We introduce a simulation technique to compute the free energy difference between two hydrate structures of different stoichiometry connected to a reservoir of gas molecules at a prescribed pressure. The method permits the determination of coexistence parameters for the system when the two hydrate structures have the same number of water molecules N_w. The approach is based on performing isobaric Lattice Switch Monte Carlo simulations to measure free energy differences between the hydrate structures when they are either fully occupied by gas molecules, or fully empty. This measurement is combined with thermodynamic integration within an ensemble in which the number of guest molecules N_g can fluctuate under the control of a chemical potential μ_g. We analyze the properties of the resulting constant-N_w,μ_g,P,T ensemble and show how it can be used to calculate coexistence points via a thermodynamic cycle. Applying the method to argon and methane structures, we find coexistence pressures that are in good agreement overall with the available experimental data.

In a recent article, Wang et al (Phys. Chem. Chem. Phys., 22, 10624 (2020)) introduced a new class of interparticle potential for molecular simulations. The potential is defined by a single range parameter, eliminating the need to decide how to truncate truly long-range interactions like the Lennard-Jones (LJ) potential. The authors explored the phase diagram for a particular value of the range parameter for which their potential is similar in shape to the LJ 12-6 potential. We have reevaluated the solid phase behaviour of this model using both Lattice Switch Monte Carlo and thermodynamic integration. In addition to finding that the boundary between hexagonal close packed (hcp) and face centred cubic (fcc) phases presented by Wang et al was calculated incorrectly, we show that owing to its finite range, the new potential exhibits several 'artifact' reentrant transitions between hcp and fcc phases. The artifact phases, which do not occur in the full (untruncated) LJ system, are also found for typically adopted forms of the truncated and shifted LJ potential. However, whilst in the latter case one can systematically investigate and correct for the effects of the finite range on the calculated phase behaviour, this is not possible for the new potential because the choice of range parameter affects the entire potential shape. Our results highlight that potentials with finite range may fail to represent the crystalline phase behaviour of systems with long-range dispersion interactions, even qualitatively.

We analyze the correspondence between two formalisms describing an interacting Bose gas, namely the standard Feynman diagrammatic expansion on the one hand, and the hierarchy equations for the imaginary-time Green functions on the other hand. We show that the Hartree–Fock approximation, as well as its first corrections at low density derived by Baym et al (2001 Eur. Phys. J. B 24 107–24), can be equivalently formulated in both formalisms. Within the hierarchy approach, the two-body correlations are expressed at lowest order in the interactions in terms of the full one-body Green function. This sheds light on the physical content of the corrections to the Hartree–Fock theory. Moreover, this representation of can be extended to higher orders, opening the way to systematic calculations of further corrections to the ideal critical temperature when the density increases.

We consider a quantum multicomponent plasma made with S species of point charged particles interacting via the Coulomb potential. We derive the screened activity series for the pressure in the grand-canonical ensemble within the Feynman-Kac path integral representation of the system in terms of a classical gas of loops. This series is useful for computing equations of state for it is nonperturbative with respect to the strength of the interaction and it involves relatively few diagrams at a given order. The known screened activity series for the particle densities can be recovered by differentiation. The particle densities satisfy local charge neutrality because of a Debye-dressing mechanism of the diagrams in these series. We introduce a new general neutralization prescription, based on this mechanism, for deriving approximate equations of state where consistency with electroneutrality is automatically ensured. This prescription is compared to other ones, including a neutralization scheme inspired by the Lieb-Lebowitz theorem and based on the introduction of (S-1) suitable independent combinations of the activities. Eventually, we briefly argue how the activity series for the pressure, combined with the Debye-dressing prescription, can be used for deriving approximate equations of state at moderate densities, which include the contributions of recombined entities made with three or more particles.

Comparisons of Gibbs ensemble Monte Carlo simulations with experimental data for the cage occupancies in N2 clathrate hydrates are performed to assess the accuracy of such simulations, to refine the effective potentials employed, and to help interpret recently measured large cage over small cage occupancy ratios [Petuya et al., J. Phys. Chem. C 122, 566 (2018)]. Different sets of interaction potentials for N2-N2, N2-H2O and H2O-H2O interactions are considered. Some of them fail to reproduce the known experimental fact that some large cages are doubly occupied at 273 K and high pressures. The best agreement between simulations and experiments is obtained when using a new N-O interaction potential derived in this work by averaging an ab-initio potential energy surface for the N2-H2O dimer.

