The difficulties of simulating ET processes relate to the three-way interaction among an electrode, either metal or a semiconductor, an electrolytic solution -- often water -- and ions in the electrolyte. "You have a very complex interface," says Voth. "There's water interacting with the metal, water interacting with the ion, and the ion interaction with the metal."
Still, the most perplexing theoretical problem has to do with how an electron from the sea of electrons in the metal jumps to a swimming ion. With ferric iron, for instance, the +3 charge of the ion will be in happy equilibrium with the water around it. It violates laws of energy conservation, explains Voth, for the ion to instantaneously gain an electron, shifting to ferrous iron (+2), without first going out of equilibrium with water.
The anomaly has been accounted for by Voth's former graduate advisor at Caltech, Rudolph Marcus, who received a Nobel prize for his theoretical picture of electron transfer. "The solvent needs to fluctuate," says Voth. "Of course, it's a liquid so it's constantly fluctuating, and instantaneous fluctuations every now and then allow that electron to transfer from the metal to the ion without this energy cost. Calculating the free energy associated with that state tells us about the rate of electron transfer."
Taking off from Marcus, Voth and his graduate students Jay Straus and August Calhoun developed a set of equations and put them into a framework that makes it possible, with the help of supercomputing, to simulate electrochemical ET processes. To "see" the transition states of the fluctuating solvent computationally, they adapted a method called "umbrella sampling" that samples different energy states of the ion-water system.
Voth and his colleagues are beginning to simulate more complex electrochemical systems such as multiple ions of different species and a first-principles treatment of the electrode surface. This visualization shows a snapshot from a simulation that includes a chlorine counterion (Cl-) and an iron ion in water with a platinum electrode. Inclusion of the counterion, more realistically represents the chemical environment of an ET reaction in electrolytic solution. Ultimately, Voth and his colleagues want to include many ions and counterions in a single simulation.
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