Hartree-Fock Cluster Calculations Research Articles

Electron transport via polaron hopping in bulkTiO2: A density functional theory characterization

This work focuses on the intrinsic electron transport in stoichiometric $\mathrm{Ti}{\mathrm{O}}_{2}$. Electron hopping is described by a polaron model, whereby a negative polaron is localized at a ${\mathrm{Ti}}^{3+}$ site and hops to an adjacent ${\mathrm{Ti}}^{4+}$ site. Polaron hopping is described via Marcus theory formulated for polaronic systems and quasiequivalent to the Emin-Holstein-Austin-Mott theory. We obtain the relevant parameters in the theory (namely, the activation energy $\ensuremath{\Delta}{G}^{*}$, the reorganization energy $\ensuremath{\lambda}$, and the electronic coupling matrix elements ${V}_{AB}$) for selected crystallographic directions in rutile and anatase, using periodic density functional theory $(\mathrm{DFT})+U$ and Hartree-Fock cluster calculations. The $\mathrm{DFT}+U$ method was required to correct the well-known electron self-interaction error in DFT for the calculation of polaronic wave functions. Our results give nonadiabatic activation energies of similar magnitude in rutile and anatase, all near $\ensuremath{\sim}0.3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The electronic coupling matrix element ${V}_{AB}$ was determined to be largest for polaron hopping parallel to the $c$ direction in rutile and indicative of adiabatic transfer (thermal hopping mechanism) with a value of $0.20\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, while the other directions investigated in both rutile and anatase gave ${V}_{AB}$ values of about one order of magnitude smaller and indicative of diabatic transfer (tunneling mechanism) in anatase.

Theory of Isotope Effects on He + Trapping in Solid Hydrogen

We are currently investigating the influence of vibrational effects on the strength of trapping of He+ in solid hydrogen. Such effects can lead to an isotope dependence of the trapping energy associated with the hydrogen molecules and He+ ion. At the present time, our focus is on the isotope effect for 3He+ and 4He+, which we are studying through the vibrational motions of the trapped He+ ions in the potential they experience as they move about their equilibrium positions. The potential governing the vibrations has been obtained from Hartree–Fock cluster calculations of the total energy of the cluster composed of the He+ ion and up to the third nearest neighbor hydrogen molecules as a function of the displacement of the He+ ion from its trapped position. The energy eigenvalues for the ground vibrational states of 3He+ and 4He+ in this potential come out as 1.29 and 0.96 meV, respectively, leading to corresponding reductions by these amounts in the binding energy of 8.6 eV for both ions without vibrational effects. The difference of these reductions can be considered as an isotope shift, its value for this case being 0.33 meV. From the analysis for these results, it is suggested that isotope shift effects for deuteron and triton in solid D–T would have the same order of magnitude. A procedure for more accurate investigations of the isotope shifts is discussed.

What is the role of the oxygen atoms of the CuO chains in the high- T c superconductivity of YBa 2Cu 3O 7−δ?

For the YBa 2Cu 3O 7 and YBa 2Cu 3O 6 systems ab initio Hartree-Fock cluster calculations have been performed using a self consistent Madelung potential for the rest of the crystal and periodic boundary conditions. Surprisingly the charge transferred (∼1.0 e) to the CuO 2YCuO 2 subsystem and the charge distribution there show no changes by removal of an oxygen atom from the CuO chain. This points besides chain-superconductivity (which is verified by recent experiments) also to the possibility that the well established hole superconductivity in the CuO 2 planes of (1 2 3) may not originate from hole doping from the CuO chains. Experimental conductivity measurements in the normal state of the (1 2 3) system shows also that the charge transport occurs dominantly along the chain directions.

Model-dependent electronic structure of the Si(111)2 x 1 surface.

