Hartree-Fock Type Research Articles

GW with hybrid functionals for large molecular systems

A low-cost approach for stochastically sampling static exchange during time-dependent Hartree–Fock-type propagation is presented. This enables the use of an excellent hybrid density functional theory (DFT) starting point for stochastic GW quasiparticle energy calculations. Generalized Kohn–Sham molecular orbitals and energies, rather than those of a local-DFT calculation, are used for building the Green function and effective Coulomb interaction. The use of an optimally tuned hybrid diminishes the starting point dependency in one-shot stochastic GW, effectively avoiding the need for self-consistent GW iterations.

Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent

Ground-state solutions of a Hartree–Fock type system involving critical Sobolev exponent

Ground-State Solutions to a Hartree–Fock Type System with a 3-Lower Nonlinearity

Ground-State Solutions to a Hartree–Fock Type System with a 3-Lower Nonlinearity

Influence of diffuseness of nuclear potential on the neutron halo structure of Zr isotopes near the neutron drip line

The single-particle characteristics of the halo structure ofZr isotopes near the neutron drip line were calculated within the dispersive optical model. The influence of the increase in the diffuseness of the nuclear Hartree–Fock type potential on the root-mean-square radii of halo states and their populations was considered. A significant difference was shown between the number of neutrons in halo states and in the r > 12 fm region, where there is no spatial correlation of neutrons with the core of nucleus.

Existence and multiplicity of the positive normalized solutions to the coupled Hartree–Fock type nonlocal elliptic system

Existence and multiplicity of the positive normalized solutions to the coupled Hartree–Fock type nonlocal elliptic system

DENSITY FUNCTIONAL AND GREEN’S FUNCTIONS METHOD TO COMPUTING SPECTRAL PARAMETERS OF DIATOMIC MOLECULES

It is presented a new effective method of calculating the energy and spectral parameters of diatomic molecules based on the hybrid theory of the quasi-particle density functional and the theory of Green's functions. As an illustration, the data of the calculation of the vertical ionization potentials and the coupling constants (vibrational structure) of the photoelectron spectra of a number of diatomic molecules, in particular, N2, are received. It is presented a detailed comparison of the received results with the data of standard theories of the Hartree-Fock type, the multi-configuration electron propagator method, and the extended theory based on Koopmans' theorem using multi-configurational self-consistent field wave functions with different sets of basis functions. Iit is shown that the consistent, maximally precise consideration of exchange-correlation effects and reorganization effects within the framework of the combined theory leads to a rather significant improvement in the agreement of theoretical and experimental data both in terms of ionization potentials and photoelectron spectra in general.

Hartree-Fock type systems: Existence of ground states and asymptotic behavior

In this paper we consider a Hartree-Fock type system made by two Schrödinger equations in presence of a Coulomb interacting term and a cooperative pure power and subcritical nonlinearity, driven by a suitable parameter β≥0. We show the existence of semitrivial and vectorial ground states solutions depending on the parameters involved. The asymptotic behavior with respect to the parameter β of these solutions is also studied.

On a planar Hartree–Fock type system

On a planar Hartree–Fock type system

Shallow dopant pairs in silicon: An atomistic full configuration interaction study

The two-electron states and exchange couplings are investigated for a phosphorous donor pair in silicon using an atomistic full configuration interaction method for donor separations spanning from 0.4 to 15 nm. Three distinct donor separation regimes appear from our large basis calculations, from which the validity of simplified methods such as Heitler-London and Hartree-Fock type approaches can be assessed. For bulk donors, the exchange coupling saturates below 5 nm due to excited bonding orbital contributions to the wave functions. Ionic contributions to the two-electron state decrease between 5 and 14 nm, and a fully correlated Heitler-London-like state is reached from 14 nm onwards. Oscillations in exchange couplings can be strongly suppressed by placing the donors in the same $z$ plane and at a small depth, $D$, from the surface. This is a consequence of the $z$-valley terms becoming dominant within the dopant's wave function and of small changes with $x$ and $y$ separations no longer having much effect. We find the depth to be an important parameter in determining the exchange coupling for subsurface dopants, not only through valley repopulation ($D<10$ nm) but also through additional interface effects for ultrashallow depths ($D<2.5$ nm). Our full configuration interaction method provides insights in the exchange interaction for various regimes of donor separation and depths, from the Heitler-London limit at large distances to the 0.4--5 nm range relevant for scanning tunneling microscope based quantum state imaging and spectroscopy experiments. The precise control of electron-electron quantum correlations in such engineered atoms in the solid state is useful to design quantum logic gates and quantum simulators.

