(422d) Large Time Scale Conformation and Phase Transition Dynamics

Transition state theory (TST) is one of several ways of quantifying the dynamic behavior of molecules, proteins, crystals and other structures as they change shape. To use TST, in principle, all stationary points (minima and saddle points) are required to accurately get a measure of the dynamics of the system. However, for most problems of appreciable size (e.g., n-alkanes with 20 or more carbons, proteins with 50 or more residues, or large molecular crystals, etc.) cataloguing all minima and saddle points is not practical. Problem dimensionality usually involves hundreds, thousands, or tens of thousands of unknown variables and the number of minima and saddle points is generally astronomical. One widely accepted theory (Onuchic et al. 1997) for explaining folding dynamics is that the large scale geometry of potential or free energy landscapes for many molecular modeling problems is funnel-shaped.

In this work, we use the funneling method of Lucia and co-workers (2004, 2007, 2009) to probe energy landscapes, to find only important stationary points, and to quantify large time scale dynamics associated with changes in molecular conformation and phase transitions characteristic of the formation of waxes in petroleum fuels. We show that the funneling method easily finds molecular conformations indicative of both rotator (R) and low temperature ordered (LO) solid n-alkane phases. The funneling method can also be used for crystal structure determination of R and LO phases and thus to study rotator to low-ordered temperature phase transitions. Several examples as well as geometric illustrations are used to illustrate key findings.