Multilevel summation for dispersion: A linear-time algorithm for r −6 potentials

Impact of the Force Field on the Calculation of Density and Surface Tension of Epoxy-Resins

The molecular simulation of interfacial systems is a matter of debate because of the choice of many input parameters that can affect significantly the performance of the force field of reproducing the surface tension and the coexisting densities. After developing a robust methodology for the calculation of the surface tension on a Lennard-Jones fluid, we apply it with different force fields to calculate the density and surface tension of pure constituents of epoxy resins. By using the model that best reproduces the experimental density and surface tension, we investigate the impact of composition in mass fraction on uncured epoxy resins and the effects of degree of cross-linking on cured resins.

Review of Electrostatic Force Calculation Methods and Their Acceleration in Molecular Dynamics Packages Using Graphics Processors

Molecular dynamics (MD) simulations probe the conformational repertoire of macromolecular systems using Newtonian dynamic equations. The time scales of MD simulations allow the exploration of biologically relevant phenomena and can elucidate spatial and temporal properties of the building blocks of life, such as deoxyribonucleic acid (DNA) and protein, across microsecond (μs) time scales using femtosecond (fs) time steps. A principal bottleneck toward extending MD calculations to larger time scales is the long-range electrostatic force measuring component of the naive nonbonded force computation algorithm, which scales with a complexity of (N, number of atoms). In this review, we present various methods to determine electrostatic interactions in often-used open-source MD packages as well as the implementation details that facilitate acceleration of the electrostatic interaction calculation.

Multilevel summation for periodic electrostatics using B-splines

Fast methods for calculating two-body interactions have many applications, and for molecular science and cosmology, it is common to employ periodic boundary conditions. However, for the 1/r potential, the energy and forces are ill-defined. Adopted here is the model given by the classic Ewald sum. For the fast calculation of two-body forces, the most celebrated method is the fast multipole method and its tree-code predecessor. However, molecular simulations typically employ mesh-based approximations and the fast Fourier transform. Both types of methods have significant drawbacks, which, in most respects, are overcome by the less well-known multilevel summation method (MSM). Presented here is a realization of the MSM, which can be regarded as a multilevel extension of the (smoothed) particle mesh Ewald (PME) method, but with the Ewald softening replaced by one having a finite range. The two-level (single-grid) version of MSM requires fewer tuning parameters than PME and is marginally faster. Additionally, higher-level versions of MSM scale well to large numbers of processors, whereas PME and other two-level methods do not. Although higher-level versions of MSM are less efficient on a single processor than the two-level version, evidence suggests that they are more efficient than other methods that scale well, such as the fast multipole method and tree codes.

Multilevel summation method for electrostatic force evaluation

The multilevel summation method (MSM) offers an efficient algorithm utilizing convolution for evaluating long-range forces arising in molecular dynamics simulations. Shifting the balance of computation and communication, MSM provides key advantages over the ubiquitous particle–mesh Ewald (PME) method, offering better scaling on parallel computers and permitting more modeling flexibility, with support for periodic systems as does PME but also for semiperiodic and nonperiodic systems. The version of MSM available in the simulation program NAMD is described, and its performance and accuracy are compared with the PME method. The accuracy feasible for MSM in practical applications reproduces PME results for water property calculations of density, diffusion constant, dielectric constant, surface tension, radial distribution function, and distance-dependent Kirkwood factor, even though the numerical accuracy of PME is higher than that of MSM. Excellent agreement between MSM and PME is found also for interface potentials of air–water and membrane–water interfaces, where long-range Coulombic interactions are crucial. Applications demonstrate also the suitability of MSM for systems with semiperiodic and nonperiodic boundaries. For this purpose, simulations have been performed with periodic boundaries along directions parallel to a membrane surface but not along the surface normal, yielding membrane pore formation induced by an imbalance of charge across the membrane. Using a similar semiperiodic boundary condition, ion conduction through a graphene nanopore driven by an ion gradient has been simulated. Furthermore, proteins have been simulated inside a single spherical water droplet. Finally, parallel scalability results show the ability of MSM to outperform PME when scaling a system of modest size (less than 100 K atoms) to over a thousand processors, demonstrating the suitability of MSM for large-scale parallel simulation.