We consider a quantum multi-component plasma made of point charged particles interacting via the two-body Coulomb potential. Within the Feynman-Kac path integral representation of the system in terms of a classical gas of loops, we derive screened activity series for the pressure in the grand-canonical ensemble. The method is based on the Abe-Meeron summations which remove all long-range Coulomb divergences. Moreover, we show that the particle densities can be inferred from the diagrammatic series for the pressure, through partial differentiations with respect to suitable effective activities, consistently with the local charge neutrality. We briefly argue how these results can be used for including, in the equation of state at moderately low densities, the contributions of recombined entities made with three or more particles.

We present a method that provides reliable equations of state for partially ionized gases at moderate densities. The gas is described within the physical picture in terms of a quantum plasma made with nuclei and electrons interacting via the Coulomb potential. The method relies on the screened cluster representation derived elsewhere and is obtained by resummations of Mayer‐like diagrammatics for the equivalent classical gas of loops. The contributions to the thermodynamics of atoms, molecules, or ions are described by cluster functions built with simple diagrams involving a few elementary particles and screened interactions. All quantum and collective mechanisms at work are embedded in these cluster functions, which can be computed numerically by sampling the corresponding path integrals. The usefulness and accuracy of this formalism is illustrated by considering a hydrogen–helium mixture under solar interior conditions. As a by‐product of our calculations, we also exhibit the density dependence of the two‐body cluster function analogous to the second virial coefficient in a hydrogen gas.

The screened Coulomb interaction φ through which particles interact in the path integral description of quantum plasmas is studied analytically and numerically. This interaction, which is a key ingredient in quantum Mayer diagrams, is closely related to the random‐phase approximation potential known from finite‐temperature many‐body perturbation theory. An efficient way to compute numerically φ and its contributions in quantum Mayer diagrams under weak degeneracy conditions is proposed. Two key contributions to the thermodynamics of a moderately dense hydrogen plasma are studied using this method: polarization of the plasma and the electron– proton cluster function which accounts for the contributions from hydrogen atoms at finite density and finite temperature. The calculations include effects from dynamical screening and from shifts as well as broadening of spectral lines. When κ λ≪1, with κ the inverse Debye screening length and λ the electronic thermal de Broglie wavelength, a simple fast‐to‐evaluate approximation for φ can be used without loss of accuracy. The error induced on the electron– proton cluster function by the common approximation of replacing φ by a statically screened Debye potential is assessed for κ λ in the range 0⩽κ λ⩽0.5.

In a recent paper [Phys. Rev. E 91, 013108 (2015)], Kraeft et al. criticize known exact results on the equation of state of quantum plasmas, which have been obtained independently by several authors. They argue about a difference in the definition of the direct two-body function Q(x), which appears in virial expansions of thermodynamical quantities, but Q(x) is not a measurable quantity in itself. Differences in definitions of intermediate quantities are irrelevant, and only differences in physical quantities are meaningful. Beyond Kraeft et al.'s broad statement that there is no agreement at order rho(5/2) in the virial equation for the pressure, we show that their published results for this quantity are in fact in perfect agreement with previous existing expressions.

We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H(-), H2(+), and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.

A transparent derivation of the Ewald formula for the electrostatic energy of a periodic three-dimensional system of point charges is presented. The problem of the conditional convergence of the lattice sum is dealt with by separating off, in a physically natural and mathematically simple way, long-range non-absolutely integrable contributions in the series. The general expression, for any summation order, of the surface (or dipole) term emerges very directly from those long-range contributions.

