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Register a new userEfficient solutions of self-consistent mean field equations for dewetting and electrostatics in nonuniform liquids
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We use a new configuration-based version of linear response theory to efficiently solve self-consistent mean field equations relating an effective single particle potential to the induced density. The versatility and accuracy of the method is illustrated by applications to dewetting of a hard sphere solute in a Lennard-Jones fluid, the interplay between local hydrogen bond structure and electrostatics for water confined between two hydrophobic walls, and to ion pairing in ionic solutions. Simulation time has been reduced by more than an order of magnitude over previous methods.
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We examine in detail the theoretical underpinnings of previous successful applications of local molecular field (LMF) theory to charged systems. LMF theory generally accounts for the averaged effects of long-ranged components of the intermolecular interactions by using an effective or restructured external field. The derivation starts from the exact Yvon-Born-Green hierarchy and shows that the approximation can be very accurate when the interactions averaged over are slowly varying at characteristic nearest-neighbor distances. Application of LMF theory to Coulomb interactions alone allows for great simplifications of the governing equations. LMF theory then reduces to a single equation for a restructured electrostatic potential that satisfies Poissons equation defined with a smoothed charge density. Because of this charge smoothing by a Gaussian of width sigma, this equation may be solved more simply than the detailed simulation geometry might suggest. Proper choice of the smoothing length sigma plays a major role in ensuring the accuracy of this approximation. We examine the results of a basic confinement of water between corrugated wall and justify the simple LMF equation used in a previous publication. We further generalize these results to confinements that include fixed charges in order to demonstrate the broader impact of charge smoothing by sigma. The slowly-varying part of the restructured electrostatic potential will be more symmetric than the local details of confinements.
We show that spherical truncations of the 1/r interactions in models for water and acetonitrile yield very accurate results in bulk simulations for all site-site pair correlation functions as well as dipole-dipole correlation functions. This good performance in bulk simulations contrasts with the generally poor results found with the use of such truncations in nonuniform molecular systems. We argue that Local Molecular Field (LMF) theory provides a general theoretical framework that gives the necessary corrections to simple truncations in most nonuniform environments and explains the accuracy of spherical truncations in uniform environments by showing that these corrections are very small. LMF theory is derived from the exact Yvon-Born-Green (YBG) hierarchy by making physically-motivated and well-founded approximations. New and technically interesting derivations of both the YBG hierarchy and LMF theory for a variety of site-site molecular models are presented in appendices. The main paper focuses on understanding the accuracy of these spherical truncations in uniform systems both phenomenologically and quantitatively using LMF theory.
We analyze the structure of fluctuations near critical points and spinodals in mean-field and near-mean-field systems. Unlike systems that are non-mean-field, for which a fluctuation can be represented by a single cluster in a properly chosen percolation model, a fluctuation in mean-field and near-mean-field systems consists of a large number of clusters, which we term fundamental clusters. The structure of the latter and the way that they form fluctuations has important physical consequences for phenomena as diverse as nucleation in supercooled liquids, spinodal decomposition and continuous ordering, and the statistical distribution of earthquakes. The effects due to the fundamental clusters implies that they are physical objects and not only mathematical constructs.
Recent numerical studies of the susceptibility of the three-dimensional Ising model with various interaction ranges have been analyzed with a crossover model based on renormalization-group matching theory. It is shown that the model yields an accurate description of the crossover function for the susceptibility.
In this work we describe the Correlative Method of Unsymmetrized Self-Consistent Field (CUSF). This method is based on a set of nonlinear integrodifferential equations for the one-particle configurational distribution functions and for the self-consistent potentials of the atoms. Here we present the fundamental concepts of the CUSF, the hypotheses of the method, the basic equations, the self-consistent potential, the thermodynamics of the anharmonic crystalline solids, and the quantum corrections in the quasi-classical approximation. Keywords: lattice theory and statistics; anharmonic crystals; thermodynamics.
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