First- and Second-Order Polarizabilities of Simple Merocyanines. An Experimental and Theoretical Reassessment of the Two-Level Model

Taking four merocyanines [(CH₃)₂N−(CHCH)_n−C(CH₃)O; n = 1−4] (Mc1−4) as test D−A systems, we performed a close experimental and theoretical examination of the two level model with reference to its ability to provide correct predictions of both absolute values and dependence on the conjugation path length of first- and second-order molecular polarizabilities. By ¹H NMR spectroscopy merocyanines Mc1−4 were found to be ∼1:1 mixtures of two planar conformers with cis and trans arrangements of the C(CH₃)O electron-acceptor group and all trans structure of the polyene like fragment. The degree of bond length alternancy (BLA) in the −(CHCH)_n− fragment, was quantified by extensive full geometry optimizations at both semiempirical and ab initio level. DFT (6-31G**/B3LYP) optimized geometries were considered to be most reliable and were used for calculations of the excited-state properties. The applicability of the two level model, reducing the general sum-over-states (SOS) expansion to only one term involving the ground state (g) and the lowest-lying ¹(ππ*) CT state (e), was checked by analysis of fluorescence and near UV absorption spectra. Measurements of the basic two-level model quantities (E_ge, μ_ge and Δμ_eg), by which the dominant components of α and β tensors are expressed (α_XX, β_XXX, X ≡ long molecular axis), were designed to give approximate free-molecule values. It is proposed, in particular, an adjustment of the solvatochromic method for the determination of Δμ_eg, based on accurate measurements of absorption spectral shifts in n-hexane/diethyl ether mixtures with small diethyl ether volume fractions. Such an approach led to Mc1−4 β_XXX’s matching well in both value and n-dependence with EFISH data reported in the literature for similar merocyanines. For the fluorescent Mc4, the results were qualitatively well reproduced by an approach, which combines absorption and fluorescence solvent shifts. All the measured quantities were calculated for both trans and cis Mc1−4 by three semiempirical INDO-based approaches aiming at evaluating the performances of different integral parametrizations and CI extensions: ZINDO/S, CS INDO SCI, CS INDO SDCI. In all cases, α_XX and β_XXX were found to rise proportionally to about n^1.3 and n², respectively, in qualitatively good agreement with the experimental values. As to the absolute values, however, experimental α_XX’s and β_XXX’s were best reproduced by CS INDO SDCI combining Ohno−Klopman parametrization and CI including both single and double excitations. The validity of the two-level model was checked by comparison with converged SOS calculations for the longest chain merocyanine (Mc4) and finite field calculations of linear polarizabilities for all of the four dyes (Mc1−4).