Ultralarge Hyperpolarizability Twisted π-Electron System Electro-Optic Chromophores: Synthesis, Solid-State and Solution-Phase Structural Characteristics, Electronic Structures, Linear and Nonlinear Optical Properties, and Computational Studies

Novel emissive styryl dyes from 9-methoxy anthracene: Synthesis, photophysical, thermal stability, viscosity, and DFT study

Novel styryl colorants based on anchoring methoxy with anthracene as a donor linked with various active methylene acceptor groups to derive a conjugated π-system along with push-pull geometry were synthesized and well characterized. Photophysical properties were studied in different polarity solvents. The impact of solvent polarizability is delivered in redshifts in absorption and emission spectra, in addition to enhancing the quantum yield. The benzoxazole and benzimidazole moieties in 4c and 4d demonstrated heat stability of more than 300 °C. Fluorescent intensity is directly proportional to the viscosity and 4a demonstrates a notable viscosity sensor through 1.36 fold increase in intensity. In comparison to other styryl dyes, 4c and 4d were shown to have higher values in DMSO for polarizability (53.3496 × 10-24 esu and 53.7459 × 10-24 esu) and first-order hyperpolarizability (86.3467 × 10-30 esu and 89.1941 × 10-30 esu) as well as second-order hyperpolarizability (1768.9121 × 10-36 esu and 1740.6940 × 10-36 esu) due to presence of heterocyclic character. NLO properties of all the styryl dyes 4a-4e are within the fundamental boundary limits. The 4d (benzoxazole) dye exhibited a small HOMO-LUMO energy gap of 2.8825 eV, whereas the 4b and 4e dyes had a larger band gap due to the presence of a carbonyl group.

Enhanced molecular first hyperpolarizabilities with Reichardt's type of zwitterions: a computational study on roles of various monocyclic aromatic bridges

CONTEXT

This work reports structure-property correlations of 27 zwitterions Reichardt's types of zwitterions. Focuses are twofold, to see the (1) impacts of metamerism with Reichardt's vs Brooker's types of zwitterions and (2) impacts of monocyclic aromatic rings as bridges. All the molecules considered here have pyridinium (common acceptor: A) and p-phenylene-dicyanomethanide (common donor: D). Fundamental molecular properties like dipole moments (μ), polarizabilities (α), hyperpolarizabilities (β), and adiabatic absorptions were computed only for the Reichardt types and compared with the literature reported respective Brooker's types of zwitterions. As an impact of metamerism, in general 2-3 times enhanced hyperpolarizabilities (β) were observed for Reichardt's compared to Brooker's types. Exceptions were observed with some triazine bridges and furan bridge, where Brooker's types were found to be more efficient. As impacts of aromatic bridges, in general, 6-sevenfold enhanced β compared to well-known traditional bridges and enhanced β were observed compared to D-A directly connected zwitterion (benzene bridge: sixfold enhanced β). Current findings show that the aromatic bridge control with Reichardt's types of zwitterions is more efficient and thus may be employed as an effective strategy for the designing of functional molecular chromophores for various other fundamental areas.

METHODS

All computations were performed with Gaussian 09. Geometry optimizations and computations of fundamental properties were carried out with HF, B3LYP, CAM-B3LYP, and ωB97xD methodologies, with 6-31G(d,p) and aug-cc-pVDZ basis sets. For adiabatic excitations, computations were carried out using TDDFT and TDHF approaches. For the computations of the response properties (like the nonlinear optical responses), CPHF approach was used.

Design of High-Performance Inorganic-Organic Hybrid Nonlinear Optical Materials Using Superhalogen Al13 and Dianhydrides

Novel inorganic-organic hybrid complexes Al13-X (X represents the dianhydrides PMDA, NTCDA, and PTCDA) are theoretically designed and studied using density functional theory (DFT) and time-dependent DFT. These conjugated dianhydrides containing four acceptor carbonyl groups are commonly used as electron acceptor materials. These compounds possess large binding energies, reflecting the sufficient binding of Al13 to the dianhydride molecule. The binding nature of the complexes is of charge transfer type, i.e., electrons are transferred from the aluminum cluster to the dianhydride. All of the aimed complexes have large mean polarizability (α0) and first hyperpolarizability (β0). The β0 values are explained on the basis of electronic transitions in crucial excited states using the TD-DFT method. Additionally, the hole-electron distribution was analyzed, revealing the nature of electronic excitation. Absorption spectra analysis shows that these complexes have an excellent infrared (IR) transparent region (1000-5000 nm). Therefore, these inorganic-organic hybrid complexes with high stability can be considered as potential candidates for new IR nonlinear optical molecules.

