Theoretical insight into the second-order NLO response of the bis{4-[2-(4-pyridyl)ethenyl]benzoato}-zinc(II) metal-organic framework

Ab initio wavefunction and density functional theory calculations have been performed to investigate the second-order nonlinear optical (NLO) properties of the bis{4-[2-(4-pyridyl)ethenyl]benzoato}-zinc(II) metal-organic framework (MOF). This has been carried out by adopting the supramolecular or cluster approach, which consists in analyzing the evolution of the first hyperpolarizability as a function of the number of units of the system. In a first step, the impact of the method of calculation has been assessed, evidencing that the exchange-correlation functional has a stronger impact on the first hyperpolarizability (β) values than the basis set. Still, the first hyperpolarizability values related to the hyper-Rayleigh scattering (HRS) (β _HRS) are slightly more sensitive to the Zn basis set than to that of the other atoms, but the combination of the LANL2DZ basis for Zn with the 6-31G* basis set for the other atoms provides stable results with respect to adding supplementary valence, polarization, and diffuse functions as demonstrated by the variations of β _HRS that remain smaller than 6%. Several structure/property relationships have then been deduced for the β of this MOF: (i) the lack of coordination of the ligands extremities enhances β because their donor/acceptor characters are not damped by the Zn ²⁺ cations, (ii) the β of clusters expanding in one direction increases almost linearly with the cluster size, (iii) the deviations with respect to linearity are smaller than 25%, which differ from organic molecular crystals, and (iv) the octupolar component of the β response is of the same order of magnitude as its dipolar counterpart, and its relative importance generally increases with the cluster size.