Hartree-Fock Approach Research Articles

On the physical interpretation of the nuclear molecular orbital energy.

Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.

Semi-empirical calculations of radiative decay rates in Mo II. A comparison between oscillator strength parametrization and core-polarization-corrected relativistic Hartree-Fock approaches

We present a semi-empirical determination of Mo II radiative parameters in a wide wavelength range 1716–8789Å. Our fitting procedure to experimental oscillator strengths available in the literature permits us to provide reliable values for a large number of Mo II lines, predicting previously unmeasured oscillator strengths of lines involving 4d45p and 4d35s5p odd-parity configurations. The extracted transition radial integral values are compared with ab-initio calculations: on average they are 0.88 times the values obtained with the basic pseudo-relativistic Hartree Fock method and they agree well when core polarization effects are included. When making a survey of our present and previous studies and including also those given in the literature we observe as general trends a decreasing of transition radial integral values with filling nd shells of the same principal quantum numbers for ndk(n + 1)s→ndk(n + 1)p transitions.

BIASING FIELD EFFECTS ON ELECTRONIC PROPERTIES IN HALOGENATED PHENYLENE ETHYNYLENE OLIGOMERS

In this paper results from ab initio simulations of the electronic structure properties of a class of halogenated phenylene ethynylene oligomers (OPE) are presented. These molecular species are investigated because of their suitable properties for application as single-molecule switches in the future emerging molecular electronic devices. Combined Hartree-Fock and Density Functional Theory approach is applied to investigate the biasing field effects on the relevant electronic properties, such as potential energy of the ground states, potential barrier height, localization of frontier molecular orbitals and the HOMO-LUMO gap. Special attention is also paid on the effects of substitution of the hydrogen atoms in the central phenylene ring of basic OPE molecule with halogen atoms. The analyses of the obtained results undoubtedly show that the biasing field has a strong impact on the potential barrier height, transition probabilities and band gap. Halogenation of the central phenylene ring does not have such a strong influence on the aforementioned properties, but it could be a useful way for fine tuning of some of the properties, especially the potential barrier height, enabling control of the torsional stochastic switching, inherent for the studied species.

Relativistic effects and three-nucleon forces in nuclear matter and nuclei

We review a large body of predictions obtained within the framework of relativistic meson theory together with the Dirac–Brueckner–Hartree–Fock approach to nuclear matter and finite nuclei. The success of this method has been largely related to its ability to take into account important three-body effects. Therefore, the overarching theme of this paper is the interpretation of the so-called “Dirac effects” as an effective three-nucleon force. We address the equation of state (EoS) of isospin symmetric and asymmetric nucleonic matter and related issues, ranging from proton and neutron density distributions to momentum distributions and short-range correlations. A central part of the discussion is devoted to the optical model potential for nucleon–nucleus scattering. We also take the opportunity to explore similarities and differences with predictions based on the increasingly popular chiral effective field theory.

The Thermal Properties of Asymmetric Nuclear Matter within the Extended Brueckner–Hartree–Fock Approach

The single-particle potentials and other properties at absolute zero temperature in isospin asymmetric nuclear matter are investigated in the frame of an extended Brueckner theory. Also thermal quantities are calculated in asymmetric nuclear matter using CD-Bonn potential and the Urbana three-body forces (3BF). Also, the effects of the hole–hole contributions are investigated within the self-consistent Greens function approach. The inclusion of 3BF or the hole–hole contributions improves the predicted saturation property of symmetric nuclear matter within the Brueckner–Hartree–Fock approach and it leads to a significant stiffening of the density dependence of symmetry energy at high densities but the exact saturation point is not reproduced. This is of great importance in astrophysical calculation. A phenomenological term simulating the three-body interaction is introduced to assure the empirical saturation property. The hot properties of asymmetric nuclear matter such as the internal energy and the press...

On the multi-layer multi-configurational time-dependent Hartree approach for bosons and fermions.

