Radial Correlation Functions Research Articles

Simulation of phase separation in alcohol/water mixtures using two‐body force field and standard molecular dynamics

Standard molecular dynamics simulations have been carried out on pure alcohols and alcohol/water mixtures. A simple atom-atom force field consisting of Lennard-Jones potentials plus coulombic terms over atomic point charges, but without explicit polarization terms, has been specifically fitted to reproduce several experimental properties of the pure alcohols, and has been used for mixtures by developing combination rules with the TIP3P water model. Densities, enthalpies of vaporization, radial distribution functions, self-diffusion coefficients, and rotational correlation functions of the pure alcohols are well reproduced and compare favorably with those from more sophisticated force fields. Some key aspects of the phase behaviour are correctly reproduced by the molecular dynamics simulation, showing a distinct demixing process for the n-butanol/water mixture as opposed to the stability of the t-butanol/water mixtures. The results demonstrate the ability of a molecular dynamics simulation, even in its standard form and with easily accessible time ranges, but with a carefully optimized force field, to simulate and, to a certain extent, predict the properties of binary mixtures.

Investigation of the possibility of using correlation reflectometry to determine the parameters of small-scale turbulence in the core of a tokamak plasma

Results are reported from investigating the possibility of using reflectometry to determine the parameters of small-scale turbulence in the core of a tokamak plasma. In particular, the extent to which the reflectometric measurements are local is estimated. Experimental data from reflectometric measurements in the gradient zone, as well as the cross spectra and radial correlation functions, are presented. A turbulence model is constructed that yields spectral, statistical, and correlation turbulent plasma properties close to the measured ones. The model is used to simulate the propagation of electromagnetic radiation in a turbulent plasma.

CONTINUITY BETWEEN DISORDER AND ORDER IN THE SEQUENTIAL DEPOSITION OF PARTICLES

ABSTRACT In previous work we pointed out that clusters of particles built through sequential quenching show increasing degrees of order as the temperature is lowered. In the low-temperature limit, a two-dimensional model system with a nondegenerate ground state would result in a perfect crystal. The opposite, high-temperature, limit corresponds to the case of random sequential addition (RSA). In the present work we study the continuous evolution from disorder to order at intermediate states using a triangular well potential to represent particle interactions. We investigate radial and bond-orientation correlation functions and the bond order parameter as measures of the degree of crystallinity of the structures up to a reduced number density of 0.65, which is close to the jamming limit of RSA.

Triplet correlations in the quantum hard-sphere fluid

A study of three-particle correlations in the quantum hard-sphere fluid far from exchange is presented. The three types of triplet correlations in a monatomic quantum fluid (instantaneous, linear response, and centroids) are analyzed by utilizing (a) the density derivatives of the corresponding quantum pair radial correlation functions, (b) closures for triplet functions, and (c) path-integral Monte Carlo (PIMC) simulations that have concentrated on the fixing of equilateral and isosceles correlations. For the sake of comparison, the classical hard-sphere fluid is also studied with tools (a) and (b) and Monte Carlo (MC) simulations. The relative usefulness of density derivatives combined with closures is discussed in light of the PIMC and MC results. The exact PIMC correlations between quantum triplets show features that resemble those known to occur at the pair level, such as the close proximity between the instantaneous and the three-particle linear response, the much more pronounced features in centroid triplet structures, and the same global patterns with changes in density and temperature such as the outward shifts of the structures with decreasing temperature and density.

NMR relaxation parameters of a Lennard-Jones fluid from molecular-dynamics simulations

Ensembles of soft spheres or of Lennard-Jones atoms were studied by molecular dynamics at reduced temperatures from 0.8 to 3, and radial distribution functions, diffusion coefficients, and magnetic dipole-dipole correlation functions were measured as functions of system size. The expected relation between the values of the correlation functions at zero lag time and the integrals of the radial distribution was verified for each system. The measured correlation functions were compared with theoretical expressions derived by [Ayant et al., J. Phys. (Paris) 36, 991 (1975)] and by [Hwang and Freed, J. Chem. Phys. 63, 4017 (1975)]. It was shown that, in order to recover the long-time behavior characteristic of diffusion-controlled relaxation processes, the simulation must comprise at least 10 000 particles. By fitting the simulation results to the Hwang-Freed function, independent values of the diffusion coefficient were obtained, similar but not identical to those computed using the Green-Kubo formalism. The spectral densities of the dipole-dipole interaction were computed as Fourier transforms of the correlation functions. These quantities are less sensitive to model imperfections and reproduce quite well the values derived from theory. The dimensionless spin-lattice and spin-spin relaxation rates were derived from the spectral densities. It was shown that the spin-lattice (longitudinal) relaxation rate goes through a maximum as the temperature increases, while the spin-spin (transverse) rate decreases monotonously.

