Hartree-Fock Field Research Articles

Inner shell photoexcitation of atoms with correlation effects on autoionization : application to the argon 2p shell

For atoms with closed shells in their ground state, a Hartree-Fock (HF) equation is obtained for the electron moving in the field of an inner shell vacancy which decays through autoionization. In this equation, the following processes are taken into account: 1) change of the HF field of the remaining atom as a result of autoionization decay of the inner shell vacancy; 2) interaction of the photoelectron with a virtual Auger electron, thus the radial correlation in their movement is accounted for. The developed method is applied to study the L II,III -photoexcitation in Ar atom

The electronic structure of Ca@C 60

The electronic structure of Ca@C 60 in the gas phase was probed by ultraviolet photoelectron spectroscopy (UPS) of Ca@C − 60. The electron affinity of Ca@C 60 was found to be 3.0 eV. The spectrum suggests that Ca donates its two 4s electrons to the C 60 t 1u LUMO. Ab initio self-consistent field Hartree-Fock calculations were performed on Ca@C 60 at four different symmetries, I h, D 3d, D 5d, and C 5v. We found that the C 5v symmetry has the lowest energy with the central Ca 2+ ion 0.7 Å away from the center of C 60 and that Ca@C 60 has a 3A 2 triplet electronic ground state in C 5v symmetry.

An efficient implementation of the direct-SCF algorithm on parallel computer architectures

The development and implementation of a parallel direct self consistent field (SCF) Hartree-Fock algorithm, with gradients and random phase approximation solutions is presented. Important details of the structure of the parallel version of DISCO and preliminary results for calculations using the Concurrent Supercomputing Consortium Intel Touchstone Delta parallel computer system are reported. The data show that the algorithms are efficiently parallelized and that throughput of a one processor CRAY X-MP is reached with about 16 nodes on the Delta. The data also indicate sequential code which was not a bottleneck on traditional supercomputers, can become time critical on parallel computers.

Quantum Monte Carlo studies of two-electron atoms constrained in spherical boxes

As part of their continuing study of the influence of the environment on the properties of atoms and molecules, the authors calculate the ground-state energies of three two-electron atoms and ions-H-, He and Li+-constrained at the centre of a hard spherical cavity. The calculations are performed using the techniques of quantum Monte Carlo (QMC); the particular QMC algorithm employed is unique in that the associated timestep error is quadratic, rather than linear, and thus yields highly accurate energies, a typical error bound being +or-0.0003 Hartree. This accuracy exceeds that previously obtained in studies employing self-consistent field Hartree-Fock and configuration interaction methods.

Finite-field fourth-order MBPT calculations of dipole moments, field, and field-gradient polarizabilities of diatomic molecules

The dipole moments and the independent components of the field polarizability α for H 2, CO, F 2,CH + and OH − and of the field-gradient polarizability A for CH +, CO and FH molecules were calculated at the self consistent field Hartree-Fock (SCF-HF) and at the complete fourth order many body perturbation theory (MBPT (4) ) level of approximation using the POL1 basis sets described recently by Sadlej. Excellent overall agreement with respect to the best values available is obtained for all electric properties and for all the species examined in this work. The only exceptions are the relatively low values obtained for the α xx component of the dipole polarizability of the OH − ion and for the A x,xz component of the FH molecule, owing to the absence of f-type GTOs in the POL1 basis.

First-Principle Cluster Investigationof Geometric and Electronic Structuresof Boron-Adsorbed Si(111) Surface

The self-consistent field Hartree-Fock cluster procedure applied to B and Al adsorbed on Si(111) surface shows a greater binding energy for the B atom when it is located in the five-fold coordinated B 5 site as compared to the four-fold T 4 site. This is in contrast to Al which prefers the T 4 site. The result demonstrates strong theoretical support for recent conclusions from measurements of the B/Si(111) surface by a number of different experimental techniques including the results of our ion channeling measurements presented.

First-Principle Cluster Investigationof Geometric and Electronic Structuresof Boron-Adsorbed Si(111) Surface

The self-consistent field Hartree-Fock cluster procedure applied to B and Al adsorbed on Si(111) surface shows a greater binding energy for the B atom when it is located in the five-fold coordinated B 5 site as compared to the four-fold T 4 site. This is in contrast to Al which prefers the T 4 site. The result demonstrates strong theoretical support for recent conclusions from measurements of the B/Si(111) surface by a number of different experimental techniques including the results of our ion channeling measurements presented.

Deformations in nuclei near N and Z=40

The authors study the deformation and the spectral structure of low-lying bands in the nuclei 80Zr, 79,81Y and 81Zr using the deformed-shell model based on Hartree-Fock fields. In their calculation, 56Ni is taken as the inert core with the model space consisting of 1p3/2, 0f5/2 1p1/2 and 0g9/2 states. An effective interaction given by Kuo (1985) and modified by Bhatt (1988) for this configuration space has been used in the calculation. The role of the g9/2 state in producing large deformations in 80Zr is analysed.

