Contribution To Pairing Correlations Research Articles

Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres.

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, , between the excess entropy per particle (relative to an ideal gas with the same temperature and density), , and the pair-correlation contribution, . Thus, the RMPE represents the net contribution to due to spatial correlations involving three, four, or more particles. A heuristic “ordering” criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension has been proposed (Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126). The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction . It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum at a packing fraction , and then rapidly increases, becoming positive beyond a certain packing fraction . Interestingly, while both and monotonically decrease as dimensionality increases, the value of exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality . A plot of the scaled RMPE shows a quasiuniversal behavior in the region .

Generalized Rosenfeld scalings for tracer diffusivities in not-so-simple fluids: Mixtures and soft particles

Rosenfeld [Phys. Rev. A 15, 2545 (1977)] originally noticed that casting the transport coefficients of simple monatomic equilibrium fluids in a specific dimensionless form makes them approximately single-valued functions of excess entropy. This observation has predictive value because, while the transport coefficients of dense fluids can be difficult to estimate from first principles, the excess entropy can often be accurately predicted from liquid-state theory. In this work, we use molecular simulations to investigate whether Rosenfeld's observation is a special case of a more general scaling law relating the tracer diffusivities of particles in mixtures to the excess entropy. Specifically, we study the tracer diffusivities, static structure, and thermodynamic properties of a variety of one- and two-component model fluid systems with either additive or nonadditive interactions of the hard-sphere or Gaussian-core form. The results of the simulations demonstrate that the effects of mixture concentration and composition, particle-size asymmetry and additivity, and strength of the interparticle interactions in these fluids are consistent with an empirical scaling law relating the excess entropy to a dimensionless (generalized Rosenfeld) form of tracer diffusivity, which we introduce here. The dimensionless form of the tracer diffusivity follows from knowledge of the intermolecular potential and the transport/thermodynamic behavior of fluids in the dilute limit. The generalized Rosenfeld scaling requires less information and provides more accurate predictions than either Enskog theory or scalings based on the pair-correlation contribution to the excess entropy. As we show, however, it also suffers from some limitations especially for systems that exhibit significant decoupling of individual component tracer diffusivities.

Composition and concentration anomalies for structure and dynamics of Gaussian-core mixtures

We report molecular dynamics simulation results for two-component fluid mixtures of Gaussian-core particles, focusing on how tracer diffusivities and static pair correlations depend on temperature, particle concentration, and composition. At low particle concentrations, these systems behave like simple atomic mixtures. However, for intermediate concentrations, the single-particle dynamics of the two species largely decouple, giving rise to the following anomalous trends. Increasing either the concentration of the fluid (at fixed composition) or the mole fraction of the larger particles (at fixed particle concentration) enhances the tracer diffusivity of the larger particles but decreases that of the smaller particles. In fact, at sufficiently high particle concentrations, the larger particles exhibit higher mobility than the smaller particles. Each of these dynamic behaviors is accompanied by a corresponding structural trend that characterizes how either concentration or composition affects the strength of the static pair correlations. Specifically, the dynamic trends observed here are consistent with a single empirical scaling law that relates an appropriately normalized tracer diffusivity to its pair-correlation contribution to the excess entropy.

Waterlike Structural and Excess Entropy Anomalies in Liquid Beryllium Fluoride

The relationship between structural order metrics and the excess entropy is studied using the transferable rigid ion model (TRIM) of beryllium fluoride melt, which is known to display waterlike thermodynamic anomalies. The order map for liquid BeF2, plotted between translational and tetrahedral order metrics, shows a structurally anomalous regime, similar to that seen in water and silica melt, corresponding to a band of state points for which average tetrahedral (q(tet)) and translational (tau) order are strongly correlated. The tetrahedral order parameter distributions further substantiate the analogous structural properties of BeF2, SiO2, and H2O. A region of excess entropy anomaly can be defined within which the pair correlation contribution to the excess entropy (S2) shows an anomalous rise with isothermal compression. Within this region of anomalous entropy behavior, q(tet) and S2 display a strong negative correlation, indicating the connection between the thermodynamic and the structural anomalies. The existence of this region of excess entropy anomaly must play an important role in determining the existence of diffusional and mobility anomalies, given the excess entropy scaling of transport properties observed in many liquids.

Entropy, local order, and the freezing transition in Morse liquids

The behavior of the excess entropy of Morse and Lennard-Jones liquids is examined as a function of temperature, density, and the structural order metrics. The dominant pair correlation contribution to the excess entropy is estimated from simulation data for the radial distribution function. The pair correlation entropy (S2) of these simple liquids is shown to have a threshold value of (-3.5+/-0.3)kB at freezing. Moreover, S2 shows a T(-2/5) temperature dependence. The temperature dependence of the pair correlation entropy as well as the behavior at freezing closely correspond to earlier predictions, based on density functional theory, for the excess entropy of repulsive inverse power and Yukawa potentials [Rosenfeld, Phys. Rev. E 62, 7524 (2000)]. The correlation between the pair correlation entropy and the local translational and bond orientational order parameters is examined, and, in the case of the bond orientational order, is shown to be sensitive to the definition of the nearest neighbors. The order map between translational and bond orientational order for Morse liquids and solids shows a very similar pattern to that seen in Lennard-Jones-type systems.

