Supramolecular step in design of nonlinear optical materials: Effect ofπ…πstacking aggregation on hyperpolarizability

Theoretical estimation of nonlinear optical (NLO) properties is an important step in systematic search for optoelectronic materials. Density functional theory methods are often used to predict first molecular hyperpolarizability for compounds in advance of their synthesis. However, design of molecular NLO materials require an estimation of the bulk properties, which are often approximated as additive superposition of molecular tensors. It is therefore important to evaluate the accuracy of this additive approximation and estimate the extent by which intermolecular interactions influence the first molecular hyperpolarizability β. Here we focused on the stacking aggregates, including up to 12 model molecules (pNA and ANS) and observed enhancement and suppression of molecular hyperpolarizability relative to the additive sum. We found that degree of nonadditivity depends on relative orientation of the molecular dipole moments and does not correlate with intermolecular interaction energy. Frenkel exciton model, based on dipole-dipole approximation can be used for qualitative prediction of intermolecular effects. We report on inaccuracy of this model for the molecules with long π-systems that are significantly shifted relative to each other, when dipole-dipole approximation becomes inaccurate. To obtain more detailed information on the effect of intermolecular interactions on β we proposed electrostatic approach which accounts for the mutual polarization of the molecules by each other. We measure the induced polarization of each molecule in the aggregate by the charge of its donor (or acceptor) group. The proposed approach demonstrates linear correlation βFF vs βelm (estimated by finite field theory and electrostatic model, respectively) and allows decomposition of the hyperpolarizability for a molecular aggregate into separate molecular contributions. We used this decomposition to analyze the reasons of deviation of aggregate β from additivity, as well as the cooperative effect of intermolecular interactions on hyperpolarizability for stacks of growing size. In cases of positive cooperativity (enhancement), we found 6–8 molecules to be necessary to reach the asymptotic limit. In more frequent cases of negative cooperativity two opposite factors play role. The first one consists of direct lowering of β due to repulsive dipole-dipole interactions. The second factor is originated in a decrease of molecular dipole moments, which in turn leads to a decrease of dipole-dipole repulsion, and therefore increases β. For strong intermolecular repulsive dipole-dipole interactions these effects nearly cancel each other. In such cases the trimers and even dimers are sufficient to reach the asymptotic limit of the infinite stacks. Based on the observed trends we estimated non-additive correction to β for well known NLO crystals NPAN and MNMA. In the case of NPAN, stacking effect on molecular hyperpolarizability represents the leading component of the crystal packing effect and improves the agreement between calculated and experimental data which is further improved when frequency dependence is taken in account.