Ab Initio Periodic Hartree-Fock Research Articles

Ab Initio Hartree-Fock Simulation of R-Plane Sapphire

Abstract R-plane sapphire is the preferred substrate material for silicon-based radiation-hard devices and RF integrated circuits. Ab initio periodic Hartree-Fock simulations of r-plane sapphire slabs are presented with a particular focus on the surface relaxation and the surface energy. The calculations show that there is a considerable relaxation of the four outermost atomic layers of r-plane sapphire. A comparison with c-, a- and m-plane sapphire shows that the surface energy of fully relaxed r-plane sapphire is considerably larger than the surface energy of c-plane sapphire, but similar to the surface energies of a- and m-plane sapphire. The implications of these findings for chemical mechanical polishing (CMP) and electrolytic in-process dressing (ELID) grinding of sapphire are discussed briefly.

Molecular dynamic study of the melting temperature in MgF 2 with the fluorite structure

The melting temperature of MgF 2 with cubic fluorite structure has been calculated by the constant temperature and pressure molecular dynamics (MD) simulation using the well-tested effective pair-wise potentials, which consist of the Coulomb, dispersion, and repulsion interaction by varying temperature from 300 to 2500 K. It is found that the potential parameters for MgF 2 derived from ab initio periodic Hartree-Fock calculations are very successful in reproducing accurately the DFT-GGA combined with quasi-harmonic Debye model calculated volumes of the cubic fluorite-type MgF 2 over a wide range of temperature at room pressure. Our simulated melting temperature of cubic fluorite-type MgF 2 is very close to the actual melting temperature 1539 K. Meanwhile, the radial distribution functions of Mg–Mg, F–F, and Mg–F ion pairs near the melting temperature are investigated from the isobaric and isothermal ensemble.

Theoretical Study of Scanning Probe Microscope Images of VTe2

Ab initio periodic Hartree-Fock calculations with the full potential and minimum basis set are applied to interpretation of scanning tunneling microscope (STM) and atomic force microscope (AFM) images on 1TVTe2. Our results show that the simulated STM image shows asymmetry while the simulated AFM image shows the circular electron densities at the bright spots without asymmetry of electron density to agree with the experimental AFM image. The bright spots of both the STM and AFM images of VTe2 are associated with the surface Te atoms, while the patterns of bright spots of STM and AFM images are different.

Universal LC Method for a Determination of Fourteen Cationic Surfactants Widely Used in Surfactant Industry

Ab initio periodic Hartree-Fock calculations with the full potential and minimum basis set are applied to interpretation of scanning tunneling microscope (STM) and atomic force microscope (AFM) images on 1TVTe2. Our results show that the simulated STM image shows asymmetry while the simulated AFM image shows the circular electron densities at the bright spots without asymmetry of electron density to agree with the experimental AFM image. The bright spots of both the STM and AFM images of VTe2 are associated with the surface Te atoms, while the patterns of bright spots of STM and AFM images are different.

Theoretical study of the interaction of molecular oxygen with a reduced TiO 2 surface

We investigate the re-oxidation of the reduced TiO 2 (1 1 0) surface by adsorption of molecular oxygen using quantum-chemical, ab-initio periodic Hartree–Fock calculations. The absorption sites considered are anion defects and cation Ti(5f) positions. The results show evidence of strong charge transfer from the defect surface to the O 2 molecule. In agreement with experiment, we find that the most stable species is one in which molecular oxygen adsorbs at the defect sites as O 2 −. Adsorption of three O 2 molecules per vacancy site is thermodynamically favored compared to one or two adsorbed molecules.

Surface Energies and Heats of Oxygen Adsorption in Ceria/Ceria-Zirconia Solid Solutions: Analysis by Semiempirical Interacting Bonds Method

Semiempirical Interacting Bonds Method (IBM) in the slab approximation with due regard to relaxation after the free surface formation was used to calculate the surface energies and enthalpies of oxygen adsorption on the surface of ceria-based solid solutions. The IBM-estimated surface energies agree well with the published values obtained using electrostatic models or the periodic ab initio Hartree-Fock code CRYSTAL. The most weakly bound forms of the surface oxygen appear to be located at the (111) face on the cerium cations which have complex defects of non-stoichiometry in the subsurface layer.

