Stability, Speed, and Constraints for Structural Coarse-Graining in VOTCA.

Structural coarse-graining involves the inverse problem of deriving pair potentials that reproduce target radial distribution functions. Despite its clear mathematical formulation, there are open questions about the existing methods concerning speed, stability, and physical representability of the resulting potentials. In this work, we make progress on several aspects of iterative methods used to solve the inverse problem. Based on integral equation theory, we derive fast Gauss-Newton schemes applicable to very general systems, including molecules with bonds and mixtures. Our methods are similar to inverse Monte Carlo in terms of convergence speed and have a similar cost per iteration as iterative Boltzmann inversion. We investigate stability problems in our schemes and in the inverse Monte Carlo method and propose modifications to fix them. Furthermore, we establish how the pair potential can be constrained at each iteration to reproduce the pressure, Kirkwood-Buff integral, or the enthalpy of vaporization. We demonstrate the potential of our approach in deriving coarse-grained force fields for nine different solvents and their mixtures. All methods described are implemented in the free and open VOTCA software framework for systematic coarse-graining.

Where Lennard-Jones Potentials Fail: Iterative Optimization of Ion-Water Pair Potentials Based on Ab Initio Molecular Dynamics Data.

The use of the Lennard-Jones (LJ) potential in computer simulations of aqueous electrolyte solutions is widespread. The standard approach is to parametrize LJ potential parameters against thermodynamic solution properties, but problems in representing the local structural and dynamic properties of ion hydration shells remain. The r-12-term in the LJ potential is responsible for this as it leads to overly repulsive ion-water interactions at short range. As a result, the LJ potential predicts blue-shifted vibrational peaks of the cations' rattling mode and too large negative ion hydration entropies. We demonstrate that cation-water effective pair potentials derived from ab initio MD data have softer short-range repulsions and represent hydration shell properties significantly better. Our findings indicate that replacing the LJ potential with these effective pair potentials offers a promising route to represent thermodynamic solution properties and local interactions of specific ions with nonpolarizable force field models.

Coarse-grained model of a nanoscale-segregated ionic liquid for simulations of low-temperature structure and dynamics.

We perform molecular dynamics simulations to study the structure and dynamics of the ionic liquid [Omim][TFSI] in a broad temperature range. A particular focus is the progressing nanoscale segregation into polar and nonpolar regions upon cooling. As this analysis requires simulations of large systems for long times, we use the iterative Boltzmann inversion method to develop a new coarse-grained (CG) model from a successful all-atom (AA) model. We show that the properties are similar for both levels of description at room temperature, while the CG model shows stronger nanoscale segregation and faster diffusion dynamics than its AA counterpart at low temperatures. Exploiting these features of the CG model, we find that the characteristic length scale of the structural inhomogeneity nearly doubles to ∼3 nm when the temperature is decreased to about 200 K. Moreover, we observe that the nanoscale segregation is characterized by a bicontinuous morphology. In worm-like nonpolar regions, the ends of the octyl rests of the cations preferentially aggregate in the centers, while the other parts of the alkyl chains tend to be aligned parallel on a next-neighbor level and point outward, allowing for an integration of the imidazolium head groups of the cations into polar regions together with the anions, resembling to some degree the molecular arrangement in cylindrical micelles.

Iterative integral equation methods for structural coarse-graining.

In this paper, new Newton and Gauss-Newton methods for iterative coarse-graining based on integral equation theory are evaluated and extended. In these methods, the potential update is calculated from the current and target radial distribution function, similar to iterative Boltzmann inversion, but gives a potential update of quality comparable with inverse Monte Carlo. This works well for the coarse-graining of molecules to single beads, which we demonstrate for water. We also extend the methods to systems that include coarse-grained bonded interactions and examine their convergence behavior. Finally, using the Gauss-Newton method with constraints, we derive a model for single bead methanol in implicit water, which matches the osmotic pressure of the atomistic reference. An implementation of all new methods is provided for the open-source VOTCA package.