Torsion Angles between Donor and Acceptor Moieties as a Descriptor for Designing Nonlinear Optics and Thermally Activated Delayed Fluorescence Materials

The performances of nonlinear optics (NLO) and thermally activated delayed fluorescence (TADF) materials are strongly related to the torsion angles (θ) between donor (D) and acceptor (A) moieties in D-A architecture molecules. However, the underlying relationships connecting θ to the performances of NLO/TADF materials remain unclear. Herein, we present a comprehensive theoretical study on NLO/TADF materials composed of a series of D-A backbone molecules (TPAAP/TPAAQ series and AQ-DMAC/AQ-MeFAC series) to shed light on these relationships. It is found that changing θ via the intramolecular locking strategy can greatly influence values of the first hyperpolarizability (β) and singlet-triplet energy gap (ΔEST), further leading to better/worse performances of NLO/TADF materials, respectively. Intriguingly, a more detailed analysis indicates that the variation trends between θ and β/ΔEST are changeable in low θ regions, exhibiting volcano-like relationships. The large coefficients of determination (R2, ranging from 0.76 to 0.93) suggest that this experimentally measurable parameter (θ) can be used as a promising descriptor to evaluate the performances of related materials. Following the revealed θ-β/θ-ΔEST correlations, the optimal/worst torsion angles for different materials are identified. These findings highlight the importance of the intrinsic structure-performance relationships, thus providing novel design strategies for high-performance NLO/TADF materials.

Lighting up Micro-/Nanorobots with Fluorescence

Micro-/nanorobots (MNRs) can be autonomously propelled on demand in complex biological environments and thus may bring revolutionary changes to biomedicines. Fluorescence has been widely used in real-time imaging, chemo-/biosensing, and photo-(chemo-) therapy. The integration of MNRs with fluorescence generates fluorescent MNRs with unique advantages of optical trackability, on-the-fly environmental sensitivity, and targeting chemo-/photon-induced cytotoxicity. This review provides an up-to-date overview of fluorescent MNRs. After the highlighted elucidation about MNRs of various propulsion mechanisms and the introductory information on fluorescence with emphasis on the fluorescent mechanisms and materials, we systematically illustrate the design and preparation strategies to integrate MNRs with fluorescent substances and their biomedical applications in imaging-guided drug delivery, intelligent on-the-fly sensing and photo-(chemo-) therapy. In the end, we summarize the main challenges and provide an outlook on the future directions of fluorescent MNRs. This work is expected to attract and inspire researchers from different communities to advance the creation and practical application of fluorescent MNRs on a broad horizon.

Dual Solution-/Solid-State Emissive Excited-State Intramolecular Proton Transfer (ESIPT) Dyes: A Combined Experimental and Theoretical Approach

Excited-state intramolecular proton transfer (ESIPT) dyes typically show strong solid-state emission, but faint fluorescence intensity is observed in the solution state owing to detrimental molecular motions. This article investigates the influence of direct (hetero)arylation on the optical properties of 2-(2'-hydroxyphenyl)benzoxazole ESIPT emitters. The synthesis of two series of ESIPT emitters bearing substituted neutral or charged aryl, thiophene, or pyridine rings is reported herein along with full photophysical studies in solution and solid states, demonstrating the dual solution-/solid-state emission behavior. Depending on the nature of substitution, several excited-state dynamics are observed: quantitative or partially frustrated ESIPT process or deprotonation of the excited species. Protonation studies revealed that pyridine substitution triggered a strong increase of quantum yield in the solution state for the protonated species owing to favorable quinoidal stabilization. These attractive features led to the development of a second series of dyes with alkyl or aryl pyridinium moieties showing strong tunable solution/solid fluorescence intensity. For each series, ab initio calculations helped rationalize and ascertain their behavior in the excited state and the nature of the emission observed by the experimental results.

