Why are some B_6-nN_nH₆ molecules planar and others not? Insights from quasi-molecule theory

It is shown by tiling that only three out of the thirteen title molecules are planar. Using our recent concept of quasi-molecule ('tile') or its generalisation, all participating tiles have been here optimised in a few spin-states both at the DFT level with the B3LYP and M06-2X functionals, and using the CCSD(T) method. While borazine (1,4,6-B3N3H6) was synthesised in the forties of the past century, its next up-lying planar isomer (1,3,4-B3N3H6 or BHNHNHBHBHNHBHNHNHBHBHNH) was not. Quasi-tetratomic tiles are then shown to be shape-determining while 5-body terms and beyond are shape-preserving. The need to bring the notion of planarity as a probabilistic outcome is also examined, and the concept of planarity likelihood ratio (index) introduced. As for the above borazine isomers, this index is also predicted to be unit for 1,4-B4N2H6, a result that is corroborated upon its optimisation at DFT/B3LYP/AVTZ level but not with M06-2X by which it is predicted as quasi-planar. Nevertheless, recent work with a derivative of diazatetraborinine where all atoms are bonded to substituent atoms or groups of atoms confirms the planarity of the B(4)N(2 )ring. Such a result is further corroborated at the gold-standard CCSD(T) level. Although planarity is also predicted for B6H6, DFT and CCSD(T) frequency calculations suggest it to be likely a saddle point.