Annalen der PhysikVolume 524, Issue 6-7 p. 103-105 Physics ForumFree Access The divergent atomic partition function or how to assign correct statistical weights to bound states V. Ballenegger, V. Ballenegger [email protected] Institut UTINAM, Université de Franche-Comté, 25030 Besançon cedex, FranceSearch for more papers by this author V. Ballenegger, V. Ballenegger [email protected] Institut UTINAM, Université de Franche-Comté, 25030 Besançon cedex, FranceSearch for more papers by this author First published: 03 July 2012 https://doi.org/10.1002/andp.201200728Citations: 8AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL References [1]W. Ebeling, W.D. Kraeft,and G. Röpke, Ann. Phys. (Berlin) 524, 311– 326 (2012). [2]A.I. Larkin, Sov. Phys.-JETP 11, 1363 (1960). [3]W. Ebeling, Physica 40, 290 (1968). [4]W. Ebeling, Physica 38, 378 (1968). [5]D. Kremp, M. Schlanges, and W.-D. Kraeft, Quantum Statistics of Non-Ideal Plasmas (Springer, Berlin Heidelberg, 2005). [6]A. Alastuey, V. Ballenegger, F. Cornu, and Ph.A. Martin, Stat. Phys. 113, 455 (2003). [7]A. Alastuey, V. Ballenegger, F. Cornu, and Ph.A. Martin, Stat. Phys. 130, 1119 (2008). [8]A. Alastuey and V. Ballenegger, J. Phys. A, Math. Theor. 42, 214031 (2009). [9]A. Alastuey and V. Ballenegger, Contrib. Plasma Phys. 50, 46 (2010). [10]W. Ebeling, W.D. Kraeft,and G. Röpke, Contrib. Plasma Phys. 52, 7 (2012). [11]F.J. Rogers, Phys. Rev. A 10, 2441 (1974). [12]D. Saumon and G. Chabrier, Phys. Rev. A 46, 2084 (1992). [13]V.K. Gryaznov et al., AIP Conf. Proc. 731, 147 (2004). Citing Literature Volume524, Issue6-7July 2012Pages 103-105 ReferencesRelatedInformation

We demonstrate explicitly how the two seemingly different particle mesh Ewald methods, the smooth particle mesh Ewald (SPME) and the particle-particle particle mesh (P3M), can be mathematically transformed into each other. This allows us in particular to convert the error estimate of the P3M method in the energy-conserving scheme (also known as "P3M with analytic differentiation") into an error estimate for the SPME method, via a simple change of the lattice Green function. Our error estimate is valid for any values of the SPME parameters (mesh size, spline interpolation order, Ewald splitting parameter, real-space cutoff distance), including odd orders of splines. The problem with the self-forces is avoided thanks to an analytical formula that allows to subtract them directly within the particle mesh calculation. Plots of the accuracy of the SPME forces are provided for a wide range of parameter values. The main use of the error estimate is to allow a simulation program to scan quickly the multidimensional parameter space to find the best set of parameters to achieve a target accuracy at the smallest computational cost. As a byproduct, we show how a SPME code can be transformed into a P3M version by changing a few lines of code. We demonstrate also that the P3M lattice Green function can be approximated by a closed form expression, computable on-the-fly, that provides essentially the same accuracy as the full function.

We study a hydrogen gas at low densities within the physical picture. Recombination processes leading to the formation of atoms and molecules are properly taken into account via the well-known Ebeling function and a new four-body partition function. Our method provides a reliable equation of state which covers the plasma, atomic and molecular phases (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact scaled low-temperature (SLT) expansion, which provides a rigorous extension of the well-known virial expansion-valid in the fully ionized phase-into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E-H|/kT) included (E-H similar or equal to -13.6 eV). Those truncated expansions describe the first five nonideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom H, ions H- and H-2(+), molecule H-2, ... ) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for the molecule H-2 and ions H- and H-2(+), for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (rho similar to 10(-2) g/cm(3)), some discrepancies among the SLT, OPAL, and PIMC results are observed. DOI: 10.1103/PhysRevE.86.066402

Dipolar soft-sphere (DSS) fluids in the dilute low-coupling regime are studied via Molecular Dynamic simulations and the extension of a theoretical formalism previously used for dipolar hard spheres in which new terms for the virial expansion of the radial distribution function corresponding to the three-particle contribution are presented and tested for the zero and non-zero magnetic field case. A thorough comparison with simulations shows that the extended formalism is able to account for the structure factors of DSS with and without externally applied magnetic fields in the dilute low-coupling regime: quantitative agreement between theory and simulations is found for dipolar coupling parameters λ≲2, and volume fraction φ≲0.25. When λ>1 the new added term to the virial expansion is observed to play a crucial role in order to match quantitatively theory and simulations at zero field. In the presence of an external magnetic field our tests show that further improvements are needed and only new terms with Langevin function dependences can significatively contribute to improve the predictions for the dilute low-coupling regime. Numerical simulations show that despite that the ferrofluids considered here are in the dilute low-coupling regime, when an external field is applied, important correlations along the parallel direction to the field and depletion phenomena along the perpendicular direction are observed in the averaged density surrounding a particle.

