βHRS Values Research Articles

Pseudo-Stilbene- and Azobenzene-Type Systems for Optical Frequency Conversion: Estimating the First-Order Molecular Hyperpolarizability

This study investigates the potential of a set of pseudo-stilbene and azobenzene molecular structures to become optical frequency converters for optical communications based on a detailed exploration of the first-order molecular hyperpolarizability (βHRS), which is the microscopic counterpart of second harmonic generation (SHG). βHRS values were obtained via quantum chemical calculations using the Gaussian 16 software package in solvent and gas-phase media at different wavelengths, i.e., 1064 nm, 1310 nm, and 1510 nm. The latter two wavelengths are of particular interest for optical communications. Our study focused on discerning how the molecular structure influences the βHRS response, explicitly highlighting the influence of the azomethine group (CH=N). The results revealed that the molecular planarity, affected by this group, plays a crucial role in modulating the optical properties. The highest βHRS value in a solvent medium using the CAM-B3LYP/6-311+G(2d,p) level of theory achieved in this work was around 1400 ×10−30cm4startvolt−1, four orders of magnitude higher than KDP (0.2 ×10−30cm4startvolt−1), which is a reference in SHG experiments at 1064 nm. The highest calculated βHRS value at the same level of theory and solvent at 1310 nm and 1550 nm was 631 × 10−30cm4startvolt−1 and 456 × 10−30cm4startvolt−1, respectively. All these values belong to molecular structures with azo-coupling with donor (4-NMe2) and acceptor (4′-NO2) peripheral groups, designated as AB-3.

Unraveling the Symmetry Effects on the Second-Order Nonlinear Optical Responses of Molecular Switches: The Case of Ruthenium Complexes.

Owing to their odd order, second-order nonlinear optical (NLO) responses are very sensitive to symmetry. Therefore, within hyper-Rayleigh scattering (HRS) technique, the symmetry impacts the amplitude of the molecular responses, the HRS first hyperpolarizability (βHRS), and the depolarization ratio (DR). Starting from a challenging octupolar structure bearing six ruthenium(II) ammine centers π-conjugated via quaterpyridyl moieties to a tris-chelated zinc(II) core, together with its Λ shape and one-dimensional analogues built by replacing one or two Ru-quaterpyridyl moieties with bipyridine moieties, (time-dependent) density functional theory calculations have been enacted to unravel the symmetry-NLO response relationships as well as their RuII/III redox-triggered switching effects. The one-dimensional and Λ-shaped NLOphores present βHRS values ∼3 times larger than those of the octupolar system, for both Ru oxidation states. However, using the few-state valence bond-charge transfer models demonstrates that the βHRS response of the octupolar complex cation can become larger than those of its one-dimensional and Λ-shaped analogues provided stronger donor-acceptor groups are employed. In parallel, the DRs decrease from a strong dipolar character (DR ≈ 6) for the one-dimensional chromophore to a weaker dipolar character (DR ≈ 5) for the Λ-shaped one and to a clear octupolar character (DR ≈ 1.7) for the last one. In all cases, the β responses originate mostly from metal-to-ligand charge transfer excited states, as revealed using a new scheme for analyzing the variations in electron density upon excitation. The RuII/III oxidations lead to a strong decrease in the βHRS responses, which is attributed to the loss of the donor character of the Ru centers and therefore to the reduction of the push-pull π-conjugation. These results demonstrate that the NLO contrast and the NLO switching behavior of these Ru cations are maintained for the different molecular symmetries. Finally, the character of the β responses of the oxidized species, as revealed by the DR values, further evidences a clear evolution from dipolar to octupolar NLOphores.

Excited-State Dynamics and Nonlinear Optical Properties of Hyperpolarizable Chromophores Based on Conjugated Bis(terpyridyl)Ru(II) and Palladium and Platinum Porphyrinic Components: Impact of Heavy Metals upon Supermolecular Electro-Optic Properties.

A new series of strongly coupled oscillators based upon (porphinato)Pd, (porphinato)Pt, and bis(terpyridyl)ruthenium(II) building blocks is described. These RuPPd, RuPPt, RuPPdRu, and RuPPtRu chromophores feature bis(terpyridyl)Ru(II) moieties connected to the (porphinato)metal unit via an ethyne linker that bridges the 4'-terpyridyl and porphyrin macrocycle meso-carbon positions. Pump-probe transient optical data demonstrate sub-picosecond excited singlet-to-triplet-state relaxation. The relaxed lowest-energy triplet (T1) excited states of these chromophores feature absorption manifolds that span the 800-1200 nm spectral region, microsecond triplet-state lifetimes, and large absorptive extinction coefficients [ε(T1 → Tn) > 4 × 104 M-1 cm-1]. Dynamic hyperpolarizability (βλ) values were determined from hyper-Rayleigh light scattering (HRS) measurements carried out at several incident irradiation wavelengths over the 800-1500 nm spectral region. Relative to benchmark RuPZn and RuPZnRu chromophores which showed large βHRS values over the 1200-1600 nm range, RuPPd, RuPPt, RuPPdRu, and RuPPtRu displayed large βHRS values over the 850-1200 nm region. Generalized Thomas-Kuhn sum (TKS) rules and experimental hyperpolarizability values were utilized to determine excited state-to-excited state transition dipole terms from experimental electronic absorption data and thus assessed frequency-dependent βλ values, including two- and three-level contributions for both βzzz and βxzx tensor components to the RuPPd, RuPPt, RuPPdRu, and RuPPtRu hyperpolarizability spectra. These analyses qualitatively rationalize how the βzzz and βxzx tensor elements influence the observed irradiation wavelength-dependent hyperpolarizability magnitudes. The TKS analysis suggests that supermolecules related to RuPPd, RuPPt, RuPPdRu, and RuPPtRu will likely feature intricate dependences of experimentally determined βHRS values as a function of irradiation wavelength that derive from substantial singlet-triplet mixing, and complex interactions among multiple different β tensor components that modulate the long wavelength regime of the nonlinear optical response.

