Short-range Behavior Research Articles

On the Short-Range Behavior of Correlated Pair Functions from the Adiabatic-Connection Fluctuation-Dissipation Theorem of Density-Functional Theory.

The short-range behavior of correlated pair functions from the adiabatic-connection fluctuation-dissipation theorem (ACFD) of density functional theory (DFT) employing local exchange-correlation kernels has been analyzed. It has been found that for large basis sets the pair function exhibits unphysical humps for small interelectronic distances if the adiabatic local density approximation kernel is used in the ACFD scheme (this method is termed ACFD/ALDA in this work). However, up to basis set sizes of quadruple-ζ type quality, the correlated pair function of ACFD/ALDA behaves physically correct and the method yields reasonable results for atomization energies, ionization potentials, and intermolecular interaction energies. In order to correct the deficiencies of the pair function of ACFD/ALDA for large basis sets, a short-range correction scheme has been devised on the basis of a combination of the ACFD/ALDA pair function for the large distance regime with a proper physically correctly behaving pair function at smaller distances. While this approach, termed as ACFD/ALDAcorr, practically yields results close to those of the ACFD/ALDA method for finite basis sets, it enables basis set extrapolation techniques and thus can take dynamic correlation effects fully into account in contrast to the ACFD/ALDA approach. This work also presents an efficient density-fitting algorithm to compute the ACFD correlation energies that enables the calculation of correlation energies of extended molecular systems.

Site-site direct correlation functions for three popular molecular models of liquid water

Direct correlation functions (DCFs) play a pivotal role in the applications of classical density functional theory (DFT) to addressing the thermodynamic properties of inhomogeneous systems beyond the local-density or mean-field approximations. Whereas numerous studies have been dedicated to the radial distribution functions of liquid water--the most important solvent on earth, relatively little attention has been given to the site-site DCFs. The water DCFs are long-ranged and difficult to calculate directly by simulation, and the predictions from conventional liquid-state theories have been rarely calibrated. Here we report a computational procedure for accurate evaluation of the site-site DCFs of liquid water based on three popular molecular models (viz., SPC, SPC∕E, and TIP3P). The numerical results provide a benchmark for calibration of conventional liquid-state theories and fresh insights into development of new DFT methods. We show that: (1) the long-range behavior of the site-site DCFs depends on both the molecular model and the thermodynamic condition; (2) the asymptotic limit of DCFs at large distance does not follow the mean-spherical approximation (MSA); (3) individual site-site DCFs are long ranged (~40 nm) but a summation of all DCF pairs exhibits only short-range behavior (~1 nm or a few water diameters); (4) the site-site bridge correlation functions behave as the DCFs, i.e., they are also long-ranged while the summation of all bridge correlation functions is short ranged. Our analytical and numerical analyses of the DCFs provide some simple strategies for possible improvement of the numerical performance of conventional liquid-state theories.

A fast method for computing 1-D wakefields due to coherent synchrotron radiation

A method for computing the free-space longitudinal wakefield due to coherent synchrotron radiation (CSR) in a one-dimensional model is developed using a fast integrated Green function approach. This approach accurately captures the short-range behavior of the CSR interaction and does not require the numerical differentiation of a noisy longitudinal charge density. The transient wakefields that occur near bend entry and exit are included. This method can also be generalized to include the effect of upstream radiation that propagates through multiple lattice elements before interacting with the bunch.

Short-range asymptotic behavior of the wave functions of interacting spin-1/2 fermionic atoms with spin-orbit coupling: A model study

We consider spin-1/2 fermionic atoms with isotropic Rashba spin-orbit coupling in three directions. The interatomic potential is modeled by a square-well potential. We derive the analytic form of the asymptotic wave functions at short range for two fermions in the subspace of zero net momentum and zero total angular momentum. We show that the spin-orbit coupling has perturbative effects on the short-range asymptotic behavior of the wave functions away from resonances. We argue that our conclusion should hold generally.

