Essential-state Model Research Articles

Dynamic effects on the nonlinear optical properties of donor acceptor stenhouse adducts: insights from combined MD + QM simulations.

The second-order nonlinear optical (NLO) responses of a donor-acceptor stenhouse adduct (DASA) are investigated by using a computational approach combining molecular dynamics simulations and density functional theory (DFT) calculations. Specific force fields for the open and closed photoswitching forms are first parameterized and validated according to the Joyce protocol, in order to finely reproduce the geometrical features and potential energy surfaces of both isomers in chloroform solution. Then, DFT calculations are performed on structural snapshots extracted at regular time steps of the MD trajectories to address the influence of the thermalized conformational dynamics on the NLO responses related to hyper-Rayleigh scattering (HRS) experiments. We show that accounting for the structural dynamics largely enhances the HRS hyperpolarizability (βHRS) compared to DFT calculations considering solely equilibrium geometries, and greatly improves the agreement with experimental measurements. Furthermore, we show that the NLO responses of the NLO-active open form are correlated with the bond order alternation along the triene bridge connecting the donor and acceptor moieties, which is rationalized using simple essential state models.

Aggregates of Cyanine Dyes: When Molecular Vibrations and Electrostatic Screening Make the Difference.

Aggregates of cyanine dyes are currently investigated as promising materials for advanced electronic and photonic applications. The spectral properties of aggregates of cyanine dyes can be tuned by altering the supramolecular packing, which is affected by the length of the dye, the presence of alkyl chains, or the nature of the counterions. In this work, we present a joint experimental and theoretical study of a family of cyanine dyes forming aggregates of different types according to the length of the polymethinic chain. Linear and nonlinear optical spectra of aggregates are rationalized here in terms of an essential-state model accounting for intermolecular interactions together with the molecular polarizability and vibronic coupling. A strategy is implemented to properly account for screening effects, distinguishing between electrostatic intermolecular interactions relevant to the ground state (mean-field effect) and the interactions relevant to the excited states (excitonic effects). To the best of our knowledge, this is the first attempt to simulate nonlinear spectral properties of aggregates of symmetric dyes accounting for molecular vibrations.

Charge Delocalization and Vibronic Couplings in Quadrupolar Squaraine Dyes.

Squaraines are prototypical quadrupolar charge-transfer chromophores that have recently attracted much attention as building blocks for solution-processed photovoltaics, fluorescent probes with large two-photon absorption cross sections, and aggregates with large circular dichroism. Their optical properties are often rationalized in terms of phenomenological essential state models, considering the coupling of two zwitterionic excited states to a neutral ground state. As a result, optical transitions to the lowest S1 excited state are one-photon allowed, whereas the next higher S2 state can only be accessed by two-photon transitions. A further implication of these models is a substantial reduction of vibronic coupling to the ubiquitous high-frequency vinyl-stretching modes of organic materials. Here, we combine time-resolved vibrational spectroscopy, two-dimensional electronic spectroscopy, and quantum-chemical simulations to test and rationalize these predictions for nonaggregated molecules. We find small Huang-Rhys factors below 0.01 for the high-frequency, 1500 cm-1 modes in particular, as well as a noticeable reduction for those of lower frequency modes in general for the electronic S0 → S1 transition. The two-photon allowed state S2 is well separated energetically from S1 and has weak vibronic signatures as well. Thus, the resulting pronounced concentration of the oscillator strength in a narrow region relevant to the lowest electronic transition makes squaraines and their aggregates exceptionally interesting for strong and ultrastrong coupling of excitons to localized light modes in external resonators with chiral properties that can largely be controlled by the molecular architecture.