A multi-layer multi-configurational time-dependent Hartree (MCTDH) approach using a second quantization representation (SQR) based on optimized time-dependent orbitals is introduced. The approach combines elements of the multi-layer MCTDH-SQR approach of Wang and Thoss, which employs a preselected time-independent orbital basis, and the MCTDH for bosons and multi-configuration time-dependent Hartree-Fock approaches, which do not use multi-layering but employ time-dependent orbital bases. In contrast to existing MCTDH-type approaches, the results of the present approach for a given number of configurations are not invariant with respect to unitary transformations of the time-dependent orbital basis. Thus a natural orbital representation is chosen to achieve fast convergence with respect to the number of configurations employed. Equations of motion for the present ansatz, called (multi-layer) MCTDH in optimized second quantization representation, are derived. Furthermore, a scheme for the calculation of optimized unoccupied single-particle functions is given which can be used to avoid singularities in the equations of motion.

Theoretical and experimental investigations on linear and nonlinear optical response of metal complexes doped PMMA films

Metal organic complexes, diaceto bis benzimidazole cobalt(II) and diaceto bis benzimidazole copper(II), are synthesized by a simple chemical route. The synthesized powders are doped in PMMA with 1, 3, 5 wt% and deposited as free standing films of thickness ∼1 μm. For theoretical simulation, metal organic complex (MOC) embedded into the PMMA matrix is subjected to polarizability and hyperpolarizability calculations using the PM6 algorithm in MOPAC2012 package. It is found that the minimum interaction distance between PMMA and MOC is about 34 nm and does not vary with respect to the dopant. The copper complex shows higher interaction energy with the polymer matrix than the cobalt complex. Time dependent Hartree Fock approach is used to calculate the α, β and γ values for static, 0.25 and 0.5 eV energies; the cobalt complex shows higher polarizability and hyperpolarizability than the copper complex. Experimentally, the optical absorption, thermo-optic coefficient, nonlinear absorption coefficient and nonlinear refractive index of the samples are determined. The thermo-optic coefficients of the samples are seen to increase with increasing dopant concentration. From open aperture Z-scan studies the films are found to exhibit reverse saturable absorption behaviour, and from the closed aperture Z-scan all samples are found to exhibit self-focusing effects. The calculated third order susceptibility is in the order of 10−5 esu. The optical limiting properties are studied at 650 nm using a 20 mW laser and all the samples are found to exhibit good optical limiting in the operating wavelength.

Microscopic optical model potential based on a Dirac Brueckner Hartree Fock approach and the relevant uncertainty analysis

A relativistic microscopic optical model potential, named CTOM , for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock approach. The microscopic feature of CTOM is guaranteed through rigorously adopting the isospin dependent DBHF calculation within the subtracted T matrix scheme. In order to verify its prediction power, a global study n , p + A scattering are carried out. The predicted scattering observables coincide with experimental data within a good accuracy over a broad range of targets and a large region of energies only with two free items, namely the free-range factor t in the applied improved local density approximation and minor adjustments of the scalar and vector potentials in the low-density region. In addition, to estimate the uncertainty of the theoretical results, the deterministic simple least square approach is preliminarily employed to derive the covariance of predicted angular distributions, which is also briefly contained in this paper.

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.

Spiral magnetic phases on the Kondo Lattice Model: A Hartree–Fock approach

We study the Kondo Lattice Model (KLM) on a square lattice through a Hartree–Fock approximation in which the local spins are treated semi-classically, in the sense that their average values are modulated by a magnetic wavevector Q while they couple with the conduction electrons through fermion operators. In this way, we obtain a ground state phase diagram in which spiral magnetic phases (in which the wavevector depends on the coupling constants and on the density) interpolate between the low-density ferromagnetic phase and the antiferromagnetic phase at half filling; within small regions of the phase diagram commensurate magnetic phases can coexist with Kondo screening. We have also obtained ‘Doniach-like’ diagrams, showing the effect of temperature on the ground state phases, and established that for some ranges of the model parameters (the exchange coupling and conduction electron density) the magnetic wavevector changes with temperature, either continuously or abruptly (e.g., from spiral to ferromagnetic).