The influence of Li+, Na+, Mg2+, Ca2+, and Zn2+ ions on the hydrogen bonds of the Watson–Crick base pairs

The interaction of mono- and divalent metal ions with the nucleic acid base pairs A:T and G:C has been studied using ab initio self-consistent field Hartree-Fock computations with minimal basis sets. Energy-optimized structures of the two base pairs with a final base-base distance of L = 10.35 A have been determined and were further used in calculations on ternary complexes Mn+ - A:B together with previously computed coordination geometries of the cations at adenine (Ade), thymine (Thy), and guanine (Gua). Besides the binding energy of the various metal ions to the base pairs, changes in the stability of the H bonds between Ade and Thy or Gua and Cyt have been determined. Polarization effects of the metal ion on the ligand turned out to increase the binding between complementary bases. Regardless of the metal species, cation binding to Gua N(3) and Thy O(2) leads to a special increase in H-bond stability, whereas binding to Ade N(3) changes the H-bond stability least. Situated in between are the stabilizing effects caused by Gua and Ade N(7) coordination. A remarkable relation between the stability of the H bond and the distance from metal binding site to H bonds was found. This relationship has been rationalized in terms of partial charges of the atoms participating in H bonding, which can reveal the trend in the electrostatic part of total H bond energy. It can be shown that a short distance between coordination site and acceptor hydrogen increases the H-bond strength substantially, while a long distance shows minor effects as supposed. On the other hand, the opposite effect is observed for the influence of the distance between binding site and donor atom. A comparison of our findings with a new model of transition metal ion facilitated rewinding of denatured DNA proposed by S. Miller, D. VanDerveer, and L. Marzilli is given [(1985) J. Am. Chem. Soc. 107, 1048-1055].

Single particle orbitals for configuration interaction derived from quantum electrodynamics

By explicitly introducing degrees of freedom for the electromagnetic field into the Hamiltonian for an N-electron system, we propose a variational procedure leading to mean fields different from the Hartree-Fock field. We show that g-Hartree equations result if the electromagnetic field is assumed to be in a coherent state. Since the solutions of these equations, the g-Hartree orbitals, are derived from a variational ansatz more general than the Hartree-Fock functional, we expect them to be particularly suitable to furnish a single-particle basis set for fast converging configuration interaction (CI) calculations. We report configuration interaction studies on the water molecule in a double zeta basis set employing various single-particle basis set transformations for the construction of the configuration state functions and investigate the convergence behaviour of the CI expansion explicitly.We find that the expansion in terms of g-Hartree orbitals receives substantially larger fractions of the total correlation energy in the case considered, if single excitations with respect to the mean field configuration are retained in the CI procedure.

Basis set dependence, precision, and accuracy of full ab initio gradient optimizations of molecular structures of nonstrained hydrocarbons. I. CC bond lengths

AbstractDifferent highly accurate experimental determinations of molecular structures (ED: rg and r0α, MW: r0, rs, and rz, and X‐ray distances) of 14 unstrained hydrocarbons have been linearly correlated with corresponding self‐consistent field Hartree Fock (SCF HF) ab initio full gradient‐optimized structures. From the eight applied basis sets (STO‐3G, STO‐6G; 3‐21G, 4‐31G, 6‐31G, 6‐311G; 6‐31G*, and 6‐31G**) the 6‐31G basis set, although not best regarding total energies, yields statistically the most precise regression equation, which allows the prediction of ED rg CC distances as reliable as the best experimental determinations. Surprisingly the accuracy of all calculated CC distances (measured as difference Δ between calculated CC distances and experimental ED rg values) depends linearly on bond distances, with the largest deviations being observed for triple bonds. This seems to be a clear indication of different influences of correlation effects on calculated geometries which are neglected in the applied HF treatment. The linear regression equations presented here allow the prediction of any kind of experimental CC distance parameters for each of the eight basis sets considered. Even experimentally unknown re CC distances may be predicted from these single determinantal HF optimizations.

Neutron-40Ca mean field between -80 and +80 MeV from a dispersive optical-model analysis.

