Recently experimentally-based asymptotic exchange energies Delta V-E between ground state atoms in Li-2, Na-2, K-2, and NaK have been determined from spectroscopically-determined potential energy curves. These empirical results are shown to be well fit by the expression -CR(alpha)e(-beta R) of Smirnov and Chibisov, where C is a positive constant and alpha and beta can be readily calculated from the atomic ionization energies. The expression should be useful for estimating the exchange energy in other alkali dimers.