A new approach is presented for obtaining coarse-grained (CG) force fields from fully atomistic molecular dynamics (MD) trajectories. The method is demonstrated by applying it to derive a CG model for the dimyristoylphosphatidylcholine (DMPC) lipid bilayer. The coarse-graining of the interparticle force field is accomplished by an application of a force-matching procedure to the force data obtained from an explicit atomistic MD simulation of the biomolecular system of interest. Hence, the method is termed a "multiscale" CG (MS-CG) approach in which explicit atomistic-level forces are propagated upward in scale to the coarse-grained level. The CG sites in the lipid bilayer application were associated with the centers-of-mass of atomic groups because of the simplicity in the evaluation of the forces acting on them from the atomistic data. The resulting CG lipid bilayer model is shown to accurately reproduce the structural properties of the phospholipid bilayer.

Coarse-grained ͑CG͒ models provide a computationally efficient method for rapidly investigating the long time-and length-scale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarse-graining ͑MS-CG͒ method ͓J. Phys. Chem. B 109, 2469 ͑2005͒; J. Chem. Phys. 123, 134105 ͑2005͔͒ for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force ͑PMF͒ that governs the equilibrium distribution of positions of the CG sites for the MS-CG models. A CG model that employs such a PMF as a "potential energy function" will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.

In order to introduce flexibility into the simple point-charge (SPC) water model, the impact of the intramolecular degrees of freedom on liquid properties was systematically studied in this work as a function of many possible parameter sets. It was found that the diffusion constant is extremely sensitive to the equilibrium bond length and that this effect is mainly due to the strength of intermolecular hydrogen bonds. The static dielectric constant was found to be very sensitive to the equilibrium bond angle via the distribution of intermolecular angles in the liquid: A larger bond angle will increase the angle formed by two molecular dipoles, which is particularly significant for the first solvation shell. This result is in agreement with the work of Hochtl et al. [J. Chem. Phys. 109, 4927 (1998)]. A new flexible simple point-charge water model was derived by optimizing bulk diffusion and dielectric constants to the experimental values via the equilibrium bond length and angle. Due to the large sensitivities, the parametrization only slightly perturbs the molecular geometry of the base SPC model. Extensive comparisons of thermodynamic, structural, and kinetic properties indicate that the new model is much improved over the standard SPC model and its overall performance is comparable to or even better than the extended SPC model.

Ionic liquids have many promising industrial applications. The side-chain length of the cations has been known to significantly influence the physical and chemical properties of those liquids, especially liquid crystal formation. 1 Because there are numerous species of possible ionic liquids, it is of great interest to understand the general physical picture behind the effect of varying the length of side chains of cations.In this work, a multiscale coarse-graining (MS-CG) method 2 has been extended to explore the effect of various cation side-chain lengths in ionic liquids. This method allows for large systems to be simulated for long times, thus revealing features of the system that are difficult to see using conventional all-atom molecular dynamics (MD) simulations. Simulations with the MS-CG models show that, with sufficient side-chain length, neutral tail groups of cations aggregate to form spatially heterogeneous domains of the tails, while the charged headgroups and anions distribute as uniformly as possible due to the strong electrostatic interactions. The geometrical constraints for head and tail groups of cations result in a novel balanced liquid crystal-like structure at suitable temperatures. This physical picture can qualitatively explain the experimentally observed ionic liquid crystal formation, the transition from liquid crystal to isotropic ionic liquid, and the changes of structural, dynamic, and thermodynamic properties when varying the sidechain length.The MS-CG method 2 has been applied here to the EMIM + NO 3 -ionic liquid to develop coarse-grained (CG) models at T ) 400 and 700 K, respectively. Details of the CG models are given in the Supporting Information. As shown in Figure 1, the nitrate anion has been coarse-grained as Site D, while the aromatic ring of the cation as Site A, the methyl group as Site B, the methylene and methyl groups on the alkyl chain as Sites C and E, respectively. To study the effect of chain-length elongation, the alkyl chain is then extended with two more methylene groups (Sites C) to form BMIM + NO 3 -. The partial charges are assigned as the numbers in Figure 1. The bonded parameters for the sites on the alkyl chain are assigned with the parameters for the sp 3 carbon (CT) sites given in ref 3. Although this model is a coarse-grained one, the qualitative results should not depend on the details of the force field parameters. For convenience, the ionic liquid systems will be denoted by the number of carbons on the alkyl chain, e.g., EMIM + NO 3 -as C 2 and BMIM + NO 3 -as C 4 . The C 4 MS-CG systems with 64, 400, and 800 ion pairs have been simulated by using the DL_POLY program 4 at T ) 700 K. The aggregation of tail groups was determined by visual examination for all three sizes of simulation. One snapshot of the simulation for 400 ion pairs is shown in Figure 2. Headgroups and anions are seen to distribute relatively homogeneously, but tail groups aggregate together and form several spatially heterogeneous domains.The heterogeneity of the tail groups is char...

We propose and implement an alternative approach to the original Car–Parrinello method where the density matrix elements (instead of the molecular orbitals) are propagated together with the nuclear degrees of freedom. Our new approach has the advantage of leading to an O(N) computational scheme in the large system limit. Our implementation is based on atom-centered Gaussian orbitals, which are especially suited to deal effectively with general molecular systems. The methodology is illustrated by applications to the three-body dissociation of triazine and to the dynamics of a cluster of a chloride ion with 25 water molecules.