SPECTRAL ANALYSIS AND TIME-DEPENDENT SCATTERING THEORY ON MANIFOLDS WITH ASYMPTOTICALLY CYLINDRICAL ENDS

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity. For the scattering theory, the existence and asymptotic completeness of the wave operators is proved in a two-Hilbert spaces setting. A stationary formula as well as mapping properties for the scattering operator are derived. The existence of time delay and its equality with the Eisenbud–Wigner time delay is finally presented. Our analysis mainly differs from the existing literature on the choice of a simpler comparison dynamics as well as on the complementary use of time-dependent and stationary scattering theories.

Fluctuations and micro-heterogeneity in mixtures of complex liquids

The role of concentration fluctuation and micro-heterogeneity in aqueous methanol mixtures are examined by two different methods: computer simulations of two systems with sizes of 2048 and 16 384 molecules, and site-site Ornstein-Zernike integral equation theory with two different closures. The focus is on the short and long range behaviour of the correlation functions, their running integrals and the structure factors. It is found that the micro-heterogeneous nature of these mixtures does not allow a proper stabilisation of the long range tail of the correlations as obtained through computer simulations, even over 6 ns runs. Similarly, approximate closures provide poor estimates of the concentration fluctuations and micro-structure of the mixtures. Interestingly, the analysis of the inadequacies of both these studies provide interesting insights about the nature and interplay of the concentration fluctuations and the micro-heterogeneity in these mixtures.

Optimization of a Coarse-Grained Force Field for Biological Simulations

The substantial gains in computational power over recent years have been the result of increased processor parallelization. For atomistic simulation, parallelization of spatial dimensions is a viable approach, leading to large length scale simulation. Parallelization of time, on the other hand, can be achieved by averaging of fast time scale motions. Coarse-Grained (CG) models accomplish this by replacing common groups of atoms with 0-dimension points (beads) and defining potentials between the beads. The challenge then is to choose functional forms and parameters for these potentials that accurately reproduce the behavior of equivalent atomistic and experimental systems. In this work, we consider the fundamental unit of water to be a bead representing four water molecules. The beads are made polarizable by the addition of a variable angular term between three charged points on each charge neutral site. Ionic beads are defined as equivalent to four water molecules solvating one atomistic ion. Further, building blocks of linear alkanes are beads of either 3 or 4 carbon units. Non-bonded, non-Coulomb interactions between beads are described by a modified Morse potential which addresses the complexity of multi-atomic beads by decoupling the short-range and long-range behavior. Instead of using a potential of relatively simple form, the comparatively complex potential is computed by lookup table. Optimization of force-field parameters is performed using FFOpt, an in-house software package. The method explores parameter space using Nelder-Mead, a simplex optimization algorithm. The error function for optimization is defined by comparison of CG simulation results to either those of atomistic simulation or experimental values. Analysis used is optimization includes density profile, diffusion coefficient, dielectric constant, and solvation free energies.

On the Radial Dependence of the Herschbach Effect

We present the first results of a study of the radial dependence of the Herschbach effect. The effect displays distinctive short-range behaviour, evidently due to a contact interaction, and also reveals mid- and long-range behaviours. Cosmological implications of the long-range Herschbach effect are explored.

Critical behavior and magnetocaloric effect of Gd65Mn35−xGex (x = 0, 5, and 10) melt-spun ribbons

Gd65Mn35−xGex (x = 0, 5, 10) alloy ribbons were prepared by melt-spinning. A fully amorphous structure was obtained for the alloys with x = 5 and 10, whereas, in melt-spun Gd65Mn35 ribbons, crystalline phases (α-Gd and GdMn2) precipitate in the amorphous matrix. The magnetic phase transition from ferromagnetic to paramagnetic is second order. The critical exponents are deduced from the Kouvel-Fisher method and scaling behavior. The obtained critical exponents are in agreement with the theoretical values of 3D Ising model. The Ising-like behavior suggests the presence of large anisotropy and short-range magnetic-coupling behavior. The maximum magnetic-entropy changes of the melt-spun alloys with x = 0, 5, and 10 for a magnetic field change from 0 to 5 T are 4.2, 4.1, and 4.5 Jkg−1 K−1, respectively. All three alloys have a broad temperature range of the magnetic-entropy peak, resulting in large refrigerant capacities.

