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

Abstract

The structural chemistry of boron goes beyond the sp, sp 2 , and sp 3 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. Allboron equivalents of cyclopropenium cation viz the flat B 3 H 5 and the nonplanar B 3 H 6 + constitute the missing links. The nonplanar B 3 H 6 + (C 3v ) is the starting point for construction of polyhedral boranes; e.g., fusion of two of them leads to octahedral B 6 H 6 2−. On the other hand, planar B 3 H 6 + and B 3 H 5 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 C 3 H 3 + 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.