Spotlight on Charge-Transfer Excitons in Crystalline Textured n-Alkyl Anilino Squaraine Thin Films

Prototypical n-alkyl terminated anilino squaraines for photovoltaic applications show characteristic double-hump absorption features peaking in the green and deep-red spectral range. These signatures result from coupling of an intramolecular Frenkel exciton and an intermolecular charge transfer exciton. Crystalline, textured thin films suitable for polarized spectro-microscopy have been obtained for compounds with n-hexyl (nHSQ) and n-octyl (nOSQ) terminal alkyl chains. The here released triclinic crystal structure of nOSQ is similar to the known nHSQ crystal structure. Consequently, crystallites from both compounds show equal pronounced linear dichroism with two distinct polarization directions. The difference in polarization angle between the two absorbance maxima cannot be derived by spatial considerations from the crystal structure alone but requires theoretical modeling. Using an essential state model, the observed polarization behavior was discovered to depend on the relative contributions of the intramolecular Frenkel exciton and the intermolecular charge transfer exciton to the total transition dipole moment. For both nHSQ and nOSQ, the contribution of the charge transfer exciton to the total transition dipole moment was found to be small compared to the intramolecular Frenkel exciton. Therefore, the net transition dipole moment is largely determined by the intramolecular component resulting in a relatively small mutual difference between the polarization angles. Ultimately, the molecular alignment within the micro-textured crystallites can be deduced and, with that, the excited state transitions can be spotted.

Dynamical effects of Pauli blocking on resonant multielectron ionization

We examine the dynamical role of the Pauli exclusion principle on resonant multielectron ionization. Using a simple essential-state model that permits us approximate but analytical solutions, we show that this principle can lead to several unexpected consequences. It has only a transient effect on the resonant multielectron dynamics and its dynamical impact decreases with increasing Rabi frequency. Due to mutually competing mechanisms, this principle can enhance the ionization probability, while at the same time it also decreases the probability for double ionization. Furthermore, it can also manifest itself in the energy distribution of the ionized electrons, but only if the energy accumulation range of the electronic detector is chosen to be sufficiently wide.

Polymorphism in Squaraine Dye Aggregates by Self‐Assembly Pathway Differentiation: Panchromatic Tubular Dye Nanorods versus J‐Aggregate Nanosheets

AbstractA bis(squaraine) dye equipped with alkyl and oligoethyleneglycol chains was synthesized by connecting two dicyanomethylene substituted squaraine dyes with a phenylene spacer unit. The aggregation behavior of this bis(squaraine) was investigated in non‐polar toluene/tetrachloroethane (98:2) solvent mixture, which revealed competing cooperative self‐assembly pathways into two supramolecular polymorphs with entirely different packing structures and UV/Vis/NIR absorption properties. The self‐assembly pathway can be controlled by the cooling rate from a heated solution of the monomers. For both polymorphs, quasi‐equilibrium conditions between monomers and the respective aggregates can be established to derive thermodynamic parameters and insights into the self‐assembly mechanisms. AFM measurements revealed a nanosheet structure with a height of 2 nm for the thermodynamically more stable polymorph and a tubular nanorod structure with a helical pitch of 13 nm and a diameter of 5 nm for the kinetically favored polymorph. Together with wide angle X‐ray scattering measurements, packing models were derived: the thermodynamic polymorph consists of brick‐work type nanosheets that exhibit red‐shifted absorption bands as typical for J‐aggregates, while the nanorod polymorph consists of eight supramolecular polymer strands of the bis(squaraine) intertwined to form a chimney‐type tubular structure. The absorption of this aggregate covers a large spectral range from 550 to 875 nm, which cannot be rationalized by the conventional exciton theory. By applying the Essential States Model and considering intermolecular charge transfer, the aggregate spectrum was adequately reproduced, revealing that the broad absorption spectrum is due to pronounced donor‐acceptor overlap within the bis(squaraine) nanorods. The latter is also responsible for the pronounced bathochromic shift observed for the nanosheet structure as a result of the slip‐stacked arranged squaraine chromophores.

Innenrücktitelbild: Polymorphism in Squaraine Dye Aggregates by Self‐Assembly Pathway Differentiation: Panchromatic Tubular Dye Nanorods versus J‐Aggregate Nanosheets (Angew. Chem. 21/2021)

Supramolekularer Polymorphismus wird im Forschungsartikel auf S. 12056 von David Bialas, Kazunori Sugiyasu, Frank Würthner und Mitarbeitern für Bis(squarain)-Farbstoffaggregate beschrieben. Das Bis(squarain) assembliert in Lösung bei schneller Abkühlung zu helikalen Nanostäbchen, während langsames Abkühlen zu thermodynamisch stabilen Nanoblattstrukturen führt. Die beiden Polymorphe zeigen völlig unterschiedliche UV/Vis/NIR-Absorptionseigenschaften mit panchromatischen Merkmalen für die Nanostäbchen, während für die Nanoblätter eine schmale, bathochrom verschobene J-Bande beobachtet wird.