The n${\mathrm{\ensuremath{-}}}^{40}$Ca complex mean field is derived from a dispersive optical-model analysis of the available experimental cross sections. In this analysis the real part of the mean field contains dispersive contributions which are derived from the imaginary part by means of a dispersion relation. These dispersive contributions must be added to the Hartree-Fock potential which is assumed to have a Woods-Saxon shape, with a depth ${V}_{H}$(E) that depends exponentially upon energy. The input experimental data are 14 differential cross sections in the energy domain (5.3, 40.0 MeV), five polarization cross sections in the domain (9.9, 16.9 MeV), and the total cross section in the domain (2.5, 80 MeV).The resulting optical-model potential is an analytic function of energy. It can thus be extrapolated towards negative energies, where it should be identified with the shell-model potential. This extrapolation yields good agreement with the experimental single-particle energies in the two valence shells of $^{40}\mathrm{Ca}$. The model also predicts the radial shape and the occupation probabilities of the single-particle orbits and the spectroscopic factors of the single-particle excitations. In order to reproduce the experimental energies of the deeply bound 1p and 1s orbits, one must use a linear rather than an exponential energy dependence of ${V}_{H}$(E) at large negative E. It is shown that this is precisely the behavior expected from the fact that the energy dependence of ${V}_{H}$(E) actually represents the nonlocality of the original microscopic Hartree-Fock field. The model also correctly predicts the distribution of the single-particle strength of the 1d(5/2 excitation in $^{39}\mathrm{Ca}$. The calculated distributions of the 1p strength in $^{39}\mathrm{Ca}$ and of the 1f(5/2 strength in $^{41}\mathrm{Ca}$ show that the available experimental information extends over less than half the expected peak, whose energy is thus poorly known experimentally. In the energy domain (2.5, 9 MeV) the predicted total cross section deviates from the experimental data; this reflects the fact that at low energy the calculated cross section is very sensitive to small modifications of the mean field.

Experimental and theoretical investigation of chemisorbed Ga on Si(111)

Study of the lattice location of Ga adsorbed from weakly acidic methanol solution on chemically cleaned Si(111) surfaces has been carried out by an x‐ray standing wave (XSW) technique using a conventional Mo Kα x‐ray source. XSW is a very sensitive and precise technique to determine impurity atom locations normal to the diffraction planes. In addition to measurements of adatom locations normal to the crystal surface plane, the atom locations relative to planes inclined to the surface were measured. Self‐consistent field Hartree–Fock cluster investigations were carried out for Ga on Si(111) surfaces for different high‐symmetry adsorption sites such as substitutional, atop, threefold open, and threefold eclipsed to determine the minimum energy positions. The effect of lattice relaxation was studied for the eclipsed site alone. Analyzing the XSW results together with the bond lengths and binding energies derived from cluster calculations indicates that Ga coadsorbs at the atop and threefold relaxed eclipse s...

Nature of bonding between alkali metals and silicon surface

In recent literature, diverse views have been expressed regarding the nature (ionic versus covalent) of bonding between alkali metals and the Si(001)-(2×1) surface. Also unsettled is the issue as to whether the metallicity upon K adsorption is due to the partial occupancy of the dangling bonds or due to the metallic K chain. The resolution of these outstanding problems is sought by performing electronic structure total energy calculations using cluster as well as slab models. The cluster model calculations have used an ab initio self-consistent field Hartree–Fock technique, whereas the slab model has employed pseudopotentials within the density functional formalism. Using a variety of criteria, we conclude that the bond is strong and ionic with negligible covalent effects. At the monolayer coverage, the charge from the adsorbed potassium atoms is transferred into the empty, antibonding dangling bond surface states resulting in the metallization of the Si(001) substrate surface. The presence of the dangling bond states prevents the alkali monolayer from metallization.

Unified description of the neutron-208Pb mean field between -20 and +165 MeV from the dispersion relation constraint.

The real part of the central neutron${\mathrm{\ensuremath{-}}}^{208}$Pb mean field is the sum of a Hartree-Fock component plus a dispersive component. In keeping with theoretical expectations, the Hartree-Fock field is assumed to have a Woods-Saxon shape whose depth decreases exponentially with increasing energy and whose radius and diffuseness are independent of energy. The dispersive component is determined from the imaginary part of the optical-model potential by making use of the dispersion relation which connects these two quantities. The imaginary part is written as the sum of a volume and a surface-peaked contribution. The dispersion relation then implies that the real dispersive contribution is also the sum of volume and surface-peaked components. The parameters of the complex mean field are determined by fitting the available differential and polarization cross sections in the energy domain [4, 40 MeV] and the total cross sections in the domain [1,120 MeV]; these data are contained in previous published or unpublished reports, but new measurements of the total cross sections are presented from 1 to 25 MeV. Good fits to these cross sections, and also to unpublished total cross sections for energies up to 165 MeV, are obtained despite the fact that the number of adjusted parameters is quite small because of our use of the constraint implied by the dispersion relation.The real part of the mean field is well approximated by a Woods-Saxon shape whose radius decreases with increasing energy between 5 and 25 MeV; its depth is approximately constant from 5 to 15 MeV and then decreases with increasing energy; these findings are in keeping with recent empirical evidence. When the neutron energy decreases below 2.5 MeV, the potential radius decreases; it increases again when the neutron energy decreases below -14.5 MeV. In the domain -20 MeV<E<0 the deduced potential accurately reproduces the experimental single-particle energies as well as the asymptotic values of the single-particle wave functions as measured from sub-Coulomb pickup reactions; it also yields excellent agreement with the spreading width of the deeply bound 1${h}_{11/2}$ hole state. The rms radii, absolute spectroscopic factors, and occupation numbers are calculated for the valence particle and hole states. At the Fermi energy (-6 MeV), the mean field can be identified with the Hartree-Fock potential, for which the present analysis yields a depth of 46.4 MeV, a radius of 1.24${A}^{1/3}$ fm, and a diffuseness of 0.68 fm. In the energy domain 4\ensuremath{\le}E\ensuremath{\le}10 MeV, the already good agreement between the predicted and measured cross sections is further improved if the imaginary part of the mean field is allowed to have its strength depend upon the neutron orbital angular momentum, and its surface diffuseness is allowed to be energy dependent.

