It is only in the last few years that for elementary reactions of organotransition-metal compounds the transition-state geometry can be optimized and the potential energy profile can be obtained from ab initio molecular orbital calculations. Elementary reactions thus studied include oxidative addition/reductive elimination, olefin insertion/..beta..-elimination carbonyl insertion, thermolysis of ketene complexes, and isomerization of metallacycle to an alkylidene-olefin complex. Despite such success, a study of an entire cycle of a catalytic process, consisting of several elementary reactions, has been a challenge to theoreticians. The authors communicate here the results of the first such study, on homogeneous olefin hydrogenation by the Wilkinson catalyst. They concentrate on the dominant catalytic cycle of the mechanism proposed by Halpern. The model of the cycle they adopted, consists of oxidative addition of H/sub 2/, coordination of ethylene, ethylene insertion, isomerization, and reductive elimination of ethane.