Structural and thermodynamic properties of hydrogen molecular clusters formed around an atomic or molecular cation are examined. The shell distribution of H2 molecules and the size of the clusters are discussed. The Bloom-Margenau model for predicting the number of neutral molecules that could bind to a cation core is investigated and its limitations are illustrated using the Li+(H2)k clusters as test case. Finally, results for the entropy of the H+n clusters (n = 5 - 27, odd) and for the Gibbs free energy variations associated to the cluster formation are presented and the spontaneity of the clustering process in different conditions is examined.