On the calculation of rate constants by approximating the Fermi–Dirac distribution with a step function

Replacing the Fermi–Dirac distribution with a step function for the purpose of calculating electron-transfer rate constants has been documented in a range of electrochemical systems. However, a misleading view of the actual electron-transfer process might result because of this substitution. While the calculations of the rate constant for the forward process (i.e. positive applied overpotential for oxidation or negative applied overpotential for reduction) agree closely with results obtained using the Fermi–Dirac distribution, the magnitudes of the reverse-reaction rate constants show a substantial discrepancy. A small improvement on the error-function expression is attained by including a secondary term in the approximation.