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

Abstract

Taking four merocyanines [(CH3)2N-(CHCH)n-C(CH 3)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 (1)H NMR spectroscopy merocyanines Mc1-4 were found to be approximately 1:1 mixtures of two planar conformers with cis and trans arrangements of the C(CH 3)O electron-acceptor group and all trans structure of the polyene like fragment. The degree of bond length alternancy (BLA) in the -(CHCH)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)(pipi*) CT state (e), was checked by analysis of fluorescence and near UV absorption spectra. Measurements of the basic two-level model quantities ( Ege, microge and Deltamicro(eg)), by which the dominant components of alpha and beta tensors are expressed (alpha XX , beta XXX , X identical with 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 Deltamicro(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 beta 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, alpha XX and beta XXX were found to rise proportionally to about n (1.3) and n (2), respectively, in qualitatively good agreement with the experimental values. As to the absolute values, however, experimental alpha XX 's and beta 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).

Chemical asymmetry and α and β polarizabilities of D-A-D′ chromophores: a three-state-model and TDDFT-SOS analysis of a penta-heptamethine ketocyanine

“…In particular, in spite of a quasi-linear structure reminiscent of centrosymmetry ( Fig. 1), the three-state modelling attributed to KC2 and KC3 significant quadratic hyperpolarizabilities (expressed by the b vec components of the b tensors), comparable with those reported for their parent merocyanines, 9 generally considered prototypes of efficient second-order NLO chromophores. [10][11][12] Interestingly, about half of the total b vec was found to come from the SOS term involving the three electronic states of the essential-state model, i.e.…”

N‐Ethyl Carbazole Derived D‐π‐A‐π‐D Based Fluorophores: Consolidated Spectroscopic, Viscosity and DFT Studies

“…For 5 a‐c , various NLO parameters were spectroscopically determined such as transition dipole moment (μ CT ), linear polarizability (α CT ), first hyperpolarizability (β CT ) and second hyperpolarizability (γ CT ). Table S13 lists the values for the above mentioned parameters obtained utilizing UV–vis absorption/emission spectroscopic data incorporating in the two‐level model . In CHCl 3 , the μ CT of the lowest lying CT excited state for 5 a , 5 b , and 5 c was found to be 5.88, 6.38, and 6.68 Debye respectively, using the solvatochromic method.…”

Experimental and theoretical investigation of linear and nonlinear optical properties of ethyl‐3‐hydroxy‐2‐napthoate azo dyes by solvatochromic, computational aspects, and Z‐scan technique

“…Oudar two‐level model equations were applied to investigate NLO characteristics using solvatochromic data . Using the solvatochromic outputs, we have evaluated the α xx or α CT (“linear polarizability”), β xx or β CT (“first‐order” hyperpolarizability), and “second‐order” hyperpolarizability, denoted as 〈 γ 〉 SD (solvatochromic descriptor) . The complete theory and equations used to evaluate “linear first‐order polarizability” ( α xx or α CT ), “first‐order hyperpolarizability” ( β xx or β CT ), and “second order hyperpolarizability” (〈 γ 〉 SD ) are produced in Equation SI 3.…”

“…The “density functional theory” (DFT) is a useful tool for the determination of NLO properties of compounds . The reliable answers were examined for the “first‐order hyperpolarizability” ( β ), “second order hyperpolarizability” ( γ ) using theoretical quantum chemical calculations DFT . However, quantitative estimation of NLO properties (ie, polarizability and hyperpolarizability parameters) is still a challenging job because of the fact that the performance of functionals needs to invariably benchmarked for a particular systems .…”