Determining landscape-based criteria for freezing of liquids

The correlation between statistical properties of the energy landscape and the number of accessible configurational states, as measured by the exponential of the excess entropy (e(Se)), are studied in the case of a simple Lennard-Jones-type liquid in the neighborhood of the thermodynamic freezing transition. The excess entropy Se is defined as the difference between the entropy of the liquid and that of the ideal gas under identical temperature and pressure conditions and is estimated using the pair correlation contribution, S2. Landscape properties associated with three categories of configurations are considered: instantaneous configurations, inherent saddles, and inherent minima. Landscape properties studied include the energy and the key parameters of the Hessian eigenvalue distribution as well as the mean distances between instantaneous configurations and the corresponding inherent saddles and minima. The signatures of the thermodynamic freezing transition are clearest in the case of inherent structure properties which show, as a function of e(S2), a pronounced change in slope in the vicinity of the solid-liquid coexistence. The mean distance between instantaneous and saddle configurations also shows a similar change in slope when the system crosses from the stable to the supercooled regime. In the case of inherent saddles, the minimum eigenvalue acts as a similar indicator of the thermodynamic freezing transition but the average and maximum eigenvalues do not carry similar signatures. In the case of instantaneous configurations, a weak indicator of the thermodynamic freezing transition is seen in the behavior of the fraction of negative curvature directions as a function of the exponential of the excess entropy.

The Scaling Ionic Partitioning Scheme for Estimating Electron Correlation Energy of A2-like and AX-Type Molecules

Based on the definition of pair correlation contribution of the individual electron pair to the system in the text and the investigation of the transferablility of some pair correlation contributions in the respective covalent systems, the total correlation energies of A2-like covalent molecules (H2NNH2, HOOH) and AX-type polar covalent molecules (CH3X (X = F, OH, NH2)) have been approximated using our simple scaling ionic partitioning scheme. The estimation results show that the absolute deviations are less than 2 kcal/mol; however, in this way, more than 90% of computational work can be saved. Incorporating our early work on the strong ionic compounds MA, we summarized the general formula to estimate the total correlation energy for different kinds of chemical bonding systems. The comparison of the numerical values of the ratio of the scaling coefficients for MA strong ionic compounds, AX polar covalent molecules, and A2 typical standard covalent molecules shows that the ratio of the scaling coefficients depends on the ionic property of the system.

Study on pair correlation energies of isoelectronic systems F−, HF and H2F+

AbstractThe intrapair and interpair correlation energies of F−, HF and H2F+ systems are calculated and analyzed using MP2‐OPT2 method of MELD program with cc‐PVSZ* basis set. From the analysis of pair correlation energies of these isoelectronic systems, it is found that the 1sF2 pair correlation energy is transferable in these three Isoelectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H–‐F bonding electron pair in HF molecule with those in H2F+ system are compared. The results indicate that the bonding effect of a molecule is one of the important factors to influence electron correlation energy of the system. The comparison of correlation energy contributions including triple and quadruple excitations with those only including singles and doubles calculated with 6–311 ++ G(d) basis set shows that the higher‐excitation correlation energy contribution gives more than 2% of the total correlation energy for these systems.

Estimating electron correlation energies of A2 from A− and A+ ionic units with a simple scaling approach

Electron pair correlation contribution from individual electron pairs of the molecular orbitals is defined and used in analyzing the correlation patterns of F2, O22−, and CH3CH3 isoelectronic covalent systems. Based on our simple strategy so-called “separating large system into smaller ones” for estimating the correlation energies by investigating both the ionic and the diradical partitioning schemes for covalent systems, a simple scaling scheme is presented for estimating the total correlation energy. It is achieved by summing the scaled correlation energies of its ionic fragments derived from the ionic partitioning scheme rather than from the diradical partitioning scheme. Of the three estimated results, the absolute deviations are less than ±0.29 kcal/mol, however, using this simple scaling approach, at least 90% of computational work can be saved. At the present condition with the computational demand for calculating the electron correlation energies of large covalent molecules, it is hopeful that this simple scaling approach could be useful to estimate the correlation energies of large CH-containing alkaline compounds.

Diffraction and transport in dense plasmas: Especially liquid metals

Recent computer experiments on liquid Mg and Bi (and also on dense hydrogen) have focussed anew on issues involving static and dynamical structure in plasmas. In Mg and Bi, under normal liquid metal conditions, separation of core and valence electrons is valuable both for thermodynamics and in interpreting diffraction experiments. Mg is considered in some detail as a specific example where there is weak electron–ion interaction. Finally, dynamical structure is considered. After a brief summary relating back to the electron–electron pair correlation contribution in X-ray scattering, attention is next focussed on the (longitudinal) viscosity of alkali metals via the Kubo formula. This viscosity is shown to be dominated by ion–ion interactions. Nevertheless, an intimate relation at the melting point is exposed between shear viscosity, thermal conductivity, and electrical resistivity, the latter two transport coefficients being dominated by electrons.

Isotopic dilution effects on the isotropic Raman spectra of methane in supercritical fluid

The Raman isotropic υ 1 band of CH 4 diluted in CD 4 has been studied along numerous isochoric lines 0.2< p/p <1.7 and over a wide range of temperature 1·10 −3 <(T-T c)/T c <5–10 −1. Comparison with published data on pure CH 4, completed by some ones near critical density, evidences the distinct pair correlation contribution to the spectrum of pure substance. Critical inhomogenous broadening observed in both cases is interpreted in terms of interaction modulation correlation time or local density distribution.