We have used the pseudopotential density-functional total-energy scheme to study the atomic and electronic structure of the Si(111)2\ifmmode\times\else\texttimes\fi{}1 surface: we examine and compare in detail both the standard Pandey's \ensuremath{\pi}-bonded chain (PC) model and the alternative three-bond scission (TBS) model including their variations. We find that while the PC model is acceptable both in energetics and in spectroscopic examination, the TBS model is energetically unfavored (0.25 eV/surface-atom higher in energy than the PC model) and does not agree in band structure with experiments. This differs from the result of the recent Hartree-Fock cluster calculations where the TBS model produces the experimental band structure. We also find that the reverse-buckled PC model is as favored in energetics as the PC model, and its band structure is also compared well with experiments. The physical relevance of the reverse-buckled PC model and the TBS model is discussed in connection with some unresolved questions concerning this surface. \textcopyright{} 1996 The American Physical Society.

Lattice dynamics and hyperfine interactions in ZnO and ZnSe at high external pressures.

The II-VI semiconductors ZnO and ZnSe have been investigated by x-ray and $^{67}\mathrm{ssbauer}$ spectroscopy at high external pressures. In ZnSe, the recoilfree fraction f increases from f=0.50% at ambient pressure to 1.19% at 6.1 GPa. It then decreases to f=0.92% as the pressure is further raised to 8.2 GPa. This decrease of f is caused by softening of phonon modes which occurs far below the crystallographic phase transition (13.5 GPa). In the high-pressure phase of ZnO (NaCl structure), low-frequency acoustic-phonon modes become harder and high-frequency optic modes become softer as compared to ZnO (wurtzite structure). Modern theoretical Hartree-Fock cluster and full potential scalar-relativistic linearized-augmented plane-wave calculations have been performed. These calculations reveal that in both systems covalent contributions to the chemical bond determine the change of the s electron density \ensuremath{\rho}(0) at the Zn nucleus between the different crystallographic phases as well as the electric-field-gradient tensor in ZnO (wurtzite). In particular, \ensuremath{\rho}(0) in ZnO (NaCl phase) is reduced compared to \ensuremath{\rho}(0) in ZnO (wurtzite phase) by -1.15e/${\mathit{a}}_{0}^{3}$. Thus, contrary to observation for ZnSe, the electrical conductivity in ZnO (NaCl phase) is not expected to increase in comparison with the low-pressure wurtzite structure. \textcopyright{} 1996 The American Physical Society.

Hartree-Fock study on the lower excited states of a Cu + impurity in NaF using large embedded clusters

We report spin-restricted and symmetry-restricted Hartree-Fock cluster calculations on the lower excited states of a Cu + impurity in NaF in order to investigate their dependence on cluster size. In contrast to previous work on smaller clusters, we found all states arising from the configurations e g 4t 2g 5a 1g 1 and e g 3t 2g 6a 1g 1 to be local. Delocalization can occur when an unbalanced choice of cluster and set of embedding point charges is made. These results confirm the local perspective from which previous spectroscopic assignments have been made. However, the inconsistency with the results from OD-EPR spectra remains.

67Zn-Mössbauer study of nanostructured ZnO

Using the 93.31 keV Mossbauer transition in67Zn we have investigated hyperfine interactions and lattice-dynamic effects of nanostructured hexagonal (wurtzite) ZnO. The nanocrystals with particle sizes between 3 and 30 ran were produced by a reactive-gas sublimation method and were subsequently compacted into solid bodies under external pressure. The nanocrystalline materials were used as sources in Mossbauer emission experiments. A drastic increase of the asymmetry parameter was found fromη=0 (single crystal) toη≈0.5 (nanostructured material). Our theoretical Hartree-Fock cluster calculations show that displacements of the Zn atoms off the hexagonal symmetry axis as small as 0.005 A can lead to such enhancedη parameters. The Lamb-Mossbauer factorf drastically drops when the particle size is reduced below ∼ 10 nm. Two lattice-dynamic models are discussed which successfully describe this behavior.

