What is the best definition of a liquid cluster at the molecular scale?

We investigate the ability of different cluster definitions to serve as a good reaction coordinate in molecular simulations of nucleation. In particular, the most commonly used Stillinger criterion [J. Chem. Phys. 38, 1486 (1963)] is compared with the cluster definition introduced by ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)]. The accuracy of these two different cluster definitions is tested by using molecular dynamics to study the vapor-liquid nucleation of Lennard-Jones argon as a model system. We are able to compare the size of the critical cluster identified by each cluster definition with a completely model-independent value provided by the nucleation theorem, aided by a recently introduced method that accurately extracts the location of the transition state directly from the kinetics. It is found that the Stillinger definition strongly overestimates the size of small molecular clusters by up to a factor of 2. A simple change of the Stillinger radius is unable to rectify this deficiency. On the contrary, the ten Wolde-Frenkel definition, while being only slightly more elaborate than a simple Stillinger criterion, is remarkably successful in identifying the correct molecular excess of the small clusters if the parameters are chosen adequately. The method described here can also be generalized to identify a proper reaction coordinate in other activated processes.