Ewald sums for Yukawa potentials

Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo

We propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn-Sham or Hartree-Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.

Collective ion dynamics in Coulomb one-component plasmas within the self-consistent relaxation theory

In this paper, we present the theoretical formalism describing the collective ion dynamics of the nonideal Coulomb classical one-component plasmas on the basis of the self-consistent relaxation theory. The theory is adapted to account for correlations between the frequency relaxation parameters that characterize the three- and four-particle dynamics and the parameters associated with the two-particle dynamics. The dynamic structure factor spectra and dispersion characteristics calculated for a wide range of wave numbers are in agreement with the molecular dynamics simulation data and the results obtained with the theory of the frequency moments. The proposed formalism reproduces all the features inherent to the Coulomb one-component plasmas and requires only knowledge of the coupling parameter and the information about the structure.

Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations

Accurate phase diagrams of multicomponent plasmas are required for the modeling of dense stellar plasmas, such as those found in the cores of white dwarf stars and the crusts of neutron stars. Those phase diagrams have been computed using a variety of standard techniques, which suffer from physical and computational limitations. Here we present an efficient and accurate method that overcomes the drawbacks of previously used approaches. In particular, finite-size effects are avoided as each phase is calculated separately; the plasma electrons and volume changes are explicitly taken into account; and arbitrary analytic fits to simulation data as well as particle insertions are avoided. Furthermore, no simulations at "uninteresting" state conditions, i.e., away from the phase coexistence curves, are required, which improves the efficiency of the technique. The method consists of an adaptation of the so-called Gibbs-Duhem integration approach to electron-ion plasmas, where the coexistence curve is determined by direct numerical integration of its underlying Clapeyron equation. The thermodynamics properties of the coexisting phases are evaluated separately using Monte Carlo simulations in the isobaric semigrand canonical ensemble (NPTΔμ). We describe this Monte Carlo-based Clapeyron integration method, including its basic physical and numerical principles, our extension to electron-ion plasmas, and our numerical implementation. We illustrate its applicability and benefits with the calculation of the melting curve of dense carbon-oxygen plasmas under conditions relevant for the cores of white dwarf stars and provide analytic fits to implement this new melting curve in white dwarf models. While this work focuses on the liquid-solid phase boundary of dense two-component plasmas, a wider range of physical systems and phase boundaries are within the scope of the Clapeyron integration method, which had until now only been applied to simple model systems of neutral particles.

Interplay of anisotropy in shape and interactions in charged platelet suspensions

Motivated by the intriguing phase behavior of charged colloidal platelets, we investigate the structure and dynamics of charged repulsive disks by means of Monte Carlo simulations. The electrostatic interactions are taken into account through an effective two-body potential, obtained within the nonlinear Poisson-Boltzmann formalism, which has the form of anisotropic screened Coulomb potential. Recently, we showed that the original intrinsic anisotropy of the electrostatic potential in competition with excluded volume effects leads to a rich phase behavior that not only includes various liquid-crystalline phases but also predicts the existence of novel structures composed of alternating nematic-antinematic sheets. Here, we examine the structural and dynamical signatures of each of the observed structures for both translational and rotational degrees of freedom. Finally, we discuss the influence of effective charge value and our results in relation to experimental findings on charged platelet suspensions.

On phase behavior and dynamical signatures of charged colloidal platelets

Charged platelet suspensions, such as swelling clays, disc-like mineral crystallites or exfoliated nanosheets are ubiquitous in nature. Their phase behaviours are nevertheless still poorly understood: while some clay suspensions form arrested states at low densities, others exhibit an equilibrium isotropic-nematic transition at moderate densities. These observations raise fundamental questions about the influence of electrostatic interactions on the isotropic-nematic transition and the organisation of charged platelets. We investigate the competition between anisotropic excluded-volume and repulsive electrostatic interactions in suspensions of charged colloidal discs, by means of Monte-Carlo simulations and characterization of the dynamics of the structures. We show that the original intrinsic anisotropy of the electrostatic potential between charged platelets not only rationalizes generic features of the complex phase diagram of charged colloidal platelets such as Gibbsite and Beidellite clays, but also predicts the existence of novel structures. Furthermore, we find evidences of a strong slowing down of the dynamics upon increasing density.

Generalized approach to Ewald sums

We derive Ewald sum formulas for potential energy and force for a system of point charges interacting with an arbitrary, long-range central potential. The system is made neutral by a uniform background of opposite charge interacting with the same potential. These formulas can be readily used in computer numerical simulations of model physical systems. In particular, expressions for the potential energy and the force have been obtained in both two and three dimensions for Coulomb and other power-law potentials, Yukawa systems, and for an electronic bilayer. We discuss numerical results and their accuracy for various systems and, based on our analysis, suggest values to be used for the parameters that appear in the Ewald sums.