Double-exponential decay of orientational correlations in semiflexible polyelectrolytes

In this paper we revisited the problem of persistence length of polyelectrolytes. We performed a series of Molecular Dynamics simulations using the Debye-Hückel approximation for electrostatics to test several equations which go beyond the classical description of Odijk, Skolnick and Fixman (OSF). The data confirm earlier observations that in the limit of large contour separations the decay of orientational correlations can be described by a single-exponential function and the decay length can be described by the OSF relation. However, at short countour separations the behaviour is more complex. Recent equations which introduce more complicated expressions and an additional length scale could describe the results very well on both the short and the long length scale. The equation of Manghi and Netz when used without adjustable parameters could capture the qualitative trend but deviated in a quantitative comparison. Better quantitative agreement within the estimated error could be obtained using three equations with one adjustable parameter: 1) the equation of Manghi and Netz; 2) the equation proposed by us in this paper; 3) the equation proposed by Cannavacciuolo and Pedersen. Two characteristic length scales can be identified in the data: the intrinsic or bare persistence length and the electrostatic persistence length. All three equations use a single parameter to describe a smooth crossover from the short-range behaviour dominated by the intrinsic stiffness of the chain to the long-range OSF-like behaviour.

Short-range behavior of some electron-pair densities

The short-range behavior of several electron-pair densities is reported to be governed in common by a quantity ρ2(0,0), which is a special value at the origin r1=r2=0 of the spherically averaged two-electron density function ρ2(r1,r2). Such electron-pair densities include the radial sum density, the outer density, the coalescence density, and the counterbalance density, appearing in the literature to clarify different aspects of the electron–electron interaction. Moreover, the two-electron value ρ2(0,0) is shown to be exactly determined by the one-electron value ρ(0) in the Hartree–Fock theory of atoms with closed s subshells, where ρ(0) is the value at the origin r=0 of the spherically averaged single-electron density function ρ(r). A small correction is added for open s subshell cases.

Statistics of low-frequency normal-mode amplitudes in an ocean with random sound-speed perturbations: Shallow-water environments

Second- and fourth-moment mode-amplitude statistics for low-frequency ocean sound propagation through random sound-speed perturbations in a shallow-water environment are investigated using Monte Carlo simulations and a transport theory for the cross-mode coherence matrix. The acoustic observables of mean and mean square intensity are presented and the importance of adiabatic effects and cross-mode coherence decay are emphasized. Using frequencies of 200 and 400 Hz, transport theory is compared with Monte Carlo simulations in a canonical shallow-water environment representative of the summer Mid-Atlantic Bight. Except for ranges less than a horizontal coherence length of the sound structure, the intensity moments from the two calculations are in good agreement. Corrections for the short range behavior are presented. For these frequencies the computed mode coupling rates are extremely small, and the propagation is strongly adiabatic with a rapid decay of cross-mode coherence. Coupling effects are predicted to be important at kilohertz frequencies. Decay of cross-mode coherence has important implications for acoustic interactions with nonlinear internal waves: For the case in which the acoustic path is not at glancing incidence with a nonlinear internal-wave front, adiabatic phase randomizing effects lead to a significantly reduced influence of the nonlinear waves on both mean and mean square intensity.

Mediation of resonance energy transfer by a third molecule

The influence of a third molecule on the rate of resonance energy transfer is studied using diagrammatic perturbation theory within the framework of molecular quantum electrodynamics. Two distinct mechanisms are identified. One corresponds to direct transfer between donor and acceptor while the other involves relay of energy by the third species. Fermi Golden rule transition rates valid for all separation distances beyond wave function overlap are evaluated for these two processes as well as for the interference term between direct and indirect exchange, thereby extending previous work which was limited to the near-zone only. Short- and long-range limits are also obtained in each case. It is found that in the near-zone the indirect rate contribution exhibits inverse sixth power dependence on relative distances of emitter and absorber relative to the third body, in contrast to its far-zone counterpart, which exhibits inverse square behavior. The interference term, however, displays inverse cubic dependence on all three distance vectors at short-range and inverse behavior in the far-zone. Interestingly, for a collinear arrangement of the three molecules in the near-zone, the interference term is negative, reducing the overall rate of energy transfer. The results obtained are interpreted in terms of microscopic and macroscopic pictures of transfer occurring within a surrounding medium.

