The CECAM electronic structure library and the modular software development paradigm.

First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community.

Can we approach the gas-liquid critical point using slab simulations of two coexisting phases?

In this paper, we demonstrate that it is possible to approach the gas-liquid critical point of the Lennard-Jones fluid by performing simulations in a slab geometry using a cut-off potential. In the slab simulation geometry, it is essential to apply an accurate tail correction to the potential energy, applied during the course of the simulation, to study the properties of states close to the critical point. Using the Janecek slab-based method developed for two-phase Monte Carlo simulations [J. Janec̆ek, J. Chem. Phys. 131, 6264 (2006)], the coexisting densities and surface tension in the critical region are reported as a function of the cutoff distance in the intermolecular potential. The results obtained using slab simulations are compared with those obtained using grand canonical Monte Carlo simulations of isotropic systems and the finite-size scaling techniques. There is a good agreement between these two approaches. The two-phase simulations can be used in approaching the critical point for temperatures up to 0.97 TC∗ (T∗ = 1.26). The critical-point exponents describing the dependence of the density, surface tension, and interfacial thickness on the temperature are calculated near the critical point.

Monte Carlo simulations of the static friction between two grafted polymer brushes.

A configurational bias Monte Carlo method has been developed to study the static friction between grafted polymers immersed in a good solvent. Simple models using the soft quadratic potential from a dissipative particle dynamics study have been used to model polyzwitterionic brushes at physiological pressures (up to 7.5 MPa). Three models of decreasing rigidity have been used to model the friction between the brushes by calculating the tangential component of the pressure induced by a mismatch in the registry of the two grafting surfaces. The static friction coefficient can be calculated for three model systems and the slip between the layers occurs at a much lower values of shear force for the more flexible polymer layer. A moderate increase in the flexibility of the chains reduces the friction coefficient by a factor of ca. 20. Tilting the layer directors of the brushes also increases the static friction between the layer when the top, tilted layer is displaced in the direction away from the tilt. Non-equilibrium dynamics techniques for the same model were performed using dissipative particle dynamics and the limiting extremes of the Stribeck curve corresponding to the boundary lubrication regime and the hydrodynamic lubrication regime were observed for these flat surfaces. As expected, µk is significantly lower than µs for the same system. The dynamical friction coefficients in the model are in good agreement with those observed in the experiment and the ratio of µk/µs of between 0.11 and 0.5 observed in the simulations is in reasonable agreement with the value of 0.5 normally observed for these seen for these systems.

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. We provide a short account of different methodological factors (size-effects, truncation procedures, long-range corrections and potential models) that can affect the results of the simulations. Accurate calculations are presented for the calculation of the surface tension as a function of the temperature, pressure and composition by considering the planar gas-liquid interface of a range of molecular fluids. In particular, we consider the challenging problems of reproducing the interfacial tension of salt solutions as a function of the salt molality; the simulations of spherical interfaces including the calculation of the sign and size of the Tolman length for a spherical droplet; the use of coarse-grained models in the calculation of the interfacial tension of liquid-liquid surfaces and the mesoscopic simulations of oil-water-surfactant interfacial systems.

Controlling the long-range corrections in atomistic Monte Carlo simulations of two-phase systems.

The long-range correction to the surface tension can amount to up to 55% of the calculated value of the surface tension for cutoffs in the range of 2.1-6.4 σ. The calculation of the long-range corrections to the surface tension and to the configurational energy in two-phase systems remains an active area of research. In this work, we compare the long-range corrections methods proposed by Guo and Lu ( J. Chem. Phys. 1997 , 106 , 3688 - 3695 ) and Janecek ( J. Phys. Chem. B 2006 , 110 , 6264 - 6269 ) for the calculation of the surface tension and of the coexisting densities in Monte Carlo simulations of the truncated Lennard-Jones potential and the truncated and shifted Lennard-Jones potential models. These methods require an estimate of the long-range correction at each step in the Monte Carlo simulation. We apply the full version of the Guo and Lu method, which involves the calculation of a double integral that contains a series of density differences, and we compare these results with the simplified version of the method which is routinely used in two-phase simulations. We conclude that the cutoff dependencies of the surface tension and coexisting densities are identical for the full versions of Guo and Lu and Janecek methods. We show that it is possible to avoid applying the long-range correction at every step by using the truncated Lennard-Jones potential with a cutoff rc ≥ 5 σ. The long-range correction can then be applied at the end of the simulation. The limiting factor in the accurate calculation of this final correction is an accurate estimate of the coexisting densities. Link-cell simulations performed using a cutoff rc = 5.5 σ require twice as much computing time as those with a more typical cutoff of rc = 3.0 σ. The application of the Janecek correction increases the running time of the simulation by less than 10%, and it can be profitably applied with the shorter cutoff.

