Reversible work, also known as the potential of mean force, is used to map explicit atom (EA) onto united atom (UA) potentials for CH, CH2, CH3, and CH4 sites. These UA potentials are found to be temperature dependent and to be described by stretched exponential-6 functions. Although this is fairly dissimilar to the Lennard-Jones 6-12 potential, the one may be mapped onto the other by requiring that the second virial coefficients and locations of the potential minimum be equal for the two forms. When this is done, good agreement with standard UA potentials is found.