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At least 1,531 records · Page 85
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DOE OSTI2014

Development of ferroelectric correlations in the quantum paraelectric and antiferrodistortive regimes in Ba{sub x}Sr{sub 1-x}TiO{sub 3} (x ≤ 0.10)

The dielectric response ε(T) of Ba{sub x}Sr{sub 1-x}TiO{sub 3} (x ≤ 0.1) for compositions at and below the critical composition for the ferroelectric transition has been studied. With progressive Ba substitution, the growth of ferroelectric correlations and the weakening of the Antiferrodistortive (AFD) and the quantum paraelectric (QPE) effects have been studied by monitoring the changes in both the in and out of phase parts of the dielectric response. For the compositions close to pure SrTiO{sub 3} (x = 0 and x = 0.02), the temperature dependence exhibits a continuous rise in the in-phase part and no ferroelectric peak, consistent with the QPE behavior. With increasing Ba substitution, the low temperature behavior of the in phase part ε{sup ′} progressively changes from a continuous rise to exhibit a weak maximum and finally to a well developed cusp. For higher Ba concentrations, the low temperature peak (T ∼ 50K), which corresponds to ferroelectric correlations, becomes increasingly sharper until at the critical composition, x = 0.10, the system shows a single well defined ferroelectric peak. However, the out of phase response of the x = 0.1 composition exhibited a succession of three BaTiO{sub 3} type ferroelectric transitions. For x≤0.04, the out of phase part shows evidence of an ordering around T ∼ 100K, which is the expected AFD ordering temperature. The deviations of the ε{sup ′}(T) data from the Curie-Weiss law have been analyzed within the frame work of two different theoretical models. It was determined that the dielectric behavior for lower concentrations of Ba (up to x ≤ 0.08) was explainable in terms of a model of non-interacting regions which are themselves homogeneously polarized and undergo a second order phase transition. For the phase boundary composition, i.e., x = 0.1, on the other hand, the data are explainable in terms of the Sherrington and Kirkpatrick model which includes the effects of weak correlations between the polar regions characterized by a glassy order parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Analytical estimation of the correlation dimension of integer lattices

Recently [L. Lacasa and J. Gómez-Gardeñes, Phys. Rev. Lett. 110, 168703 (2013)], a fractal dimension has been proposed to characterize the geometric structure of networks. This measure is an extension to graphs of the so called correlation dimension, originally proposed by Grassberger and Procaccia to describe the geometry of strange attractors in dissipative chaotic systems. The calculation of the correlation dimension of a graph is based on the local information retrieved from a random walker navigating the network. In this contribution, we study such quantity for some limiting synthetic spatial networks and obtain analytical results on agreement with the previously reported numerics. In particular, we show that up to first order, the correlation dimension β of integer lattices ℤ{sup d} coincides with the Haussdorf dimension of their coarsely equivalent Euclidean spaces, β = d.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Towards numerically accurate many-body perturbation theory: Short-range correlation effects

The example of the uniform electron gas is used for showing that the short-range electron correlation is difficult to handle numerically, while it noticeably contributes to the self-energy. Nonetheless, in condensed-matter applications studied with advanced methods, such as the GW and random-phase approximations, it is common to neglect contributions due to high-momentum (large q) transfers. Then, the short-range correlation is poorly described, which leads to inaccurate correlation energies and quasiparticle spectra. To circumvent this problem, an accurate extrapolation scheme is proposed. It is based on an analytical derivation for the uniform electron gas presented in this paper, and it provides an explanation why accurate GW quasiparticle spectra are easy to obtain for some compounds and very difficult for others.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Stability conditions for exact-exchange Kohn-Sham methods and their relation to correlation energies from the adiabatic-connection fluctuation-dissipation theorem

The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N{sub 2}, O{sub 2}, and the polyyne C{sub 10}H{sub 2}) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Narrowing the error in electron correlation calculations by basis set re-hierarchization and use of the unified singlet and triplet electron-pair extrapolation scheme: Application to a test set of 106 systems

