Multi-scale modeling: From atoms to the continuum

Multi-scale modeling

Computational studies play an important role in our understanding of complex fluids. They can provide physical insight and molecular information that is hard to obtain from experiment. The most important part of a computer simulation is the choice of molecule model. In classical models each molecule is represented by a collection of sites.  In an atomistic model each site represents a single atom, in a united atom model each site represents one heavy atom and associated hydrogen atoms, and in coarse-grained models each site represents several heavy atoms.

The choice of model depends on the problem and the relevant physics.  More detailed models more faithfully represent the physical system.  However, they are computationally intensive and cannot efficiently sample all configurations.  The process of coarse-graining results in a hierarchy of models that sample increasingly more efficiently, but are less representative of the system, and are likely to be less transferable to other conditions or molecules.

Force Field Development

The starting point is the development of a fully polarizable atomistic model for the system.  In our group we use symmetry adapted perturbation theory (SAPT) based on quantum density functional theory (DFT) as a starting point and then empirically introduce additional sites and interactions to reproduce the behavior of hydrogen bonding systems.  DFT-SAPT has unique advantages for force-field development, including its inherent energy decomposition and prediction of non-covalent interaction energies with comparable accuracy to coupled-cluster.

The robust and transferable character of the SAPT force fields is largely due to the parameterization methodology, in which all asymptotic interaction parameters are obtained from monomer properties.  The static polarizabilities are converted to a shell-model (Drude oscillators), for ease of implementation in standard MD simulation packages.  Dispersion coefficients are then generated from the frequency-dependent polarizabilities, and the remaining force field parameters, namely short-range terms describing exchange-repulsion and charge penetration (and potentially charge-transfer), are fit to the residual of the asymptotic force field description and SAPT intermolecular interaction energies of dimer species.

We make adjustments to the SAPT force field protocol to treat hydrogen bonding systems.  We add additional sites to better represent the angular dependence of the interaction, adjust the polarizability to reproduce crystal properties, and adjust short-ranged interactions to better reproduce the liquid structure as observed in first principles molecular dynamics simulations.  The resulting approach gives excellent results, for example, for urea water mixtures.

Hierarchical Coarse-Graining

We develop a hierarchy of coarse-grained models using a “top-down” approach.  We vary the polarization and atomistic resolution of functional groups and parameterize the models using SAPT to the same DFT calculations.   The approach has been successful in the study of room temperature ionic liquids.

BMW-MARTINI: Bottom-Up Coarse-Graining

An alternative approach is to start with a heuristic simpler representation and adjust the force fields to reproduce experimental data.  In the MARTINI approach 4 heavy atoms are mapped to a single site with the parameters obtained by comparing to experiment.  Our group has developed a coarse-grained force field for simulations of lipids, peptides, and polymers.  The basis is the big multipole water (BMW) model.

The new BMW-MARTINI force field reproduces many fundamental membrane properties and also yields improved energetics (when compared to the original MARTINI force-field) for the interactions between charged amino acids with lipid membranes, especially at the membrane/water interface. The simulations emphasize the importance of a reasonable description of the electrostatic properties of water in coarse-grained simulations.