
Surface Reaction Kinetics from First Principles
Emily A. Carter
Department of Chemistry and Biochemistry, Box 951569
University of California, Los Angeles, CA 900951569, U. S. A.
Kinetics and dynamics of reactions and phase transitions are difficult to probe experimentally on the atomic level. It is for this reason that theorists have jumped into the fray to invent methods that will yield such information. A very important factor determining the outcome of possible processes is the nature of the transition state (TS)  the saddle point on the potential energy surface connecting the initial and final states. There are many ways to locate TS's, and this talk will discuss two different methods constructed at UCLA. One was derived in the early 1990's, the socalled Ridge method (I.V. Ionova and E. A. Carter,J. Chem. Phys., 98, 6377 (1993) and J. Chem. Phys., 103, 5437 (1995)), which utilizes only energies and gradients to find saddle points via walking along a high energy ridge to its minimum. The other is a new method, applicable not only for the usual molecular reaction paths but also for examining processes in bulk materials (e.g., diffusion, reactions and phase transitions). We call this the hyperplane transition state method (A. Christensen and E. A. Carter, to be published). The HTS method, which also only requires energies and gradients, divides the ndimensional coordinate space into a continuum of (n1)dimensional hyperplanes, parameterized by a single reaction coordinate (defined similarly to the Ridge method) and locates the lowest energy configuration in a discrete set of these hyperplanes. The reaction path is then the totality of these restricted minima. The HTS technique is a bit more general than previous TS search algorithms in that it extends the coordinate space beyond the usual atomic coordinates to include the unit cell size and shape. The method has been implemented in a code for DFT with periodic boundary conditions.
After introducing these two methods, we will give examples of applications to both surface reactions and to bulk processes related to materials science. We will also show how finding transition states is a necessary but not sufficient ingredient in determining how processes proceed. In particular, following the dynamics  via ab initio molecular dynamics [A. J. R. da Silva, M. R. Radeke, and E. A. Carter, Surf. Sci. Lett., 381, L628 (1997)], calculating the rate constants from first principles [C. J. Wu, I. V. Ionova, and E. A. Carter, Phys. Rev. B, 49, 13488 (1994) and M. R. Radeke and E. A. Carter, Phys. Rev. B, 54, 11803 (1996)], and calculating the kinetic order of reactions [M. R. Radeke and E. A. Carter, Phys. Rev. B, 55, 4649 (1997)] is critical to obtaining a full picture of what is happening at the atomic level. For further information, see my web page at http://www.chem.ucla.edu/carter/. See also a review in Ann. Rev. Phys. Chem., 48, 243 (1997). To search for the references above, see, for example:http://prbo.aps.org/ for recent Phys. Rev. B articles, http://prola.aps.org/ for older Phys. Rev. B articles, and http://ojps.aip.org/journals/doc/JCPSA6home/top.html for J. Chem. Phys.