Hartree-Fock Results Research Articles

Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation

We present a dynamical second-order kernel for the Bethe-Salpeter equation to calculate electronic excitation energies. The derivation takes explicitly the functional derivative of the exact second-order self energy with respect to the one-particle Green's function. It includes naturally a frequency dependence, going beyond the adiabatic approximation. Perturbative calculations under the Tamm-Dancoff approximation, using the configuration interaction singles (CIS) eigenvectors, reveal an appreciable improvement over CIS, time-dependent Hartree-Fock, and adiabatic time-dependent density functional theory results. The perturbative results also compare well with equation-of-motion coupled-cluster and experimental results.

Topological antiferromagnetic phase in a correlated Bernevig-Hughes-Zhang model

Topological properties of antiferromagnetic phases are studied for a correlated topological band insulator by applying the dynamical mean field theory to an extended Bernevig-Hughes-Zhang model including the Hubbard interaction. The calculation of the magnetic moment and the spin Chern number confirms the existence of a non-trivial antiferromagnetic (AF) phase beyond the Hartree-Fock theory. In particular, we uncover the intriguing fact that the topologically non-trivial AF phase is essentially stabilized by correlation effects but not by the Hartree shifts alone. This counterintuitive effect is demonstrated, through a comparison with the Hartree-Fock results, and should apply for generic topological insulators with strong correlations.

An Improvement on Noninteger n-Generalized Exponential Type Orbitals with Hyperbolic Cosine in Atomic Calculations

Abstract An improvement on the total energy results reported in Ref. 9 in atomic calculations based on a modified type hyperbolic cosine function cosh(βrμ + γ) is presented. It is shown that the noninteger n-generalized exponential type orbitals rn* - 1e- ζ rμ with modified type hyperbolic cosine as radial basis functions are a much better approximation to the Hartree–Fock orbitals than a double-zeta basis set of Slater type functions. The efficiency of the new basis function is tested by application to some closed and open shell neutral atoms and their ions. A substantial improvement in both the total and orbital energies is obtained within the minimal basis sets framework. The total energy values obtained in this work are significantly close to the numerical Hartree–Fock results. These results supersede all previous minimal basis function total energies achieved in the literature.

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.

Hyperpolarizability of two electron atoms under spherically confined Debye plasma

Pilot calculations on the hyperpolarizability of He, the first neutral member of the two electron sequence, have been performed under spherical confinement with a view to analyse the effect of pressure on such non linear optical properties. Detailed investigations have also been performed for the first time on the hyperpolarizability due to the effect of screened Coulomb potential obtained from a surrounding Debye plasma environment. Variation perturbation theory within coupled Hartree-Fock scheme has been adopted to estimate the non linear optical properties under such external confinement. For a given plasma coupling strength, the hyperpolarizability value is found to reduce systematically with decrease of radius of confinement, while the same is found to increase continuously with increasing plasma coupling strength determined by gradual enhancement of the screening parameter for a given radius of confinement. Under strong confinement the hyperpolarizability value is found to be negative. The estimated free atom hyperpolarizability is consistent with the existing coupled Hartree-Fock result.

Symmetry energy within the BHF approach

We analyze the correlations of the slope and curvature parameters of the symmetry energy with the neutron skin thickness of neutron-rich isotopes, and the crust-core transition density in neutron stars. Microscopic Brueckner–Hartree–Fock results are compared with those obtained with several Skyrme and relativistic mean field models. Our results confirm that there is an inverse correlation between the neutron skin thickness and the transition density.

Koopmans’ Transfer Integral Calculation: A Comparison between the Hartree-Fock and the Density Functional Results

The prediction of the charge mobility in conjugated organic systems is of great interest in order to evaluate their potential use as active materials in a wide class of devices. In this field, one of the most used approaches for modeling this process is the Marcus theory, where one of the key parameters to be calculated is the intermolecular transfer integral, J. Different methods have been developed for J calculations, based initially on the Hartree-Fock Hamiltonian and more recently on the density functional ones. However, in literature only few works were focused on the reliability of the values of the intermolecular transfer integrals obtained with density functional calculations. Here, by using the energy-splitting-in-dimer approach we discuss the results of a study on the dependence of J on the type of the density functional approach used and compare them with data from Hartree-Fock Hamiltonian. We found that, under the hypothesis of the Koopmans approach, the Hartree-Fock and density functional results can be seen as the upper and lower limits, respectively, of the corresponding experimental value.