Unusual Non-Kasha Photophysical Behavior of Aggregates of Push–Pull Donor–Acceptor Chromophores

Unlike the Frenkel exciton model, the essential state model (ESM) for aggregates of donor–acceptor (DA) chromophores accounts self-consistently for the effect of the reaction field on the ground an...

Davydov Splitting in Squaraine Dimers

The essential states model (ESM) for donor–acceptor–donor (D–A–D) chromophores is used to explore absorption and photoluminescence (PL) in molecular dimers composed of centrosymmetric and non-centrosymmetric squaraine molecules. The spectral line shapes and shifts relative to the monomer spectrum are due to an interesting interplay between three-center charge distributions responsible for ground- and excited-state (permanent) dipole and quadrupole moments and two-center charge distributions responsible for transition dipole moments. The Davydov splitting is sensitive only to the interactions between the (extended) transition dipoles , whereas the permanent dipole-dipole and quadruple-quadrupole interactions impact the midpoint frequency of the two Davydov components, leading to a generally asymmetric splitting relative to the peak monomer transition frequency. The theory accurately reproduces the steady-state absorption and PL line shapes recently obtained for covalently bound squaraine dimers. The ESM also predicts an extreme type of non-Kasha behavior, where both Davydov components are blue-shifted above the monomer transition frequency.

Essential States Model for Merocyanine Dye Stacks: Bridging Electronic and Optical Absorption Properties

An extension of the essential states model is developed to investigate the absorption and electronic properties of a highly dipolar merocyanine dye and double and quadruple π-stacks formed upon the folding and self-assembly of appropriate spacer-tethered bis(merocyanine) dyes. Our analysis reveals that a simple two-state model is not sufficient to adequately describe the absorption features of a single chromophore. However, by including an additional bridge state, the absorption features are well described and reasonable values for the permanent and transition dipole moments are obtained. We show that the low-energy absorption band of the folded double stack results from vibronic coupling, whereas the additional absorption shoulder observed in the spectrum of the self-assembled quadruple stack is due to a transition to a lower excited state. Furthermore, the chromophores within both π-stacks exhibit an increase in the charge-transfer character in the ground state with respect to the single chromophore arising from polarizability effects, which are not accounted for in the conventional Frenkel exciton theory. These insights are of significant importance for the proper design of functional materials based on merocyanines and dipolar chromophores in general.

Non-Kasha Behavior in Quadrupolar Dye Aggregates: The Red-Shifted H-Aggregate

Aggregates of quadrupolar DAD-type chromophores are investigated theoretically using the essential states model (ESM) enhanced to include vibronic coupling. On the basis of vibronic signatures in the absorption and photoluminescence spectra, important connections are made to the Frenkel exciton model, which is the basis for defining conventional H- and J-aggregates. In contrast to the exciton theory, the ESM allows for an unusual type of the red-shifted H-aggregate, driven by the large quadrupole–quadrupole interaction. Except for the red shift of the main absorption peak, such aggregates display all of the characteristics of conventional H-aggregates, including suppressed radiative decay rates and all of the vibronic signatures in the absorption and photoluminescence spectra consistent with Frenkel exciton models. Red-shifted H-dimers occur for a range of slip angles, which separate conventional H- and J-aggregate behavior, with the slip range diminishing with increasing intermolecular separation. Davydo...

Measuring local conformations and conformational disorder of (Cy3)2 dimer labeled DNA fork junctions using absorbance, circular dichroism and two-dimensional fluorescence spectroscopy.

