Experimental and Theoretical Investigation of the First-Order Hyperpolarizability of Octupolar Merocyanine Dyes

Merocyanines: Electronic Structure and Spectroscopy in Solutions, Solid State, and Gas Phase

Merocyanines, owing to their readily tunable electronic structure, are arguably the most versatile functional dyes, with ample opportunities for tailored design via variations of both the donor/acceptor (D/A) end groups and π-conjugated polymethine chain. A plethora of spectral properties, such as strong solvatochromism, high polarizability and hyperpolarizabilities, and sensitizing capacity, motivates extensive studies for their applications in light-converting materials for optoelectronics, nonlinear optics, optical storage, fluorescent probes, etc. Evidently, an understanding of the intrinsic structure-property relationships is a prerequisite for the successful design of functional dyes. For merocyanines, these regularities have been explored for over 70 years, but only in the past three decades have these studies expanded beyond the theory of their color and solvatochromism toward their electronic structure in the ground and excited states. This Review outlines the fundamental principles, essential for comprehension of the variable nature of merocyanines, with the main emphasis on understanding the impact of internal (chemical structure) and external (intermolecular interactions) factors on the electronic symmetry of the D-π-A chromophore. The research on the structure and properties of merocyanines in different media is reviewed in the context of interplay of the three virtual states: nonpolar polyene, ideal polymethine, and zwitterionic polyene.

Elucidating the Photophysics and Nonlinear Optical Properties of a Novel Azo Prototype for Possible Photonic Applications: A Quantum Chemical Analysis

The photophysics and nonlinear optical responses of a novel nitrothiazol-methoxyphenol molecule were investigated using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) methods with the polarizable continuum model to take the solvent effect into account. Special attention is paid to the description of the lowest absorption band, characterized as a strong π → π* state in the visible region of the spectrum. The TD-DFT emission spectrum analysis reveals a significant Stokes shift of more than 120 nm for the π → π* state in gas phase condition. The results show a great influence of the solvent polarity on the nonlinear optical (NLO) response of the molecule. Specifically, the second harmonic generation hyperpolarizability β(-2ω; ω, ω) shows a large variation from gas to aqueous solvent (82 × 10-30 to 162 × 10-30 esu), exhibiting notably higher values than those reported for standard compounds such as urea (0.34 × 10-30 esu) and p-nitroaniline (6.42 × 10-30 esu). Furthermore, a two-photon absorption analysis indicates a large cross-section (δ2PA = 77 GM) with superior performance compared to several dyes. These results make the molecule quite interesting for nonlinear optics.

Second-order nonlinear optical properties of X-shaped pyrazine derivatives

This work reports an investigation of the second-order NLO properties of two isomer series of X-shaped pyrazine derivatives, by means of HRS measurements and DFT calculations. The systems differ in the relative position of the donor and acceptor substituents with respect to the axis formed by the nitrogen atoms of the central pyrazine ring. Although the magnitude of the second harmonic signal is similar, HRS measurements revealed that the anisotropy of the NLO response strongly differs in the two chromophore series, the one of the 2,3-isomers being strikingly dipolar, while the one of the 2,6-isomers is mostly octupolar. The experimental observations are well supported by DFT calculations. In particular, the sum-over-states approach allows us to rationalize the different NLO anisotropies observed in the two isomer series through a detailed analysis of the symmetry of the low-lying excited states.

First hyperpolarizability of the di-8-ANEPPS and DR1 nonlinear optical chromophores in solution. An experimental and multi-scale theoretical chemistry study

The solvent effects on the linear and second-order nonlinear optical properties of an aminonaphtylethenylpyridinium (ANEP) dye are investigated by combining experimental and theoretical chemistry methods. On the one hand, deep near infrared (NIR) hyper-Rayleigh scattering (HRS) measurements (1840-1950 nm) are performed on solutions of di-8-ANEPPS in deuterated chloroform, dimethylformamide, and dimethylsulfoxide to determine their first hyperpolarizablity (βHRS). For the first time, these HRS experiments are carried out in the picosecond regime in the deep NIR with very moderate (≤3 mW) average input power, providing a good signal-to-noise ratio and avoiding solvent thermal effects. Moreover, the frequency dispersion of βHRS is investigated for Disperse Red 1 (DR1), a dye commonly used as HRS external reference. On the other hand, these are compared with computational chemistry results obtained by using a sequential molecular dynamics (MD) then quantum mechanics (QM) approach. The MD method allows accounting for the dynamical nature of the molecular structures. Then, the QM part is based on TDDFT/M06-2X/6-311+G* calculations using solvation models ranging from continuum to discrete ones. Measurements report a decrease of the βHRS of di-8-ANEPPS in more polar solvents and these effects are reproduced by the different solvation models. For di-8-ANEPPS and DR1, comparisons show that the use of a hybrid solvation model, combining the description of the solvent molecules around the probe by point charges with a continuum model, already achieves quasi quantitative agreement with experiment. These results are further improved by using a polarizable embedding that includes the atomic polarizabilities in the solvent description.

