of ∼ 17 GPa for β-MgCl 2 → rutile and ∼ 77 GPa for rutile → fluorite.

Periodic ab initio study of silico-faujasite

Silico-faujasite (144 atoms in the unit cell) has been investigated using an ab initio periodic Hartree-Fock scheme and an all-electron basis set. The structure has been fully optimized; it turns out that this system is less stable than α-quartz by about 4 kcal mol −1 per SiO 2 unit. The electron density and electrostatic potential maps are used for discussing the differences between pores limited by 6- and 12-membered rings in faujasite.

Ionic solids at elevated temperatures and high pressures: MgF2

A combination of periodic Hartree–Fock theory, quasiharmonic lattice dynamics, and molecular dynamics is used to study the behavior of MgF2 at elevated temperatures and/or high pressures. Particular attention is paid to the pressure-induced transition from the rutile to the fluorite structure in view of earlier theoretical estimates of the transition pressure, which differ widely. It is shown that previously reported potentials obtained by fitting to empirical data fail to reproduce thermodynamic properties. To rectify this, a new set of consistent two-body potentials has been derived from ab initio periodic Hartree–Fock calculations. Lattice dynamics calculations in the quasiharmonic approximation based on these potentials has been used to study the two phases of MgF2 at high T and P. The resulting transition pressure and that obtained directly from Hartree–Fock calculations in the static limit are both ⩽30 GPa, which is close to the experimental value but appreciably lower than a previous molecular dynamics value of over 130 GPa. The variation of quantities such as (∂P/∂T)V which play a central role in the formulation of approximate equations of state is also considered.

Electronic structure and properties ofCu2O

The structural and electronic properties of ${\mathrm{Cu}}_{2}\mathrm{O}$ have been investigated using the periodic Hartree-Fock method and a posteriori density-functional corrections. The lattice parameter, bulk modulus, and elastic constants have been calculated. The electronic structure of and bonding in ${\mathrm{Cu}}_{2}\mathrm{O}$ are analyzed and compared with x-ray photoelectron spectroscopy spectra, showing a good agreement for the valence-band states. To check the quality of the calculated electron density, static structure factors and Compton profiles have been calculated, showing a good agreement with the available experimental data. The effective electron and hole masses have been evaluated for ${\mathrm{Cu}}_{2}\mathrm{O}$ at the center of the Brillouin zone. The calculated interaction energy between the two interpenetrated frameworks in the cuprite structure is estimated to be around -6.0 kcal/mol per ${\mathrm{Cu}}_{2}\mathrm{O}$ formula. The bonding between the two independent frameworks has been analyzed using a bimolecular model and the results indicate an important role of ${d}^{10}{\ensuremath{-}d}^{10}$ type interactions between copper atoms.

Structure and Energetics of the Water/NaCl(100) Interface

A series of correlation-corrected periodic Hartree−Fock (PHF) calculations have been performed to evaluate the structure of a single layer of water adsorbed on NaCl(100). This work was motivated by differing experimental observations which assign the water/NaCl interface structure as either a monolayer, with a single adsorbate binding site, or a 4×2 bilayer model. Quantum mechanical binding energies were computed for several adsorbate/surface geometries corresponding to 1×1 and 2×1 monolayer structures and 4×2 bilayer structures. The calculations indicate that the binding energy per water molecule for the monolayer and bilayer models are very similar; the estimated PHF and correlation-corrected binding energies are 10 and 14 kcal/mol, respectively, for both models. When measured per unit surface area the 4×2 bilayer is energetically favored because it has a 50% greater packing density than the monolayer. The computed binding energies are consistent with experiment. These data show that the monolayer struc...

Periodic ab initio Hartree-Fock study of trigonal and orthorhombic phases of boric oxides

The structure and electronic properties of trigonal and orthorhombic boric oxide (B2O3) are studied using periodic ab initio Hartree-Fock method. The optimised structural parameters for two B2O3 polymorphs are in good agreement with experimental data. The analyses of their electronic structures provide insights into the chemical nature of the B–O bond and the way in which it changes with the coordination number around boron and oxygen. Our quantum-chemical study suggests that the orthorhombic form is more ionic than the trigonal form and that the coordination number of boron around oxygen plays a more dominant role than that of oxygen around boron in B2O3 crystals.

An ab initio Hartree-Fock study of the electron-excess gap states in oxygen-deficient rutile TiO 2

Ab initio spin-unrestricted periodic Hartree-Fock calculations have been used to study the electron-excess gap states in rutile TiO 2 which result from the formation of oxygen vacancies in the bulk and at the surface of an isolated slab of infinite {110} planes. These states are found to be insulating and occur at ∼ 1–2 eV above the O 2p band edge. It is shown that while the O 2p band undergoes small changes in both width and shape as a result of these defects, it remains essentially spin-paired. On the other hand, gap states associated with these defects are largely spin-polarised states corresponding to excess electron density trapped at bulk vacancies and local Ti 3d 1 and Ti 3d 2 configurations in both the bulk and at the surface. In the bulk the lowest energy state is one in which the majority of the excess charge is localised at the vacant oxygen site, whereas at the surface the redistribution is essentially at the surface Ti atoms. For the oxygen-deficient {110} surface with an entire plane of missing oxygen atoms, an antiferromagnetic spin arrangement is found consisting of localised spins on the surface titanium atoms.