Structure and rheology of star polymers in confined geometries: a mesoscopic simulation study.

Mesoscopic simulations of star polymer melts adsorbed onto solid surfaces are performed using the dissipative particle dynamics (DPD) method. A set of parameters is developed to study the low functionality star polymers under shear. The use of a new bond-angle potential between the arms of the star creates more rigid chains and discriminates between different functionalities at equilibrium, but still allows the polymers to deform appropriately under shear. The rheology of the polymer melts is studied by calculating the kinetic friction and viscosity and there is good agreement with experimental properties of these systems. The study is completed with predictive simulations of star polymer solutions in an athermal solvent.

The gas-liquid surface tension of argon: a reconciliation between experiment and simulation.

We present a simulation of the liquid-vapor interface of argon with explicit inclusion of the three-body interactions. The three-body contributions to the surface tension are calculated using the Kirkwood-Buff approach. Monte Carlo calculations of the long-range corrections to the three-body contribution are calculated from the radial distribution function g((2))(z1, cos θ12, r12). Whereas the effective two-body potentials overestimate the surface tension by more than 15%, the inclusion of the three-body potential provides an excellent agreement with the experimental results for temperatures up to 15 K below the critical temperature. We conclude that the three-body interactions must be explicitly included in accurately modelling the surface tension of argon.

Mesoscale modeling of polyelectrolyte brushes with salt.

We report dissipative particle dynamics (DPD) simulations of a polyelectrolyte brush under athermal solvent conditions. The electrostatic interactions are calculated using the particle-particle particle-mesh (PPPM) method with charges distributed over the particles. The polymer beads, counterions, co-ions, and solvent particles are modeled explicitly. The DPD simulations show a dependence of the brush height on the grafting density and the charge fraction that is typical of the nonlinear osmotic brush regime. We report the effect of the addition of salt on the structural properties of the brush. In the case of a polyelectrolyte brush with a high surface coverage, the simulations reproduce the transition between the nonlinear osmotic brush regime where the thickness of the brush is independent of the salt concentration and the salted regime where the brush height decreases weakly with the salt concentration.

Electrostatic Interactions in Dissipative Particle Dynamics: Toward a Mesoscale Modeling of the Polyelectrolyte Brushes.

We report mesoscopic simulations of bulk electrolytes and polyelectrolyte brushes using the dissipative particle dynamics (DPD) method. The calculation of the electrostatic interactions is carried out using both the Ewald summation method and the particle-particle particle-mesh technique with charges distributed over the particles. The local components of the pressure tensor are calculated using the Irving and Kirkwood, and the method of planes and mechanical equilibrium is demonstrated. The profiles of the normal component of the pressure tensor are shown to be similar for both the Ewald and particle-particle particle-mesh methods for a single polyelectrolyte brush. We show that the PPPM method with the MOP technique is the appropriate choice for simulations of this type. The mesoscale modeling of a strongly stretched polylectrolyte brush formed by strong charged polymer chains at a high grafting density shows that the polyelectrolyte follows the nonlinear osmotic regime, as expected from the calculation of the Gouy-Chapman length and the dimensionless Manning ratio.

Mesoscopic simulation of entanglements using dissipative particle dynamics: application to polymer brushes.

We use a simple spring-spring repulsion to model entanglements between polymers in dissipative particle dynamics (DPD) simulations. The model is applied to a polymer brushes system to study lubrication. We demonstrate that this method leads to mechanical equilibrium in polymer brushes using the normal DPD time step. The number of bond crossings is calculated to provide a quantitative description of the entanglement. We demonstrate that it is possible to avoid 99% of the bond crossings with the values of spring-spring repulsion that can be used without significantly decreasing the time step. A shear force is applied to the system to study the effect of the decrease in the bond crossings on the structure and rheological properties of the brushes. In particular, we show how the friction coefficient increases with the decrease in the bond crossings of the polymers.

Dissipative particle dynamics simulations in the grand canonical ensemble: applications to polymer brushes.

We have used the dissipative particle dynamics (DPD) method in the grand canonical ensemble to study the compression of grafted polymer brushes in good solvent conditions. The force-distance profiles calculated from DPD simulations in the grand canonical ensemble are in very good agreement with the self-consistent field (SCF) theoretical models and with experimental results for two polystyrene brush layers grafted onto mica surfaces in toluene.