Dynamical properties of two- and three-dimensional colloidal clusters of six particles.

Colloidal clusters are important systems for studying self-assembly. Clusters of six colloidal particles attracting each other via short-ranged interactions have been recently studied both theoretically and experimentally. Here we present a computer modelling study of the thermodynamics and dynamics of these clusters using a short-ranged Morse potential in two and three dimensions. We combine energy landscape methods with comprehensive sampling, both of configurations using Markov chain Monte Carlo and also of trajectories using Langevin molecular dynamics propagation. We show that the interaction energies between the particles are probably greater than previously assumed. The rates predicted by transition state theory using harmonic vibrational densities of states are off by four orders of magnitude, since the effects of viscosity are not accounted for. In contrast, sampling short trajectories using an appropriate friction constant and discrete relaxation path sampling produces reasonable agreement with the experimental rates.

Markov state modeling and dynamical coarse-graining via discrete relaxation path sampling.

A method is derived to coarse-grain the dynamics of complex molecular systems to a Markov jump process (MJP) describing how the system jumps between cells that fully partition its state space. The main inputs are relaxation times for each pair of cells, which are shown to be robust with respect to positioning of the cell boundaries. These relaxation times can be calculated via molecular dynamics simulations performed in each cell separately and are used in an efficient estimator for the rate matrix of the MJP. The method is illustrated through applications to Sinai billiards and a cluster of Lennard-Jones discs.