Hartree-Fock Cluster Research Articles

First-Principles Study of Arsenic Atom, Its Irons and Molecule

In the present work, we have performed the ground state energy calculations for arsenic atom, its ions and molecule using Hartree-Fock (HF) cluster approximation. The correlation effects in the HF calculations have been taken into account by considering the Møller-Plesset second order perturbation (MP2) and truncated form of Configurational Interaction (CI) that includes single, double, and quadruple excitations, also known as QCISD implemented by the Gaussian 03 sets of program. Our study shows that the ground state of arsenic atom is a quadrate state i.e., charge zero and multiplicity four with ground state energy - 60796.66 eV in MP2 levels of calculation with cc-pVDZ basis set. We have performed the first-principles calculation to study the first electron affinity and ionization energies of arsenic atom up to tenth level. The first-principles calculation has been also carried out to study the equilibrium configuration of arsenic molecule (As2). The bond length and binding energy of arsenic molecule (As2) is found to be 2.15 Å and 3.65 eV in MP2 levels of approximation with basis set 6-311G(3df). Our study has been extended to calculate electrostatic potential for arsenic molecule (As2), whose values at global maxima and minima are found to be 0.30 eV and - 0.20 eV respectively. The calculation of HOMO-LUMO energy gap for the arsenic molecule (As2) is almost independent of choice of basis sets as well as levels of approximation. The HF, MP2, and QCISD calculations also have been carried out to estimate the electric field gradient (EFG) parameters for the excited nuclear state in arsenic molecule (As2). Our results show that the HF, MP2, and QCISD values for the EFG parameters do not differ significantly, indicating that electron correlation effects do not contribute for the determination of EFG parameter.The Himalayan Physics Year 5, Vol. 5, Kartik 2071 (Nov 2014)Page : 17-21

Electron Exchange and Conduction in Nontronite from First-Principles

Fe-bearing clay minerals serve as an important source and sink for electrons in redox reactions in various subsurface geochemical environments. We apply first-principles calculations using a small polaron hopping approach and Marcus electron transfer theory to examine electron exchange mobilities in an Fe-rich smectite, nontronite Fe2Si4O10(OH)2. GGA+U calculations provide rates of electron hopping that agree very well with values deduced from variable-temperature Mossbauer data (Schaefer et al. Environ. Sci. Technol.2011, 45, 540), indicating a surprisingly fast electron mobility at room temperature. Evaluation of the electron transfer (ET) rates within the Hartree–Fock cluster framework for the Fe2+/Fe3+ electron hopping in tetrahedral (TS) and octahedral sheets (OS), as well as across the sheets (TS–OS), shows that the dominant contribution to the bulk electronic conductivity should come from the ET within the OS. Deprotonation of structural OH groups mediating ET between the Fe ions in the OS is found...

Scalar-relativistic 5f-in-core pseudopotentials and core-polarization potentials for trivalent actinides: calibration calculations for Ac3+, Cm3+ and Lr3+ complexes

The performance of recently proposed 5f-in-core pseudopotentials for the trivalent actinides was investigated in calculations for model complexes An3+Ln− for three selected actinides (An3+ = Ac3+, Cm3+, Lr3+) and eight simple ligands with atoms from the first three periods of the table of elements (Ln− = F−, Cl−, OH−, SH−, CO, NH2−, H2O, H2S, NH3). Results of Hartree-Fock and Coupled Cluster with singles, doubles and perturbative triples calculations using basis sets of quadruple-zeta quality are compared to corresponding reference data obtained with scalar-relativistic energy-adjusted 5f-in-valence small-core pseudopotentials. The inclusion of core-polarization potentials in the 5f-in-core pseudopotential calculations and corrections of the basis set superposition error by the counterpoise correction leads to very good agreement between the 5f-in-valence and 5f-in-core pseudopotential results for bond lengths, bond angles and binding energies. Results from 5f-in-core pseudopotential calculations using different density functionals also show reasonable agreement with the more rigorous Coupled Cluster results. It is argued that the An 5f rather than the An f population is a useful criterion for the applicability of a specific An 5f-in-core pseudopotential.

First-principles study of location of Er3 + ion—relationship to understanding of hyperfine interactions in the optoelectronic erbium–silicon system

The importance of hyperfine interactions in the Erbium-Silicon system is underscored by our first-principles Hartree-Fock Cluster investigations on the location of Erbium in Silicon. Our theoretical studies show that both substitutional and tetrahedral interstitial sites are stable for Er3+ ion with the latter having a larger binding energy. This conclusion is not completely supported by channeling experiments. It is suggested that Mossbauer measurements on 166Er isotope would be valuable to compare experimental results with theoretical predictions of the hyperfine interactions of both magnetic and quadrupolar types to provide additional information about the location of Er3+.