A method previously suggested to calculate the correlation energy at the complete one-electron basis set limit by reassignment of the basis hierarchical numbers and use of the unified singlet- and triplet-pair extrapolation scheme is applied to a test set of 106 systems, some with up to 48 electrons. The approach is utilized to obtain extrapolated correlation energies from raw values calculated with second-order Møller-Plesset perturbation theory and the coupled-cluster singles and doubles excitations method, some of the latter also with the perturbative triples corrections. The calculated correlation energies have also been used to predict atomization energies within an additive scheme. Good agreement is obtained with the best available estimates even when the (d, t) pair of hierarchical numbers is utilized to perform the extrapolations. This conceivably justifies that there is no strong reason to exclude double-zeta energies in extrapolations, especially if the basis is calibrated to comply with the theoretical model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Correlated electron pseudopotentials for 3d-transition metals

A recently published correlated electron pseudopotentials (CEPPs) method has been adapted for application to the 3d-transition metals, and to include relativistic effects. New CEPPs are reported for the atoms Sc − Fe, constructed from atomic quantum chemical calculations that include an accurate description of correlated electrons. Dissociation energies, molecular geometries, and zero-point vibrational energies of small molecules are compared with all electron results, with all quantities evaluated using coupled cluster singles doubles and triples calculations. The CEPPs give better results in the correlated-electron calculations than Hartree-Fock-based pseudopotentials available in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Correlation consistent basis sets for the atoms In–Xe

In this work, the correlation consistent family of Gaussian basis sets has been expanded to include all-electron basis sets for In–Xe. The methodology for developing these basis sets is described, and several examples of the performance and utility of the new sets have been provided. Dissociation energies and bond lengths for both homonuclear and heteronuclear diatomics demonstrate the systematic convergence behavior with respect to increasing basis set quality expected by the family of correlation consistent basis sets in describing molecular properties. Comparison with recently developed correlation consistent sets designed for use with the Douglas-Kroll Hamiltonian is provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Relativistic four-component calculations of indirect nuclear spin-spin couplings with efficient evaluation of the exchange-correlation response kernel

In this work, we report on the development and implementation of a new scheme for efficient calculation of indirect nuclear spin-spin couplings in the framework of four-component matrix Dirac-Kohn-Sham approach termed matrix Dirac-Kohn-Sham restricted magnetic balance resolution of identity for J and K, which takes advantage of the previous restricted magnetic balance formalism and the density fitting approach for the rapid evaluation of density functional theory exchange-correlation response kernels. The new approach is aimed to speedup the bottleneck in the solution of the coupled perturbed equations: evaluation of the matrix elements of the kernel of the exchange-correlation potential. The performance of the new scheme has been tested on a representative set of indirect nuclear spin-spin couplings. The obtained results have been compared with the corresponding results of the reference method with traditional evaluation of the exchange-correlation kernel, i.e., without employing the fitted electron densities. Overall good agreement between both methods was observed, though the new approach tends to give values by about 4%-5% higher than the reference method. On the average, the solution of the coupled perturbed equations with the new scheme is about 8.5 times faster compared to the reference method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The Coulomb, exchange, and correlation components of the electron-electron repulsion in harmonium atoms

Highly accurate Coulomb, exchange, and correlation components of the electron-electron repulsion energies of the three-electron harmonium atoms in the {sup 2}P{sub −} and {sup 4}P{sub +} states are obtained for 19 values of the confinement strength ω ranging from 10{sup −3} to 10{sup 3}. The computed data are consistent with their ω → 0 and ω → ∞ asymptotics that are given by closed-form algebraic expressions. Robust approximants that accurately reproduce the actual values of the energy components while strictly conforming to these limits are constructed, opening an avenue to stringent tests capable of predicting the performance of electronic structure methods for systems with varying extents of the dynamical and nondynamical electron correlation. The values of the correlation components, paired with the computed 1-matrices are expected to be particularly useful in the context of benchmarking of approximate density matrix functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

One-electron reduced density matrices of strongly correlated harmonium atoms

Explicit asymptotic expressions are derived for the reduced one-electron density matrices (the 1-matrices) of strongly correlated two- and three-electron harmonium atoms in the ground and first excited states. These expressions, which are valid at the limit of small confinement strength ω, yield electron densities and kinetic energies in agreement with the published values. In addition, they reveal the ω{sup 5/6} asymptotic scaling of the exchange components of the electron-electron repulsion energies that differs from the ω{sup 2/3} scaling of their Coulomb and correlation counterparts. The natural orbitals of the totally symmetric ground state of the two-electron harmonium atom are found to possess collective occupancies that follow a mixed power/Gaussian dependence on the angular momentum in variance with the simple power-law prediction of Hill’s asymptotics. Providing rigorous constraints on energies as functionals of 1-matrices, these results are expected to facilitate development of approximate implementations of the density matrix functional theory and ensure their proper description of strongly correlated systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Dynamical correlation effects on structure factor of spin-polarized two-dimensional electron gas