Ultrafast photoionization dynamics at high laser intensities in the xuv regime

We study the ionization dynamics in the soft-x-ray regime for high intensities and short pulses for excitations near the ionization threshold. Using a one-dimensional helium atom model, we compare exact numerical solutions with time-dependent Hartree-Fock results in order to identify the role of electron-electron correlations. At moderate intensities but still in the x-ray and short-pulse regime, we find that the Hartree-Fock theory reproduces well the dynamics of the ground-state occupation, while at high intensities strong correlation effects occur for excitations close to the threshold. From their characteristic momentum distributions, we can identify contributions to the double ionization from sequential three-photon and nonsequential or sequential two-photon processes. At elevated intensities these contributions deviate from their usual intensity scaling due to saturation effects, even though the total double-ionization probability stays below 10%. Furthermore, analysis of the time evolution of the momentum distribution reveals signatures of the energy-time uncertainty which indicate a coherent regime of the dynamics.

Nonequilibrium steady states for interacting open systems: Exact results

Under certain conditions we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our time-dependent scattering approach is {\it exact} and proves, among other things the independence of the steady-state quantities from the initial state of the sample. Closed formulas for the steady-state current amenable for perturbative calculations w.r.t. the interaction strength are also derived. In the partitioning case we calculate the first order correction and recover the mean-field (Hartree-Fock) results.

Average Local Ionization Energies as a Route to Intrinsic Atomic Electronegativities

Historically, two important approaches to the concept of electronegativity have been in terms of: (a) an atom in a molecule (e.g., Pauling) and (b) the chemical potential. An approximate form of the latter is now widely used for this purpose, although it includes a number of deviations from chemical experience. More recently, Allen introduced an atomic electronegativity scale based upon the spectroscopic average ionization energies of the valence electrons. This has gained considerable acceptance. However it does not take into account the interpenetration of valence and low-lying subshells, and it also involves some ambiguity in enumerating d valence electrons. In this paper, we analyze and characterize a formulation of relative atomic electronegativities that is conceptually the same as Allen's but avoids the aforementioned problems. It involves the property known as the average local ionization energy, I̅(r), defined as [Formula: see text], where ρi(r) is the electronic density of the i(th) orbital, having energy εi, and ρ(r) is the total electronic density. I̅(r) is interpreted as the average energy required to remove an electron at the point r. When I̅(r) is averaged over the outer surfaces of atoms, taken to be the 0.001 au contours of their electronic densities, a chemically meaningful scale of relative atomic electronegativities is obtained. Since the summation giving I̅(r) is over all occupied orbitals, the issues of subshell interpenetration and enumeration of valence electrons do not arise. The procedure is purely computational, and all of the atoms are treated in the same straightforward manner. The results of several different Hartree-Fock and density functional methods are compared and evaluated; those produced by the Perdew-Burke-Ernzerhof functional are chemically the most realistic.

Support vector machine regression (LS-SVM)—an alternative to artificial neural networks (ANNs) for the analysis of quantum chemistry data?

A multilayer feed-forward artificial neural network (MLP-ANN) with a single, hidden layer that contains a finite number of neurons can be regarded as a universal non-linear approximator. Today, the ANN method and linear regression (MLR) model are widely used for quantum chemistry (QC) data analysis (e.g., thermochemistry) to improve their accuracy (e.g., Gaussian G2-G4, B3LYP/B3-LYP, X1, or W1 theoretical methods). In this study, an alternative approach based on support vector machines (SVMs) is used, the least squares support vector machine (LS-SVM) regression. It has been applied to ab initio (first principle) and density functional theory (DFT) quantum chemistry data. So, QC + SVM methodology is an alternative to QC + ANN one. The task of the study was to estimate the Møller-Plesset (MPn) or DFT (B3LYP, BLYP, BMK) energies calculated with large basis sets (e.g., 6-311G(3df,3pd)) using smaller ones (6-311G, 6-311G*, 6-311G**) plus molecular descriptors. A molecular set (BRM-208) containing a total of 208 organic molecules was constructed and used for the LS-SVM training, cross-validation, and testing. MP2, MP3, MP4(DQ), MP4(SDQ), and MP4/MP4(SDTQ) ab initio methods were tested. Hartree-Fock (HF/SCF) results were also reported for comparison. Furthermore, constitutional (CD: total number of atoms and mole fractions of different atoms) and quantum-chemical (QD: HOMO-LUMO gap, dipole moment, average polarizability, and quadrupole moment) molecular descriptors were used for the building of the LS-SVM calibration model. Prediction accuracies (MADs) of 1.62 ± 0.51 and 0.85 ± 0.24 kcal mol(-1) (1 kcal mol(-1) = 4.184 kJ mol(-1)) were reached for SVM-based approximations of ab initio and DFT energies, respectively. The LS-SVM model was more accurate than the MLR model. A comparison with the artificial neural network approach shows that the accuracy of the LS-SVM method is similar to the accuracy of ANN. The extrapolation and interpolation results show that LS-SVM is superior by almost an order of magnitude over the ANN method in terms of the stability, generality, and robustness of the final model. The LS-SVM model needs a much smaller numbers of samples (a much smaller sample set) to make accurate prediction results. Potential energy surface (PES) approximations for molecular dynamics (MD) studies are discussed as a promising application for the LS-SVM calibration approach.