An ab initio Hartree-Fock study of the [formula omitted] adsorption system

The adsorption of boron onto the Si(001)2 × 1 surface is studied at 0.5 monolayer (ML) coverage using the linear combination of atomic Orbitals (LCAO) pseudopotential Hartree-Fock method for periodic systems embodied in the CRYSTAL program. Four stable structures are determined within a range of 0. 13 Hartree (2 × 2 surface unit cell) . The minimum energy configuration is an ad-dimer on-top configuration in which the B dimers are oriented parallel to the adjacent Si dimers. The only stable structure exhibiting a 2 × 1 surface periodicity is one in which the boron lies just below the surface. These results are compared with ab initio Hartree-Fock cluster calculations and with experimental data.

Electronic structure of Zn in oxide spinels

Using67Zn Mossbauer absorption and emission spectroscopy, we have investigated the electronic structure at the A and B sites in the normal spinels (Zn)[Al2]O4, (Zn)[Fe2]O4 and (Zn)[Ga2]O4. Within each system, the center shift Sc at the A site is more positive. In all systems investigated, the electric field gradientV u at the B site is negative. The values for SC andV U scale with oxygen nearest-neighbour distance to Zn. In the Fe spinel, a transferred magnetic hyperfine field is observed at the Zn site below the antiferromagnetic ordering temperatureTN=10 K. For a more detailed discussion of the chemical bond, we have performed ab initio Hartree-Fock cluster calculations for the Al and Fe spinels. Our experimental and theoretical results show that all hyperfine parameters are essentially determined by covalency effects. Our data on the Ga spinel raise the question of a partially inverse structure.

Investigation of electronic structure and anisotropy of the Lamb-Mössbauer factor in ZnF2 single crystals

Using the 93.3 keV resonance in67Zn the isomer shift, the quadrupole interaction, and the anisotropy of the Lamb-Mossbauer factor (LMF) in ZnF2 single crystals have been investigated. The main component of the electric field gradient (efg) tensorVzz=+(2.18+-0.22)×1017V/cm2 andη=0.29±0.03 are derived.Vzz is oriented perpendicular to the crystallographicc axis. The anisotropy of the LMF is large:fx=(2.4±0.1)%,fy=(2.3±0.2)%, andfz=(1.4±0.2)%. Ab initio Hartree-Fock cluster calculations gave a detailed description of the observed charge distribution including the orientation of the efg tensor. Using a force constant model (shell model), we solved the eigenvalue problem of the dynamic matrix and quantitatively reproduced the anisotropy of the LMF.

High-pressure phase transition in ZnSe

A high-pressure Mossbauer spectrometer for the 93.3-keV resonance in67Zn and an X-ray diffractometer of the Guinier type are used to investigate67ZnSe powder at high external pressures. At ∼ 13 GPa, a phase transition from the zinc blende to the fcc (NaCl) structure is observed. The transition is accompanied by a 15.2% decrease of the volume of the unit cell. The Lamb-Mossbauer factor (LMF) increases fromf=0.53% at ambient pressure tof=1.07% at 6.1 GPa. It thendecreases tof=0.91% as the pressure is further increased to 8.2 GPa. This behavior is investigated by lattice-dynamical calculations using an 11-parameter rigid-ion model. The decrease of the LMF at high pressures is caused by the softening of the TA phonon modes, which occurs already far below the phase transition. The s-electron density ρ(0) at the67Zn nucleus increases with reduced volume. The change of ρ(0) as well as theoretical Hartree-Fock cluster calculations show that covalency of bonding 4s/4p states of Zn and Se plays an essential role and determines the isomer shift.

Investigation of the Ligand Exchange Reaction for the Aqueous Be2+ Ion

The geometry and energy of the transition state for the exchange of water-coordinating Be{sup 2+} in aqueous solution has been investigated by Hartree-Fock (HF) cluster calculations, which include the ion and its near-neighbors. The calculated activation parameters, {Delta}V* and {Delta}H*, are compared to the spectroscopic values. The HF activation volume {Delta}V* was found to be approximately 0 compared to the experimental value of -13.6 cm{sup 3}/mol. The discrepancy is attributed to an incomplete description of the second coordination shell, which is needed to accurately define the volume of the transition-state complex. Including a continuum approximation for the solvent did not improve the agreement. The HF activation enthalpy for the exchange reaction, 0.65 eV, is in good agreement with the experimentally determined value of 0.61 eV. A qualitative description of the reaction mechanism has been developed from calculations on 5-fold coordinated Be{sup 2+} with one Be-OH{sub 2} distance constrained to the reaction coordinate. The results suggest a reaction scheme where the exchanging water from the second coordination shell is oriented along a 2-fold axis of the tetramer. 31 refs., 8 figs., 6 tabs.