Dielectric Constant and Density Dependence of the Structure of Supercritical Carbon Dioxide Using a New Modified Empirical Potential Model: A Monte Carlo Simulation Study

Two modified versions of the Elementary Physical Model (EPM) [J. Phys. Chem. 1995, 99, 12021] for supercritical carbon dioxide have been proposed in this work and their validities are affirmed by computing the thermodynamic properties and dielectric constant up to 910 kg/m3 with use of canonical ensemble Monte Carlo simulation. Simulations performed for 500 molecules with the EPM2-M model reproduce the experimental data accurately at all thermodynamic states. The structural analyses demonstrate that the aggregation is strong at low density while the coordination number is large at high density. In addition, a detailed study on the radial and angular correlation functions reveals that the T-shaped geometry is dominate while a variety of other structures still appear in the first coordination shell. Furthermore, the angular correlation functions show that the probability of a molecule being oriented toward the convex side of another molecule is equal to that pointing toward the concave side since the molecular nonlinearity of carbon dioxide is only marginal. As the distance between two molecules increases, the preferred orientations disappear quickly and all the results are in good agreement with the prior ab initio calculation [J. Chem. Phys. 2004, 120, 9694].

Statistical mechanics of a colloidal suspension in contact with a fluctuating membrane

Surface effects are generally prevailing in confined colloidal systems. Here we report on dispersed nanoparticles close to a fluid membrane. Exact results regarding the static organization are derived for a dilute solution of nonadhesive colloids. It is shown that thermal fluctuations of the membrane broaden the density profile, but on average colloids are neither accumulated nor depleted near the surface. The radial correlation function is also evaluated, from which we obtain the effective pair potential between colloids. This entropically driven interaction shares many similarities with the familiar depletion interaction. It is shown to be always attractive with range controlled by the membrane correlation length. The depth of the potential well is comparable to the thermal energy, but depends only indirectly upon membrane rigidity. Consequences for the stability of the suspension are also discussed.

Quantum statistical mechanics with Gaussians: Equilibrium properties of van der Waals clusters

The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.

Computation of the equation of state of the quantum hard-sphere fluid utilizing several path-integral strategies.

The compressibility factor of the quantum hard-sphere fluid within the region (rho(N) (*)</=0.8,lambda(B) (*)</=0.9) is computed by following four distinct routes involving the three pair radial correlation functions that are significant in the path-integral context, namely, instantaneous, pair linear response, and centroids. These functions are calculated with path-integral Monte Carlo simulations involving the Cao-Berne propagator. The first route to the equation of state is the instantaneous standard one, i.e., the usual volume derivative of the partition function expressed in terms of the instantaneous pair radial correlations. The other three routes stem from the extended compressibility theorem, which associates the isothermal compressibility with the three pair radial structures mentioned above and involves the solving of appropriate Ornstein-Zernike equations. An analysis of the error bars in the quantities computed is reported, and it is proven the usefulness of the centroid pair correlations to fix quantum equations of state. Also, the regions where the fluid-solid changes of phase should take place are identified with the use of indicators sensitive to order in the sample. The consistency of the current results is assessed and comparison with data available in the literature is made wherever possible.

The compressibility theorem for quantum simple fluids at equilibrium

An extension of the compressibility theorem for quantum simple fluids within the pathintegral approach is presented. First, it is demonstrated that in the absence of quantum exchange, the isothermal compressibility can be formulated in an exact manner with the use of the pair radial correlation function of the path-integral centroids corresponding to the particles of the fluid. This adds up to the two known formulations based on the pair correlations between true quantum particles, namely the instantaneous and the pair linear response correlations. To complement this extension, an exact Ornstein-Zernike equation for pair centroid correlations is derived, which permits accurate estimates for the isothermal compressibility to be obtained. Several fluids are studied, new numerical results for the latter quantity are reported to support the theoretical points, and some difficulties present in this sort of calculation are discussed. The systems studied are the following: the quantum hard sphere fluid with and without attractive Yukawa interaction, liquid helium-4 and liquid para-hydrogen. Finally, the possibilities of extending the theorem to deal with quantum exchange are considered, and it is shown that the extension and its computational Ornstein-Zernike scheme also hold for a Bose fluid.

