Hartree-Fock Field Research Articles

О расширенном пространстве Гильберта

The construction of the extended Hilbert space is presented in the form of a direct sum of the spaces of vectors of finite and infinite norms as the main space in the mathematical formalism of quantum mechanics of a many-electron atom. On the example of constructing the analytical structure of the probability amplitude 1s-3p of photoexcitation of a neon atom, the implementation of the EHS-construct for solving the equations of the self-consistent Hartree-Fock field is given.

Chiral symmetry breaking and topological charge of zigzag graphene nanoribbons

Interacting quasi-one-dimensional zigzag graphene nanoribbons display gapped edge excitations. Although the self-consistent Hartree–Fock fields break chiral symmetry, our work demonstrates that zigzag graphene nanoribbons maintain their status as short-range entangled symmetry-protected topological insulators. The relevant symmetry involves combined mirror and time-reversal operations. In undoped ribbons displaying edge ferromagnetism, the band gap edge states with a topological charge form on the zigzag edges. An analysis of the anomalous continuity equation elucidates that this topological charge is induced by the gap term. In low-doped zigzag ribbons, where the ground state exhibits edge spin density waves, this topological charge appears as a nearly zero-energy edge mode. Our system is outside the conventional classification for topological insulators.

Effect of electronic concentration on the self-trapping transition of polaron for the weakly correlated system in the adiabatic limit

The self-trapping transition of the polaron is investigated for the two-dimensional extended Holstein-Hubbard model. A series of canonical transformations are performed on the Hamiltonian followed by a many phonon averaging, to eliminate the phonon degrees of freedom from the system. The mean field Hartree-Fock calculation has been done to solve the effective electronic Hamiltonian and the ground state energy is obtained variationally. The effect of electronic concentration on the polaronic hopping parameter is studied with respect to the electron–phonon interaction strengths in the weak Coulomb correlation limit. The transition from a delocalized mobile polaron to a localized self-trapped polaron has been found to be discontinuous for the adiabatic motion of the polaron and the self-trapping transition needs stronger electron–phonon interaction strength as the electronic concentration minimizes.

Finite-size instabilities in finite-range forces

It has been recently shown that some Gogny finite-range interactions suffer from finite-size instabilities in coordinate-space calculations [Eur. Phys. J. A 55, 150 (2019)]. We confirm this finding by using the Hartree-Fock (HF) method in the quasilocal approximation to finite-range forces. The use of the quasilocal approximation substantially simplifies the calculations as compared with those including the exact exchange contribution to the energy and HF fields. The quantity most affected by the finite-size instabilities in the coordinate-space calculations is the spatial density at the origin that wildly oscillates as the HF iterative process proceeds. In addition to the recent ${\mathrm{D1M}}^{*}$ parametrization of the Gogny force, we find that the D1M parametrization also shows this deficiency in several nuclei. We find that the harmonic-oscillator basis with its ultraviolet cutoff provides converged results in a wide and realistic range of basis sizes. This result serves as a justification of the numerous calculations with D1M and ${\mathrm{D1M}}^{*}$ in finite nuclei that show no trace of instability.

Convergence of nuclear magnetic shieldings and one-bond 1 J(11 B1 H) indirect spin-spin coupling constants in small boron molecules.

Self-consistent field Hartree-Fock, density functional theory, and coupled-cluster calculations of the nuclear magnetic shielding constants of BH and BH3 molecules have been conducted to characterize the convergence of individual results obtained with correlation-consistent and polarization-consistent basis sets. The individual 11 B and 1 H NMR parameters were estimated in the complete basis set limit and compared with benchmark results. Only the KT3 density functional accurately reproduced 11 B shielding in BH molecule.

