The recent development and application of the method of kinetically controlled selective ionization has produced detailed and reliable data on the collisional energy transfer kernel P(E-',E) entering master equation theories of unimolecular reaction rates. Here we test the ability of our partially ergodic collision theory (PECT) to predict the functional form of the observed kernel leaving only one parameter, the first moment of the distribution , to be input from other sources. The data explored here include two reactant molecules, toluene and azulene, in collisions with 18 and 8 medium molecules, respectively, ranging from inert gas atoms to n-heptane. The initial energy of the reactant molecule is varied from 10 000 cm(-1) to 49 000 cm(-1) and 30 000 cm(-1), respectively. The energy transfer efficiency beta(E) is about one-tenth of its ergodic collision limit of unity. The PECT is found to fit the monoexponential form of the kernel determined from the experimental data over a broad range of initial energies E including tail regions of very low probability. A minor but systematic deviation is observed for nearly elastic collisions of large medium molecules. The functional fit is good enough to effectively allow the three parameters of the monoexponential experimental kernel to be replaced by a single parameter representing energy transfer efficiency. (C) 2003 American Institute of Physics.