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.

Understanding of nuclear quadrupole interactions of 35 Cl, 79 Br and 129 I and binding energies of solid halogens at first-principles level

This paper deals with the understanding at a first-principles level of the nuclear quadrupole interaction (NQI) parameters of solid chlorine, bromine and iodine as well as the intermolecular binding of these molecules in the solid. The electronic structure investigations that we have carried out to study these properties of the solid halogens are based on the Hartree-Fock Cluster approach using the Roothaan variational procedure with electron correlation effects included using many-body perturbation theory with the empty orbitals used in the perturbation theory investigations for the excited states. The results of our investigations provide good agreement with the measured NQI parameters primarily from the Hartree-Fock one electron wave-functions with many-body effects making minor contributions. The binding (dissociation) energies for the molecules with the solid state environment on the other hand arises from intermolecular many body effects identified as the Van der Waals attraction with one-electron Hartree-Fock contribution being repulsive in nature.

Ab Initio Study of the On-Site Potential for Divalent Impurities in Dilute Sr1−x A x TiO3 Solid Solutions

The off-center impurity model for divalent impurities in SrTiO3 (Mn, Mg, Ca, Cd, Pb, Zn substituted for Sr) is checked. The results of ab initio Hartree-Fock and density functional theory (DFT) B3LYP cluster calculations of the local adiabatic potential for impurity atoms are presented. The results show that all impurity atoms, except Zn and Mg, move in single-well potentials, whereas Zn and Mg in Sr1−x A xTiO3 are found to occupy off-center positions, as does the Li in K1−xLixTaO3, and move in the six-well local potential. It is found that Mn2+ion in a high spin state moves in a flat potential well. The strong effect of electron correlations on the local potentials for Zn and Mg is revealed.

Study of muon magnetic hyperfine and nuclear quadrupole interactions and easy axis in the organic ferromagnet p-Cl-Ph-CHN-TEMPO

The first-principles Hartree–Fock cluster procedure has been used for studying the electronic structure of the organic ferromagnetic p-Cl-Ph-CHN-TEMPO (4-(p-chlorobenzylideneamino)-2,2,6,6-tetramethylpiperidin-1-yloxyl) radical system with and without positive muon or muonium. Theory is able to provide quantitative information about the trapping sites for muon and muonium and the associated muon hyperfine interaction parameters. Using this information, two sites, one with muonium trapped near oxygen in the electronic singlet state of the muonium–radical pair system involved and the other with muon trapped near chlorine, are identified as likely candidates for the source of the experimentally observed μSR frequency of 3.2 MHz from zero-field measurement. The easy axis is obtained in both cases as the b-axis in the monoclinic lattice in agreement with the results of our magnetic dipole–dipole interaction studies using the magnetic moment distributions in the ferromagnetic state in the absence of muon and muonium. Nuclear quadrupole interaction parameters for nuclei adjacent to the trapped muon and muonium have been evaluated and their role in distinguishing between alternate trapping sites is discussed.

First-principles calculation of electronic structures and hyperfine interactions for muonium centers in ZnO

The first-principles Hartree–Fock cluster method is applied to investigate the possible positions and associated hyperfine properties of the muonium centers in the II–VI semiconductor ZnO. Two clusters are used to simulate the local environments around the anti-bonding (AB) ∥ and bond-center (BC) ∥ muonium with axial symmetry along the c-axis, to try to understand the natures of the two centers whose axially symmetric hyperfine tensors have been observed experimentally. Our results show that the muonium center at the anti-bonding site close to oxygen (AB O) ∥ is more stable and its charge state is +0.44, which indicates a donor state in the semiconductor, but the associated hyperfine parameters are only in reasonable order of magnitude agreement with the experiments. The results for the (BC) ∥ center show a smaller binding energy than for the (AB O) ∥ center, and hyperfine parameters three orders of magnitude larger than the experiment but still an order of magnitude smaller than for free muonium.

