Resonant and static cubic hyperpolarizabilities of push-pull dipolar and quadrupolar chromophores: toward enhanced two-photon absorption

Recent reports of push-pull dipolar and quadrupolar chromophores with enhanced two-photon absorption have generated considerable interest in these two molecular systems. Two photon absorption is related to the imaginary part of the two-photon resonant cubic hyperpolarizability Im[gamma(omega)]. In this work, we have described both push-pull dipolar and quadrupolar chromophores using multi valence-bond states models based on measurable parameters of the valence-bond forms. We have derived analytical expressions of their non-resonant static cubic hyperpolarizability gamma(0) and of Im[gamma(omega)]. Comparison between the transparency / Im[gamma(omega)] trade-off and Im[gamma(omega)] / gamma(0) correlation helps understand the advantages and drawbacks of each of these two push-pull systems. Furthermore by understanding how the valence-bond parameters are related to the molecular structure and its environment, it is possible to predict how Im[gamma(omega)] will be affected by changing either the conjugation size, the donor-acceptor pair or the solvent polarity for both of these push-pull systems. The results of this study suggest common guidelines for the molecular engineering of both the push-pull dipolar and quadrupolar chromophores.