An Extended Rudolph Diagram: B₃H₅ and B₃H₆+ Relate 3D-, 2D-, 1D-, and 0D-Boron Allotropes

The structural chemistry of boron goes beyond the sp, sp2, and sp3 hybridization paradigms of carbon chemistry. We relate the apparently unconnected polyhedral boranes and 3D allotropes on the one hand and 2D clusters, borophenes, and multilayer borophenes on the other hand, through an extended Rudolph diagram. All-boron equivalents of cyclopropenium cation viz the flat B3H5 and the nonplanar B3H6+ constitute the missing links. The nonplanar B3H6+ (C3v) is the starting point for construction of polyhedral boranes; e.g., fusion of two of them leads to octahedral B6H62–. On the other hand, planar B3H6+ and B3H5 relate to borophenes with hexagonal holes. These borophene sheets can be further stacked with diverse interlayer BB bonds, ranging from bilayers to infinite layers. The tendency to achieve electron sufficiency as in the parent C3H3+ dictates the preference for hexagonal holes in the constituent layers and the interlayer bonds between them in multilayer borophenes. The design principles and theoretical validations for the formation of multilayer borophenes are also presented, indicating the variety and complexities involved.