Time-dependent second-order Born calculations for model atoms and molecules in strong laser fields

Using the finite-element discrete variable representation of the nonequilibrium Green's function (NEGF) we extend previous work [K. Balzer et al., Phys. Rev. A 81, 022510 (2010)] to nonequilibrium situations and compute---from the two-time Schwinger-Keldysh-Kadanoff-Baym equations---the response of the helium atom and the heteronuclear molecule lithium hydride to laser fields in the uv and xuv regimes. In particular, by comparing the one-electron density and the dipole moment to time-dependent Hartree-Fock results on one hand and the full solution of the time-dependent Schr\"odinger equation on the other hand, we demonstrate that the time-dependent second Born approximation carries valuable information about electron-electron correlation effects. Also, we outline an efficient distributed memory concept which enables a parallel and well-scalable algorithm for computing the NEGF in the two-time domain.

The electronic spectrum of AgBr 2: Ab initio benchmark vs. DFT calculations on the lowest ligand-field states including spin–orbit effects

The X 2Π g, 2Σ g + and 2Δ g states of AgBr 2 have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) and DFT calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges and spin densities. The spin–orbit (SO) effects were included through the effective hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. At the ACPF level, the ground state is 2Π g, in contradiction with ligand-field theory and Hartree–Fock results. The ACPF adiabatic excitation energies of the 2Σ g + and 2Δ g states are 3825 and 20 152 cm −1, respectively. The inclusion of the SO effects leads to a pure Ω = 3/2 ( 2Π g) ground state, a Ω = 1/2 (97% 2Π g + 3% 2Σ g +) A state, a Ω = 1/2 (3% 2Π g + 97% 2Σ g +) B state, a Ω = 5/2 ( 2Δ g) C state and a Ω = 3/2 (99% 2Δ g) D state. The B97, B3LYP and PBE0 functionals, which were shown to yield accurate transition energies for CuCl 2, overestimate the X 2Π g– 2Σ g + T e by around 25% but provide a qualitative energetic ordering in agreement with CASSCF and ACPF results. The nature of the bonding in the X 2Π g ground state is different from that of AgCl 2 since the Mulliken charge on the metal is 0.95 while the spin density is only 0.39. DFT strongly delocalizes the spin density providing even smaller values of around 0.13 on Ag not only for the ground state, but also for the 2Σ g + state.

Hartree–Fock perturbative corrections for total and reaction energies

We have performed an assessment of the Hartree-Fock perturbative correction (HFPC) on a large and diverse set of molecules and reactions. Errors in both absolute and reaction energies with respect to converged secondary basis Hartree-Fock results are reported for a wide spectrum of primary/secondary basis set combinations. These results show that using an adequate primary basis, HFPC can accurately reproduce secondary basis energies at a substantially reduced cost. Comparisons of HFPC with the related dual basis Hartree-Fock (DBHF) scheme are also made for several molecules and target secondary basis sets. Our results indicate that HFPC is faster and more accurate than DBHF for approaching triple-zeta basis sets. For quadruple-zeta secondary basis sets, HFPC is capable of yielding more accurate energies at a marginally increased cost over DBHF.

Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states

We explain how to implement, in the context of projected entangled-pair states (PEPS), the general procedure of fermionization of a tensor network introduced in [P. Corboz, G. Vidal, Phys. Rev. B 80, 165129 (2009)]. The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the t-J model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.