Numerical study of a binary Yukawa model in regimes characteristic of globular proteins in solutions

The main goal of this paper is to assess the limits of validity, in the regime of low concentration and strong Coulomb coupling (high molecular charges), of a simple perturbative approximation to the radial distribution functions (RDF's), based upon a low-density expansion of the potential of mean force and proposed to describe protein-protein interactions in a recent small-angle-scattering (SAS) experimental study. A highly simplified Yukawa (screened Coulomb) model of monomers and dimers of a charged globular protein (beta-lactoglobulin) in solution is considered. We test the accuracy of the RDF approximation, as a necessary complementary part of the previous experimental investigation, by comparison with the fluid structure predicted by approximate integral equations and exact Monte Carlo (MC) simulations. In the MC calculations, an Ewald construction for Yukawa potentials has been used to take into account the long-range part of the interactions in the weakly screened cases. Our results confirm that the perturbative first-order approximation is valid for this system even at strong Coulomb coupling, provided that the screening is not too weak (i.e., for Debye length smaller than monomer radius). A comparison of the MC results with integral equation calculations shows that both the hypernetted-chain (HNC) and Percus-Yevick closures have a satisfactory behavior under these regimes, with the HNC being superior throughout. The relevance of our findings for interpreting SAS results is also discussed.

Phase diagram of a binary symmetric hard-core Yukawa mixture

We assess the accuracy of the self-consistent Ornstein-Zernike approximation for a binary symmetric hard-core Yukawa mixture by comparison with Monte Carlo simulations of the phase diagrams obtained for different choices of the ratio alpha of the unlike-to-like interactions. In particular, from the results obtained at alpha=0.75 we find evidence for a critical endpoint in contrast to recent studies based on integral equation and hierarchical reference theories. The variation of the phase diagrams with range of the Yukawa potential is investigated.

Phase diagrams of hard-core repulsive Yukawa particles

We determine the phase behavior of hard spheres interacting with repulsive Yukawa (screened Coulomb) interaction using computer simulations. We study the effect of the hard-core diameter on the phase behavior of repulsive Yukawa particles by comparing our phase diagrams with that of repulsive point Yukawa particles. We show that for sufficiently high contact values of the pair potential (betaepsilon=20, 39, 81, and higher), the fluid-face-centered-cubic (fcc) solid, at high screening, the fluid-body-centered-cubic (bcc) solid and the bcc-fcc coexistence for packing fractions eta less, similar 0.5 are well described by the phase boundaries of point Yukawa particles, by employing a mapping of the point Yukawa system onto a hard-core repulsive Yukawa system. While the bcc-fcc coexistence is well described by the point Yukawa limit for eta<0.5, we find a deviation at higher eta as the hard-core repulsion favors the fcc solid for eta>/=0.5, independent of the screening. Consequently, a second triple point appears in the phase diagram in the weak screening regime. In addition, we find that all the phase coexistence regions in our phase diagrams for hard-core repulsive Yukawa system are very narrow, i.e., a small density jump in the coexisting phases.

Transport coefficients of the Yukawa one-component plasma

We present equilibrium molecular-dynamics computations of the thermal conductivity and the two viscosities of the Yukawa one-component plasma. The simulations were performed within periodic boundary conditions, and Ewald sums were implemented for the potentials, the forces, and for all the currents which enter the Kubo formulas. For large values of the screening parameter, our estimates of the shear viscosity and the thermal conductivity are in good agreement with the predictions of the Chapman-Enskog theory.

Ab initio study of deuterium in the dissociating regime: sound speed and transport properties

The sound speed and the transport properties of dense hydrogen (deuterium) are computed from local spin-density approximation molecular-dynamics simulations in the dissociating regime. The sound speed c(s) is evaluated from the thermodynamical differentiation of the equation of state in the molecular phase and is in very good agreement with recent experiments. The diffusion constant D and the viscosity eta are extracted from simulations performed at V=6, 4, and 2.7 cm(3)/mole, corresponding, respectively, for deuterium at rho=0.672, 1.0, and 1.5 g/cm(3) in a range of temperatures 1000 K<T<50,000 K. In the dissociated regime, the diffusion coefficient is well predicted by one-component plasma formulas using a renormalized coupling parameter recently proposed by Murillo [M. S. Murillo, Phys. Rev. B 62, 4115 (2000)]. The behavior of the shear viscosity in the dissociated regime is more complex and exhibits a crossover between atomic and screened plasma formulation. A comparison with recent molecular-dynamics simulations of Yukawas systems shows that the inverse of the screening length must lie between 1 and 2, in nearest-neighbor radius units, as suggested by the results on the diffusion.