Following work by Slater and Bunker, the unimolecular rate constant versus collision frequency, k(uni)(omega,E), is expressed as a convolution of unimolecular lifetime and collisional deactivation probabilities. This allows incorporation of nonexponential, intrinsically non-RRKM, populations of dissociating molecules versus time, N(t)/N(0), in the expression for k(uni)(omega,E). Previous work using this approach is reviewed. In the work presented here, the biexponential f(1) exp(-k(1)t) + f(2) exp(-k(2)t) is used to represent N(t)/N(0), where f(1)k(1) + f(2)k(2) equals the RRKM rate constant k(E) and f(1) + f(2) = 1. With these two constraints, there are two adjustable parameters in the biexponential N(t)/N(0) to represent intrinsic non-RRKM dynamics. The rate constant k(1) is larger than k(E) and k(2) is smaller. This biexponential gives k(uni)(omega,E) rate constants that are lower than the RRKM prediction, except at the high and low pressure limits. The deviation from the RRKM prediction increases as f(1) is made smaller and k(1) made larger. Of considerable interest is the finding that, if the collision frequency omega for the RRKM plot of k(uni)(omega,E) versus omega is multiplied by an energy transfer efficiency factor beta(c), the RRKM k(uni)(omega,E) versus omega plot may be scaled to match those for the intrinsic non-RRKM, biexponential N(t)/N(0), plots. This analysis identifies the importance of determining accurate collisional intermolecular energy transfer (IET) efficiencies.