Periodic Hartree–Fock study of the adsorption of molecular oxygen on a reduced TiO2 (110) surface

We present a theoretical analysis of O2 adsorption on a reduced TiO2 (110) rutile surface, based on periodic ab initio Hartree–Fock calculations. Three different orientational approaches, three different spin symmetries, and two different adsorption sites are considered. We also consider the possibility that the surface can absorb more than one oxygen molecule. Positions of the surface ions, oxygen ions belonging to the third and fourth layers of the slab, and the bond lengths of the O2 and O2-substrate distances are optimized. Adsorption energies, admolecule-substrate bond lengths, spin densities and Mulliken charges are analyzed. The model is tested by comparing spin densities and relaxation parameters obtained for the reduced TiO2 (110) system to previous theoretical results. Finally, we discuss the relationship of our results to experimental observations of thermal desorption rates at low temperatures (100–600 K).

CO/MgO(0 0 1) at different CO coverages: a periodic ab initio Hartree–Fock and B3-LYP study

The adsorption of CO at various coverages on the regular MgO(0 0 1) surface has been studied using a rigorous ab initio approach based on the solution of the periodic Schrödinger equation at both Hartree–Fock and DFT levels. The crystal orbitals are expanded in Gaussian atomic orbitals and the Coulomb and exchange series are treated rigorously as implemented in the crystal-98 computer code, ensuring the correct behavior of electric field outside the crystalline surfaces. For DFT calculations, the B3-LYP functional coupled with Gaussian basis sets of high quality for periodic calculations have been adopted. Three different CO coverages (namely 1×2(CO×Mg), 1×4 and 1×8) have been considered. Because of the very small binding energies (BEs), a careful analysis of the effects of the basis set superposition error as well as the computation of the harmonic CO frequency shift with numerical procedures of better quality than in the past have been carried out. Comparison with the results obtained for the CO/Na + and CO/CO 2 complexes has also been made in order to clarify the bonding at ionic surfaces. Neither charge transfer nor polarization play a significant role, and the weak BE results from a large cancellation between electrostatic and exchange repulsion components as formerly suggested by accurate cluster calculations embedded in total-ion ab initio model potential. Our best binding energy and CO frequency shift are still underestimated with respect to the most updated experimental data and in good agreement with the best data from embedded cluster calculations. The disagreement with experiment seems to suggest that the dispersive contribution to the BE, unfortunately not accounted for by the Hamiltonians encoded in the available computer periodic codes, may play an important role to reconcile the data of computer simulation with those from experiment.

Direct wide band gap material: a Hartree–Fock study of α-Be 3N 2

The ground state electronic structure of the beryllium nitride alpha phase has been investigated using the all-electron ab initio periodic Hartree–Fock (HF) approach, with a posteriori density-functional (DFT) correlation corrections. The computed HF lattice constant (8.144 Å) agrees with experiment (8.145 Å) and the calculations predict a bulk modulus of 2.52 Mbar and cohesive energy of 1.24 a.u./formula unit. The band gap is found to be direct of 4.43 eV at the Γ point, including corrections with DFT. This material might have application in the area of optoelectronics.

Lower order atomic multipole moments of the oxygen atoms of “small size” H-form aluminosilicate frameworks

The geometries of all possible SiO(H)Al Brönsted centres within five hydrogen form (H-form) aluminosilicate frameworks, ABW, CAN, CHA, EDI, and NAT, were optimised using a full periodic ab initio Hartree–Fock LCAO scheme at the STO-3G level. A distributed multipole analysis (DMA) was then applied at the ps-21G ∗(Al, Si)/6-21G ∗(O, H) level in order to obtain the multipole moments. Simple analytical approximations of the dependence of the Mulliken charges and atomic dipole moments with respect to the average bond distance, the anisotropy between the AlO and SiO distances, and the SiOAl angle for all crystallographically independent types of oxygen atom were derived on the basis of all optimised models. The nuclear quadrupole coupling constants for 17O are calculated for all oxygen positions and compared to the experimental values measured for zeolites A, LSX, and Y.