Spontaneous Combustion of 2-Bromo-3-Methoxythiophene: A Study on Reaction Pathways and Energetics by Quantum Chemical Calculations

Reaction pathways and energetics for the dimerization and trimerization reactions of 2-bromo-3-methoxythiophene (2Br-3Met) molecules are investigated using hybrid density functional theory (DFT) calculations to obtain insight into the oligomerization reaction observed in the spontaneous combustion of pure liquid 2Br-3Met. The calculations show that the carbon-bromine bond in a 2Br-3Met molecule elongates easily, and the trans addition of this C-Br bond to a double bond in the neighboring 2Br-3Met molecule occurs easily at room temperature, reflecting the evaluated activation energy of ΔH_a = 12.46 kcal/mol (enthalpy) or ΔG_a = 35.68 kcal/mol (Gibbs free energy, 298.150 K and 1 atm). The formation process of trimers is calculated in a similar way. A model for the explanation of spontaneous combustion is proposed; large oligomers of the 2Br-3Met molecule are produced spontaneously following the initial formation of dimers or trimers. UV-vis spectra and vibration spectra are obtained for related molecular species, which show reasonable agreement with the experimental results.

What Leads to Aggregation-Induced Emission?

Aggregation-induced emission (AIE), usually referring to the phenomenon in which molecules emit more strongly in the aggregate state than in the solution state, is intriguing and promising in various optoelectronic and biosensing applications. In this Perspective, the basic principles that can lead to AIE and experimental evidence to reveal the AIE mechanism of tetraphenyl ethylene (TPE)-type molecules are discussed. AIE is the consequence of two factors: (1) the fast energy dissipation by crossing a conical intersection (CI) in solutions but not in solids results in low luminescence efficiencies in the solutions, and (2) the weak intermolecular coupling and thus slow intermolecular energy/charge transfers in the AIE solids effectively prevent quenching and result in relatively high luminescence efficiencies. The key to AIE is that the luminescence efficiency is tuned by controlling molecules to cross or not to cross a CI by changing the phase of molecules. How fast a molecule can cross a CI is dependent on the energy barrier of isomerization, which can be tuned in many ways, including mechanical or electrical stimuli, in addition to changing phases. Barrier-dependent crossing CI also results in a very important consequence: excitation-wavelength-dependent fluorescence yield within one electronic excited state, an anti-Vavilov's rule phenomenon. In principle, there can be an alternative way to tune luminescence efficiency by manipulating the formation of CIs instead of crossing or not crossing them. This approach relies on the fact that the electronic ground state and the excited state have many different properties, e.g., dipole moment. By tuning the environment, e.g., dielectric constant, to favor or disfavor one state, one may be able to lift or lower the potential surface of one state so that the potential surfaces of two states can vary between intersected and not contacted.

Unlocking the Remarkable Influence of Intramolecular Group Rotation for Third-order Nonlinear Optical Properties

This work exposes for the first time the remarkable influence of intramolecular group rotation on third-order nonlinear optical (NLO) performance. In order to prove the role of group rotation, we designed and synthesized two photo-response compounds tetramethyl 5,5'-(((diazene-1,2-diylbis(4,1-phenylene))bis(oxy))bis(methylene))diisophthalate (1) and 5,5'-(((diazene-1,2-diylbis(4,1-phenylene))bis(oxy))bis(methylene))diisophthalic acid (2) and investigated their NLO performance under different substituent (benzyloxy group) rotation states. 1 and 2 have dynamic benzyloxy group rotation in dilute solution and shows reverse saturated absorption (RSA). When the benzyloxy group rotation of 1 and 2 was restricted by PMMA, their NLO performance not only converted into saturated absorption (SA) and NLO refraction behaviours, but also hardly changed after isomerization. Interestingly, we also restricted the benzyloxy group rotation in solution to a certain extent through photo-induced trans→cis isomerization, and found that the NLO performances of cis isomers of 1 and 2 exhibit SA and positive refraction and are similar to those of 1-PMMA and 2-PMMA. This work provides a new exploratory method for studying the influencing factors of third-order NLO performance.

Similarities and differences between Mn(II) and Zn(II) coordination polymers supported by porphyrin-based ligands: synthesis, structures and nonlinear optical properties