Anisotropic coarse-grained statistical potentials improve the ability to identify nativelike protein structures

We present a new method to extract distance and orientation dependent potentials between amino acid side chains using a database of protein structures and the standard Boltzmann device. The importance of orientation dependent interactions is first established by computing orientational order parameters for proteins with α-helical and β-sheet architecture. Extraction of the anisotropic interactions requires defining local reference frames for each amino acid that uniquely determine the coordinates of the neighboring residues. Using the local reference frames and histograms of the radial and angular correlation functions for a standard set of nonhomologue protein structures, we construct the anisotropic pair potentials. The performance of the orientation dependent potentials was studied using a large database of decoy proteins. The results demonstrate that the new distance and orientation dependent residue–residue potentials present a significantly improved ability to recognize native folds from a set of native and decoy protein structures.

Control of electron correlations in a spherical quantum dot

Spherical quantum dots containing several electrons are considered for different values of the total spin. Numerical calculations are carried out using the quantum path-integral Monte Carlo method. The dependence of the electron correlations on the dimensionless control quantum parameter q associated with the steepness of the confinement potential is studied. The quantum transition from a Wigner crystal-like state (i.e., from the regime of strongly correlated electrons) to a Fermi-liquid state (“cold” melting) driven by the parameter q is studied in detail. The behavior of the radial and pair correlation functions, which characterize quantum delocalization of the electrons, is considered.

Magnetism of amorphous FeB in the Bennett model

We investigate magnetic properties of amorphous clusters, containing 10 4 atoms of two kinds: magnetic and nonmagnetic. Atoms are represented as hard spheres. The clusters are obtained with the sequential deposition algorithm. The ratio of radii of two kinds of spheres is chosen as to reproduce the density of FeB amorphous alloy. Then, calculated spectra of the Fe–Fe radial correlation functions also agree with experimental data. The magnetization is obtained within the Ising model. We reproduce the experimental thermal dependence of spontaneous magnetization of Fe 80B 20. This gives information on the Slater–Néel curve and allows to calculate the Arrott plots. We observe also a direct proportionality between the paramagnetic spin–spin correlation function and the Slater–Néel curve.

The use of distributed partial wave basis for accurate atom–molecule statistical distributions

We apply the distributed partial wave formulation to the calculation of atom–molecule statistical distributions. Site radial correlation functions are computed accurately by coupling multicenter contributions using the spherical harmonics expansion of three-dimensional intramolecular correlation functions. The results are systematically improved as the order of expansions increases. It is shown that the technique using spherical Bessel transforms with logarithmic grids, is particularly cost effective for accurate statistical distribution functions. We compared some numerical results with exact functions obtained by numerical integrations.

Properties of the path-integral quantum hard-sphere fluid in k space

The properties of quantum fluids in Fourier space, as the system response functions to weak external fields, are analyzed taking the quantum hard-sphere fluid as a probe. This serves to clarify the physical meaning of the different radial correlation functions that can be defined in a path-integral quantum fluid, since these functions are the r-space counterparts of the response functions. The basic feature of the external field relevant to this discussion is connected with its localizing/nonlocalizing effect on the quantum particles composing the fluid (i.e., a localizing field causes the collapse of the particle thermal packet). Fields that localize the quantum particles reveal the so-called instantaneous quantities (e.g., the conventional static structure factor), which are related with the diagonal elements of the density matrix. Fields that do not localize the quantum particles show the so-called linear response quantities, which are related to the diagonal and the off-diagonal density matrix elements. To perform this study the path-integral formalism is considered from the functional analysis approach. Given that the Gaussian Feynman–Hibbs effective potential picture is known to represent well many structural features of the quantum hard-sphere fluid, the parallel study of the response functions within this picture is also presented. In particular, the latter picture provides an accurate Ornstein–Zernike scheme that can be used for numerical calculations of response functions over a wide range of conditions, and also gives fine estimates for quantities difficult to compute with the path integral. Results for the quantum hard-sphere fluid obtained within the latter scheme are reported, tests of consistency are given, and the possibility of approximating the instantaneous response function by means of the coherent part of the linear response function is assessed.

Strong heterogeneity caused by deep mantle layering

Numerical simulations are used to characterize the volumetric heterogeneity associated with proposed chemical layering in the deep mantle. A globally continuous, undulating layer generates enormous amounts of volumetric heterogeneity, which is caused by lateral variations in the layer boundary depth and by strong hot upwellings arising from the top of the layer, in the middle lower mantle region. In contrast, the heterogeneity in the deepest mantle is very weak. Partial cancellation of the temperature and compositional contributions to seismic velocity could mask the layer itself, but the strong signatures of the thermochemical boundary layer and induced upwellings remain, even when fields are filtered to approximate the resolution of global seismic tomographic models. This distinctive heterogeneity is not observed in global seismic tomographic models. Dense material that is restricted to discontinuous “piles” generates heterogeneity that is more consistent, although not entirely, with seismic observations, with strong heterogeneity at the core‐mantle boundary. Radial correlation functions display a characteristic narrowing in the vicinity of any chemical layer but are very sensitive to the applied “seismic tomographic” filtering.

