Effect of chain length and donor–acceptor substitution on the electrical responsive properties of conjugated biphenyls: a DFT-based computational study

<p>The effect of donor–acceptor (D-A) substituent and chain length on the electrical polarisabilities and first hyper polarisability of cis and trans biphenyl oligomeric compounds have been investigated using density functional theory-based hybrid functional CAM-B3LYP with 6-311G (2d,2p) basis set. Our extensive computational study reveals that both average polarisability and first hyper polarisability of the studied compounds increase with the increasing ethylene spacer chain length. Again the substitution of donor (NMe₂) and acceptor (C≡N) at the para position of the phenyl rings to each oligomer shows order of magnitude increase of both <i>α</i>_av and <i>β</i>_av value compared to the unsubstituted one. This increased <i>α</i>_av and <i>β</i>_av values have been explained due to increasing charge transfer contribution resulting from decreasing optical energy gap (Δ<i>E</i> = <i>S</i>₁ − <i>S</i>₀) upon D-A substitution. It is also observed that the charge transfer contribution to first hyperpolarisability (<i>β</i>_CT) is more than the polarisability (<i>α</i>_CT) for the studied molecules. The electronic spatial extent (<<i>R</i>²>) which is a measure of electron density volume around the molecule is found to play a major role along with the intramolecular charge transfer character to explain the non-linear variation of first hyperpolarisability (<i>β</i>_av) as a function of ethylene spacer chain length (<i>n</i>) and D-A substitution.</p

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_av), 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_av, η, ω for DBC and α_av 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_av) 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>₀ − <i>S</i>₁ optical energy gap rather than HOMO–LUMO gap of the titled compounds.</p