Ga–In intermixing, intrinsic doping, and Wigner localization in the emission spectra of self-organized InP/GaInP quantum dots

We present study of structural and optical properties of InP/GaInP quantum (QDs) providing a weak quantum confinement and creating a platform to study Wigner localization (WL) effects using high spatial resolution optical spectroscopy. Self-organized QD structures were grown using metal-organic chemical phase epitaxy by using different substrate misorientations and cap layer deposition temperatures. Using transmission electron microscopy and energy dispersive x-ray spectroscopy, we demonstrated a bimodal height distribution with peaks at ~5 and ~20 nm and a control of both the lateral size distribution, peaked from ~100 to ~160 nm, and the amount of Ga–In intermixing in the QDs (up to 20%). Using photoluminescence (PL) spectroscopy in combination with circular polarization degree and time resolved micro-PL measurements, we demonstrated control of the emission energy, the intrinsic doping, and the emission decay of these In(Ga)P QDs. Using high-spatial-resolution near-field PL spectra and imaging of single dots, we demonstrated WL effects in dots having a population of up to nine electrons and a parabolic confinement down to ħω0 ~ 1 meV. We performed a self-consistent calculation of exciton transitions using an effective mass, mean field theory with an isotropic elasticity model to describe the effect of Ga–In intermixing on the emission properties of these dots; and we used calculations of shell splitting, using mean field Hartree–Fock approach and calculations of electron density distribution using configuration interaction approach, to described effects of enhancement of WL in non-circular dots with hard-wall potentials.

Anomalous D'yakonov-Perel' spin relaxation in InAs (110) quantum wells under strong magnetic field: Role of Hartree-Fock self-energy

We investigate the influence of the Hartree-Fock self-energy, acting as an effective magnetic field, on the anomalous D'yakonov-Perel' spin relaxation in InAs (110) quantum wells when the magnetic field in the Voigt configuration is much stronger than the spin-orbit-coupled field. The transverse and longitudinal spin relaxations are discussed both analytically and numerically. For the transverse configuration, it is found that the spin relaxation is very sensitive to the Hartree-Fock effective magnetic field, which is very different from the conventional D'yakonov-Perel' spin relaxation. Even an extremely small spin polarization ($P=0.1\%$) can significantly influence the behavior of the spin relaxation. It is further revealed that this comes from the {\em unique} form of the effective inhomogeneous broadening, originated from the mutually perpendicular spin-orbit-coupled field and strong magnetic field. It is shown that this effective inhomogeneous broadening is very small and hence very sensitive to the Hartree-Fock field. Moreover, we further find that in the spin polarization dependence, the transverse spin relaxation time decreases with the increase of the spin polarization in the intermediate spin polarization regime, which is also very different from the conventional situation, where the spin relaxation is always suppressed by the Hartree-Fock field. It is revealed that this {\em opposite} trends come from the additional spin relaxation channel induced by the HF field. For the longitudinal configuration, we find that the spin relaxation can be either suppressed or enhanced by the Hartree-Fock field if the spin polarization is parallel or antiparallel to the magnetic field.

Evolution of the persistent spin helix in the presence of Hartree-Fock fields

We derive a spin diffusion equation for a spin-orbit coupled two-dimensional electron gas including the Hartree-Fock field resulting from 1st order electron-electron interactions. We find that the lifetime of the persistent spin helix, which emerges for equal linear Rashba- and Dresselhaus spin-orbit interactions, can be enhanced considerably for large initial spin polarizations due to the Hartree-Fock field. The reason is a reduction of the symmetry-breaking cubic Dresselhaus scattering rate by the Hartree-Fock field. Also higher harmonics are generated and the polarization of the persistent spin helix rotates out of the (Sy,Sz)-plane acquiring a finite Sx-component. This effect becomes more pronounced, when the cubic Dresselhaus spin-orbit interaction is large.

Mobility edge phenomenon in a Hubbard chain: A mean field study

We show that a tight-binding one-dimensional chain composed of interacting and non-interacting atomic sites can exhibit multiple mobility edges at different values of carrier energy in presence of external electric field. Within a mean field Hartree-Fock approximation we numerically calculate two-terminal transport by using Green's function formalism. Several cases are analyzed depending on the arrangements of interacting and non-interacting atoms in the chain. The analysis may be helpful in designing mesoscale switching devices.

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.: (VII) hfodd (v2.49t): A new version of the program

We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.