Four coordination polymers (CPs) Mn-TMPP (1), Zn-TMPP (2), Mn-THPP (3), and Zn-THPP (4) have been synthesized and characterized (H2TMPP = meso-tetrakis (6-methylpyridin-3-yl) porphyrin; H2THPP = meso-tetrakis (6-(hydroxymethyl) pyridin-3-yl) porphyrin). The one-dimensional (1D) chain compound 1 is formed via a head-to-tail connection of the Mn-TMPP unit, wherein the central Mn2+ features a square pyramidal geometry coordinated by four N atoms from the porphyrin skeleton and one additional N atom from an adjacent Mn-TMPP unit. Compound 2 features an octahedral Zn2+ center associated with four N atoms from the porphyrin skeleton to define the equatorial plane and two additional N donors at the axial positions to give a two-dimensional (2D) CP. The 1D chain of 1 and the 2D layer of 2 possess distinctive molecular structures but nearly identical molecular arrangements in their unit cells viewed along all three crystallographic axes. By contrast, Mn- and Zn-based CPs 3 and 4 supported by the THPP ligand share both identical molecular connectivities and crystal packing. In 3/4, each Mn/Zn center is chelated by four N donors of the porphyrin interior to define the equatorial plane of an octahedron, whose axial sites are occupied by two alcoholic OH groups from a pair of trans-located pyridinemethanol moieties. The third-order nonlinear optical properties of 1-4 investigated using the Z-scan technique at 532 nm revealed reverse saturable absorption and self-focusing effects for all four CPs, with hyperpolarizability values (γ) in the range 1.42 × 10-28 esu to 7.64 × 10-28 esu. These high γ values are comparable to the best porphyrin-based molecular assemblies, demonstrating potential for these materials in optical limiting applications.

Electric-Field-Induced Second Harmonic Generation Nonlinear Optic Response of A4 β-Pyrrolic-Substituted ZnII Porphyrins: When Cubic Contributions Cannot Be Neglected

In this work, we have prepared a series of A₄ Zn^II porphyrins, carrying in the β-pyrrolic-position one or two π-delocalized ethynylphenyl moieties with a -NO₂ acceptor or a -NMe₂ donor pendant, and measured their second-order NLO response in CHCl₃ solution at 1907 nm via the electric-field-induced second harmonic generation (EFISH) technique. For some of these compounds, we have recorded an unexpected sign and/or absolute value of μβ₁₉₀₇. Since their sterically hindered A₄ structure should ensure the lack of significant aggregation processes in solution, we explain such anomalous EFISH results by invoking a non-negligible contribution of the electronic cubic term γ(-2ω; ω, ω, 0) to γ_EFISH, as supported by a qualitative evaluation of the third-order response through the measure of the cubic hyperpolarizability (γ_THG) and by computational evidence.

Extremely twisted and bent pyrene-fused N-heterocyclic germylenes

The first examples of pyrene-fused Janus-type N-heterocyclic germylenes (NHGe) are reported. Remarkably, the pyrene linker and the germanium containing rings are extremely twisted, with "twist angles" up to 64°. Coordination of a Lewis base modifies the twisting of pyrene to an overall bent core (141° bend angle).

A Twist on Nonlinear Optics: Understanding the Unique Response of π-Twisted Chromophores

Materials with large nonlinear optical (NLO) response have the ability to manipulate the frequency and phase of incident light and exhibit phenomena that form the basis of modern telecommunication systems. In molecule-based materials, the second- and third-order NLO performance is related to the hyperpolarizability (β) and second hyperpolarizability (γ) of the constituent molecules. The search for higher β materials is driven by the desire to keep pace with expanding demand for high speed data transmission, while discovery of high γ chromophores is crucial for the development of emergent photonic technologies reliant on manipulation of "light-with-light". For decades, it was believed that for highest performance, organic NLO materials must be composed of planar π-system chromophores, and much exploratory research focused on subtle molecular modifications, which generally yielded incremental increases in μβ, where μ is the molecular dipole moment. The surprising recent discovery that twisted π-system chromophores can exhibit dramatically higher β values than their planar analogues has revealed a new design paradigm and stimulated the development of high performance twisted intramolecular charge transfer (TICT) chromophores, which are composed of electron-donating and electron-accepting π-substituents joined by a sterically constrained twisted biaryl fragment. In such chromophores, the twisting of the π-system enforces charge separation in the electronic ground state, leading to large dipole moments and low-lying charge-transfer excitations. This unique electronic structure forms the basis for enhanced NLO response, with an archetypal TICT chromophore, TMC-2, exhibiting very large second- ( μβ = 24 000 × 10^-48 esu) and third-order (γ = 1.4 × 10^-33 esu) metrics in dilute low-polarity solutions. This Account summarizes several approaches to enhance μβ in various environments, including (1) manipulating the biaryl torsional angle, (2) modifying the electron accepting fragment, (3) extending conjugation, (4) adding multiple twisted fragments, (5) modifying chromophore side chains, and (6) tuning the chromophore environment. Another set of modifications is explored to enhance γ, including (1) coupling to a cyanine dye to hybridize the cyanine and TICT orbitals, (2) manipulating the donor and acceptor group identity. The extensive modifications described above yield a detailed understanding of TICT chromophore molecular NLO response and unambiguous evidence that such chromophores have the potential to revolutionize organic electro-optics.