CH 3CN⧸alkali coadsorption at metal surfaces: model studies for alkali induced adsorbate geometry changes

From near edge X-ray absorption fine structure (NEXAFS) measurements of the coadsorption of acetonitrile (CH 3CN) and K on the Au(100) surface it has been concluded that the C-N bond length in adsorbed CH 3CN is shortened by 0.13 bohr due to the interaction with the alkali coadsorbate. This conclusion was based on a “bond-length-with-a-ruler” interpretation of respective shifts of the σ CN ∗ shape resonance. In order to understand the details of the coadsorptive interaction and its consequences for molecular geometries ab initio Hartree-Fock cluster calculations are performed on CH 3CNK + model systems. Full geometry optimizations of the CH 3CN molecule with and without the coadsorbate confirm the decreased C-N bond length due to the coadsorbate interaction but the effect (0.04 bohr) is much smaller than suggested from experiment. Calculations on selected CH 3CN core-to-valence excitations (determining the NEXAFS absorption peaks) show that the presence of the K+ ion results in field induced shifts of the excitation energies which are larger than those due to geometry changes. This suggests for the CH 3CN , K Au(100) system that the observed NEXAFS peak shifts are determined by electrostatic field effects in the coadsorbate system and may not reflect actual adsorbate geometry changes.

First-principles investigation of 67Zn isomer shifts in ZnF2 and the chalcogenides ZnO, ZnS, ZnSe, and ZnTe.

All-electron, self-consistent, Hartree-Fock cluster calculations have been carried out to derive electron densities at the zinc nucleus in the series of compounds ${\mathrm{ZnF}}_{2}$ (rutile-type structure), ZnO (rocksalt structure), ZnO (wurtzite structure), and the compounds ZnS, ZnSe, and ZnTe (all with the sphalerite structure). The derived density differences show a very good linear correlation with the experimental isomer shifts. The isomer shifts and results for the densities at the zinc nucleus have been combined to calculate a value for the change of the mean-square nuclear charge radius for the M\"ossbauer transition in $^{67}\mathrm{Zn}$ of \ensuremath{\Delta}〈${\mathit{r}}^{2}$〉=+(13.9\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ ${\mathrm{fm}}^{2}$. Our calculations clearly show the importance of the covalency of the Zn-ligand bond for the origin of the isomer shift and fully corroborate the experimental linear correlation between decreasing isomer shift values and increasing electronegativity of the ligands. The most important contribution to the electron-density differences at the zinc nucleus comes from the Zn(4s) electrons with a smaller but significant contribution from the Zn(3s) electrons appearing to arise primarily from the repulsive influence of the ligand-ion orbitals.

A theoretical study of H-centre migration in alkali halide crystals KCl and NaCl

Abstract Two different theoretical techniques, ab initio Hartree-Fock cluster calculations, and that of atom-atom potentials, as implemented in the CASCADE code, are employed for simulating on-site and saddle-point positions of primary Frenkel defects (H centres) in NaCl and KCl crystals. In both types of calculations H centres are found to be oriented along , which agrees with experimental data for NaCl but contradicts that for KCl. Reasons for the latter result are discussed. The activation energy for H-centre migration obtained by both methods agrees with experiment. The conformation of the saddle point is analysed.