The adsorption of stiff magnetic filaments close to an attractive surface is studied thoroughly via extensive Langevin dynamics simulations (LD). Magnetic filaments are represented by a coarse-grained bead-spring model where each bead bears a point dipole located at its center and the excluded volume interaction is introduced via a soft-core repulsive potential. We find strong evidence for the existence of two transitions as the temperature is lowered. First, the system undergoes a continuum phase transition from the desorbed to the adsorbed state. This transition is followed by a second structural transition that takes place when the filaments are already adsorbed. The adsorption transition is found to be very similar to the one observed for stiff non-magnetic polymer chains [Sintes et al., Macromolecules 2001, 34, 1352–1357] where the chain bending interaction plays a similar role as the magnetic component of the present case. However, the tendency of the magnetic chains to stretch is reversed by a further reduction in temperature and the chains tend to form closed adsorbed loops leading to a second structural transition. A representation of the phase diagram for the adsorption of magnetic filaments is determined here for the first time. We also present a novel way to determine the temperature at which the chain is adsorbed that is based on the analysis of the change in the number of trains, tails and loops developed by the polymer chain during the adsorption process.

We derive an analytic formula for subtracting the spurious self-forces in particle–mesh methods that use the analytical differentiation scheme, such as the Smooth Particle Mesh Ewald (SPME) method and the Particle–Particle Particle–Mesh (P3M) method with analytical differentiation. The impact of the self-forces on the accuracy of the particle–mesh methods is investigated, and it is shown that subtracting them can improve the accuracy of the calculation for some choices of the methodʼs parameters. It is also suggested to subtract exactly the approximate, mesh-computed, self-energy of each particle, replacing them by the exact value. Subtracting in this way the self-energy and self-force of each particle not only improves the accuracy, but also reduces the violation of momentum and energy conservation in particle–mesh methods with analytical differentiation.

The interlaced and non-interlaced versions of the dipolar particle-particle particle-mesh (P(3)M) method implemented using the analytic differentiation scheme (AD-P(3)M) are presented together with their respective error estimates for the calculation of the forces, torques, and energies. Expressions for the optimized lattice Green functions, and for the Madelung self-forces, self-torques and self-energies are given. The applicability of the theoretical error estimates are thoroughly tested and confirmed in several numerical examples. Our results show that the accuracy of the calculations can be improved substantially when the approximate (mesh computed) Madelung self-interactions are subtracted. Furthermore, we show that the interlaced dipolar AD-P(3)M method delivers a significantly higher accuracy (which corresponds approximately to using a twice finer mesh) than the conventional method, allowing thereby to reduce the mesh size with respect to the non-interlaced version for a given accuracy. In addition, we present similar expressions for the dipolar ik-differentiation interlaced scheme, and we perform a comparison with the AD interlaced scheme. Rough tests for the relative speed of the dipolar P(3)M method using ik-differentiation and the interlaced/non-interlaced AD schemes show that when FFT computing time is the bottleneck, usually when working at high precisions, the interlaced AD-scheme can be several times faster than the other two schemes. For calculations with a low accuracy requirement, the interlaced version can perform worse than the ik and the non-interlaced AD schemes.

A theoretical formalism to predict the structure factors observed in dipolar soft-sphere fluids based on a virial expansion of the radial distribution function is presented. The theory is able to account for cases with and without externally applied magnetic fields. A thorough comparison of the theoretical results to molecular-dynamics simulations shows a good agreement between theory and numerical simulations when the fraction of particles involved in clustering is low; i.e., the dipolar coupling parameter is lambda less, similar 2, and the volume fraction is phi less, similar 0.25. When magnetic fields are applied to the system, special attention is paid to the study of the anisotropy of the structure factor. The theory reasonably accounts for the structure factors when the Langevin parameter is smaller than 5.