Using the CRAY C90, Voth and his co-workers simulated an iron ion in water at 300¡ Kelvin interacting with the surface of a platinum electrode. To realistically represent the ion's interactions with the water around it, the simulation included 671 water molecules. The first part of the work applied an essentially Newtonian scheme for calculating the forces between atoms. The results show an energy barrier (about 10 kilocalories per mole) that must be overcome for the ion to shift between the ferrous and ferric state.
"There's been debate for years," says Voth, "about whether the solvent really influences an electrochemical electron transfer reaction. We showed fairly conclusively that under these conditions it does. This information can be very difficult, if not impossible, to get from experiment."
The next phase was to treat the water quantum mechanically, which meant quantizing the hydrogen nuclei of each water molecule. Voth and his co-workers applied the Feynman path integral technique, an approach to quantum computations that Voth adapted to predict the rate of ET processes. "There are in principle very large quantum effects in water from a variety of sources," says Voth, "and we wanted to investigate what difference this could make."
With 400 hours on a CRAY C90 processor and an additional eight months on five workstations, Voth believes this is the largest liquid-state Feynman path integral simulation carried out to date. "What we found was this striking effect that, given the same parameters, the quantum modes in water are very significant in determining the free energy of the reaction. You see that the barrier is lowered going from left to right in the free energy curve, which means the reaction will happen faster. More than that there's now a driving force. You go downhill from left to right, which means the reaction will occur spontaneously in that direction, whereas in the classical case, it's just as happy to go in either direction."
Free energy for electron transfer at the water-metal interface. The two wells in the curve correspond to the Fe2+ (left) and Fe3+ (right) state of the ion. The hump between the wells indicates the "energy barrier," approximately 10 kilocalories per mole, between the two states.
Voth and his colleagues are now working out a mathematical theory to describe this quantum effect. "That's the beauty of computer simulation. This study exemplifies how it adds a third tier to science, on top of theory and experiment. You can find novel effects that you wouldn't have expected. And now we're going to develop the theories to explain their origin."
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