Existence of excitonic insulator phase in the extended Falicov-Kimball model: SO(2)-invariant slave-boson approach

We re-examine the three-dimensional spinless Falicov-Kimball model with dispersive $f$ electrons at half-filling, addressing the dispute about the formation of an excitonic condensate, which is closely related to the problem of electronic ferroelectricity. To this end, we work out a slave-boson functional integral representation of the suchlike extended Falicov-Kimball model that preserves the $SO(2)\otimes U(1)^{\otimes 2}$ invariance of the action. We find a spontaneous pairing of $c$ electrons with $f$ holes, building an excitonic insulator state at low temperatures, also for the case of initially non-degenerate orbitals. This is in contrast to recent predictions of scalar slave-boson mean-field theory but corroborates previous Hartree-Fock and RPA results. Our more precise treatment of correlation effects, however, leads to a substantial reduction of the critical temperature. The different behavior of the partial densities of states in the weak and strong inter-orbital Coulomb interaction regimes supports a BCS-BEC transition scenario.

Simplified one-dimensional calculation of 13.5 nm emission in a tin plasma including radiation transport

Many next generation lithography schemes for the semiconductor industry are based on a 13.5 nm tin plasma light source, where hundreds of thousands of 4d-4f, 4p-4d, and 4d-5p transitions from Sn5+–Sn13+ ions overlap to form an unresolved transition array. To aid computation, transition arrays are treated statistically, and Hartree–Fock results are used to calculate radiation transport in the optically thick regime with a one-dimensional Lagrangian plasma hydrodynamics code. Time-dependent spectra and conversion efficiencies of 2% in-band 13.5 nm emission to laser energy are predicted for a Nd:YAG (yttrium aluminum garnet) laser incident on a pure tin slab target as a function of laser power density and pulse duration at normal incidence. Calculated results showed a maximum conversion efficiency of 2.3% for a 10 ns pulse duration at 8.0×1010 W/cm2 and are compared to experimental data where available. Evidence for the need to include lateral expansion is presented.

Quantum Monte Carlo study of the two-dimensional electron gas in presence of Rashba interaction

We introduce a variant to the Diffusion Monte Carlo algorithm that can be employed to study the effects of the Rashba interaction in a many electron systems. Because of the spin--orbit nature of Rashba interaction a standard algorithm cannot be applied and therefore a specific imaginary time spin dependent propagator has been developed and implemented following previous work developed in the framework of nuclear physics. We computed the ground state energy of the 2D electron gas at different densities for several values of the Rashba interaction strength as a function of "Rashba spin states" polarization. Comparison is given with analytically known Hartree-Fock results and for the system in absence of Coulomb interaction.

Neural network approach to quantum-chemistry data: Accurate prediction of density functional theory energies

Artificial neural network (ANN) approach has been applied to estimate the density functional theory (DFT) energy with large basis set using lower-level energy values and molecular descriptors. A total of 208 different molecules were used for the ANN training, cross validation, and testing by applying BLYP, B3LYP, and BMK density functionals. Hartree-Fock results were reported for comparison. Furthermore, constitutional molecular descriptor (CD) and quantum-chemical molecular descriptor (QD) were used for building the calibration model. The neural network structure optimization, leading to four to five hidden neurons, was also carried out. The usage of several low-level energy values was found to greatly reduce the prediction error. An expected error, mean absolute deviation, for ANN approximation to DFT energies was 0.6+/-0.2 kcal mol(-1). In addition, the comparison of the different density functionals with the basis sets and the comparison of multiple linear regression results were also provided. The CDs were found to overcome limitation of the QD. Furthermore, the effective ANN model for DFT/6-311G(3df,3pd) and DFT/6-311G(2df,2pd) energy estimation was developed, and the benchmark results were provided.

Theoretical considerations on high Tc superconductivity

In the Introduction of the paper the different theoretical models for the prediction of high Tc superconductivity, which were done before its discovery in ceramic materials, are reviewed. After this a number of models to interpret the experimentally found high superconductive transition temperature are mentioned. In the second part of the paper the results of Hartree-Fock and DODS band structure calculations on (Cu–O)x chains and on the 2-dimensional Cu–O plane are presented. We have found that in the 2D case the Fermi level is in a broad band due to O 2p orbitals, while there are narrow Cu 3d bands in the valence band region. This gives the possibility that the polarization of the localized electrons in the narrow bands provide an effective attraction between the mobile electrons in the broad band which can lead to formation of Cooper pairs and therefore also to a superconductive state. The DODS calculation of the (Cu–O)x chain leads to a spin alternation on the O atom in agreement with the experimentally found antiferromagnetic behavior of the ceramic materials. This gives rise to a spin-polaron (through a spin-flip) mechanism of superconductivity if positive holes are formed. Finally it is discussed how the band structures of the ceramic materials could be improved by taking into account charge transfer between the planes (via different cluster calculations), the effect of the Madelung potential of the crystal and last but not least correcting the bands for correlation effects using a generalized electronic polaron model.