Why are some B6-nNnH6 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-{\rm B}_3{\rm N}_3{\rm H}_6 $ 1 , 4 , 6 − B 3 N 3 H 6 ) was synthesised in the forties of the past century, its next up-lying planar isomer ( $ 1,3,4-{\rm B}_3{\rm N}_3{\rm H}_6 $ 1 , 3 , 4 − B 3 N 3 H 6 or $ {\rm BHNHNHBHBHNH} $ BHNHNHBHBHNH ) 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-{\rm B}_4{\rm N}_2{\rm H}_6 $ 1 , 4 − B 4 N 2 H 6 , 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 $ {\rm B}_4{\rm N}_2 $ B 4 N 2 ring. Such a result is further corroborated at the gold-standard CCSD(T) level. Although planarity is also predicted for $ {\rm B}_6{\rm H}_6 $ B 6 H 6 , DFT and CCSD(T) frequency calculations suggest it to be likely a saddle point. [ABSTRACT FROM AUTHOR]