Cumulative coordinates for approximations of high‐order atomic multipole moments in aluminosilicate and aluminophosphate sieves*

AbstractA scheme to obtain approximate analytical functions for the atomic distributed multipole moments of the crystallographically different atoms within aluminosilicate and aluminophosphate sieves is discussed. Respective atomic multipole moments are derived within the CRYSTAL95 ab initio periodic Hartree–Fock code with different basis sets, from minimal STO‐3G to 6‐21G*. In order to illustrate the possible applications, distributed analyses are carried out for various structural models from all‐siliceous zeolites and aluminophosphates with ratio Al/P=1 to hydrogen forms of aluminosilicates. Simple approximate forms based on charge and geometry coordinates are proposed for the high‐order moments of each atom, which are further required for the calculation of the electrostatic field within the structures. The possibility to use this analytical approach to evaluate the electrostatic field within embedded cluster models is also shortly discussed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 70–85, 2001

Basis set choice and basis set superposition error (BSSE) in periodic Hartree–Fock calculations on molecular crystals

Periodic ab initio Hartree–Fock calculations on molecular crystals using the CRYSTAL programs are increasingly common, but to date basis set choice for these calculations seems to have been dictated more by convention rather than an informed choice from numerous alternatives. This work compares the use of basis sets built on 6-21G and 6-31G molecular basis sets with one double-zeta alternative. We show that the use of unmodified DZP basis sets is not only routinely possible, but results in substantially smaller basis set superposition error in the estimation of lattice energies. Through atomic calculations we demonstrate that, in part, this can be attributed to inherent deficiencies in the 6-21G and 6-31G basis sets, namely the constraining of valence s and p exponents to be equal. The analysis also sheds some light on the frequently cited but often poorly understood numerical instabilities that occur in calculations on some molecular crystals with the 6-31G basis set.

Quadrupole coupling constants CQQ for 2H, 27Al, and 17O atoms calculated at the periodic Hartree–Fock level for understanding the geometry of H‐form aluminosilicates

AbstractThe coordinates of crystallographically different atomic types of Si–O(H)–Al Brönsted centers within five H‐form aluminosilicate frameworks—ABW, CAN, CHA, EDI, and NAT—were optimized using a full periodic ab initio Hartree–Fock scheme at the STO‐3G level. Single‐point calculations were then carried out at the ps‐21G* (Al, Si)/6‐21G*(O, H) and 6‐21G*(Al, Si)/6‐21G*(O, H) levels to obtain the 2H, 27Al, and 17O respective nuclear quadrupole coupling constants and electrostatic field gradient anisotropies. The latter are discussed and compared to the experimental values measured for different zeolites. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 182–192, 2001

Ab initio 2-D periodic Hartree-Fock study of Fe-substituted lizardite 1 T - a simplified cronstedtite model

A 2-D periodic ab initio Hartree–Fock LCAO study was performed on Fe-substituted 1:1 sheet silicate, lizardite. The atomic orbitals were described by large-core pseudopotentials (Fe atoms) and a sp basis set (the other atoms). Calculated atomic charges and the results of bond population analysis indicate that the Fe-O bond was as ionic as the Mg-O. This hypothesis was supported by calculated density of states and electron density maps. Increasing Fe for Mg substitution changed the shape of projected density of states (PDOS) of O(p) orbitals.

Ab initiostudy ofMF2(M=Mn,Fe,Co,Ni)rutile-type compounds using the periodic unrestricted Hartree-Fock approach

