For simulation studies of (macro) molecular liquids it would be of significant interest to be able to adjust or increase the level of resolution within one region of space, while allowing for the free exchange of molecules between open regions of different resolution or representation. We generalize the adaptive resolution idea and suggest an interpretation in terms of an effective generalized grand canonical approach. The method is applied to liquid water at ambient conditions.

For theoreticians, ionic liquids represent a major challenge. This is due to the fact that intermolecular interactions are particularly strong because of ionic liquids' ionicity. This, in turn, causes a subtle interplay between different scales which is encoded in the measured macro- and mesoscopic properties and also in the molecular electrostatic characteristics. Therefore, force fields have to describe the microscopic processes correctly in order to reproduce macroscopic properties accurately over a large range of state variables. Herein, imidazolium-based ionic liquids were studied at different scales, going from the detailed quantum electronic scale to the classical atomistic scale. It is indicated how the information gained at each level could be used for the other scales. In particular, the issue of deriving suitable partial charges for use in classical force fields is addressed. The Blöchl method was employed to generate partial charges reproducing the multipole distribution accurately for bulk systems. This led naturally to absolute ionic charges of less than |1 e|, i.e. charge scaling. So, the monopole structure of the herein introduced force field mimics the quantum chemical behaviour observed in the liquid phase. This led to a substantial improvement in the description of dynamical properties of immediate experimental interest, such as electric conductivity. For further insight, the electric dipole moment of the ions was taken as physical indicator of their electronic structure. The electric dipole moment was found to fluctuate strongly and to depend on polarisation. Hence, our scale-combined study offers a gateway to rational design of models, based on the relevant underlying physics rather than on mere numerical parameterisation, and thereby to (possibly) more direct physical interpretation of experimental results.

In this work, we provide a detailed theoretical analysis, supported by numerical tests, of the reliability of the adaptive-resolution-simulation (AdResS) technique in sampling the grand-canonical ensemble. We demonstrate that the correct density and radial distribution functions in the hybrid region, where molecules change resolution, are two necessary conditions for considering the atomistic and coarse-grained regions in AdResS to be equivalent to subsystems of a full atomistic system with an accuracy up to the second order with respect to the probability distribution of the system. Moreover, we show that the work done by the thermostat and a thermodynamic force in the transition region is formally equivalent to balancing the chemical potential difference between the different resolutions. From these results follows the main conclusion that the atomistic region exchanges molecules with the coarse-grained region in a grand-canonical fashion with an accuracy up to (at least) second order. Numerical tests, for the relevant case of liquid water at ambient conditions, are carried out to strengthen the conclusions of the theoretical analysis. Finally, in order to show the computational convenience of AdResS as a grand-canonical setup, we compare our method to the insertion particle method in its most efficient computational implementation. This fruitful combination of theoretical principles and numerical evidence makes the adaptive-resolution technique a candidate for a natural, general, and efficient protocol for grand-canonical molecular dynamics for the case of large systems.

Adaptive-resolution molecular dynamics (MD) schemes allow for changing the number of degrees of freedom on the fly and preserve the free exchange of particles between regions of different resolution. There are two main alternatives on how to design the algorithm to switch resolution using auxiliary “switching” functions: force based and potential energy based approaches. In this work we show that, in the framework of classical MD, the latter presents fundamental conceptual problems which make unlikely, if not impossible, the derivation of a robust algorithm based on the potential energy.