A screened potential molecular-orbital calculation of the π-electron systems of metalloporphin, metallochlorin, and metallobacteriochlorin

The excitation energies and oscillator strengths of the lowest (π,π*) excited states of metalloporphin, -chlorin, and -bacteriochlorin were calculated by the screened potential molecular-orbital theory. The screened potential incorporates instantaneous polarization effects in the molecular Hartree–Fock field. The model reproduced the spectra of the lowest excited states fairly well without use of empirical parameters. The calculated energies of the lowest excited triplets and the Q singlet state were in good agreement with those observed, while the B state was correctly predicted only for the reduced resonance integrals.

First principles investigation of chemisorption of moderately heavy atoms on semiconductor surfaces—bromine on silicon

Self‐consistent field Hartree–Fock cluster investigations have been carried out for bromine atoms chemisorbed on Si (111) surface using 5, 14, and 27 atom clusters. For the first two clusters, both all‐electron and pseudopotential procedures have been used and the total energy curves as a function of adatom position have been found to compare very well. The third cluster has been studied by the pseudopotential procedure alone. For the five‐atom cluster which corresponds to the SiH3Br molecule, the Si–Br bond distance and 79Br quadrupole coupling constant (e2qQ) are obtained as 2.20 A and 355.4 MHz, respectively, in very good agreement with the experimental values from microwave measurements of 2.21 A and 346 MHz. For the surface chemisorbed system, we have studied the location of the bromine atom, the local density of states (LDOS), the frequencies and amplitudes of the Si–Br vibrations and the 79Br quadrupole coupling constant. The calculated Si–Br bond distance of 2.23 A agrees very well with two experi...

Conformation and electronic structure of the di-sulfur nitride (S 2N − anion : A Hartree—Fock—Slater analysis

The total statistical energy and Mulliken's population analysis obtained through the self-consistent field Hartree—Fock—Slater method are applied to the study of the S 2N − ion. The results suggest that the ground state of this anion has a symmetrical C 2v conformation with an SNS angle of 110° and SN distances of 1.57 å. The electronic structure and electronic spectrum of this species are discussed.

Excitonic fine structure of the arsenic K-edge in AsF n ( n = 3,5,6) cage molecules

We present self-consistent field Hartree-Fock calculations of the excitonic fine structure of the arsenic K-edge for several arsenic fluorine cage molecules AsF n ( n = 3, 5, 6). Ground-state energies and K-shell ionization energies are computed. The binding energies relative to the K-shell ionization energy of several excitonic states, made up of a 1s core hole and an electron in a valence or Rydberg final state, are found. The relative oscillato, strengths for X-ray absorption to these states are determined and good agreement with experimental X-ray absorption data on AsF 5 in the gas phase is found.

The electronic structure and the solid state properties of the one-dimensional tetraza porphin nickel (II ) system. A self-consistent-field Hartree-Fock crystal-orbital approach based on a semiempirical Hamiltonian

The electronic structure and the solid state properties of tetraza porphin nickel (II), 1, have been studied by means of self-consistent field (SCF) Hartree-Fock (HF) crystal-orbital (CO) calculations that are derived in the framework of a semiempirical INDO Hamiltonian. The iterative SCF procedure is based on an algorithm where Hartree damping of the bond-order matrices and a direct steepest-descent formalism have been combined in order to avoid SCF difficulties in the CO method as a result of the closely spaced occupied and virtual Fermi seas. The diatomic intercell energies are mainly determined by electrostatic contributions. The NiNi coupling is highly repulsive, large stabilising two-centre pairs are found for the interaction between the 3d centre of the reference cell and the heteroatoms (N) in the neighbouring fragments. A large number of ligand, pi , lone-pair and sigma bands are predicted to be on top of dispersion curves with substantial Ni3d character. Oxidation processes in 1 are ligand-centred leading to organic pi radical cations. The INDO CO results for 1 are compared with experimental data derived for nickel phthalocyanine, NiPc, and halogenated NiPc derivatives.