Spin-vortices and Spin-vortex-induced Loop Currents in the Pseudogap Phase of Cuprates

We explain several anomalous phenomena observed in the pseudogap phase of hole-doped cuprates based on the recently proposed spin-vortex superconductivity theory. In this theory, doped-holes become almost immobile small polarons, and spin-vortices are formed with those small polarons as their centers. A Hartree–Fock field for conduction electrons that is optimized for the interaction energy of local moments is derived; it contains a fictitious magnetic field arising from spin-vortices, and yields current carrying states. The obtained currents are loop currents around spin-vortices, i.e., the spin-vortex-induced loop currents (SVILCs), and a collection of them produces a macroscopic current. The SVILC explains (1) nonzero Kerr rotation in zero-magnetic field after exposed in a strong magnetic field; (2) the change of the sign of the Hall coefficient with temperature change; (3) the suppression of superconductivity in the x=1/8 static-stripe ordered sample; and (4) a large anomalous Nernst signal, including its sign-change with temperature change. We show that the hourglass-shaped magnetic excitation spectrum is the evidence for the existence of spin-vortices. We further argue that the “Fermi-arc” in the ARPES is a support for the presence of localized moments in the bulk; a disconnected arc-shaped Fermi surface is obtained by assuming an antiferromagnetic interaction between the localized moments in the bulk and itinerant electrons in the surface region.

Magnetic response in mesoscopic Hubbard rings: A mean field study

The present work proposes an idea to remove the long standing controversy between the calculated and measured current amplitudes carried by a small conducting ring upon the application of an Aharonov–Bohm (AB) flux ϕ . Within a mean field Hartree–Fock (HF) approximation we numerically calculate persistent current, Drude weight, low-field magnetic susceptibility and related issues. Our analysis may be inspiring for studying magnetic response in nano-scale loop geometries.

Calculation of the zero-field splitting tensor on the basis of hybrid density functional and Hartree-Fock theory

The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.

Elongation method and supermolecule approach for the calculation of nonlinear susceptibilities. Application to the 3-Methyl-4-Nitropyridine 1-Oxide and 2-Methyl-4-Nitroaniline crystals

The linear and nonlinear optical properties of the 3-methyl-4-nitropyridine-1-oxyde (POM) and 2-methyl-4-nitroaniline (MNA) crystals are evaluated using the elongation method and the supermolecule approach. The elongation calculations adopt the finite field Hartree-Fock numerical scheme to get the static polarizability, first and second hyperpolarizabilities of large one-dimensional clusters, allowing a very accurate extrapolation of the crystal packing ratios to the infinite one-dimensional arrays. The supermolecule approach employs the analytical time-dependent Hartree-Fock scheme for evaluating the static and dynamic polarizability and first hyperpolarizabilities of smaller clusters. Most of the calculations are performed using the semiempirical AM1 Hamiltonian. Preliminary results are also carried out at the ab initio level using a minimal basis set. These polarizability and hyperpolarizability results are then used to estimate the effective (hyper)polarizabilities of the unit cell in the whole crystals and subsequently their linear and nonlinear susceptibilities. The inclusion of electron correlation effects is also discussed.

Resonant inelastic contact scattering of X-ray photons on atoms and ions

The existence of an extended resonance structure outside the X-ray emission regions is theoretically predicted in the total double differential cross section for the scattering of linearly polarized photons on free atoms (ions). This structure is almost entirely determined by inelastic photon scattering of the contact type. The amplitude of the inelastic contact scattering probability is described using an analytical expression for a non-relativistic transition operator, which was previously obtained by the author outside the dipole and momentum approximations. The resonant inelastic contact scattering of X-ray photons on a neon atom and neonlike ions of argon, titanium, and iron has been studied. Calculations were performed in a nonrelativistic approximation for the wave functions of the scattering states, with allowance for many-body effects of the radial relaxation of one-electron orbitals in the Hartree-Fock field of a deep 1s vacancy and (for neon atom) the double excitation/ionization of the ground atomic state.

