Simulation Methodologies
Real-space Electrostatics
In molecular simulations, proper accumulation of the electrostatic interactions is essential and is one of the most computationally-demanding tasks. The common molecular mechanics force fields represent atomic sites with full or partial charges protected by Lennard-Jones (short range) interactions. This means that nearly every pair interaction involves a calculation of charge-charge forces. Coupled with relatively long-ranged r-1 decay, the monopole interactions quickly become the most expensive part of molecular simulations. Historically, the electrostatic pair interaction would not have decayed appreciably within the typical box lengths that could be feasibly simulated, so the standard approach is to use a mixed (real and reciprocal) space approach called the Ewald summation.

In the larger systems that are more typical of modern simulations, large cutoffs should be used to incorporate electrostatics correctly. The Gezelter group has been working on new real-space methods to handle electrostatics that scale linearly with system size, but still give results of similar accuracy to the Ewald summation.

Historically, only small electrostatic systems could be studied, and the Ewald sum replicated the simulation box to convergence. Today, radial cutoff methods should be able to reach convergence for larger systems of charges.

Algorithms for Langevin Dynamics
The use of rigid molecular substructures has become quite common in our group. We use coarse grained models for lipids, and these models often contain which have rigid unified-atom head groups, or even rigid ellipsoidal approximations to the molecular bodies themselves. We are also interested in some exciting new liquid crystalline phases which have been exhibited by "banana" shaped molecules.

There are a number of excellent algorithms in the literature for integrating the Newtonian mechanics of these bodies. However, we often want to place these rigid bodies in an environment of implicit solvent (instead of simulating each of the solvent molecules explicitly). To do this, one would traditionally use Langevin dynamics.

Algorithms for simulating Langevin dynamics for atomic systems have become common features in many molecular dynamics packages. We are developing methods for performing Langevin simulations on rigid particles of arbitrary shape. To do this, we are integrating accurate estimations of the friction tensor from hydrodynamics theory into some new sophisticated rigid body dynamics algorithms.

Molecular structure, rigid ellipsoid approximation, and rough-shell hydrodynamic model for the liquid crystal mesogen 5CB.