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

Abstract

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.

DFT investigation of structural and optoelectronic properties of glassy chalcogenide CuXY2 (X = Sb, Bi; Y = S, Se, Te) molecules

“…Relativistic effects are known to make significant contributions to the electronic structure spectra and optical properties of molecules containing very heavy atoms [45][46][47][48][49]. Consequently, relativistic effects such as mass-velocity, Darwin and spin-orbit effects are expected to be significant for Bi-containing molecules, as shown in previous studies [46][47][48][49].…”

“…Relativistic effects are known to make significant contributions to the electronic structure spectra and optical properties of molecules containing very heavy atoms [45][46][47][48][49]. Consequently, relativistic effects such as mass-velocity, Darwin and spin-orbit effects are expected to be significant for Bi-containing molecules, as shown in previous studies [46][47][48][49]. Furthermore, Bi is quite interesting from a relativistic standpoint since its electronic configuration 6s 2 6p 3 suggests that the 6s 2 part of the valence shell is inert due to the relativistic contraction of the 6s orbital.…”

Investigation of the Spin Competition in the Al6 Cluster

“…Metallic clusters in their ground-state geometries can present Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects that break the orbital symmetry. − It has been shown that DFT methods can handle the JT and PJT contributions in geometry optimizations, reproducing the breaking of high-symmetry configurations in metallic clusters; , however, spin–orbit effects could compensate for JT contributions, producing high-symmetry structures. , JT distortions are present in both the GS and MECP geometries in Al 6 clusters. As can be seen in Table , SO coupling makes a low-energy contribution in Al 6 [14 cm –1 (i.e., 0.04 kcal/mol) on the g CP–3 geometry].…”

Relativistic structural characterization of molybdenum and tungsten disulfide materials

“…[ 10 ] These large spin‐orbit effects manifest themselves in the optical, trion, and excitonic properties and spin valley dynamics of WS 2 , all of which are attributed to the large spin‐orbit splitting of W. Spin‐orbit effects not only influence the geometries of the molecules and materials containing heavy atoms but also completely alter the topological structures of potential energy surfaces. [ 36,37 ] That is, the spin‐orbit coupling is so large that it overtakes Jahn‐Teller distortions, thus modifying the potential energy surfaces of such molecules. [ 37 ] This arises from the fact that the overall symmetry of the molecule or material under consideration is altered when spin‐orbit coupling is included from the usual point group to the double group, [ 9,37 ] thereby allowing for the mixing of two electronic states that would otherwise not mix.…”

“…[ 36,37 ] That is, the spin‐orbit coupling is so large that it overtakes Jahn‐Teller distortions, thus modifying the potential energy surfaces of such molecules. [ 37 ] This arises from the fact that the overall symmetry of the molecule or material under consideration is altered when spin‐orbit coupling is included from the usual point group to the double group, [ 9,37 ] thereby allowing for the mixing of two electronic states that would otherwise not mix. Such singlet‐triplet mixings of electronic states caused by spin‐orbit coupling result in very interesting topological spintronics in heavy materials such as WS 2 .…”