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At least 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Electronic correlation without double counting via a combination of spin projected Hartree-Fock and density functional theories

Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+f{sub c}DFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+f{sub c}DFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+f{sub c}DFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+f{sub c}DFT scheme are discussed in light of these results.

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

Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum golden-rule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems.

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

Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media

Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Order and correlation contributions to the entropy of hydrophobic solvation

The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom’s test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by identifying the structural feature responsible for the entropy change, and point to a possible explanation for the observed dependence on length scale. Our key results are that the hydrophobic effect, i.e. the signature, temperature-dependent, solvation entropy of nonpolar molecules in water, is largely due to a dispersion force arising from correlations between rotating permanent dipole moments, that the strength of this force depends on the Kirkwood g-factor, and that the strength of this force may be obtained exactly without simulation.

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

Calculation of the molecular integrals with the range-separated correlation factor

Explicitly correlated quantum chemical calculations require calculations of five types of two-electron integrals beyond the standard electron repulsion integrals. We present a novel scheme, which utilises general ideas of the McMurchie-Davidson technique, to compute these integrals when the so-called “range-separated” correlation factor is used. This correlation factor combines the well-known short range behaviour resulting from the electronic cusp condition, with the exact long-range asymptotics derived for the helium atom [Lesiuk, Jeziorski, and Moszynski, J. Chem. Phys. 139, 134102 (2013)]. Almost all steps of the presented procedure are formulated recursively, so that an efficient implementation and control of the precision are possible. Additionally, the present formulation is very flexible and general, and it allows for use of an arbitrary correlation factor in the electronic structure calculations with minor or no changes.

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

The correlation study of parallel feature extractor and noise reduction approaches

This paper presents literature reviews that show variety of techniques to develop parallel feature extractor and finding its correlation with noise reduction approaches for low light intensity images. Low light intensity images are normally displayed as darker images and low contrast. Without proper handling techniques, those images regularly become evidences of misperception of objects and textures, the incapability to section them. The visual illusions regularly clues to disorientation, user fatigue, poor detection and classification performance of humans and computer algorithms. Noise reduction approaches (NR) therefore is an essential step for other image processing steps such as edge detection, image segmentation, image compression, etc. Parallel Feature Extractor (PFE) meant to capture visual contents of images involves partitioning images into segments, detecting image overlaps if any, and controlling distributed and redistributed segments to extract the features. Working on low light intensity images make the PFE face challenges and closely depend on the quality of its pre-processing steps. Some papers have suggested many well established NR as well as PFE strategies however only few resources have suggested or mentioned the correlation between them. This paper reviews best approaches of the NR and the PFE with detailed explanation on the suggested correlation. This finding may suggest relevant strategies of the PFE development. With the help of knowledge based reasoning, computational approaches and algorithms, we present the correlation study between the NR and the PFE that can be useful for the development and enhancement of other existing PFE.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Analysis of the correlation dimension for inertial particles

We obtain an implicit equation for the correlation dimension which describes clustering of inertial particles in a complex flow onto a fractal measure. Our general equation involves a propagator of a nonlinear stochastic process in which the velocity gradient of the fluid appears as additive noise. When the long-time limit of the propagator is considered our equation reduces to an existing large-deviation formalism from which it is difficult to extract concrete results. In the short-time limit, however, our equation reduces to a solvability condition on a partial differential equation. In the case where the inertial particles are much denser than the fluid, we show how this approach leads to a perturbative expansion of the correlation dimension, for which the coefficients can be obtained exactly and in principle to any order. We derive the perturbation series for the correlation dimension of inertial particles suspended in three-dimensional spatially smooth random flows with white-noise time correlations, obtaining the first 33 non-zero coefficients exactly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Radial and poloidal correlation reflectometry on Experimental Advanced Superconducting Tokamak

An X-mode polarized V band (50 GHz–75 GHz) radial and poloidal correlation reflectometry is designed and installed on Experimental Advanced Superconducting Tokamak (EAST). Two frequency synthesizers (12 GHz–19 GHz) are used as sources. Signals from the sources are up-converted to V band using active quadruplers and then coupled together for launching through one single pyramidal antenna. Two poloidally separated antennae are installed to receive the reflected waves from plasma. This reflectometry system can be used for radial and poloidal correlation measurement of the electron density fluctuation. In ohmically heated plasma, the radial correlation length is about 1.5 cm measured by the system. The poloidal correlation analysis provides a means to estimate the fluctuation velocity perpendicular to the main magnetic field. In the present paper, the distance between two poloidal probing points is calculated with ray-tracing code and the propagation time is deduced from cross-phase spectrum. Fluctuation velocity perpendicular to the main magnetic field in the core of ohmically heated plasma is about from −1 km/s to −3 km/s.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Examining the impact of harmonic correlation on vibrational frequencies calculated in localized coordinates

Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Synchronous correlation matrices and Connes’ embedding conjecture

In the work of Paulsen et al. [J. Funct. Anal. (in press); preprint arXiv:1407.6918], the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain C*-algebras. In particular, synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters. In this paper, we develop these ideas further, focusing on the relations between synchronous correlation matrices and microstates. We prove that Connes’ embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices. We prove that if Connes’ embedding conjecture has a positive answer, then the tracial rank and projective rank are equal for every graph. We then apply these results to more general non-local games.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

GRB physics and cosmology with peak energy-intensity correlations

Gamma Ray Bursts (GRBs) are immensely energetic explosions radiating up to 10{sup 54} erg of energy isotropically (E{sub iso}) and they are observed within a wide range of redshift (from ∼ 0.01 up to ∼ 9). Such enormous power and high redshift point at these phenomena being highly favorable to investigate the history and evolution of our universe. The major obstacle in their application as cosmological study-tools is to find a way to standardize the GRBs, for instance similar to SNe Ia. With respect to this goal, the correlation between spectral peak energy (E{sub p,i}) and the “intensity” is a positively useful and investigated criterion. Moreover, it has been demonstrated that, through the E{sub p,i} – E{sub iso} correlation, the current data set of GRBs can already contribute to the independent evidence of the matter density Ω{sub M} being ∼ 0.3 for a flat universe scenario. We try to inspect and compare the correlations of E{sub p,i} with different intensity indicators (e.g., radiated energy, average and peak luminosity, bolometric vs. monochromatic quantities, etc.) both in terms of intrinsic dispersion and precise estimation of Ω{sub M}. The outcome of such studies are further analyzed in verifying the reliability of the correlations for both GRB physics and their standardization for cosmology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Modeling the influence of string collective phenomena on the long range rapidity correlations between the transverse momentum and the multiplicities

The long-range rapidity correlations between the multiplicities (n-n) and the transverse momentum and the multiplicity (pT-n) of charge particles are analyzed in the framework of the simple string inspired model with two types of sources. The sources of the first type correspond to the initial strings formed in a hadronic collision. The sources of the second type imitate the appearance of the emitters of a new kind resulting from interaction (fusion) of the initial strings. The model enabled to describe effectively the influence of the string fusion effects on the strength both the n-n and the pT-n correlations. It was found that in the region, where the process of string fusion comes into play, the calculation results predict the non-monotonic behaviour of the n-n and pT-n correlation coefficients with the growth of the mean number of initial strings, i.e. with the increase of the collision centrality. It was shown also that the increase of the event-by-event fluctuation in the number of primary strings leads to the change of the pT-n correlation sign from negative to positive. One can try to search these signatures of string collective phenomena in interactions of various nuclei at different energies varying the class of collision centrality and its width.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Tunable two-photon correlation in a double-cavity optomechanical system

Correlated photons are essential sources for quantum information processing. We propose a practical scheme to generate pairs of correlated photons in a controllable fashion from a double-cavity optomechanical system, where the variable optomechanical coupling strength makes it possible to tune the photon correlation at our will. The key operation is based on the repulsive or attractive interaction between the two photons intermediated by the mechanical resonator. The present protocol could provide a potential approach to coherent control of the photon correlation using the optomechanical cavity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Locality of correlation in density functional theory

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ + B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Exchange correlation potentials from full configuration interaction in a Slater orbital basis

Ryabinkin–Kohut–Staroverov (RKS) theory builds a bridge between wave function theory and density functional theory by using quantities from the former to produce accurate exchange-correlation potentials needed by the latter. In this work, the RKS method is developed and tested alongside Slater atomic orbital basis functions for the first time. To evaluate this approach, full configuration interaction computations in the Slater orbital basis are employed to give quality input to RKS, allowing full correlation to be present along with correct nuclei cusps and asymptotic decay of the wavefunction. SlaterRKS is shown to be an efficient algorithm to arrive at exchange-correlation potentials without unphysical artifacts in moderately-sized basis sets. Furthermore, enforcement of the nuclear cusp conditions will be shown to be vital for the success of the Slater-basis RKS method. As a result, examples of weakly and strongly correlated molecular systems will demonstrate the main features of SlaterRKS.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Scattering evidence of positional charge correlations in polyelectrolyte complexes

