Semi-empirical in nature, Marcus theory has also been used to calculate the rate internal conversion, which suggests the vibronic transition scale to be significantly smaller than other vibronic energy scales. Building on the Arrhenius expression (Equation ), the activation energy is replaced with the Gibbs free energies of reaction, and the pre-exponential factor is formally defined similar to Fermi's Golden Rule. In addition, if it is assumed that the nuclear modes are harmonic and can be treated classically, this density of states can be examined analytically . In its full form, it is cast as :