Evolution of B₁₃ⁿ (n = + 3 to - 3) wheel with electron injection/abstraction: an insight from electronic structure...

The planar B₁₃⁺¹ cluster, a prototypical molecular 'Wankel motor', has captivated the scientific community with its exceptional stability as well as rotor action. The present study is an exploration of how incremental electron injection/abstraction influences the electronic structure of B₁₃ clusters with B₁₃⁺¹ as a reference one. It has been found that seven different charge states (from + 3 to - 3) of B₁₃ cluster are possible, among which B₁₃^-1 triplet is the lowest energy cluster. For B₁₃ⁿ clusters, n =  + 3 to - 2, the clusters are planar and possess C_2v symmetry and their relative atomic arrangement is similar to B₁₃⁺¹ ground state (GS) structure in which a triangular boron core is encircled by ten peripheral boron atoms. B₁₃^-3 cluster has a different geometric arrangement of atoms like that of the B₁₃⁺¹ transition state (TS) structure; remains planar, possesses C_2v symmetry. The different atomic arrangement of B₁₃^-3 can be assigned to the electronic structural relaxation to reduce the electronic stress arising from high negative charge. B₁₃⁺¹ cluster is characterized by a unique electron density distribution in the cluster plane which is analogous to a 'tri-spoke wheel' configuration. In it, three spokes of electron dense lines connect the triangular core to the nearly circular periphery. The present study unveils how the injection or abstraction of electrons modifies the electronic topology in the cluster plane and how the spoke-wheel geometry evolves. It has been found that, in the + 3 and + 2 charge states, the wheel consists of four and five spokes respectively. On the other hand, for all other clusters, the overall electronic topology resembles that of the tri-spoke wheel-like B₁₃⁺¹ cluster. AIM analysis helped to trace out and characterize the evolution of the spoke-wheel topology with electron density at ring critical points and the bond paths.

Density Functional Theory (DFT), utilizing the 6-311 + G(d) basis set and the PBE1PBE hybrid density functional, has been employed to determine the minimum energy structures of B₁₃ clusters with different charged states. The calculations have been performed using a superfine integration grid and very tight optimization settings, as implemented in GAUSSIAN 09 Revision D.01. To address potential instabilities in SCF calculations, wavefunction stability has been thoroughly analysed. AIM analysis and various real-space functions, including electron density, Localized Orbital Locator (LOL), Phase-Space defined Fisher Information Density (PS-FID), and Electron Localization Function (ELF), have been investigated. Multiwfn 3.8 was utilized for plotting these functions.