To cite this article: Krishnan Balasubramanian (2009) Group theoretical treatment of Jahn-Teller versus spin-orbit effects on geometries, rovibronic levels and nuclear spin species of bismuth and antimony clusters, Clusters of very heavy group 15 elements, particularly those of Sb and Bi are intriguing due to the interplay of vibronic and relativistic effects, which quench the Jahn-Teller distortion, and thus resulting in the retention of higher symmetry in the double group. Group theoretical treatment of Bi n clusters and comparisons with Sb n clusters as a function of cluster size and coordination polyhedra has been carried out. The spin-orbit and Jahn-Teller effects have dual roles, thus resulting in interesting rovibronic and nuclear spin species arising from spin-9/2 209 Bi. The rovibronic and nuclear spin species of 121 Sb and 123 Sb are also quite interesting due to their equal relative abundance and high nuclear spin. It has been shown by using group theoretical and combinatorial methods that these clusters exhibit interesting nuclear spin multiplets and distributions of rovibronic levels as a function of polyhedral geometry, which is influenced by the quenching of Jahn-Teller pseudorotation by spin-orbit effects in heavier Bi n clusters. The results are contrasted with Sb n clusters which undergo Jahn-Teller pseudorotations. It is also pointed out how the techniques considered here can be applied to Tl n and In n clusters.