The effect of the complete restriction of rotatory Brownian motion of donor and acceptor molecules on the extent of nonradiative energy transfer in systems containing many donors and acceptors has been investigated. It is assumed that the molecules under discussion are randomly distributed and randomly oriented in space at the moment of excitation. The number of donor molecules which retain their excitation energy at time t after excitation is found to decrease exponentially with the sum of two terms: one proportional to t and the other proportional to t1/2. This time dependence is similar in form to that found by Förster for systems in which donor and acceptor molecules undergo rapid rotatory diffusion. While the coefficient of -t in the exponent is the same in both cases, the coefficient of -t1/2 is smaller for systems in which molecular rotation is frozen than for systems in which rotatory Brownian motion is rapid.