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.

Computer modelling of the surface tension of the gas–liquid and liquid–liquid interface

This review presents the state of the art in molecular simulations of interfacial systems and of the calculation of the surface tension from the underlying intermolecular potential.

Direct-Space Corrections Enable Fast and Accurate Lorentz-Berthelot Combination Rule Lennard-Jones Lattice Summation

Long-range lattice summation techniques such as the particle-mesh Ewald (PME) algorithm for electrostatics have been revolutionary to the precision and accuracy of molecular simulations in general. Despite the performance penalty associated with lattice summation electrostatics, few biomolecular simulations today are performed without it. There are increasingly strong arguments for moving in the same direction for Lennard-Jones (LJ) interactions, and by using geometric approximations of the combination rules in reciprocal space, we have been able to make a very high-performance implementation available in GROMACS. Here, we present a new way to correct for these approximations to achieve exact treatment of Lorentz-Berthelot combination rules within the cutoff, and only a very small approximation error remains outside the cutoff (a part that would be completely ignored without LJ-PME). This not only improves accuracy by almost an order of magnitude but also achieves absolute biomolecular simulation performance that is an order of magnitude faster than any other available lattice summation technique for LJ interactions. The implementation includes both CPU and GPU acceleration, and its combination with improved scaling LJ-PME simulations now provides performance close to the truncated potential methods in GROMACS but with much higher accuracy.

Extension and evaluation of the multilevel summation method for fast long-range electrostatics calculations

Several extensions and improvements have been made to the multilevel summation method (MSM) of computing long-range electrostatic interactions. These include pressure calculation, an improved error estimator, faster direct part calculation, extension to non-orthogonal (triclinic) systems, and parallelization using the domain decomposition method. MSM also allows fully non-periodic long-range electrostatics calculations which are not possible using traditional Ewald-based methods. In spite of these significant improvements to the MSM algorithm, the particle-particle particle-mesh (PPPM) method was still found to be faster for the periodic systems we tested on a single processor. However, the fast Fourier transforms (FFTs) that PPPM relies on represent a major scaling bottleneck for the method when running on many cores (because the many-to-many communication pattern of the FFT becomes expensive) and MSM scales better than PPPM when using a large core count for two test problems on Sandia's Redsky machine. This FFT bottleneck can be reduced by running PPPM on only a subset of the total processors. MSM is most competitive for relatively low accuracy calculations. On Sandia's Chama machine, however, PPPM is found to scale better than MSM for all core counts that we tested. These results suggest that PPPM is usually more efficient than MSM for typical problems running on current high performance computers. However, further improvements to MSM algorithm could increase its competitiveness for calculation of long-range electrostatic interactions.

Atomistic potentials for trisiloxane, alkyl ethoxylate, and perfluoroalkane-based surfactants with TIP4P/2005 and application to simulations at the air-water interface

The mechanism of superspreading, the greatly enhanced spreading of water droplets facilitated by trisiloxane surfactants, is still under debate, largely because the role and behavior of the surfactants cannot be sufficiently resolved by experiments or continuum simulations. Previous molecular dynamics studies have been performed with simple model molecules or inaccurate models, strongly limiting their explanatory power. Here we present a force field dedicated to superspreading, extending existing quantum-chemistry-based models for the surfactant and the TIP4P/2005 water model ( Abascal et al. J. Chem. Phys. , 2005 , 123 , 234505 ). We apply the model to superspreading trisiloxane surfactants and nonsuperspreading alkyl ethoxylate and perfluoroalkane surfactants at various concentrations at the air-water interface. We show that the developed model accurately predicts surface tensions, which are typically assumed important for superspreading. Significant differences between superspreading and traditional surfactants are presented and their possible relation to superspreading discussed. Although the force field has been developed for superspreading problems, it should also perform well for other simulations involving polymers or copolymers with water.