Solution of the Kohn–Sham equations for many-electron atoms confined by penetrable walls

The solution of the Kohn–Sham equations in the Roothaan’s context is presented for atoms confined by penetrable walls. A new basis set is employed in this work, which was designed within the Hartree–Fock approach to ensure a correct decay on the electron density. Exchange-correlation functionals from local density and generalized gradient approximation are considered in the implementation of the Kohn–Sham method. The confinement effects on energies (total and orbital) and on the exchange potential are discussed when two exchange-only functionals are compared with the Hartree–Fock method, for closed-shell atoms confined by finite potentials. Clearly, the wrong asymptotic behavior exhibited by the exchange-only Kohn–Sham potentials, considered in this work, has a large impact on orbital energies when several confinements are tested. In fact, such exchange potentials predict orbital energies which are drastically different than those predicted by the Hartree–Fock method. These differences are not restricted just to absolute values, also the trend observed for exchange and orbital energies is quite different than that predicted by Hartree–Fock. Effects of the correlation contribution are also discussed on total and orbital energies, which show same trends than those obtained by exchange-only functionals. Unfortunately, there are no implementations of correlated methods based on the wave-function for this kind of problems, and consequently our results for correlation energy cannot be compared with a reference. With this implementation there is one possibility to test the performance of approximate exchange-correlation functionals, in addition to the sets commonly used in the design of new functionals.

Nuclear matter saturation with chiral three-nucleon interactions fitted to light nuclei properties

Abstract The energy per particle of symmetric nuclear matter and pure neutron matter is calculated using the many-body Brueckner–Hartree–Fock approach and employing the Chiral Next-to-next-to-next-to leading order (N3LO) nucleon–nucleon (NN) potential, supplemented with various parametrizations of the Chiral Next-to-next-to leading order (N2LO) three-nucleon interaction. Such combination is able to reproduce several observables of the physics of light nuclei for suitable choices of the parameters entering in the three-nucleon interaction. We find that some of these parametrizations provide a satisfactory saturation point of symmetric nuclear matter and values of the symmetry energy and its slope parameter L in very good agreement with those extracted from various nuclear experimental data. Thus, our results represent a significant step toward a unified description of few- and many-body nuclear systems starting from two- and three-nucleon interactions based on the symmetries of QCD.

Sensitivity of the fusion cross section to the density dependence of the symmetry energy

It is the aim of this paper to discuss the impact of nuclear fusion on the EOS. This is a timely subject given the expected availability of increasingly exotic beams at rare isotope facilities\,\cite{balantekin2014}. In practice, we focus on $^{48}$Ca+$^{48}$Ca fusion. We employ three different approaches to calculate fusion cross-sections for a set of energy density functionals with systematically varying nuclear matter properties. Fusion calculations are performed using frozen densities, using a dynamic microscopic method based on density-constrained time-dependent Hartree-Fock (DC-TDHF) approach, as well as direct TDHF study of above barrier cross-sections. For these studies, we employ a family of Skyrme parametrizations with systematically varied nuclear matter properties. We find a slight preference for forces which deliver a slope of symmetry energy of $L\approx 50$\,MeV that corresponds to a neutron-skin thickness of $^{48}$Ca of $R_\mathrm{skin}\!=\!(0.180\!-\!0.210)$\,fm.

Extension and parametrization of high-order density dependence in Skyrme forces

The three-body force is indispensable in nuclear energy density functionals which leads to a density dependent two-body term in the Hartree-Fock approach. Usually a single factional power of density dependency has been adopted. We consider the possibility of an additional higher-order density dependence in extended Skyrme forces. As a result, new extended Skyrme parametertizations based on the SLy4 force are obtained and the improvements in descriptions of global nuclei have been demonstrated. The higher-order term can also substantially affect nuclear properties in the high density region in general ways.

Theoretical study of the effect of π-conjugated transmitter of D–π–A ruthenium systems on the quadratic NLO properties

In this work, we present the theoretical quantum chemical calculation of effect of π-conjugated transmitter variation of two types of acceptor based on barbituric acid (with R=H or R=Me) of the organometallic molecules. The one-photon absorption OPA, dipole moments (μ), first hyperpolarizabilities (β), frontier molecular orbital energies based on the semi-empirical ZINDO/1 method within a framework of the restricted Hartree–Fock approach have been calculated. This method was employed to study relationship between first hyperpolarizabilities and the a kind of transmitter of π-conjugated ligand in the investigated organometallic compounds. Using this method, we found excellent agreement with experimental S1 → S0 excitation energies. The investigated complexes show large optical second order nonlinearities in comparison with metal alkynyl and related complexes.