Substituent effects on linear and nonlinear optical properties of fluorescent (E)-2-(4-halophenyl)-7-arlstyrylimidazo[1,2-A]pyridine: spectroscopic and computational methods

Effects of alkylamino and bromo substituents on imidazo[1,2-a]pyridines containing donor-π-acceptor type groups were comprehensively investigated for their linear and nonlinear optical properties by solvatochromic and DFT (CAM-B3LYP and BHandHLYP) methods. The difference between the ground and excited dipole moments as well as their ratios obtained by solvatochromic analysis indicate that the excited state is more polar than the ground state for both the bromo and diethyl amino derivative. More than twofold enhancement in the excited state dipole moments was observed as revealed by the difference and ratio of dipole moment upon the introduction of alkylamino donor group and these suggest large intramolecular charge transfer in the dyes. Stabilization energy above 20 kJ/mol was observed for large number of electron donor–acceptor interactions in Natural Bonding Orbital (NBO) analysis. Bond length alternation (BLA) and Bond order alternation (BOA) values tend to zero suggesting a high degree of polarization in the dyes. Enhancement in mean polarizability (α0), first hyperpolarizability (β0) and second static hyperpolarizabilities ( $\bar \gamma$) were observed by the introduction of alkylamino and bromo group in place of chloro in spite of the fact that Hammett constant of chloro and bromo are the same. The dyes have fundamental and intrinsic properties within the Hamiltonian limits. The two-photon absorption cross section value (≈100 GM) is comparable with LDS-698, a commercial TPA dye. This investigation is important for understanding the electronic structure of imidazo[1,2-a]pyridine with active functional groups and extending the potential for optical applications.

Push–pull unsymmetrical substitution in nickel(ii) complexes with tetradentate N2O2 Schiff base ligands: synthesis, structures and linear–nonlinear optical studies

Push–pull unsymmetrical substitution efficiently modulates the electronic, linear and nonlinear optical properties of nickel(ii) complexes with salen-type ligands.

Resemblances of experiment and theory on aryl substituted luminogenic polypyrazolines

Polyarylpyrazolines (PPB, PPA, PPT, PPBt) containing various aryl substituents emit light in a broad color range from orange to blue, making them suitable for optoelectronics.

Structural Properties and Nonlinear Optical Responses of Halogenated Compounds: A DFT Investigation on Molecular Modelling

Computational chemistry is used to evaluate structures of different compounds by using principles of theoretical and quantum chemistry integrated into useful computer programs. It is used to determine energies, dipole moments and thermodynamic properties of different compounds. The present work reports the computational study of six donor-acceptor dyes. The computational method CAM-B3LYP with 6-31G(d,p) was used in this research to determine the effect of halogens on non-linear optical compounds. HOMO-LUMO energy gaps, dipole polarizabilities, first hyperpolarizabilities, and absorption spectra of six studied compounds (dye 1: 4-(2-(4-fluorophenyl)ethynyl)benzenamine; dye 2: 4-(2-(4-chlorophenyl)ethynyl)benzenamine; dye 3: 4-(2-(4-bromophenyl)ethynyl)benzenamine; dye 4: 5-(2-(4-fluorophenyl)ethynyl)benzene-1,2,3-triamine; dye 5: 5-(2-(4-chlorophenyl)ethynyl)benzene-1,2,3-triamine; dye 6: 5-(2-(4-bromophenyl)ethynyl)benzene-1,2,3-triamine) with aniline and halo phenyl segments were computed by using density functional theory (DFT) and time-dependent density functional theory (TDDFT). Results indicate that all dyes showed wavelengths of maximum absorbance in the visible region. Small HOMO-LUMO energy gaps were observed in all investigated dyes. The present calculations on these dyes (1-6) offer an understanding of the direction of charge transfer (CT) and how NLO behavior can be explained. The aniline-to-halo phenyl CT, caused by the combination of the donor amino group and the acceptor halo group, could be a reason for NLO behavior of these sorts of compounds. These compounds exhibit significant molecular second-order NLO responses, especially dyes (6) and (5), with second-order polarizability determined to be approximately 4600 a.u.