The sugar-phosphate backbone of DNA near single-stranded (ss)-double-stranded (ds) junctions likely fluctuates within a broad distribution of conformations to permit the proper binding of genome regulatory proteins that function at these sites. In this work we use absorbance, circular dichroism (CD), and two-dimensional fluorescence spectroscopy (2DFS) to study the local conformations and conformational disorder within chromophore-labeled DNA constructs. These constructs employ dimers of the fluorescent chromophore Cy3 that are site-specifically incorporated into the sugar-phosphate backbones of DNA strands at ss-ds DNA fork junctions. We show that these data can be analyzed to determine the local conformations of the (Cy3)2 dimer, and the degree of conformational disorder. Our analysis employs an essential-state Holstein-Frenkel Hamiltonian model, which takes into account the internal electronic-vibrational motions within each Cy3 chromophore, and the resonant electronic interaction that couples the two chromophores together. Our results suggest that this approach may be applied generally to understand local backbone conformation and conformational disorder at ss-ds DNA fork junctions.

Investigation of nondegenerate two-photon absorption in common fluorescent dyes

The nondegenerate two-photon excited fluorescence (ND-TPEF) and nondegenerate two-photon absorption (ND-TPA) cross-sections of two common fluorescent dyes were investigated using the femtosecond pump-probe technique at several wavelength combinations. Time-resolved and laser intensity dependent fluorescence revealed that the fluorescence was originated from the ND-TPA effect. Experimental ND-TPA cross-section exhibited larger values than corresponding degenerate two-photon absorption case. Additionally, an improved essential-state model involving multiple TPA excited states was proposed to evaluate the TPA cross-section of organic molecules, which showed good agreement with experimental results. This study indicates that the investigated fluorescent dyes would play important roles in multicolor two-photon imaging.

Electronic Nature of Nonlinear Optical Properties of a Symmetrical Two-Photon Absorbing Fluorene Derivative: Experimental Study and Theoretical Modeling

A comprehensive experimental and theoretical study of linear photophysical properties, such as excited-state relaxation, two-photon absorption, and stimulated emission spectra of the symmetrical fluorene derivative 2,2′-((1E,1′E)-(9,9-diethyl-9H-fluorene-2,7-diyl)bis(ethene-2,1-diyl))bis(1-methyl-1H-pyrrole) (1), is presented. The steady-state absorption, fluorescence, excitation, and excitation anisotropy spectra of 1 in organic solvents of different polarities are investigated experimentally and modeled. The fluorescence solvatochromism of 1 suggests the occurrence of symmetry breaking in the first excited state. The nature of fast relaxation processes in the excited state of 1, with the characteristic times of several picoseconds, is investigated by transient absorption femtosecond pump–probe spectroscopy. The spectral properties of 1 are satisfactorily described by an essential-state model that, accounting for electron–vibration coupling and for polar solvation, addresses spectroscopic features not on...

Spectroscopic Investigation and Theoretical Modeling of Benzothiadiazole-Based Charge-Transfer Chromophores: From Solution to Nanoaggregates

Experimental and theoretical investigations are presented on four quadrupolar molecules constituted of a central electron-acceptor 2,1,3-benzothiadiazole conjugated at both sides with electron-donating thiophene (or 2,2′-bithiophene) substituted groups. Previous investigation of their physicochemical properties demonstrated that thermally induced self-organization might be achieved for one of them. In this study, we further explore the structure–properties relationships for these quadrupolar chromophores also examining their aggregation behavior in organic nanoparticles. Strong spectroscopic evidence of J-aggregates formation is obtained, favored by the presence of branched terminal alkyl chains. The surprisingly low fluorescence quantum yield of these J-aggregates is rationalized within the essential-state model approach.

Quasi-three-level model applied to measured spectra of nonlinear absorption and refraction in organic molecules

Materials with a large nonlinear refractive index (n2) and relatively small linear and nonlinear absorption losses, namely, two-photon absorption (2PA, of coefficient α2), have long been sought after for applications such as all-optical switching (AOS). Here we experimentally determine the linear and 2PA properties of several organic molecules, which we approximate as centrosymmetric, and use a simplified essential-state model (quasi-three-level model) to predict the dispersion of n2. We then compare these predictions with experimental measurements of n2 and find good agreement. Here “quasi”-three-level means using a single one-photon allowed intermediate state and multiple (here two) two-photon allowed states. This also allows predictions of the figure-of-merit (FOM), defined as the ratio of nonlinear refractive phase shift to the 2PA fractional loss, that determines the viability for such molecules to be used in device applications. The model predicts that the optimized wavelength range for a large FOM lies near the short wavelength linear absorption edge for cyanine-like dyes where the magnitude of n2 is quite large. However, 2PA bands lying close to the linear absorption edge in certain classes of molecules can greatly reduce this FOM. We identify two molecules having a large FOM for AOS. We note that the FOM is often defined as the ratio of real to imaginary parts of the third-order susceptibility (χ(3)) with multiple processes leading to both components. As explained later in this paper, such definitions require care to only include the 2PA contribution to the imaginary part of χ(3) in regions of transparency.