Efficient calculation of electronic coupling integrals with the dimer projection method via a density matrix tight-binding potential

Designing organic semiconductors for practical applications in organic solar cells, organic field-effect transistors, and organic light-emitting diodes requires understanding charge transfer mechanisms across different length and time scales. The underlying electron transfer mechanisms can be efficiently explored using semiempirical quantum mechanical (SQM) methods. The dimer projection (DIPRO) method combined with the recently introduced non-self-consistent density matrix tight-binding potential (PTB) [Grimme et al., J. Chem. Phys. 158, 124111 (2023)] is used in this study to evaluate charge transfer integrals important for understanding charge transport mechanisms. PTB, parameterized for the entire Periodic Table up to Z = 86, incorporates approximate non-local exchange, allowing for efficient and accurate calculations for large hetero-organic compounds. Benchmarking against established databases, such as Blumberger's HAB sets, or our newly introduced JAB69 set and comparing with high-level reference data from ωB97X-D4 calculations confirm that DIPRO@PTB consistently performs well among the tested SQM approaches for calculating coupling integrals. DIPRO@PTB yields reasonably accurate results at low computational cost, making it suitable for screening purposes and applications to large systems, such as metal-organic frameworks and cyanine-based molecular aggregates further discussed in this work.

Predicting the Second-Order Nonlinear Optical Responses of Organic Materials: The Role of Dynamics

The last 30 years have witnessed an ever-growing application of computational chemistry for rationalizing the nonlinear optical (NLO) responses of organic chromophores. More specifically, quantum chemical calculations proved highly helpful in gaining fundamental insights into the factors governing the magnitude and character of molecular first hyperpolarizabilities (β), be they either intrinsic to the chromophore molecular structure and arising from symmetry, chemical substitution, or π-electron delocalization, or induced by external contributions such as the laser probe or solvation and polarization effects. Most theoretical reports assumed a rigid picture of the investigated systems, the NLO responses being computed solely at the most stable geometry of the chromophores. Yet, recent developments combining classical molecular dynamics (MD) simulations and DFT calculations have evidenced the significant role of structural fluctuations, which may induce broad distributions of NLO responses, and even generate them in some instances.This Account presents recent case studies in which theoretical simulations have highlighted these effects. The discussion specifically focuses on the simulation of the second-order NLO properties that can be measured experimentally either from Hyper-Rayleigh Scattering (HRS) or Electric-Field Induced Second Harmonic Generation (EFISHG). More general but technical topics concerning several aspects of the calculations of hyperpolarizabilities are instead discussed in the Supporting Information.Selected examples include organic chromophores, photochromic systems, and ionic complexes in the liquid phase, for which the effects of explicit solvation, concentration, and chromophore aggregation are emphasized, as well as large flexible systems such as peptide chains and pyrimidine-based helical polymers, in which the relative variations of the responses were shown to be several times larger than their average values. The impact of geometrical fluctuations is also illustrated for supramolecular architectures with the examples of nanoparticles formed by organic dipolar dyes in water solution, whose soft nature allows for large shape variations translating into huge fluctuations in time of their NLO response, and of self-assembled monolayers (SAMs) based on indolino-oxazolidine or azobenzene switches, in which the geometrical distortions of the photochromic molecules, as well as their orientational and positional disorder within the SAMs, highly impact their NLO response and contrast upon switching. Finally, the effects of the rigidity and fluidity of the surrounding are evidenced for NLO dyes inserted in phospholipid bilayers.

Modeling the First-Order Molecular Hyperpolarizability Dispersion from Experimentally Obtained One- and Two-Photon Absorption

The search for optical materials, particularly organic compounds, is still an attractive and essential field for developing several photonic devices and applications. For example, some applications are based on light scattering with twice the energy of the incoming photon for selected compounds, that is, the nonlinear optical effect related to the second-order susceptibility term from the electronic polarization expression. The microscopic interpretation of this phenomenon is called the first-order molecular hyperpolarizability or incoherent second harmonic generation of light. Understanding such phenomena as a function of the incoming wavelength is crucial to improving the optical response of future materials. Still, the experimental apparatus, hyper-Rayleigh scattering, apparently simple, is indeed a challenging task. Therefore, we proposed a proper alternative to obtain the dispersion of the first-order hyperpolarizability using the well-known one- and two-photon absorption techniques. By the spectral analysis of both the spectra, we gathered spectroscopic parameters and applied them for predicting the first-order hyperpolarizability dispersion. This prediction is based on an n-level energy system, taking into account the position and magnitude of transition dipole moments and the difference between the permanent dipole moment of the n-excited states. Moreover, using the presented method, we can avoid underestimating the first-order hyperpolarizability by not suppressing higher-energy transitions. Quantum chemical calculations and the hyper-Rayleigh scattering technique were used to validate the proposed method.

Performance of DFT functionals for calculating the second-order nonlinear optical properties of dipolar merocyanines

Evolution of the static HRS hyperpolarizability of a tricyanopropylidene-based merocyanine dye with the length of the polyenic bridge, as calculated using various ab initio and DFT approximations.

First molecular electronic hyperpolarizability of series of π-conjugated oxazole dyes in solution: an experimental and theoretical study

In this work, we report the experimental and theoretical first molecular electronic hyperpolarizability (β HRS) of eleven π-conjugated oxazoles compounds in toluene medium. The Hyper-Rayleigh Scattering (HRS) technique allowed the determination of the experimental dynamic β HRS values, by exciting the compounds with a picosecond pulse trains from a Q-switched and mode-locked Nd:YAG laser tuned at 1064 nm. Theoretical predictions based on time-dependent density functional theory level using the Gaussian 09 program package were performed with three different functionals (B3LYP, CAM-B3LYP, and M06-2X), to calculate both static and dynamic theoretical β HRS values. Good accordance was found between the experimental and theoretical values, in particular for the CAM-B3LYP and M06-2X functionals.