Organic Salts Suppress Aggregation and Enhance the Hyperpolarizability of a π-Twisted Chromophore

Twisted intramolecular charge-transfer (TICT) chromophores exhibit extraordinary hyperpolarizabilities, β, and are therefore promising for electro-optic technologies. Nevertheless, centrosymmetric aggregate formation severely diminishes β in concentrated solutions or in polymer matrices. Herein, the remarkable effects of organic salts on the linear and nonlinear optical response of a high β benzimidazolium-based TICT chromophore, B2TMC-2, are reported. Addition of Bu₄ P⁺ Br^- to B2TMC-2 solution in CHCl₃ induces a halochromic blueshift, primarily reflecting interactions between Bu₄ P⁺ Br^- and the B2TMC-2 cationic portion. DC electric-field induced second-harmonic generation (EFISH) measurements on B2TMC-2+Bu₄ P⁺ Br^- solution reveal a large μβ=-22,160×10^-48  esu, unprecedented for any chromophore with such a broad optical transparency window. Moreover, Bu₄ P⁺ Br^- is shown to suppress B2TMC-2 aggregation, thereby preserving high μβ in concentrated solutions. This phenomenon should be applicable to many other NLO chromophores.

Porphyrins for Second Order Nonlinear Optics (NLO): An Intriguing History

This short review outlines the main results obtained by our research group over the last 15 years in the field of porphyrins and metal porphyrins for second order nonlinear optics (NLO). This overview aims to provide a general framework of the key factors which affect the second order NLO response of porphyrin chromophores. The pivotal role of the porphyrin ring as π-conjugated linker, the nature of the metal center, the substitution pattern which features the geometrical arrangement of donor and acceptor substituents in the different classes of porphyrin NLO-phores, as well as the aggregation phenomena and the role of solvents are addressed in detail.

Unprecedented Large Hyperpolarizability of Twisted Chromophores in Polar Media

Twisted intramolecular charge transfer (TICT) chromophores exhibit uniquely large second-order optical nonlinearities ( μβ). However, their promise as electro-optic (E-O) materials is yet untapped, reflecting a strong tendency to aggregate in low-polarity media, leading to a dramatic fall in μβ. Until now, TICT chromophores in deaggregating polar solvents suffered decreased response due to polarity-driven changes in electronic structure. Here we report a new series of benzimidazolium-based TICT chromophores with interaryl torsional angles in the range of 64-77°. The most twisted, B2TMC-2, exhibits a large μβ_vec = -26,000 × 10^-48 esu (at 1907 nm) in dilute nonpolar CH₂Cl₂ solution, which is maintained in polar DMF ( μβ_vec= -20,370 × 10^-48 esu) as measured by DC electric field-induced second harmonic generation (EFISH). Sterically enforced interaryl torsional angles are confirmed by single-crystal X-ray diffraction and solution phase Nuclear Overhauser Effect (NOE) NMR, and spectroscopic characterization reveals a zwitterionic/aromatic ground state electronic structure associated with the high μβ. We show that increasingly disrupted conjugation is correlated with increased μβ even at intermediate twist angles. The excellent performance and reduced aggregation in polar solvents opens new avenues for bridging microscopic and macroscopic chromophore performance.

Evaluating the component contribution to nonlinear optical performances using stable [Ni4O4] cuboidal clusters as models

Cuboidal [Ni₄O₄]-based clusters are systematically studied with the purpose of evaluating the component contribution to the overall nonlinear optical performances.

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

A comparative theoretical study on the electrical and nonlinear optical properties of Li atom adsorbed on AlN and BN single-walled nanotubes

The geometrical structures, electrical properties, and nonlinear optical (NLO) properties of AlNNT-Li and BNNT-Li nanotube systems were investigated by means of the density functional theory (DFT) method. Frontier molecular orbitals and density of states analyses show that adsorption of the Li atom can significantly narrow the wide HOMO-LUMO gaps of pure AlNNT and BNNT. The results reveal that AlNNT-Li and BNNT-Li systems containing diffuse excess electrons can be regarded as inorganic electrides. The formation of diffuse excess electrons leads to a decrease in transition energies, thereby increasing the first hyperpolarizabilities (β ₀) of AlNNT-Li and BNNT-Li. This work may contribute to the development of potential high-performance NLO materials. Graphical abstract The structural characteristics and nonlinear optical properties of the AlNNT-Li and BNNT-Li systems were studied by means of density functional theory. Introduction of Li atoms greatly enhances the static first hyperpolarizabilities of AlNNT-Li and BNNT-Li.

