Bismuth-containing solid-state compounds pose an interest to both the physical inorganic chemists as well as condensed matter physicists due to the element's massive spin-orbit coupling, stabilization of lower oxidation states, and the inert pair effect.^[1] Additionally, the stabilization of the Bi in the +1 oxidation state gives rise to a plethora of subhalide compounds with interesting electronics and 3D structures.^[2][3][4]

Bismuth subhalides, such as Bi₄Br₄ and β-Bi₄I₄, have been recently reported as topological insulators.^[2][3] Topological insulators have caught attention of physical inorganic chemists as well as condensed matter physicists due to the unique physicochemical properties emerging upon transition from bulk to surface states.^[5] Exhibiting an energy band gap of classic insulator, the edge/surface states of the material acquire dissipationless electric transport. The subject has been investigated by condensed matter physicists as well as mathematicians to provide a link between the experimental emerging properties and the modeled topology. Broadly, the material's physics pertains to the Quantum Hall effect relying upon two pillars: time-reversal symmetry and spin orbit coupling, the latter dependent on the elemental material composition.^[5] Bismuth's heavy pnictogen nature yields a large spin-orbit coupling.^[1] Additionally, when bound to heavy halogens, bismuth subhalides give rise to a low-dimensional van der Waals bonded structure, exfoliatable into nanowires.^[3]

Low dimensional van der Waals bonded materials display a fundamental material unit, usually depicted as the simplest molecular formula obeying stoichiometry. A series of such fundamental units align in the bulk material phase due to weak van der Waals interactions. Overall, key advantages conferred by the chemical structure are the ease to scale the materials down to nanostructures under simultaneous conservation of the bulk structure and the reduction in defects amount.^[6]

Belonging to the larger class of quasi 1-dimensional van der Waals bonded materials, β-Bi₄I₄ has been recently reported as a novel topological insulator.^[2] The binary bismuth-iodine family class includes the known bismuth(III) iodide along with additional representatives such as α-Bi₄I₄, Bi₁₄I₄, Bi₁₆I₄, and Bi₁₈I₄.^[2] Having the same stoichiometric chemical formula, α-Bi₄I₄ and β-Bi₄I₄ show similar solid-state structures yet critically different physicochemical properties.^[8] Specifically, α-Bi₄I₄ represents the trivial insulator phase, while stacking of the bismuth atoms along the b crystallographic axis in the β-Bi₄I₄ phase yield a different topological insulator phase. Both isoforms crystallyse in the C2/m space group, with α-Bi₄I₄ having a unit cell volume almost double of its topological insulator counterpart.^[7] The β crytallographic angle is higher in the β-Bi₄I₄: 107.87 vs 92.96, making the β-Bi₄I₄ more tilted (see images above).^[7]

Crystal growth of β-Bi₄I₄ was achieved through a solid-state reaction between Bi and HgI₂ in a ratio of 1:2. The mixture of solid-state precursors was sealed under dynamic vacuum in a quartz ampoule and subjected to a temperature gradient of 250°C - 210°C in a two-zone furnace for 20 days.^[2][8] Needle-like blue crystals were obtained with sizes varying from a couple of mm in length and tenths of mm in diameter.^[2]

Key to modeling the topology of a material are the special points along k-vector of the Brillouin zone, accounting for the accurate depiction of the density of states emerging from the electronics of the material. Density functional theory (DFT) analyses predicted an indirect band gap of 0.158 eV in the β-Bi₄I₄ phase with the valence and conduction band maxima localized at the Γ and M k-space points, respectively.^[2] Interestingly enough, the major contributors to the band structure around the Fermi level are bismuth's p orbitals of even and odd parity, thus giving the gerade and ungerade points of symmetry.

The allowed electron energies in the topological insulator were probed with the well-employed angle-resolved photoemission spectroscopy (ARPES).^[2] Γ and M space points were found to exhibit binding energies of 0.3 eV and 0.8 eV, respectively.^[2] ARPES also probed the Fermi electron velocities along the x and y axes to be 0.1(1)×106 m*s^-1 and 0.60(4)×106 m*s^-1.^[2] The emerging non-trivial states of the topological insulator are expected to show at the space point where the conductive and valence bands almost cross or, in other words, display the smallest band gap. This point indeed showed a binding energy of 0.06 eV as measured by ARPES.^[2] ARPES measurements on a different β-Bi₄Br₄ topological insulator phase show similarity to its iodine counterpart.^[9]

A ternary rhodium-centered bipyramidal dibismuth complex is an example of subhalide complexes with interesting geometry and unusual electronic properties, particularly what has been reported as an example of Möbius aromaticity.^[4][10] The complex exhibits a 4-electron-5-centered bond in the central plane occupied by a Bi₅ equatorial pentagon with the rhodium center in the middle.^[10] Based on the electronic analysis carried out by Ruck (2003), the bismuth bonding consists of 2-centered-2-electron bonds, namely, Bi-Rh and Bi-Br one (see structure on the right).

The electronic analysis was carried out starting with counting the available skeletal electrons. Each of the 7 bismuth atoms contribute a total of 3x7=21 electrons (3 per each atom), while Rh gives all of its 9 electrons and the 8 bridging bromide atoms yield 3 electrons each. The total skeletal electron count is thus 54. The total skeletal electron count gets distributed as follows: 2 electrons per each of the 16 2c-2e^- Bi-Br bond, 2 electrons per each of the 7 2c-2e^- Rh-Bi metallic bond, 2 rhodium lone pairs remaining on the Rh centre (total of 4e^-), and 4 electrons for 5c-4e^- bond pertaining to the central pentagon. The sum of electrons used in bonding is therefore 54. Hence, the subhalide complex is electron-precise, i.e., with all of its skeletal electrons involved in chemical bonding.^[10]

The bonding in such a system was compared to the aromatic cyclopentadienyl aromatic anion. Contrary to the π-type all in-phase orbital overlap exhibited by the organic cyclopentadienyl anion, σ-type bonding of the RhBi₅ unit yields a phase change for an orbital pair (see figure).^[10]

The relative orbital energy diagram is rationalized for each of the systems relying on the Frost-Musulin mnemonic.^[11] The two lone pairs stemming from the rhodium metallic center are localized on the lowest-lying twicely degenerate set of molecular orbitals, consistent with the Möbius-type aromaticity. For reference, the electronics of the aromatic organice cyclopentadienyl unit is shown to the right of the rhodium-centered pentagonal Bi₅ unit. As can be seen, Hückel rules dictate the molecular orbital splitting is inverted compared to its metallic counterpart, the highest-occupied molecular orbitals this time being twicely degenerate.

• Solid-state chemistry
• Topological insulator
• Bismuth compounds