Tipping point to explain melamine’s non-planarity or otherwise. Can quasi-molecules be “seen” in the parent molecule?

The structure of melamine is optimized both at the DFT level with B3LYP and M06-2X functionals using AVTZ basis sets, and at ab initio level using DF-CCSD(T)/VDZ. Predicted planar with DFT when adding the zero-point-energy correction, it is a planar but distorted hexagonal triazine ring with three pyramidal amino groups at the coupled-cluster level. The potential energy surface of melanine is then expected to be rather flat near equilibrium. Both its planarity at the saddle point and non-planarity at equilibrium are deciphered, and pinpointed the role played by the embedded CNH2 quasi-molecules (tiles).