Intriguing Influence of -COOH-Driven Intermolecular Aggregation and Acid-Base Interactions with N,N-Dimethylformamide on the Second-Order Nonlinear-Optical Response of 5,15 Push-Pull Diarylzinc(II) Porphyrinates

A series of 5,15 push-pull meso-diarylzinc(II) porphyrinates, carrying one or two -COOH or -COOCH₃ acceptor groups and a -OCH₃ or a -N(CH₃)₂ donor group, show in N,N-dimethylformamide and CHCl₃ solutions a negative and solvent-dependent second-order nonlinear-optical (NLO) response measured by the electric-field-induced second-harmonic generation (EFISH) technique, different from the structurally related zinc(II) porphyrinate carrying a -N(CH₃)₂ donor group and a -NO₂ acceptor group, where a still solvent-dependent but positive EFISH second-order response was previously reported. Moreover, when a -N(CH₃)₂ donor group and a -COOH acceptor group are part of a sterically hindered 2,12 push-pull β-pyrrolic-substituted tetraarylzinc(II) porphyrinate, the EFISH response is positive and solvent-independent. In order to rationalize these rather intriguing series of observations, EFISH measurements have been integrated by electronic absorption and IR spectroscopic investigations and by density functional theory (DFT) and coupled-perturbed DFT theoretical and ¹H pulsed-gradient spin-echo NMR investigations, which prompt that the significant concentration effects and the strong influence of the solvent nature on the NLO response are originated by a complex whole of different aggregation processes induced by the -COOH group.

Triphenylamine-Based Fluorescent Styryl Dyes: DFT, TD-DFT and Non-Linear Optical Property Study

The electronic structures and spectroscopic properties of triphenylamine-based monostyryl and bis(styryl) dyes were studied using quantum chemical methods. The ground-state geometries of these dyes were optimized using the density functional theory (DFT) method. The lowest singlet excited state was optimized using time-dependent density functional theory (TD-DFT). The absorption was also calculated using the ground-state geometries. All the calculations were carried out in the gas phase and in solvent. The results indicate that the absorption maxima calculated using the TD-DFT are in good agreement with those obtained experimentally. These dyes possess a large second-order non-linear property and this is mainly due to the strong donor-π-acceptor conjugation which is attributed to the excited state intramolecular charge transfer (ICT). There is a relationship between the hardness and first hyperpolarizability and second hyperpolarizability of mono- and bis(styryl) dyes. The efficiency of the intersystem crossing process can be improved by reducing the energy gap between the singlet and triplet excited states.

Large Hyperpolarizabilities at Telecommunication-Relevant Wavelengths in Donor-Acceptor-Donor Nonlinear Optical Chromophores

Octopolar D₂-symmetric chromophores, based on the MPZnM supermolecular motif in which (porphinato)zinc(II) (PZn) and ruthenium(II) polypyridyl (M) structural units are connected via ethyne linkages, were synthesized. These structures take advantage of electron-rich meso-arylporphyrin or electron-poor meso-(perfluoroalkyl)porphyrin macrocycles, unsubstituted terpyridyl and 4'-pyrrolidinyl-2,2';6',2″-terpyridyl ligands, and modulation of metal(II) polypyridyl-to-(porphinato)zinc connectivity, to probe how electronic and geometric factors impact the measured hyperpolarizability. Transient absorption spectra obtained at early time delays (t_delay < 400 fs) demonstrate fast excited-state relaxation, and formation of a highly polarized T₁ excited state; the T₁ states of these chromophores display expansive, intense T₁ → T _n absorption manifolds that dominate the 800-1200 nm region of the NIR, long (μs) triplet-state lifetimes, and unusually large NIR excited absorptive extinction coefficients [ε(T₁ → T _n ) ∼ 10⁵ M^-1 cm^-1]. Dynamic hyperpolarizability (β_λ) values were determined from hyper-Rayleigh light scattering (HRS) measurements, carried out at multiple incident irradiation wavelengths spanning the 800-1500 nm spectral domain. The measured β_HRS value (4600 ± 1200 × 10^-30 esu) for one of these complexes, RuPZnRu, is the largest yet reported for any chromophore at a 1500 nm irradiation wavelength, highlighting that appropriate engineering of strong electronic coupling between multiple charge-transfer oscillators provides a critical design strategy to realize octopolar NLO chromophores exhibiting large β_HRS values at telecom-relevant wavelengths. Generalized Thomas-Kuhn sum (TKS) rules were utilized to compute the effective excited-state-to-excited-state transition dipole moments from experimental linear-absorption spectra; these data were then utilized to compute hyperpolarizabilities as a function of frequency, that include two- and three-state contributions for both β _zzz and β _xzx tensor components to the RuPZnRu hyperpolarizability spectrum. This analysis predicts that the β _zzz and β _xzx tensor contributions to the RuPZnRu hyperpolarizability spectrum maximize near 1550 nm, in agreement with experimental data. The TKS analysis suggests that relative to analogous dipolar chromophores, octopolar supermolecules will be likely characterized by more intricate dependences of the measured hyperpolarizability upon irradiation wavelength due to the interactions among multiple different β tensor components.

