[en] An energy transfer probability distribution function, P(E,E), for the collisional relaxation of a highly vibrationally excited donor molecule (C₆F₆, pyrazine) is constructed for the first time from experimental data on the bath (CO₂) energy gain. A prescription for mapping bath quantum state resolved data onto P(E,E) is described in detail. Analysis of earlier experimental data allows a calculation of the high ΔE=E-E region (-7000 cm^-1< E-E<-1500 cm^-1) of P(E,E) for the above systems. Comparison of the P(E,E) functions reveals that C₆F₆ is a more efficient donor molecule than pyrazine, in agreement with previous experiments and trajectory calculations. In addition, resonance like structures in the P(E,E) functions arising from long range force mediated, V endash V excitation of the carbon dioxide ν₃ mode are discussed. These results indicate that accurate P(E,E) functions can be determined from experiments involving probes of the bath energy gain. This technique can be expected to provide stringent tests of current energy transfer theory and can, in principle, be used in conjunction with measurements of thermal kinetics to obtain energy dependent unimolecular rate constants, k_E. copyright 1997 American Institute of Physics