Basic Research Needs for Geosciences - Energetics Meetings and ...

GRAND CHALLENGE: COMPUTATIONAL THERMODYNAMICS OF COMPLEX FLUIDS AND SOLIDSCourtesy of John Weare, UC San DiegoFigure 25. Water exchange in the hydration shell of Ca 2+ +64H 2 O first-principles simulations. Note that in thetrajectories in the right panel the change in structure occurs in a few ps, whereas the process occurs on a time scaleof greater than 40 ps.temperature dynamics or by modifying the energy landscape so that rare events become moreprobable (Laio et al. 2002; Voter et al. 2002). This class of methods has the advantage that localminima in the system do not have to be determined before the search starts. In another class ofmethods, it is presumed that the local minima are known (very often this is the case in chemicalreactions with known mechanisms), and the focus of the method is on determining the barrier totransition. There are several methods for doing this; for example, the Nudged Elastic Band(NEB) method (Henkelman and Jonsson 2000). This method works well for systems with fewdegrees of freedom. However, in a noisy system with many degrees of freedom, a method ofaveraging out unimportant environmental variations in the structure is necessary. New methodsneed to be developed that search for reaction pathways, including minima in noisy, manydimensionalenvironments. An example of such a method combines minimum free energy pathfinding and sampling to average out the environmental noise (Weinan et al. 2005). Given rareevent paths, methods may be introduced to calculate the free energy and estimate the reactionrate using absolute rate theory. With these rate estimates, much longer time scales can besimulated using kinetic Monte Carlo dynamics (Voter et al. 2002).Equations of State for complex systemsTo translate the advances in atomic level dynamical simulation described above into usefulapplications at the macroscopic level, efficient equations that succinctly summarize experimentaland computational data for use on the macroscopic level must be available (e.g., a rate equationor, more commonly, an EOS). The EOS should provide a succinct representation of thethermodynamics of the system that can capture the variation of the free energy, includingchanges in phase, speciation in solution, etc., for a wide range of intensive variables. There hasbeen considerable research effort in this area. However, there are very few EOS that representthermodynamic behavior with the accuracy that is required for energy applications. For many ofthese problems the molecular understanding is so poor that it is not possible to developthermodynamic models at the macroscopic scale. The best way to begin to obtain thisunderstanding may be through molecular level simulation as discussed above. It is likely that toobtain the required accuracy it will be necessary to develop models tailored to describe specificstates (e.g., solids, liquids, gases, polyions, colloids, solid solutions) rather than search for asingle EOS representation that will describe all physical states.Basic Research Needs for Geosciences: Facilitating 21 st Century Energy Systems 73