Existence of normalized solutions for the coupled Hartree–Fock type system

AbstractStanding waves solutions for a coupled Hartree–Fock type nonlocal elliptic system are considered. This nonlocal type problem was considered in the basic quantum chemistry model of small number of electrons interacting with static nucleii which can be approximated by Hartree or Hartree–Fock minimization problems. First, we prove the existence of normalized solutions for different ranges of the positive (attractive case) coupling parameter for the stationary system. Then we extend the results to systems with an arbitrary number of components. Finally, the orbital stability of the corresponding solitary waves for the related nonlocal elliptic system is also considered.

Counterexamples to Lp collapsing estimates

We show that certain L2 space-time estimates for generalized density matrices which have been used by several authors in recent years to study equations of BBGKY or Hartree-Fock type, do not have non-trivial LpLq generalizations.

Axionic dark matter halos in the gravitational field of baryonic matter

We consider a dark matter halo (DMH) of a spherical galaxy as a Bose–Einstein condensate (BEC) of the ultra-light axions (ULA) interacting with the baryonic matter. In the mean-field (MF) limit, we have derived the integro-differential equation of the Hartree–Fock type for the spherically symmetrical wave function of the DMH component. This equation includes two independent dimensionless parameters: (i) [Formula: see text] is the ratio of baryon and axion total mases and (ii) [Formula: see text] is the ratio of characteristic baryon and axion spatial parameters. We extended our “dissipation algorithm” for studying numerically the ground state of the axion halo in the gravitational field produced by the baryonic component. We calculated the characteristic size, [Formula: see text] of DMH as a function of [Formula: see text] and [Formula: see text] and obtained an analytical approximation for [Formula: see text].

Calculation Some Atomic Properties For Three and Four Electron Systems by Using Hartree- Fock Method

In this paper many physical properties evaluated like two particles radial density distribution function D (r1, r2), one-particle radial density distribution function D) (r1) has been evaluated by using Hartree-Fock type wave function for three and four electron systems (Li, Li−1, Be, Be+1, B+2) and the inter particle expectation values 〈r〉 has been evaluated too. Also it was calculation the expectation values for all energies 〈Ven〉, 〈Vee〉, 〈V〉, 〈T〉 and 〈EHF〉. All the results and the behaviors obtained in this work have been discussed, interpreted and compared with those previously obtained. It was found that the maximum of one-particle density distribution is shifting to the origin by increasing the atomic number (Z), due to the attraction forces between the nucleus and the electron clouds, As atomic number is Z increase, all the total energies are increases because the increasing nuclear charge effect. The results also indicate that attraction energy expectation values 〈Ven〉 are larger than the repulsion energy expectation value 〈Vee〉.

Microscopic tight-binding study of the interplay between on-site and inter-site Coulomb interactions in Graphene

It is realized that the Coulomb interaction plays a vital role in describing the magnetic properties of graphene-on-substrate. We attempt here to study the competition between on-site and inter-site repulsive Coulomb interactions, with impurities at both the sub-lattices in graphene-on-substrate .The Hamiltonian describes the electron hopping up to third-nearest-neighbors within tight-binding approximation. Due to substrate effect, A-sub lattice is raised by energy and B-sub lattice acquired energy , besides impurity effects at both the sub lattices. The model consists of on-site repulsive Coulomb interaction at two sublattices with same on-site Coulomb energy U and nearest-neighbor inter-site Coulomb interactions between A and B sub lattice with inter site Coulomb energy . The Coulomb interaction is considered within Hartree-Fock type mean-field approximation. The Hamiltonian is solved by Zubarev's Green's function technique and an expression for temperature dependent difference in electron occupancies between two sub-lattices is calculated and solved self-consistency. Finally the charge gap and hence modified substrate induced gap is computed numerically by varying different physical parameters of the system like on-site and inter-site Coulomb interactions and substrate induced gap, impurity concentration and electron occupancy. It is observed that inter-site Coulomb interaction is smaller than on-site Coulomb interaction and plays an important role in describing the properties of graphene.