On the calculation of the static structure factor of path-integral quantum simple fluids far from exchange

This paper addresses several points of interest concerning the computation of the static structure factor of path-integral monatomic quantum fluids. First of all, the connection between the structure factor and the path-integral linear response pair radial correlation function is shown as its defining quantity by assuming a generalized Fermi's potential for the neutron-nuclei interactions, which is to be included in the general expression of the dynamic structure factor. Second, the possibilities of finding Ornstein-Zernike equations for full path-integral fluids, and also for the effective potential models of fluids derived from the path-integral formalism, are explored by working in the grand canonical ensemble. By so doing, the success and features for improvement of the weak-field approach used previously in this context of determining quantum static structure factors [SESÉ, L. M., 1996, Molec. Phys., 89, 1783; SESÉ, L. M., and LEDESMA, R., 1997, J. chem. Phys., 106, 1134] can be understood. New numerical applications are performed within this weak-field approach taking as probes the quantum hard-sphere fluid and dense fluid helium-4, the latter being described through Lennard-Jones and Aziz-Slaman underlying interactions. The results show that the structure factors associated with the linear response and instantaneous path-integral pair radial correlation functions differ noticeably from each other with increasing quantum effects. In particular, the linear response description leads to more compressible fluids than the instantaneous one. Besides, the equality between the isothermal compressibilities fixed via the linear response and the quantum particle centre-of-gravity pair radial correlation functions does not hold beyond the situations that can be treated with the Gaussian Feynman-Hibbs effective potential picture. Comparison with experiment in the case of helium-4 (T = 4.2 K) reveals clearly that, under strong quantum conditions, an operative framework more elaborate than the weak-field approach is needed.

Orientational correlations in liquid and supercritical CO2: neutron diffraction experiments and molecular dynamics simulations

Neutron diffraction data from sub- and supercritical CO2, collected over three different experimental runs, are analysed together, in order to investigate the evolution of the microscopic structure with the thermodynamic parameters. The relative orientations of neighbouring molecules are analysed also in terms of the angular radial correlation function, obtained by molecular dynamics simulation runs compatible with the total neutron weighted radial distribution function. Orientational correlations between neighbouring molecules are seen to persist across the whole thermodynamic range investigated. However, these are limited to the first neighbouring shell, and mainly ascribable to the quadrupolar interaction.

Path-integral Monte Carlo study of the structural and mechanical properties of quantum fcc and bcc hard-sphere solids

Path-integral Monte Carlo simulations involving the Cao–Berne’s hard-sphere propagator and aimed at exploring the high-density region (ρ*=0.8, 0.9) of the quantum hard-sphere (QHS) system are reported. By starting from single cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices, the following range of temperatures defined by the reduced de Broglie’s wavelengths 0.116⩽λB*⩽0.5 is studied. The r-space structural quantities computed are pair radial correlation functions (instantaneous, linear response, and necklace center of mass) and necklace radii of gyration. In addition, the following quantities related to the necklace centers of mass are calculated: maximal structure factor values, Steinhardt et al.’s orientational order parameters, and Lindemann’s index. The thermodynamic properties evaluated are energies and pressures. Comparison with Scheraga et al.’s results available in the literature [J. Chem. Phys. 96, 7005 (1992)] is made wherever possible. As shown, only the fcc lattice maintains its features under the strong QHS repulsions, whereas bcc and sc cannot cope with these effects transforming into striking partially crystalline [bcc(q)] and fluid phases, respectively. Conclusions on the features of the resulting phases which can help to explain the stages of the partial crystallization of the QHS fluid are also drawn.

A study of the condensed phases and solid–solid phase transition in toluene: A Monte Carlo investigation

A Monte Carlo study of the orthorhombic(β), monoclinic(α), and liquid phases of toluene in the isobaric isothermal ensemble employing variable shape simulation cell is reported here. The intermolecular potential of Williams and Starr is seen to reproduce the lattice parameters and other known properties reasonably well for the α-phase. The β-phase is not reproduced as well. The structure has been characterized in terms of the radial distribution functions and orientational correlation functions. The transition from the orthorhombic low temperature β-phase to the high temperature monoclinic α-phase has been successfully simulated. The transition is first order and lies between 140 and 145 K in agreement with experiment. The reverse transition from the α- to the β-phase does not take place in agreement with experiment. The liquid phase density and the heat of vaporization are reproduced well. The potential employed predicts an interaction energy which is about 5% in excess of the experimental value. The orientational correlation function and the radial distribution functions are sensitive to the potential and suggest where improvements are possible.