Modulation of Aphid Vector Activity by Potato virus Y on In Vitro Potato Plants.

The effects of the infection of potato (Solanum tuberosum) plants by the nonpersistent Potato virus Y (PVY) were studied on the host plant colonization behavior of different colonizing (Myzus persicae) and noncolonizing (Aphis fabae, Brevicoryne brassicae, and Sitobion avenae) aphid species. The underlying questions of this study were to know how aphids respond when faced with PVY-infected plants and whether plant infection can modify the aphid behavior involved in PVY spread. Short-range orientation behavior was observed using a dual-choice set-up and aphid feeding behavior was monitored using the electrical penetration graph technique. None of the aphid species discriminated between healthy and PVY-infected plants. Nevertheless, most individuals of M. persicae landed on and probed only in one plant whereas noncolonizing aphid species exhibited interplant movements. Study of the aphid feeding behavior showed that PVY infection essentially modified phloem and xylem ingestion. M. persicae and S. avenae exhibited an increased duration of phloem phases on PVY-infected plants whereas A. fabae showed a decreased duration of phloem phases that benefited from an increased duration of xylem ingestion phases. None of these parameters were changed in B. brassicae. These data present evidence that aphids can respond to plants infected by nonpersistent viruses. Such behavioral modifications are discussed within the context of PVY spread in potato crops.

Syntheses, characterizations and properties of [Mo2O2S2]-based oxothiomolybdenum wheels incorporating bisphosphonate ligands

We report the syntheses and characterizations of the first polyoxothiometalate complexes isolated from the reaction of the oxothiocationic [Mo(V)(2)O(2)S(2)](2+) precursor and bisphosphonate ligands H(2)O(3)PCR(OH)PO(3)H(2) (R = C(4)H(5)N(2), zoledronic acid; R = C(3)H(6)NH(2), alendronic acid). [(Mo(2)O(2)S(2)(H(2)O))(4)(O(3)PC(O)(C(4)H(6)N(2))PO(3))(4)](8-) (Mo(8)S(8)(Zol)(4)) and [(Mo(2)O(2)S(2)(H(2)O))(4)(O(3)PC(O)(C(3)H(6)NH(3))PO(3))(4)](8-) (Mo(8)S(8)(Ale)(4)) contain four Mo(V) dimers connected via bisphosphonate ligands. These compounds offer a unique opportunity to compare the structures and properties of cyclic compounds obtained with [Mo(2)O(2)S(2)](2+) and with [Mo(2)O(4)](2+). The oxothio compounds appear less stable in solution than the oxo analogue, confirming the higher lability and versatility of [Mo(2)O(2)S(2)]-based compounds compared to [Mo(2)O(4)]-based POMs. Multinuclear and multidimensional solid-state NMR studies were carried out to complement X-ray diffraction analysis. Information on short-range interactions, dynamic behaviors, and local disorder within the crystalline materials are therefore reported. Furthermore, the electrocatalytic properties of Mo(8)S(8)(Ale)(4) and of the analogous [(Mo(2)O(4)(H(2)O))(4)(O(3)PC(O)(C(3)H(6)NH(3))PO(3))(4)](8-) (Mo(8)O(8)(Ale)(4)) immobilized onto the surface of a glassy carbon electrode were studied, thus evidencing the ability of [Mo(2)O(2)S(2)]-based cycles to promote the reduction of protons into hydrogen, whereas the oxo analogue appeared inactive.

