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Register a new userOn the efficient and accurate short-ranged simulations of uniform polar molecular liquids
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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.
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Coulomb interactions are present in a wide variety of all-atom force fields. Spherical truncations of these interactions permit fast simulations but are problematic due to their incorrect thermodynamics. Herein we demonstrate that simple analytical corrections for the thermodynamics of uniform truncated systems are possible. In particular results for the SPC/E water model treated with spherically-truncated Coulomb interactions suggested by local molecular field theory [Proc. Nat. Acad. Sci. USA 105, 19136 (2008)] are presented. We extend results developed by Chandler [J. Chem. Phys. 65, 2925 (1976)] so that we may treat the thermodynamics of mixtures of flexible charged and uncharged molecules simulated with spherical truncations. We show that the energy and pressure of spherically-truncated bulk SPC/E water are easily corrected using exact second-moment-like conditions on long-ranged structure. Furthermore, applying the pressure correction as an external pressure removes the density errors observed by other research groups in NPT simulations of spherically-truncated bulk species.
Current all-atom potential based molecular dynamics (MD) allow the identification of a proteins functional motions on a wide-range of time-scales, up to few tens of ns. However, functional large scale motions of proteins may occur on a time-scale currently not accessible by all-atom potential based molecular dynamics. To avoid the massive computational effort required by this approach several simplified schemes have been introduced. One of the most satisfactory is the Gaussian Network approach based on the energy expansion in terms of the deviation of the protein backbone from its native configuration. Here we consider an extension of this model which captures in a more realistic way the distribution of native interactions due to the introduction of effective sidechain centroids. Since their location is entirely determined by the protein backbone, the model is amenable to the same exact and computationally efficient treatment as previous simpler models. The ability of the model to describe the correlated motion of protein residues in thermodynamic equilibrium is established through a series of successful comparisons with an extensive (14 ns) MD simulation based on the AMBER potential of HIV-1 protease in complex with a peptide substrate. Thus, the model presented here emerges as a powerful tool to provide preliminary, fast yet accurate characterizations of proteins near-native motion.
It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the efficiency of particle swaps into equilibrium molecular dynamics (MD) simulations. We first develop a hybrid MD/MC scheme combining molecular dynamics with the original swap Monte Carlo. We implement this hybrid method in LAMMPS, a software package employed by a large community of users. Secondly, we define a continuous time version of the swap algorithm where both the positions and diameters of the particles evolve via Hamiltons equations of motion. For both algorithms, we discuss in detail various technical issues as well as the optimisation of simulation parameters. We compare the numerical efficiency of all available swap algorithms and discuss their relative merits.
Spherical truncations of Coulomb interactions in standard models for water permit efficient molecular simulations and can give remarkably accurate results for the structure of the uniform liquid. However truncations are known to produce significant errors in nonuniform systems, particularly for electrostatic properties. Local molecular field (LMF) theory corrects such truncations by use of an effective or restructured electrostatic potential that accounts for effects of the remaining long-ranged interactions through a density-weighted mean field average and satisfies a modified Poissons equation defined with a Gaussian-smoothed charge density. We apply LMF theory to three simple molecular systems that exhibit different aspects of the failure of a naive application of spherical truncations -- water confined between hydrophobic walls, water confined between atomically-corrugated hydrophilic walls, and water confined between hydrophobic walls with an applied electric field. Spherical truncations of 1/r fail spectacularly for the final system in particular, and LMF theory corrects the failings for all three. Further, LMF theory provides a more intuitive way to understand the balance between local hydrogen bonding and longer-ranged electrostatics in molecular simulations involving water.
In our first paper, we showed how a non-local effective Hamiltionian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Greens function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zig-zag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed.
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