We report a theoretical study on static density structure factor S(q) of a spin-polarized two-dimensional electron gas over a wide range of electron number density r{sub s}. The electron correlations are treated within the dynamical version of the self-consistent mean-field theory of Singwi, Tosi, Land, and Sjolander, the so-called qSTLS approach. The calculated S(q) exhibits almost perfect agreement with the quantum Monte Carlo simulation data at r{sub s}=1. However, the extent of agreement somewhat diminishes with increasing r{sub s}, particularly for q around 2k{sub F}. Seen in conjunction with the success of qSTLS theory in dealing with correlations in the unpolarized phase, our study suggests that the otherwise celebrated qSTLS theory is not that good in treating the like-spin correlations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach

The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approach enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF{sup −} systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF{sup −} system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Some properties of correlations of quantum lattice systems in thermal equilibrium

Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of McBryan and Spencer for the 2D classical XY model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Correlation of structure and ion conduction in La{sub 2−x}Y{sub x}Mo{sub 2}O{sub 9} (0 ≤ x ≤ 0.2) oxygen ion conductors

Correlation of structure and ion conduction of La{sub 2−x}Y{sub x}Mo{sub 2}O{sub 9} (0 ≤ x ≤ 0.2) has been investigated. The cubic symmetry with space group P2{sub 1}3 and other structural parameters are obtained from Rietveld refinement of X-ray diffraction patterns of Y doped samples. The average lanthanum-oxygen and molybdenum-oxygen distances are obtained from the electron density contour plot. The transmission electron microscopic study confirms the cubic nature of the samples and also provides an estimate of thickness of the grain boundary. The scanning transmission electron microscope energy dispersive spectrometer mapping confirms the different orientations of grains. The composition dependence of the ionic conductivity has been correlated with that of O2 and O3 site occupancies in the [O1La{sub 3}Mo] antitetrahedral unit. The different vibrational modes in the low frequency region due to vibration of Mo-O bands are confirmed from the analysis of FTIR and Raman spectra. The full widths at half maximum of most of the Mo-O bands are found to be independent of Y doping. Additionally, the shifts in the position of Raman bands are correlated with unit cell parameter using Grüneisen constant.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Reduced density-matrix functional theory: Correlation and spectroscopy

In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Wake potential with exchange-correlation effects in semiconductor quantum plasmas

Using the non-relativistic quantum hydrodynamic model, wake potential has been studied in a magnetized semiconductor quantum plasma in the presence of upper hybrid wave which is excited via externally injected electron beam. The quantum effect contains electron exchange and correlation potential, Fermi degenerate pressure, and Bohm potential. It is found that the contribution of quantum mechanical electron exchange and correlation potential significantly modifies the amplitude and the effective length of the oscillatory wake potential. In the electron-hole plasma systems, electron exchange-correlation effects tend to increase the magnitude of the wake potential and are much effective at the distances of the order of Debye-length. The application of the work in context of the semiconductor plasmas have also been analyzed graphically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach

Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

We present single and double particle-hole excitations in the recently revived spin-projected Hartree-Fock. Our motivation is to treat static correlation with spin-projection and recover the residual correlation, mostly dynamic in nature, with simple configuration interaction (CI). To this end, we introduce the Wick theorem for nonorthogonal determinants, which enables an efficient implementation in conjunction with the direct CI scheme. The proposed approach, termed spin-extended CI with singles and doubles, achieves a balanced treatment between dynamic and static correlations. To approximately account for the quadruple excitations, we also modify the well-known Davidson correction. We report that our approaches yield surprisingly accurate potential curves for HF, H{sub 2}O, N{sub 2}, and a hydrogen lattice, compared to traditional single reference wave function methods at the same computational scaling as regular CI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