Group theoretical treatment of Jahn–Teller versus spin-orbit effects on geometries, rovibronic levels and nuclear spin species of bismuth and antimony clusters

Abstract

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 ²⁰⁹Bi. The rovibronic and nuclear spin species of ¹²¹Sb and ¹²³Sb 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.

Keywords:

• bismuth clusters
• spin-orbit effects of bi-cluster
• nuclear spin statistics
• bin cluster
• Jahn–Teller effect

Acknowledgements

This research at California State University was supported by the office of basic energy sciences, chemical science division of US Department of Energy. The work at Lawrence Livermore National Laboratory was performed under the auspices of US Department of Energy under Contract No.W-7405-Eng-48.