Ultrafast spectroscopy, superluminescence and theoretical modeling of a two-photon absorbing fluorene derivative

A comprehensive study of photophysical and photochemical properties of an unsymmetrical fluorene derivative is presented, including linear absorption, fluorescence excitation anisotropy, photochemical stability, steady-state fluorescence, and fluorescence lifetimes in organic solvents of different polarities. Nonlinear optical properties were investigated using Z-scan measurements of degenerate two-photon absorption and femtosecond pump-probe spectroscopy. The strongly fluorescent compound exhibited good photostability, positioning it for use in a number of applications. A dramatic increase in fluorescence intensity along with spectral narrowing was observed under femtosecond pumping, demonstrating amplified spontaneous emission. An extensive set of experimental data is rationalized based on essential state models.

Aggregates of quadrupolar dyes for two-photon absorption: the role of intermolecular interactions.

We present a theoretical investigation of small aggregates of quadrupolar (A-π-D-π-A or D-π-A-π-D) charge-transfer dyes, with attention focused on the role of intermolecular interactions in determining their optical properties. We tackle the theoretical issue by adopting essential-state models (ESMs), which describe an isolated molecule in terms of a minimal number of electronic states, corresponding to the resonance structures. ESMs quite naturally describe intermolecular interactions relaxing the dipolar approximation and accounting for molecular polarizabilities. The approach is applied to curcuminoid and squaraine dyes, two families of chromophores with weak and strong quadrupolar character, respectively. The method is validated against experiment and for curcuminoids also against time-dependent density functional theory. ESMs rationalize the strong ultra-excitonic effects recurrently observed in the experimental optical spectra of aggregates of highly polarizable quadrupolar dyes, offering a valuable tool to exploit the supramolecular design of material properties.

Confirmation of the Origins of Panchromatic Spectra in Squaraine Thin Films Targeted for Organic Photovoltaic Devices

Squaraines offer significant potential for organic photovoltaics because of their broad absorbance and high extinction coefficients as well as their expected use as mechanistic probes in such devices. In this work steps are taken to develop a comprehensive understanding of the excited-state properties of squaraines on the basis of their molecular structure and the resulting solid-state packing. Accurate assignments of the absorption spectral peaks are made on the basis of an essential states model, expanded to include intermolecular charge transfer (ICT). A comparison of simulated spectra with spectra for two symmetric squaraine derivatives confirms that ICT has a major influence on the optical and electronic properties of squaraine aggregates, fully accounting for the origin of the strong panchromaticity of these systems.

Nonlinear Optical Properties of X(C6H5)4 (X = B(-), C, N(+), P(+)): A New Class of Molecules with a Negative Third-Order Polarizability.

Organic π-conjugated materials have been widely used for a variety of nonlinear optical (NLO) applications. Molecules with negative real components Re(γ) of the third-order polarizability, which leads to nonlinear refraction in macroscopic systems, have important benefits for several NLO applications. However, few organic systems studied to date have negative Re(γ) in the long wavelength limit, and all inorganic materials show positive nonlinear refraction in this limit. Here, we introduce a new class of molecules of the form X(C6H5)4, where X = B(-), C, N(+), and P(+), that have negative Re(γ). The molecular mechanism for the NLO properties in these systems is very different from those in typical linear conjugated systems: These systems have a band of excited states involving single-electron excitations within the π-system, several of which have significant coupling to the ground state. Thus, Re(γ) cannot be understood in terms of a simplified essential-state model and must be analyzed in the context of the full sum-over-states expression. Although Re(γ) is significantly smaller than that of other commonly studied NLO chromophores, the introduction of a new molecular architecture offering the potential for a negative Re(γ) introduces new avenues of molecular design for NLO applications.