Monolayer chemisorption of HCl and Cl 2 on the Si(001)2 × 1 surface

In an earlier paper results were reported for monolayer chemisorption of HCl, Cl 2 and F 2 onto the Si(001) surface. It has now been discovered that the Cl interactions were not treated correctly in these SLAB-MINDO molecular orbital calculations. The main purpose of this Letter is thus to present the corrected results for both HCl and Cl 2 chemisorption. Dangling bond configurations are now found to represent the lowest energy configurations for both chemisorption processes. This is in contrast to the previously published results in which a bridge site-topology was determined to be the minimum energy structure for Cl 2 chemisorption onto the Si(001)2 × 1 reconstructed surface. These new results are shown to be in good agreement with self-consistent ab-initio Hartree-Fock cluster calculations, with the first-principles local-density calculations of Kruger and Pollmann, and with experiment.

Monolayer chemisorption of HCl and Cl 2 on the Si(001)2 × 1 surface

In an earlier paper results were reported for monolayer chemisorption of HCl, Cl 2 and F 2 onto the Si(001) surface. It has now been discovered that the Cl interactions were not treated correctly in these SLAB-MINDO molecular orbital calculations. The main purpose of this Letter is thus to present the corrected results for both HCl and Cl 2 chemisorption. Dangling bond configurations are now found to represent the lowest energy configurations for both chemisorption processes. This is in contrast to the previously published results in which a bridge site-topology was determined to be the minimum energy structure for Cl 2 chemisorption onto the Si(001)2 × 1 reconstructed surface. These new results are shown to be in good agreement with self-consistent ab-initio Hartree-Fock cluster calculations, with the first-principles local-density calculations of Kruger and Pollmann, and with experiment.

Stability of Transition-Metal Impurities in Ionic Fluorides from Approximate Hartree-Fock Cluster Calculations

The location of the 3d levels of 10 transition-metal impurities in the band gaps of four ionic fluorides has been investigated by independent Hartree-Fock (HF) cluster calculations on open-shell M Fn-6 systems [M = Crz+ (z = 1-3), Mnz+ (z = 1-3), Fez+ (z = 1-2), and Vz+ (z = 2-3)] and closed-shell AFn-6 systems (A = Li+, Na+, Mg2+ and Zn2+). The variation of the 3d orbital energies of the impurities with the M-F distance has been deduced from the corresponding MFn-6 calculations at different cluster sizes. The band gap edges for LiF, NaF, KMgF3, and KZnF3 have been estimated from the A Fn-6 calculations: the highest occupied level has been estimated from HF orbital energies of the 1A1g ground state, and the lowest unoccupied level, from HF orbital energies of the first excited 3T1u state. These orbital energies have been combined to prepare approximate energy-distance diagrams that describe the location of the 3d impurity levels relative to the band gap of the host crystal. The diagrams give very valuable information on the stability of the 3d impurity in the host and the probable lattice relaxation induced upon impurity substitution. Such information is difficult to obtain either experimentally or by means of large-scale quantum-mechanical calculations.

A theoretical comparison of CO bonding on the Fe(100) surface

Unrestricted Hartree-Fock (UHF) cluster calculations with the Constrained Space Orbital Variation (CSOV) analysis are used to compare the bonding in vertical on-top, vertical bridging and tilted CO on the Fe(100) surface. Large charge transfers and strong back donation effects are found in the tilted CO cluster consistent with the expectation that this structure is a precursor to CO dissociation. The UHF calculations also reveal that mainly minority spin Fe d electrons are donated to the CO π ∗ orbitals. A qualitative interpretation of the recent spin polarized photoemission spectra for tilted CO on Fe(100) is presented.

A theoretical comparison of CO bonding on the Fe(100) surface

Unrestricted Hartree-Fock (UHF) cluster calculations with the Constrained Space Orbital Variation (CSOV) analysis are used to compare the bonding in vertical on-top, vertical bridging and tilted CO on the Fe(100) surface. Large charge transfers and strong back donation effects are found in the tilted CO cluster consistent with the expectation that this structure is a precursor to CO dissociation. The UHF calculations also reveal that mainly minority spin Fe d electrons are donated to the CO π ∗ orbitals. A qualitative interpretation of the recent spin polarized photoemission spectra for tilted CO on Fe(100) is presented.