The theory of local random matrix models has provided a way for understanding many aspects of quantum ergodicity and energy flow in molecules. In this paper quantitative results are presented for a random matrix model that yields analytical expressions for the degree of vibrational mixing and flow rates in polyatomics in terms of a small number of parameters. The results of these generally applicable expressions are compared with large scale computation on energy flow in several organic molecules studied experimentally : formaldehyde, thiophosgene, and propyne. We show these systems are respectively below, at, and significantly above the quantum ergodicity transition. Effects of finite molecular size on the quantum ergodicity transition are also discussed.