Relativity and the Jahn–Teller, Berry pseudorotations of TBP clusters: group theory, spin–orbit and combinatorial nuclear spin statistics of TBP Desargues–Levi isomerization graph

Abstract

Jahn–Teller and Berry pseudorotations in transition metal and main group clusters such as Hf5, Ta5, W5 and Bi5 are interesting because of the competition between relativistic effects and pseudorotations. Topological representations of various isomerization pathways arising from the Berry pseudorotation of pentamers constitute the edges of the Desargues–Levi graph. We have computed the combinatorics for multinomial colorings of the vertices, edges and 10-faces of the Desargues–Levi isomerization graph for all irreducible representations and the nuclear spin statistics of spin-7/2 181Ta5 as well as the TBP composite cluster particles. Topological insights into Jahn–Teller and Berry pseudorotations and relativistic effects are provided.