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the groundstate structural, electronic, and magnetic properties of the rutile-type compounds MF2 ( M5Mn, Fe, Co, and Ni!. All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the @001#, @111#, and @100 #~ or @010#! directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed. Several transition-metal ~TM! oxides and fluorides crystallize in the rutile-type structure, which is the simplest and most common MX 2 structure, where each M atom is octahedrally coordinated by the X ligands. Slight distortions of the MF6 structural units are present due to electrostatic and/or Jahn-Teller effects. The physical properties of the TM compounds with rutile-type structure vary considerably: from ionic or covalent insulators to metals, from diamagnetic to strong ferromagnetic or antiferromagnetic semimetallic or insulating systems. This feature is a challenge to modern theoretical methods. In this context a series of compounds whose physical properties exhibits a smooth variation from one member to the other provide a suitable test of theory. This is precisely the case of the MF2 ( M5Mn, Fe, Co, and Ni! family of ionic compounds in which the interplay between structural parameters, chemical bonding, and magnetic coupling may be expected to display such a smooth variation. Two different ab initio periodic approaches are commonly used in solid-state physics to study TM compounds: the Hartree-Fock, 1,2 and the density-functional ~in its local or gradient corrected variants 3 ! schemes. In the latter both the exchange and correlation parts of the electron-electron interaction are taken into account in an approximate way. In the former the electron exchange part is treated exactly while electron correlation is neglected. When the spin-unrestricted form of the Hartree-Fock approach ~UHF! is used in the study of insulating magnetic systems, the correct sign and a reasonably good description of the magnitude of the magnetic coupling constants usually results. The ab initio UHF

Interpretation of scanning probe microscope image of the structure of atomic vacancy on graphite: ab initio periodic Hartree–Fock calculations

By using the CRYSTAL 95 program, ab initio periodic Hartree–Fock (PHF) calculations with the full potential and 6-21G∗ basis set are applied to the interpretation of scanning tunneling microscope (STM) and atomic force microscopy (AFM) image of the structure of atomic vacancy in graphite. Our results show that change in the total electron density when compared with the ideal structure is considerable at the missing atom site, but it is not considerable beyond a distance upon the missing atom site. However, the partial charge density, which originates from the states near the Fermi energy is enhanced at the atoms surrounding the vacancy. These results are in a good agreement with those of Hahn et al. (Phys. Rev. B 53 (1996) R1725), who take that vacancies are transparent in AFM but imaged as surface protrusions in STM. In conclusion, our results should clarify the reason why vacant sites of graphite are visible shown in STM, while they are not easy to detect in AFM.

Periodic Hartree–Fock study of the adsorption of formic acid on ZnO( [formula omitted

Adsorption of formic acid (HCOOH) on ZnO( 10 10 ) surfaces has been investigated by means of quantum-chemical ab initio periodic Hartree–Fock calculations. One `bridging' structure, characterized by a formate anion symmetrically bonded via its two oxygens to two surface Zn atoms and the acidic proton bound to a surface oxygen, and two `unidentate' structures, characterized by one Zn surf–O ads bond and the acidic proton bound to a surface oxygen, were investigated. It was found that a tilted bridging geometry represents the most stable adsorption mode, with an adsorption energy of 52.4 kcal/mol. A bridging structure tilted by 15° is energetically favourable compared to an upright bridging structure by 6.9 kcal/mol, which makes the bridging adsorption mode 6.3 kcal/mol more favourable than the most stable unidentate adsorption mode. The dependence of the adsorption energy on the surface coverage was also investigated. In addition, the structures of the ZnO bulk and of the clean surface have been calculated.

