Because knowledge about homogeneous nucleation in supercooled molecular liquids is largely indirect, a molecular dynamics investigation of the freezing of liquid clusters was initiated to furnish a plausible account of the molecular behavior involved. Results of the first stage of research are reported. Clusters with free boundaries were chosen instead of bulk systems in order to avoid the interference introduced by periodic boundary conditions. Systems of 150-molecule clusters of SF6, SeF6, and TeF6 were examined. Analyses of Voronoi polyhedra in the warm systems prepared confirmed that the clusters were genuinely liquid, containing no crystalline seeds capable of initiating freezing. As the clusters cooled, random structural fluctuations created short-lived embryonic nuclei. At deeper supercooling, a nucleus of critical size ultimately appeared in each cluster and freezing began. When cooled at a rate of 2 x 10(10) K/s or more slowly, all clusters froze to bcc single crystals and these transformed to monoclinic single crystals upon further cooling. Voronoi polyhedra gave much more delicate and definitive analyses of the presence of solid nuclei than did other common indices such as the Lindemann delta. The polyhedra, however, were quite blind to the solid-state transition to monoclinic. It was found that the threshold value of the Lindemann index for freezing decreased systematically with increasing size of the molecules. The reported failure of similar systems to freeze in prior molecular dynamics simulations may have been due to the faster cooling rates adopted.