Structural and magnetic characterization of the complete delafossite solid solution (CuAlO2)1−x(CuCrO2)x

We have prepared the complete delafossite solid solution series between diamagnetic CuAlO2 and the t2g3frustrated antiferromagnet CuCrO2. The evolution with composition x in CuAl1−xCrxO2 of the crystal structure and magnetic properties has been studied and is reported here. The room-temperature unit cell parameters follow the Végard law and increase with x as expected. The μeff is equal to the Cr3+ spin-only S = 3/2 value throughout the entire solid solution. ΘCW is negative, indicating that the dominant interactions are antiferromagnetic, and its magnitude increases with Cr substitution. For dilute Cr compositions, the nearest-neighbor exchange coupling constant JBB was estimated by mean-field theory to be 3.0 meV. Despite the sizable ΘCW, long-range antiferromagnetic order does not develop until x is almost 1, and is preceded by glassy behavior. The data presented here, and those on dilute Al substitution from Okuda et al, suggest that the reduction in magnetic frustration due to the presence of non-magnetic Al does not have as dominant an effect on magnetism as chemical disorder and dilution of the magnetic exchange. For all samples, the 5 K isothermal magnetization does not saturate in fields up to 5 T and minimal hysteresis is observed. The presence of antiferromagnetic interactions is clearly evident in the sub-Brillouin behavior with a reduced magnetization per Cr atom. An inspection of the scaled Curie plot reveals that significant short-range antiferromagnetic interactions occur in CuCrO2 above its Néel temperature, consistent with its magnetic frustration. Uncompensated short-range behavior is present in the Al-substituted samples and is likely a result of chemical disorder.

Molecular oxygen tetramer (O2)4: Intermolecular interactions and implications for theεsolid phase

Recent data have determined that the structure of the high pressure $\epsilon$ phase of solid oxygen consists of clusters composed of four O$_2$ molecules. This finding has opened the question about the nature of the intermolecular interactions within the molecular oxygen tetramer. We use multiconfigurational ab initio calculations to obtain an adequate characterization of the ground singlet state of (O$_2$)$_4$ which is compatible with the non magnetic character of the $\epsilon$ phase. In contrast to previous suggestions implying chemical bonding, we show that (O$_2$)$_4$ is a van der Waals like cluster where exchange interactions preferentially stabilize the singlet state. However, as the cluster shrinks, there is an extra stabilization due to many-body interactions that yields a significant softening of the repulsive wall. We show that this short range behavior is a key issue for the understanding of the structure of $\epsilon$-oxygen.

Growth mechanism and magnon excitation in NiO nanowalls

The nanosized effects of short-range multimagnon excitation behavior and short-circuit diffusion in NiO nanowalls synthesized using the Ni grid thermal treatment method were observed. The energy dispersive spectroscopy mapping technique was used to characterize the growth mechanism, and confocal Raman scattering was used to probe the antiferromagnetic exchange energy J2 between next-nearest-neighboring Ni ions in NiO nanowalls at various growth temperatures below the Neel temperature. This study shows that short spin correlation leads to an exponential dependence of the growth temperatures and the existence of nickel vacancies during the magnon excitation. Four-magnon configurations were determined from the scattering factor, revealing a lowest state and monotonic change with the growth temperature.PACS: 75.47.Lx; 61.82.Rx; 75.50.Tt; 74.25.nd; 72.10.Di

Bound States and Scattering Resonances Induced by Spatially Modulated Interactions

We study the two-body problem with a spatially modulated interaction potential using a two-channel model, in which the interchannel coupling is provided by an optical standing wave and its strength modulates periodically in space. As the modulation amplitudes increase, there will appear a sequence of bound states. Part of them will cause a divergence of the effective scattering length, defined through the phase shift in the asymptotic behavior of scattering states. We also discuss how the local scattering length, defined through short-range behavior of scattering states, modulates spatially in different regimes. These results provide a theoretical guideline for a new control technique in the cold atom toolbox, in particular, for alkaline-earth(-like) atoms where the inelastic loss is small.

BEC-BCS crossover and universal relations in unitary Fermi gases

The contact parameter in unitary Fermi Gases governs the short-distance, high-momentum, and high-energy properties of the system. We perform accurate quantum Monte Carlo calculations with highly optimized trial functions to precisely determine this parameter at T=0, demonstrate its universal application to a variety of observables, and determine the regions of momentum and energy over which the leading short-range behavior is dominant. We derive Tan's expressions for the contact parameter using just the short-range behavior of the ground-state many-body wave function, and use this behavior to calculate the two-body distribution function, one-body density matrix, and the momentum distribution of unitary Fermi gases; providing a precise value of the contact parameter that can be compared to experiments.