Computation of global reactivity descriptors and first hyper polarisability as a function of torsional angle of donor–acceptor substituted biphenyl ring system

<p>Global reactivity descriptors, e.g. average polarisabilty (α<sub>av</sub>), chemical hardness (η), electrophilicity index (ω) of two donor–acceptor substituted biphenyl, i.e. Dimethyl-(4ʹ-Nitro-biphenyl-4-yl)-amine (NBA) and 4ʹ-Dimethylamino-biphenyl-4carbonitrile (DBC), were computed along the torsional potential of two biphenyl ring systems. Density functional-based hybrid functional B3LYP with 6-31G(d) basis were used to all the computational study. It is observed that variation of the global reactivity descriptors η, ω as a function of torsional angle of biphenyl ring of NBA are in accordance with the maximum hardness and minimum electrophilicity principle. But the variations of α<sub>av</sub>, η, ω for DBC and α<sub>av</sub> for NBA are not in accordance with the respective extremum principles. These apparent violations of extremum principles have been explained as the non-constancy of external potential within the tolerance limit for the respective parameters during the variation of torsional angle. The variation of first hyperpolarisability (β<sub>av</sub>) as a function of dihedral angle has been explained with the extent of charge transfer character of conformers for both NBA and DBC. It is also observed that the variation of first hyper polarisability is a function of <i>S</i><sub>0</sub> − <i>S</i><sub>1</sub> optical energy gap rather than HOMO–LUMO gap of the titled compounds.</p>