Role of a singlet diradical character in carbon nanomaterials: a novel hot spot for efficient nonlinear optical materials

Carbon atoms have the potential to produce a variety of fascinating all-carbon structures with amazing electronic and mechanical properties. Over the last few decades, several efforts have been made using experimental and computational techniques to functionalize graphene, carbon nanotubes and fullerenes for potential use in modern hi-tech electronic, medicinal, optical and nonlinear optical (NLO) applications. Since photons replaced electrons as a carrier of information, the field of NLO material design has drawn immense interest in contemporary materials science. There have been several reports of bridging the gap between the exciting fields of carbon nanomaterials and NLO materials by functionalizing carbon nanomaterials for potential NLO applications. In contrast to previous reports of the design of third-order NLO materials using conventional closed-shell materials, a novel strategy using open-shell diradical molecular systems has recently been proposed. Quantum chemically, diradical character is explained in terms of the instability of the chemical bonds in open-shell molecular systems. Interestingly, several carbon nanomaterials, which naturally possess open-shell singlet configurations, have recently gained momentum in the design of these classes of open-shell NLO materials with excellent NLO properties, stability and diversity. The present review establishes a systematic sequence of different studies (spanning over two decades of intense research efforts), starting from the simplest theoretical two-site diradical model, continuing to its experimental and theoretical realization in actual chemical systems, and finally applying the abovementioned model/rule to novel carbon nanomaterials to tune their NLO properties, particularly their second hyperpolarizability (γ). In the present report, we highlight several recent efforts to functionalize carbon nanomaterials by exploiting their open-shell diradical character to achieve efficient third-order NLO properties. Several issues and opportunities are discussed, including the inherited disadvantages of both experimental (the high reactivity and short life of diradical compounds) and quantum (need for multi-reference methodology) techniques when dealing with carbon nanomaterials. A comparative analysis of several quantum chemical investigations, along with contemporary experimental results, will be performed to emphasize the core issues and opportunities related to carbon nanomaterials with singlet open-shell diradical character. Thus, the present review will highlight carbon nanomaterials with diradical/biradical character for their prospective applications in the NLO field.

Tailoring of spectral response and intramolecular charge transfer in β-enaminones through band gap tuning: synthesis, spectroscopy and quantum chemical studies

In this paper, we investigate the synthetic tailoring of the spectral response and intramolecular charge transfer (ICT) of β-enaminones through bandgap modulation.

First Principle Study of Electronic and Non-Linear Optical (NLO) Properties of Triphenylamine Dyes: Interactive Design Computation of New NLO Compounds

In this study, density functional theory and time-dependent density functional theory are used to determine how the size of π-conjugated system influences the absorption spectra and non-linear optical (NLO) properties of dyes. Double and triple bonds, as well the benzene rings, are used in conjugated systems. The results of the theoretical computation show that the absorption spectra are gradually broadened and red-shifted with increases in the conjugation length. Theoretical examination of the NLO properties was performed on the key parameters of polarizability and hyperpolarizability. A notable increase in the non-linear optical response was observed with an increase in the conjugation length of the π-spacer.

Donor–acceptor organo-imido polyoxometalates: high transparency, high activity redox-active NLO chromophores

Organoimido polyoxometalates are a powerful new class of acceptor for non-linear optics. As a basis for donor–acceptor systems, they offer an excellent transparency/non-linearity trade-off and break through empirical performance limits for comparable organic materials.

Rotamerism-driven large magnitude host–guest binding change in a crown ether derivatized pyridinium-phenolate series

A large magnitude host–guest binding change driven by transducting rotamerism effects is demonstrated within a crown ether modified pyridinium-phenolate series.