Polyelectrolyte complexation plays an important role in materials science and biology. The internal structure of the resultant polyelectrolyte complex (PEC) phase dictates properties such as physical state, response to external stimuli, and dynamics. Small-angle scattering experiments with X-rays and neutrons have revealed structural similarities between PECs and semidilute solutions of neutral polymers, where the total scattering function exhibits an Ornstein–Zernike form. In spite of consensus among different theoretical predictions, the existence of positional correlations between polyanion and polycation charges has not been confirmed experimentally. Here, we present small-angle neutron scattering profiles where the polycation scattering length density is matched to that of the solvent to extract positional correlations among anionic monomers. The polyanion scattering functions exhibit a peak at the inverse polymer screening radius of Coulomb interactions, q* ≈ 0.2 Å –1 . This peak, attributed to Coulomb repulsions between the fragments of polyanions and their attractions to polycations, is even more pronounced in the calculated charge scattering function that quantifies positional correlations of all polymer charges within the PEC. Screening of electrostatic interactions by adding salt leads to the gradual disappearance of this correlation peak, and the scattering functions regain an Ornstein–Zernike form. Experimental scattering results are consistent with those calculated from the random phase approximation, a scaling analysis, and molecular simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

REIONIZATION ON LARGE SCALES. II. DETECTING PATCHY REIONIZATION THROUGH CROSS-CORRELATION OF THE COSMIC MICROWAVE BACKGROUND

We investigate the effect of patchy reionization on the cosmic microwave background (CMB) temperature. An anisotropic optical depth τ( n-hat ) alters the TT power spectrum on small scales l > 2000. We make use of the correlation between the matter density and the reionization redshift fields to construct full sky maps of τ( n-hat ). Patchy reionization transfers CMB power from large scales to small scales, resulting in a non-zero cross correlation between large and small angular scales. We show that the patchy τ correlator is sensitive to small root mean square (rms) values τ{sub rms} ∼ 0.003 seen in our maps. We include frequency-independent secondaries such as CMB lensing and kinetic Sunyaev-Zel'dovich (kSZ) terms, and show that patchy τ may still be detected at high significance. Reionization models that predict different values of τ{sub rms} may be distinguished even for the same mean value (τ). It is more difficult to detect patchy τ in the presence of larger secondaries such as the thermal Sunyaev-Zel'dovich, radio background, and the cosmic infrared background. In this case, we show that patchy τ may be detected if these frequency-dependent secondaries are minimized to ∼< 5 μK (rms) by means of a multi-frequency analysis. We show that the patchy τ correlator provides information that is complementary to what may be obtained from the polarization and the kSZ power spectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SELECTION EFFECTS IN GAMMA-RAY BURST CORRELATIONS: CONSEQUENCES ON THE RATIO BETWEEN GAMMA-RAY BURST AND STAR FORMATION RATES

Gamma-ray bursts (GRBs) visible up to very high redshift have become attractive targets as potential new distance indicators. It is still not clear whether the relations proposed so far originate from an unknown GRB physics or result from selection effects. We investigate this issue in the case of the L{sub X} -T{sub a}{sup ∗} (hereafter LT) correlation between the X-ray luminosity L{sub X} (T{sub a} ) at the end of the plateau phase, T{sub a} , and the rest-frame time T{sub a}{sup ∗}. We devise a general method to build mock data sets starting from a GRB world model and taking into account selection effects on both time and luminosity. This method shows how not knowing the efficiency function could influence the evaluation of the intrinsic slope of any correlation and the GRB density rate. We investigate biases (small offsets in slope or normalization) that would occur in the LT relation as a result of truncations, possibly present in the intrinsic distributions of L{sub X} and T{sub a}{sup ∗}. We compare these results with the ones in Dainotti et al. showing that in both cases the intrinsic slope of the LT correlation is ≈ – 1.0. This method is general and therefore relevant for investigating whether or not any other GRB correlation is generated by the biases themselves. Moreover, because the farthest GRBs and star-forming galaxies probe the reionization epoch, we evaluate the redshift-dependent ratio Ψ(z) = (1 + z){sup α} of the GRB rate to the star formation rate. We found a modest evolution –0.2 ≤ α ≤ 0.5 consistent with a Swift GRB afterglow plateau in the redshift range 0.99 < z < 9.4.

79 ASTRONOMY AND ASTROPHYSICS↗