Periodic unrestricted Hartree-Fock study of corundumlikeTi2O3andV2O3

The ground-state electronic and magnetic properties of rhombohedral ${\mathrm{Ti}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ have been investigated by ab initio all-electron periodic Hartree-Fock calculations. Both unrestricted open-shell and restricted closed-shell methods have been employed, with basis sets of atomic orbitals represented by contracted Gaussian-type functions. The ${\mathrm{t}}_{2\mathrm{g}}$ degeneracy of d electrons is removed by the rhombohedral field, giving rise to orbital ordering between ${\mathrm{a}}_{1\mathrm{g}}$ and ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\ensuremath{\pi}}}$ levels. The self-consistent-field variational solutions are spin-polarized insulating states with single (${\mathrm{a}}_{1\mathrm{g}}$) and double (${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\ensuremath{\pi}}}$) electron occupations for ${\mathrm{Ti}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$, respectively. Conducting or semiconducting states, with different relative energies of ${\mathrm{a}}_{1\mathrm{g}}$ and ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\ensuremath{\pi}}}$ bands, have also been obtained by changing the c/a ratio of the hexagonal unit cell. The charge transfer into ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\ensuremath{\sigma}}}$ levels is discussed and compared to the ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$ behavior.

Proton-ordered models of ordinary ice for quantum-mechanical studies

A periodic Hartree-Fock ab initio study is presented concerning two proton-ordered structures of ordinary ice: one ferro-electric (C-ice), the other anti-ferro-electric (P-ice). The calculated energies are practically coincident, and in good agrement with the experimental stability of disordered ice Ih. Slabs are cut out from these crystals in order to formulate a model for studying the surface properties of ordinary ice. The stability of these two-dimensional periodic systems is discussed, and the relaxation of the P-ice slab formed by two bilayers parallel to the (001) face is considered. Finally, an embedded cluster method is adopted to calculate geometric and energetic properties of KOH and NaOH dissolved in C- and P-ice at low concentration. This study permits us to discuss the role of KOH in promoting the transition from disordered Ih to ordered C-ice, which has been observed to occur at 72 K [Leadbetter et al., J. Chem. Phys. 82, 424 (1985)].

Ab initio periodic pseudopotential Hartree-Fock calculations of O 2 dissociation on perfect Si(100) surface

This paper investigates the cleavage of O 2 adsorbed on clean Si(100) surfaces with ab initio periodic pseudopotential Hartree-Fock calculations. For the adsorption of the O 2 molecular precursors at coverage ϑ = 1 (one O 2 per dimer), the Si(100) surface remains reconstructed and O 2 are adsorbed on the dimers, parallel to the surface; the sites between the dimers are vacant. For the atomic adsorption at the same coverage (representing then one O per surface Si) the surface reconstruction nearly disappears; the oxygen atoms are adsorbed over the successive spaces between adjacent surface Si atoms along the (110) directions (those of the elongated dimers and those between them) in asymmetric fashion. The dissociation of O 2 requires the breaking of two bonds, the SiSi and OO bonds and the migration of an oxygen atom. It therefore implies the presence of a high activation energy. Two paths are investigated for the O 2 dissociation and the migration of an atomic oxygen on the surface. The migration of O 2 from the best adsorption mode to least favourable one where the dissociation is easier is also discussed.

Periodic ab initio study of the oxidizing sites in Ti-containing zeolites

A periodic Hartree-Fock study of Ti-containing zeolites was performed. The zeolitic framework was modeled by means of the chabazite structure. Two framework compositions were considered ( Ti (Si + Ti) = 0 and 0.5 ) and the corresponding periodic structures were optimized in order to evaluate the structural and electronic features of the Ti sites. Cluster models were also considered for comparison. Despite the high Ti concentration, the theoretical cell expansion coefficient, 0.394, agrees very well with accurate experimental values. The adsorption of a single water molecule on a Ti site was studied and it was observed that a 5-fold coordination holds for the Ti atom in a deformed trigonal dipyramid.

Quantum ab initio study of acetylene adsorption on NaCl(100) I. Topology and adsorption energy

The quantum periodic Hartree-Fock study of acetylene adsorption on the NaCl(100) surface is carried out for three model structures, the admolecule being parallel or perpendicular to the surface. Two surface coverages ( τ = 1 4 and 1 ) are investigated for these three adsorption sites. In the most favorable situation, the adsorption energy for the monolayer is calculated as 8.0 kcal mol −1. The lateral interaction is extrapolated to 1.6 kcal mol −1 by surface coverage analysis. These calculated results are in good agreement with the experiment values. The approaches are discussed and compared to a semi-classical study of acetylene adsorption on MgO(100).