Quantitative test of electronic structures of organic ferromagnet systems from first-principles investigations using muon spin rotation data

The electronic structure of the organic ferromagnet 4-(p-chlorobenzylideneamino)-TEMPO is determined by the first-principles unrestricted Hartree-Fock cluster procedure, with and without muon (μ) and muonium (Mu), and itsaccuracy is tested by investigating μ and Mu trapping sites and corresponding muon hyperfine interaction tensors. The results provide good agreement with the observed muon spin rotation frequency, site assignment, and also easy-axis direction in agreement with that from dipole-dipole interactions between the calculated distributed magnetizations in the molecules.

Theory of 14N and 17O Nuclear Quadrupole Interactions in Polyglycine and Glycine in the Protein Chain of Cytochrome c

As part of our ongoing investigations on hyperfine properties of nuclei and attached probes (like muon and muonium) in the protein chain of Cytochrome c (Cyt c), we have been studying the 14N and 17O nuclear quadrupole interactions in the amino acids in the protein chain at different sites where they occur. As a specific example of one of the amino acids in this context, we shall present our results on Glycine in the homo-molecular polymer Polyglycine and expectations for the hetero-molecular environment occurring at a particular region of the protein chain of Cyt c which is far enough away from the heme unit to make the results more characteristic of the chain. In the Polyglycine polymer, our results for the 14N and 17O coupling constants e2qQ and asymmetry parameters for a central Glycine in a chain of odd numbered molecules are used to study how the e2qQ and vary with the chain length and to compare with the results for the isolated Glycine molecule. The aim is to study the convergence of the results with respect to chain length to find out the appropriate length at which the results become characteristic of the polymer chain. This conclusion is expected to provide insights into the chain length to be used in the protein to simulate the results for the protein chain in Cyt c. The Hartree-Fock Cluster procedure is being used for the investigations for all the results to be reported

Ab Initio Investigation of Helium Bubble Formation from Trapped He+ Ions in Solid Hydrogen

We are involved in a program aimed at a first-principles examination of the possibility of helium bubble formation in solid hydrogen. Our procedure is based on an extension of the Hartree–Fock cluster approach that we have been using for study of individual He+ ions in solid hydrogen. The preliminary results of our cluster investigations of a particular configuration of two He+ ions in neighboring tetrahedral interstitial positions are presented here. It has been found that the hydrogen molecules common to the two He+ ions lead to a substantial attractive force between the ions that almost overcomes their inherent repulsion, leading to a binding energy for this configuration only slightly less than the binding energy for two well separated trapped He+ ions. The analysis of our results have suggested future investigations of different pairs of trapping sites which appear to be more favorable for providing higher binding energies for the He+ pairs.

Theoretical Study of Trapping Sites for Muon in the Heme Group of Cytochrome c and Associated Shifts in Muon Spin Relaxation Frequencies

Muon Spin Relaxation (μSR) experiments are currently being conducted on the important electron transfer molecule cytochrome c (cyt c) with the goal to find out about microscopic details of the path the moving electron is taking. Simultaneously we are using the Unrestricted Hartree–Fock Cluster Procedure to determine the trapping sites for muon (μ+) and muonium (Mu) in the heme unit of cyt c and the associated hyperfine interactions. For the trapping sites with the highest binding energies for μ+, namely the nitrogen and the carbon of the pyrrole rings, we have used the available magnetic susceptibility data together with our calculated hyperfine fields to predict the Knight-shifts. At room-temperature we found 88.4 ppm and 79.0 ppm for the most attractive N- and adjacent C-site, respectively. At 150 K, these shifts increase to 172.7 ppm for the N-site and 153.7 ppm for the C-site.

First-Principles Theory of Muon and Muonium Trapping in the Protein Chain of Cytochrome c and Associated Hyperfine Interactions

The microscopic details of the electron transfer in cytochrome c (cyt c) are being investigated by the Muon Spin Relaxation (μSR) technique. We are using the Hartree–Fock Cluster Procedure to determine the most likely trapping sites for μ+ and muonium (Mu) in the protein chain, and have performed extensive calculations in single amino acid molecules of the protein chain of cyt c. The double-bonded oxygen atom of the carboxyl group was identified as the trapping site for both μ+ and Mu. Utilizing the wave functions we obtained from the Hartree–Fock calculations, we have determined the hyperfine field that the μ+ in Mu experiences while the latter is trapped at the oxygen.

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.

