Axel Arnold

ESPResSo—an extensible simulation package for research on soft matter systems

Abstract We describe a new program package that is designed to perform numerical Molecular Dynamics (MD) and Monte Carlo (MC) simulations for a broad class of soft matter systems in a parallel computing environment. Our main concept in developing ESPResSo was to provide a user friendly and fast simulation tool which serves at the same time as a research platform capable of rapidly incorporating the latest algorithmic developments in the field of soft matter sciences. A particular strength of ESPResSo is its efficient treatment of long range interactions for various geometries using sophisticated algorithms like P 3 M, MMM2D, MMM1D and ELC. It is already equipped with a broad variety of interaction potentials, thermostats, and ensemble integrators; it offers the usage of constraints, masses and rotational degrees of freedom; it allows to move between different ensembles on-the-fly. An efficient MPI parallelization allows the usage of multi-processor architectures. Strict usage of ANSI-C for the core functions and a Tcl -script driven user interface makes ESPResSo platform independent. This also ensures easily modifiable interfaces to communicate with other MD/MC Packages, real-time visualization and other graphic programs. We tried to maintain a clear program structure to keep ESPResSo extensible for future enhancements and additions. ESPResSo is implemented as an open source project with the goal to stimulate researchers to contribute to the package.

Harvesting graphics power for MD simulations

We discuss an implementation of molecular dynamics (MD) simulations on a graphic processing unit (GPU) in the NVIDIA CUDA language. We tested our code on a modern GPU, the NVIDIA GeForce 8800 GTX. Results for two MD algorithms suitable for short-ranged and long-ranged interactions, and a congruential shift random number generator are presented. The performance of the GPUs is compared to their main processor counterpart. We achieve speedups of up to 40, 80 and 150 fold, respectively. With the latest generation of GPUs one can run standard MD simulations at 107 flops/

Electrostatics in periodic slab geometries. I

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ESPResSo 3.1: Molecular Dynamics Software for Coarse-Grained Models

We propose a new method to sum up electrostatic interactions in two-dimensional (2D) slab geometries. It consists of a combination of two recently proposed methods: the 3D Ewald variant of Yeh and Berkowitz [J. Chem. Phys. 111, 3155 (1999)] and the purely 2D method MMM2D by Arnold and Holm [Chem. Phys. Lett. 354, 324 (2002). The basic idea involves two steps: First we use a three-dimensional summation method whose summation order is changed to sum up the interactions in a slab-wise fashion. Second we subtract the unwanted interactions with the replicated layers analytically. The resulting method has full control over the introduced errors. The time to evaluate the layer correction term scales linearly with the number of charges, so that the full method scales like an ordinary 3D Ewald method, with an almost linear scaling in a mesh based implementation. In this paper we will introduce the basic ideas, derive the layer correction term, and numerically verify our analytical results.

MMM2D: A fast and accurate summation method for electrostatic interactions in 2D slab geometries

ESPResSo is a package for Molecular Dynamics (MD) simulations of coarse-grained models. We present the most recent version 3.1 of our software, highlighting some recent algorithmic extensions to version 1.0 presented in a previous paper (Limbach et al. Comput Phys Commun 174:704–727, 2006). A major strength of our package is the multitude of implemented methods for calculating Coulomb and dipolar interactions in periodic and partially periodic geometries. Here we present some more recent additions which include methods for systems with dielectric contrasts that frequently occur in coarse-grained models of charged systems with implicit water models, and an alternative, completely local electrostatic solver that is based on the electrodynamic equations. We also describe our approach to rigid body dynamics that uses MD particles with fixed relative positions. ESPResSo now gained the ability to add bonds during the integration, which allows to study e.g. agglomeration. For hydrodynamic interactions, a thermalized lattice Boltzmann solver has been built into ESPResSo, which can be coupled to the MD particles. This computationally expensive algorithm can be greatly accelerated by using Graphics Processing Units. For the analysis of time series spanning many orders of magnitude in time scales, we implemented a hierarchical generic correlation algorithm for user-configurable observables.

Attraction and unbinding of like-charged rods

We present a new method, in the following called MMM2D, to accurately calculate the electrostatic energy and forces on charges being distributed in a two dimensional periodic array of finite thickness. It is not based on an Ewald summation method and as such does not require any fine-tuning of an Ewald parameter for convergence. We transform the Coulomb sum via a convergence factor into a series of fast decaying functions which can be easily evaluated. Rigorous error bounds for the energies and the forces are derived and numerically verified. Already for small systems our method is much faster than the traditional 2D–Ewald methods, but for large systems it is clearly superior because its time demand scales like O(N 5/3 ) with the number N of charges considered. Moreover it shows a rapid convergence, is very precise and easy to handle.

Time scale of entropic segregation of flexible polymers in confinement: implications for chromosome segregation in filamentous bacteria.

We investigate the effective interaction between two like-charged rods in the regime of large coupling parameters using both Molecular Dynamics simulation techniques and the recently introduced strong-coupling theory. We obtain attraction between the rods for elevated Manning parameters accompanied by an equilibrium surface-to-surface separation of the order of the Gouy-Chapman length. A continuous unbinding between the rods is predicted at a threshold Manning parameter ξc = 2/3.

A novel method for calculating electrostatic interactions in 2D periodic slab geometries

We report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. We find that the entropic repulsion between chains can be sufficiently strong to cause segregation on a time scale that is short compared to the one for diffusion. This result implies that entropic driving forces are sufficiently strong to cause rapid bacterial chromosome segregation.

Simulations of non-neutral slab systems with long-range electrostatic interactions in two-dimensional periodic boundary conditions

Abstract We present a new method to accurately calculate the electrostatic energy and forces on charges being distributed in a two-dimensional periodic array of finite thickness. We transform the Coulomb sum via a convergence factor into a series of fast decaying functions which can be easily evaluated. Rigorous error bounds for the energies and the forces are derived and numerically verified. Already for small systems our method is much faster than the traditional 2D-Ewald methods, but for large systems it is clearly superior because its time demand scales like O (N 5/3 ) with the number N of charges considered. Moreover it shows a rapid convergence, is very precise and easy to handle.

MMM1D: A method for calculating electrostatic interactions in one-dimensional periodic geometries

We introduce a regularization procedure to define electrostatic energies and forces in a slab system of thickness h that is periodic in two dimensions and carries a net charge. The regularization corresponds to a neutralization of the system by two charged walls and can be viewed as the extension to the two-dimensional (2D)+h geometry of the neutralization by a homogeneous background in the standard three-dimensional Ewald method. The energies and forces can be computed efficiently by using advanced methods for systems with 2D periodicity, such as MMM2D or P3M/ELC, or by introducing a simple background-charge correction to the Yeh-Berkowitz approach of slab systems. The results are checked against direct lattice sum calculations on simple systems. We show, in particular, that the Madelung energy of a 2D square charge lattice in a uniform compensating background is correctly reproduced to high accuracy. A molecular dynamics simulation of a sodium ion close to an air/water interface is performed to demonstrate that the method does indeed provide consistent long-range electrostatics. The mean force on the ion reduces at large distances to the image-charge interaction predicted by macroscopic electrostatics. This result is used to determine precisely the position of the macroscopic dielectric interface with respect to the true molecular surface.