Graph-theoretical parameters for π-MO calculation of a series of aromatic amines in the light of DFT theory: comparison with experimental CT transition energies

Abstract

Expressions for the energies of the highest occupied π-molecular orbitals of a series of aromatic amines have been derived in terms of the vertex weight h _N (for amine nitrogen) and edge weight k _C–N (for the C–N bond) by representing the amine molecule in terms of vertex- and edge-weighted graphs. Graph-theoretical methods have been used to evaluate the quantities involved in such expressions. The HOMO energies of the amines calculated by density functional theory using the 6-31++G** basis set have been correlated with these expressions to estimate the perturbational parameter h _N and the Coulomb integral α. The acceptability of the estimated values of α and h _N has been tested by their ability to explain the experimentally observed trends in the CT transition energies of a series of charge-transfer complexes of amines with tetracyanoethylene. An important structural feature, namely rotation of the –NH₂ group about the C–N bond due to steric repulsion with the nearest H-atom in the case of 1-amino compounds, has been observed by such a correlation. The result agrees well with the DFT-optimized geometries of the structures.

Keywords:

• graph theory
• DFT
• aromatic amines
• perturbation
• charge transfer

Acknowledgement

The authors thank the referee for valuable comments and suggestions.