Theoretical description of hole localization in a quartz Al center: The importance of exact electron exchange

The ``classical'' model of the ${[\mathrm{AlO}}_{4}{]}^{0}$ defect center in irradiated quartz, an Al impurity having replaced a four-coordinated Si atom, is that a hole forms in a nonbonding orbital of an oxygen atom, with consequent asymmetric relaxation along that particular Al-O direction. This model has been proposed years ago, based on the analysis of the electron-paramagnetic-resonance spectra of Al-containing crystalline ${\mathrm{SiO}}_{2}$ and analysis of Hartree-Fock cluster model calculations. Three recent theoretical studies based on first-principle density-functional theory (DFT) and band-structure plane-wave calculations proposed an alternative model where the hole is completely delocalized over four oxygen neighbors to the Al impurity, at 0 K. Using cluster models containing as many as 104 Si and O atoms and various theoretical approaches, we show that the delocalized picture is an artifact of the DFT approach and that a fully localized hole is obtained when an exact treatment of the exchange term is used. The validity of this conclusion is based on the direct comparison of computed and measured quantities such as the ${}^{17}\mathrm{O}$ hyperfine and ${}^{27}\mathrm{Al},$ ${}^{29}\mathrm{Si}$ superhyperfine coupling parameters, the ${}^{27}\mathrm{Al}$ nuclear quadrupole effect, and the derivable local distortion around the defect. This work shows that great care is needed when DFT is used to describe localized holes in insulators.

First-principles theoretical investigation of neutral vacancy-associated muonium center in silicon

To understand the nature of the recently discovered vacancy-associated center Mu V in silicon and its H counterpart V H, we have carried out a first-principles Hartree–Fock cluster investigation mainly on the cluster Si 4H 12Mu involving the muonium and the four silicon neighbors nearest to the vacancy in a neutral vacancy-associated environment, including lattice relaxation effects. Our results demonstrate that the neutral vacancy-associated model is able to explain the non-axial symmetry of the Mu V center through Jahn–Teller distortion and provides reasonable quantitative agreement with experimental hyperfine data.

Similarities and differences in the Hartree–Fock and density-functional description of the chemisorption bond

The similarities and differences between the ab initio Hartree–Fock (HF) and density-functional theory (DFT) descriptions of the chemisorption bond have been explored by applying the constrained space orbital variation (CSOV) method to obtain and analyze the HF and DFT total energies of cluster models representing the interaction of CO and NH 3 on Cu(100) and Pt(111). The qualitative picture of the chemisorption bond arising from ab initio HF and DFT quantum-chemical approaches is essentially the same; the relative importance of the different mechanisms remains unchanged. The main quantitative effect of electronic correlation is to increase the inter-unit charge transfer but substrate polarization is also affected. A very important consequence emerges: it is not necessary to revise the physical mechanisms that have been previously proposed from the ab initio Hartree–Fock cluster model approach.

Ab initioand semiempirical calculations ofH−centers in MgO crystals

The atomic and electronic structure of ${\mathrm{H}}^{\ensuremath{-}}$ ions substituting for ${\mathrm{O}}^{2\ensuremath{-}}$ ions in regular sites in MgO crystals are calculated using an ab initio Hartree-Fock (HF) cluster approach and its semiempirical version, intermediate neglect of the differential overlap. The theoretical optical absorption energy is predicted to be 10 eV, which is supported by analysis of experimental data for the ${\mathrm{H}}^{\ensuremath{-}}$ centers in a series of ionic crystals. The HF simulations of ${\mathrm{H}}^{\ensuremath{-}}$ ion diffusion via direct interstitial hops along the [100] axis predict an activation energy of about 3 eV.

Locations of implanted 19F* atoms in Si, Ge and diamond studied through their nuclear quadrupole interactions

The Hartree-Fock cluster procedure was used to obtain the associated electronic distributions for 19F* (I = 5/2, Ex = 197 KeV excited nuclear state of the 19F atom) at possible sites in crystalline Si, Ge and diamond and to calculate nuclear quadrupole coupling constants vQ and the asymmetry parameter η of the electric field gradient at the modelled sites. Lattice relaxation effects have been incorporated by employing a geometry optimization method to obtain minimum energy configurations for the clusters modelling each site. The intrabond (IB), antibonding (AB) and substitutional (S) sites in the bulk and the atop site on the surface were studied. From a comparison with vQ and η values observed in time differential perturbed angular distribution (TDPAD) measurements we were able to identify the high frequency component in Si and Ge with 19F* at the intrabond site. In diamond two high frequency components are observed. These are identified with 19F* at intrabond and substitutional sites. For the low frequency site in Si and Ge the assignment is made to 19F* implants at dangling bonds in the bulk resulting from implantation damage. In diamond none of the sites studied could provide lower frequency nuclear quadrupole parameters close to the observed ones.