Coulomb and tunneling-coupled trilayer systems at zero magnetic field

The ground-state electronic configuration of three coupled bidimensional electron gases has been determined using a variational Hartree-Fock approach, at zero magnetic field. The layers are Coulomb coupled, and tunneling is present between neighboring layers. In the limit of small separation between layers, the tunneling becomes the dominant energy contribution, while for large distance between layers the physics is driven by the Hartree electrostatic energy. Transition from tunneling to hartree dominated physics is shifted towards larger layer separation values as the total bidimensional density of the trilayers decreases. The inter-layer exchange helps in stabilize a "balanced" configuration, where the three layers are approximately equally occupied; most of the experiments are performed in the vicinity of this balanced configuration. Several ground-state configurations are consequence of a delicate interplay between tunneling and inter-subband exchange.

ROLE OF NUCLEONIC FERMI SURFACE DEPLETION IN NEUTRON STAR COOLING

ABSTRACT The Fermi surface depletion of beta-stable nuclear matter is calculated to study its effects on several physical properties that determine the neutron star (NS) thermal evolution. The neutron and proton Z factors measuring the corresponding Fermi surface depletions are calculated within the Brueckner–Hartree–Fock approach, employing the AV18 two-body force supplemented by a microscopic three-body force. Neutrino emissivity, heat capacity, and in particular neutron 3 PF 2 superfluidity, turn out to be reduced, especially at high baryonic density, to such an extent that the cooling rates of young NSs are significantly slowed.

Characterization of the copper Kβ x-ray emission profile: an ab initio multi-configuration Dirac–Hartree–Fock approach with Bayesian constraints

We investigate the characteristic radiation and the complex asymmetric structure of photoemission lines of copper, which provides a benchmark for theoretical and experimental studies of x-ray calibration series in transition metals. Ab initio multi-configuration Dirac–Hartree–Fock (MCDHF) calculations have been performed to study the complex open-shell many-electron problem in copper. The biorthogonalization technique permits determination of transition intensities and Einstein A coefficients. The results from our MCDHF calculations demonstrate excellent convergence in transition energies and intensities, as well as gauge invariance to 0.6%. Shake processes caused by single and double spectator vacancies from 3d, 3p, 3s and 4s subshells have also been investigated extensively. MCDHF has been performed to calculate energies and relative intensities of 3d, 3d2, 3p, 3s and 4s satellites, resulting in the total number of configuration states exceeding 100 000 and more than 1500 transition components. Our theoretical calculations of shake-off probabilities using the multi-configuration method in the sudden limit have a high degree of internal consistency with the best available experimental data for copper . This supports the validity of relativistic atomic theory and sets a new benchmark even for poorly resolved characteristic spectra using current techniques of analysis.

Quasifission dynamics in TDHF

For light and medium mass systems the capture cross-section may be considered to be the same as that for complete fusion, whereas for heavy systems leading to superheavy formations the evaporation residue cross-section is dramatically reduced due to the quasifission (QF) and fusion-fission processes thus making the capture cross-section to be essentially the sum of these two cross-sections, with QF occurring at a much shorter time-scale. Consequently, quasifission is the primary reaction mechanism that limits the formation of superheavy nuclei. Within the last few years the time-dependent Hartree-Fock (TDHF) approach has been utilized for studying the dynamics of quasifission. The study of quasifission is showing a great promise to provide insight based on very favorable comparisons with experimental data. In this article we will focus on the TDHF calculations of quasifission observables for the $^{48}$Ca+$^{249}$Bk system.

Superfluid fission dynamics with microscopic approaches

Recent progresses in the description of the latter stage of nuclear fission are reported. Dynamical effects during the descent of the potential towards scission and in the formation of the fission fragments are studied with the time-dependent Hartree-Fock approach with dynamical pairing correlations at the BCS level. In particular, this approach is used to compute the final kinetic energy of the fission fragments. Comparison with experimental data on the fission of 258Fm are made.