Methods for calculating rates of transitions with application to catalysis and crystal growth
Henkelman, Graeme, 1974-
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An important problem in theoretical chemistry is the calculation of reaction rates. This is challenging because most interesting chemical reactions occur much slower than the vibrational period of atoms. Even though it is in principle possible to directly simulate the classical dynamics of atomic systems, reactions of interest can almost never be observed this way. Fortunately it is possible to focus on just those slow events in which the system passes from one basin on the potential energy surface to another. If the bottleneck, or transition state, through which the system must pass in order to undergo a transition can be found, transition state theory can be used to calculate the reaction rate. For tightly bound systems the problem of finding transition states reduces to the problem of finding saddle points on the potential surface.Two methods are developed for finding saddle points efficiently---the dimer method which is used when only the initial state of the reaction is known and the climbing image nudged elastic band method which is used when the final state is also known. Both methods only require first derivatives of the potential energy, and can therefore be used with ab-initio calculations like density functional theory. The methods are applied to a variety of systems including the dissociation of methane on the Ir(111) surface and the diffusion of aluminum atoms on the Al(100) surface.In many cases, finding the rate of one process is not enough, rather, many transitions are required in order to see interesting phenomena. For these types of problems, the dimer method is used to find many different possible processes available to the system. When many processes are found, they are weighted by their rates at the simulation temperature, and one is chosen through which the system is advanced. In this way, the dimer method is combined with kinetic Monte Carlo, so that the traditional limitation of having to know all possible processes a priori is relaxed. This method for determining the long time scale dynamics of a system was applied to island formation and growth of the Al(100) surface.
- Chemistry