A re-examination of the highly floppy melamine molecule and predictability of quasi-molecule theory

Abstract

With atoms assumed as points, the query is whether melamine is $2D$ or $3D$. The answer from this work is $3D$ at its equilibrium geometry but it may assume both forms when the zero-point harmonic vibrational energy is considered. Reasons for melamine’s high floppiness are discussed and the role of the “tiles” embedded on it examined using popular quantum chemistry methods in the spirit of quasi-molecule theory and a fragmentation approach. It is argued that melamine is yet another case of spontaneously broken symmetry. The validity of the reverse of the Lemma that grounds the theory for planarity is also discussed.