Study of frequency- and temperature-dependent electrical transport in heavy fermion systems

This paper focuses on the frequency- and temperature-dependent electrical transport properties of heavy fermion (HF) systems. For this, Kondo lattice model (KLM) with Coulomb correlation between [Formula: see text]–[Formula: see text] electrons at the same site is considered. The Hamiltonian is treated in mean-field approximation (MFA) for the Kondo hybridization and Heisenberg-type interaction to get mean-field Hamiltonian and it is written after the Fourier transformation. The Hartree–Fock-type approximation is considered for the Coulomb repulsion between [Formula: see text]–[Formula: see text] electrons, the perturbed part of the Hamiltonian. The two Green’s functions for the conduction and [Formula: see text]-electrons are calculated to define the self-energy. Then the frequency- and temperature-dependent optical conductivity and resistivity are calculated by using the Kubo’s formula within the linear dynamical response approach. They are studied by varying the model parameters. The anomalies and results obtained are compared with experimental data.

Charge modulation as fingerprints of phase-string triggered interference

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high $T_c$ cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock type mean field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite $t-J$ ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.

A simple way to test for collinearity in spin symmetry broken wave functions: general theory and application to generalized Hartree Fock.

We introduce a necessary and sufficient condition for an arbitrary wavefunction to be collinear, i.e., its spin is quantized along some axis. It may be used to obtain a cheap and simple computational procedure to test for collinearity in electronic structure theory calculations. We adapt the procedure for Generalized Hartree Fock (GHF), and use it to study two dissociation pathways in CO2. For these dissociation processes, the GHF wave functions transform from low-spin Unrestricted Hartree Fock (UHF) type states to noncollinear GHF states and on to high-spin UHF type states, phenomena that are succinctly illustrated by the constituents of the collinearity test. This complements earlier GHF work on this molecule.

Space group symmetry applied to SCF calculations with periodic boundary conditions and Gaussian orbitals

Space group symmetry is exploited and implemented in density functional calculations of extended systems with periodic boundary conditions. Our scheme for reducing the number of two-electron integrals employs the entire set of operations of the space group, including glide plains and screw axes. Speedups observed for the Fock matrix formation in simple 3D systems range from 2X to 9X for the near field Coulomb part and from 3X to 8X for the Hartree-Fock-type exchange, the slowest steps of the procedure, thus leading to a substantial reduction of the computational time. The relatively small speedup factors in special cases are attributed to the highly symmetric positions atoms occupy in crystals, including the ones tested here, as well as to the choice of the smallest possible unit cells. For quasi-1D systems with most atoms staying invariant only under identity, the speedup factors often exceed one order of magnitude reaching almost 70X (near-field Coulomb) and 57X (HFx) for the largest tested (16,7) single-walled nanotube with 278 symmetry operations.

Momentum Dependent Local-Ansatz with Hybrid Wavefunction from Weak to Strong Electron Correlations

The variational theory of momentum dependent local-ansatz (MLA) has been generalized by introducing a hybrid (HB) wavefunction as a starting wavefunction, whose potential can flexibly change from the Hartree–Fock type to the alloy-analogy type by varying a weighting factor from zero to one. Numerical results based on the half-filled band Hubbard model on the hypercubic lattice in infinite dimensions show up that the new wavefunction yields the ground-state energy lower than that of the Gutzwiller wavefunction (GW) in the whole Coulomb interaction regime. Calculated double occupation number is smaller than the result of the GW in the weak Coulomb interaction regime, and remains finite in the strong regime. Furthermore, the momentum distribution shows a distinct momentum dependence, which is qualitatively different from that of the GW.

Momentum Dependent Local-Ansatz Wavefunction from Weak to Strong Electron Correlations

Momentum dependent local-ansatz (MLA) wavefunction describes accurately electron correlations from the weak to intermediate Coulomb interaction regimes. We point out that the MLA can describe the correlations from the weak to strong Coulomb interaction regimes by modifying the starting wavefunction from the Hartree-Fock (HF) type to an alloy-analogy (AA) type wavefunction. Numerical results based on the half-filled band Hubbard model on the hypercubic lattice in infinite dimensions show up that the new wavefunction yields the ground-state energy lower than the Gutzwiller wavefunction (GW) in the whole Coulomb interaction regime. Calculated double occupation number is smaller than the result of the GW in the metallic regime, and is finite in the insulator regime. Furthermore, the momentum distribution shows a distinct momentum-dependence in both the metallic and insulator regions, which are qualitatively different from those of the GW.