Many-particle effects in resonant inelastic scattering of an X-ray photon by an atom

The influence of many-particle effects on the shape and values of the double differential cross section for the resonant inelastic scattering of a linearly polarized X-ray photon by a free atom near the K and KL23 ionization thresholds has been theoretically analyzed for the neon atom. The calculations have been performed using the nonrelativistic Hartree-Fock approximation for single-electron wavefunctions and the dipole approximation for the anomalous dispersion component of the cross section. The analytical structure of the contact part of the scattering cross section has been obtained beyond the dipole approximation. The effects of the radial relaxation of electron shells, spin-orbit and multiplet splitting, and configuration interaction in the doubly excited atomic states, as well as the Auger and radiative decays of the produced vacancies, are taken into account. The nature and role of the effect of correlation amplitudes, which is responsible for the appearance of the nonzero amplitudes of nonradiative transitions between intermediate and final single-electron states of the same symmetry that are obtained in different Hartree-Fock fields, have been analyzed also. The calculations are predictive and, for an incident-photon energy of 5.41 keV, agree well with experimental results for the Kα X-ray emission spectrum of the neon atom.

Giant resonances in exotic spherical nuclei within the RPA approach with the Gogny force

Theoretical results for giant resonances in the three doubly magic exotic nuclei 78Ni, 100Sn and 132Sn are obtained from Hartree-Fock (HF) plus Random Phase Approximation (RPA) calculations using the D1S parameterization of the Gogny two-body effective interaction. Special attention is paid to full consistency between the HF field and the RPA particle-hole residual interaction. The results for the exotic nuclei, on average, appear similar to those of stable ones, especially for quadrupole and octupole states. More exotic systems have to be studied in order to confirm such a trend. The low energy of the monopole resonance in 78Ni suggests that the compression modulus in this neutron-rich nucleus is lower than the one of stable ones.

THE PROBLEM OF UNIVERSALITY OF NUCLEAR MEAN-FIELD PARAMETRIZATIONS

Most of the microscopic self-consistent approaches such as Hartree-Fock and/or Relativistic Mean Field theories use ensembles of a few adjustable parameters that are independent of the proton and neutron numbers and fixed once for all. This feature is referred to as the universality of the parametrization. It is further developed for the case of the phenomenological description of the nuclear deformed mean-field e.g. in the Woods-Saxon form and discussed in view of obtaining the parametrizations that are most stable with respect to extrapolations for the unknown nuclear ranges as e.g. in the case of various groups exotic nuclei. A new universal parametrization is obtained and an illustration presented.

Calculation of bridging oxygen [formula omitted] quadrupolar coupling parameters in alkali silicates: A combined ab initio investigation

Ab initio band-structure calculations based on the density functional theory have been performed for several crystalline Li, Na, and K-silicates to obtain electric-field gradients (efg) for oxygen atoms. The efg for bridging oxygen environments in these compounds were also investigated by performing ab initio self-consistent field Hartree–Fock molecular orbital calculations on silicate clusters, and there is good agreement between these two approaches. By performing additional ab initio quantum chemistry calculations on model silicate clusters the factors influencing the O 17 quadrupole coupling parameters for bridging oxygen environments in alkali silicates have been examined. The quadrupolar asymmetry parameter was found to be dependent on the Si–O–Si angle and the nature of the modifier cation, in agreement with previous studies. In contrast, the quadrupolar coupling constant was found to have a strong dependence on Si–O distance, as well as Si–O–Si angle and the nature of the modifier cation. Analytical expressions describing these dependencies are proposed, which should assist in describing the local environments of bridging oxygen in crystalline and amorphous materials.

Endofullerenes with small silver and copper clusters

AbstractModels of endofullerenes C60 with small metal clusters Agn and Cun (n < 5) were built and calculated with the self‐consistent field Hartree–Fock (SCF HF) MOLCAO method, using an effective core potential for silver and all‐electronic basis sets for copper. Binding energies of the clusters shows that monoatomic M@C60 structures are stable for both silver and copper. The models Mn@C60 (n = 2, 3, 4) with copper are much more favorable than those with silver. Metal atoms and clusters in the C60 molecule provide noticeable changes in its geometry, but the large distortion of the clusters does not correspond to stable structures. Stable Mn@C60 with MCu reveal the electronic charge transfer from metal atoms to the carbon cage, resulting in the positive charge of metal atoms. Models Cu2@C60 and Cu4@C60 with tetrahedron Cu4 are proposed as possible candidates in real metal–fullerene systems. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005