Ab initio study of ground and excited states of NiO(100) monolayer

Ab initio periodic Hartree-Fock calculations are reported of ground and dd excited states of an unsupported NiO(100) monolayer in the ferromagnetic, ferrimagnetic, antiferromagnetic and fully frustrated spin alignments as a function of the lattice constant. The ground state is found to be highly ionic and insulating with a minimum energy lattice constant of 4.0 Å. The Ni(d8) configuration is [(xz)2(yz)2(xy)2(z2)1(x2-y2)1], as found previously for the bulk, despite the reduced dimensionality leading to a reduction in the number of nearest neighbours and difference in the ligand-field ordering. The valence band DOS resembles closely that of the bulk with a majority weight of O(p) states at the upper edge leading to a charge-transfer system. The Ni d states occur ~1 eV below the O(p) band and are dispersed over ~4.5 eV in three distinct sub-bands. The relative stability of the four spin alignments is antiferromagnetic > ferrimagnetic > ferromagnetic > fully frustrated, with differences in energy of 10.779 meV, 10.017 meV and 1.675 meV respectively at 4.0 Å. Values of -0.84 meV and -10.78 meV can be deduced for the direct spin-spin, Ed, and superexchange, Ese, interaction energies respectively, which compare with values of -1.5 meV and -7.0 meV found previously for the bulk at a lattice constant of 4.265 Å. Ese is found to decrease rapidly to -3.66 meV at 4.5 Å, unlike Ed which remains fairly constant. This reduction in Ese is attributed largely to the increase in the band gap of the monolayer compared with the bulk. For the ferromagnetic spin alignment at 4.0 Å variationally converged solutions have been obtained for the one-electron dxydz2, dxydx2-y2 and spin-forbidden dx2-y2dz2 excited states and the two-electron dxy/dyzdz2/dx2-y2 excited state with excitation energies of 1.16 eV, 1.09 eV, 1.84 eV and 1.79 eV respectively. These are close to values that have been deduced from optical and EEL spectra and high-level cluster calculations. Converged solutions for the dxydz2 excited state in the ferromagnetic alignment have been obtained for the concentration range 1-4 excited states per 2 × 2 unit cell and in the other spin alignments for complete excitation at lattice constants from 3.9 to 5.0 Å. These show dxydz2 excitations, and by implication other dd excitations, to be highly local with an interaction energy of <0.1 eV per excitation at saturation, to be independent of the spin alignment and to increase slightly with lattice constant. The favourable arrangement of the nearest neighbour unpaired spins in the dxydz2 excited state leads to values of Ed, the direct spin-spin coupling energy, which are an order of magnitude greater than the ground state values and appreciably in excess of the bulk value. Ese, on the other hand, remains approximately the same. The first ionized state is found to be essentially d8, as it is in the bulk, with strong localization of the hole in a p orbital of a single O atom and retention of the local Ni moments. By direct analogy with the changes in the oxygen k-edge spectrum of LixNi1-xO the band gap in the NiO(100) monolayer is estimated to be ~5.3 eV from the gap between the hole band and the conduction band edge. The first electron addition state is found to be essentially d9[(dz2)2]. The energy of the single charge-transfer excitonic state of a 2 × 2 unit cell is estimated to be to be ~5.6 eV, in close agreement with the band gap deduced from the DOS of the first ionized state.

VOH center in magnesium oxide: an ab initio supercell study

The V OH trapped-electron-hole center in magnesium oxide is studied with the periodic ab initio Hartree–Fock program crystal by using the supercell scheme. The H atom that formally is substituted for a Mg atom at its lattice position migrates towards one of the neighboring O atoms, forming a strong covalent bond with it, whereas the hole localizes at the opposite O atom completely. The electronic structure of the defect is discussed in terms of electron charge and spin density maps and band structure. The isotropic and anisotropic components of the hyperfine coupling constant between the H nucleus and the unpaired electron are calculated and are in quite good agreement with ENDOR results.

Theoretical study of the termination of the Fe 3O 4 (111) surface

Ab-initio periodic Hartree–Fock calculations for the structure of the (111) surface of Fe 3O 4 (magnetite) are presented. The slabs that are derived by an ideal bulk truncation that leaves one or two iron monolayers outside oxygen layers are found to be more stable than others since they preserve most of the coordination of the surface atoms. The stability of the slabs that represent the surface layers depends on the overall composition, specifically on the deviation from stoichiometry, and on the dipole moment perpendicular to the surface. The symmetrical slab with the layer sequence Fe 2O 4Fe 3O 4Fe 2, terminated on each side by iron bilayers, is the best compromise since symmetry insures the neutrality of the dipole moment. This slab is oxygen-deficient. The energetically preferred structure relaxes so that one of the two outermost iron layers moves toward the slab center plane, exchanging sequence with the oxygen layer. The slab with the layer sequence FeO 4Fe 3O 4Fe, which is also symmetric, is terminated by iron single monolayers, would represent an excessive oxidation of the iron atoms. This slab may be reduced by hydrogenation; it is then strongly stabilized and the vertical displacement of the oxygen atoms agrees with the structure determined by LEED (the LEED study would not have detected hydrogen).