Molecular Structure-Optical Property Relationship of Salicylidene Derivatives: A Study on the First-Order Hyperpolarizability.

The first-order hyperpolarizability of π-conjugated organic molecules is of particular interest for the fabrication of electro-optical modulators. Thus, we investigated the relationship between the molecular structure and the incoherent second-order nonlinear optical response (βHRS) of four salicylidene derivatives (salophen, [Zn(salophen)(OH2)], 3,4-benzophen, [Zn(3,4-benzophen)(OH2)]) dissolved in DMSO. For that, we employed the Hyper-Rayleigh Scattering technique with picosecond pulse trains. Our experimental results pointed out dynamic βHRS values between 32.0 ± 4.8 × 10-30 cm5/esu and 58.5 ± 8.0 × 10-30 cm5/esu at 1064 nm, depending on the molecular geometry of the salicylidene molecules. More specifically, the outcomes indicate a considerable increase of βHRS magnitude (∼30%) when in the ligands are incorporated the Zn(II) ion. We ascribed such results to the rise of the planarity of the π-conjugated backbone of the chromophores caused by the Zn(II). Furthermore, we observed an increase of ∼50% in dynamic βHRS when there is a replacement of one hydrogen atom (salophen molecule) by an acetophenone group (3,4-benzophen). This result is related to the increase of the effective π-electron number and the higher charge transfer induced at the excited state. All these findings were interpreted and supported in the light of time-dependent density functional theory (DFT) calculations. Solvent effects were considered in the quantum chemical calculations using the integral equation formalism variant of the polarizable continuum model.

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 (βHRS) of eleven π-conjugated oxazoles compounds in toluene medium. The Hyper-Rayleigh Scattering (HRS) technique allowed the determination of the experimental dynamic βHRS 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 βHRS values. Good accordance was found between the experimental and theoretical values, in particular for the CAM-B3LYP and M06-2X functionals.

Structural, optical and nonlinear optical properties and TD-DFT analysis of heteroleptic bis-cyclometalated iridium(III) complex containing 2-phenylpyridine and picolinate ligands

In this work, we studied the structural, optical and nonlinear optical properties and UV–visible absorption spectrum of the heteroleptic bis-cyclometalated iridium(III) complex (tfmppy)2Ir(pic) recently synthesized with tfmppy = 5-trifluoromethyl-2-phenylpyridine and pic = picolinate. The calculations were performed by means of density functional theory (DFT) and time-dependent density functional (TD-DFT) methods using four functionals B3LYP, PBE0, CAM-B3LYP and M06-2X. Calculated geometric parameters agree with the experimental data. CAM-B3LYP and M06-2X lower the HOMO energy level and give a large energy gaps compared with B3LYP and PBE0. The four functionals show that LUMO is delocalized over $$ \pi_{\text{ppy}}^{ * } $$ orbital, and HOMO is contributed by $$ \pi_{\text{ppy}} $$ and dIr orbitals. The studied complex gets a remarkably large first-order NLO response. B3LYP would provide good estimates of the energy gap and shows the strongest values of the first hyperpolarizabilities βHRS; M06-2X and CAM-B3LYP functionals overestimate the gaps and lower βHRS values. PBE0 and B3LYP spectra agree better with the experimental spectrum in the visible region, while CAM-B3LYP and M06-2X are more accurate in UV-C region. Natural transition orbital analysis shows that the weak band observed at 468 nm corresponds to MLCT/LLCT charge transfer transitions and the intense band observed at 270 nm is mainly assigned to intra-ligand state.

Unexpected High Second-Order Nonlinear Optical Activity of Metal Complexes with Three-Branched Hexadentate 2,2'-Bipyridine Ligands.

Two hexadentate bipyridine ligands and their RuII and NiII complexes were prepared. The helical alignment of the three electron-donor-π-bridge-electron-acceptor (d-π-A) single-strands with bundle architecture in cooperation with the metal center can strongly enhance the nonlinear optical (NLO) properties. The complexation of the novel cage-type hexadentate ligands with a paramagnetic NiII -core almost doubles the βHRS values compared with the corresponding diamagnetic RuII complexes. The hyper-Rayleigh scattering (HRS) was performed with a highly sensitive setup for simultaneous discrimination between multi-photon fluorescence and the molecular first hyperpolarizability.

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 (tdelay < 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 → Tn 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 → Tn) ∼ 105 M–1 cm–1]. Dynamic hyperpolarizability (βλ) 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 βHRS 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 βHRS 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 βzzz and βxzx tensor components to the RuPZnRu hyperpolarizability spectrum. This analysis predicts that the βzzz and βxzx 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.

Oxazines: A New Class of Second-Order Nonlinear Optical Switches.

A combined experimental-theoretical investigation has revealed that oxazine-based compounds are multiaddressable, multistate, and multifunctional molecular switches exhibiting contrasts of both linear and second-order nonlinear optical properties. The switching properties are particularly large when the substituent is a donor group. In this study, the cleavage of the C-O bond at the junction of the indole and oxazine cycles (of the closed a forms) is acido-triggered, leading to an open form (b(+)) characterized by larger first hyperpolarizabilities (βHRS) and smaller excitation energies than in the closed form. These results are confirmed and interpreted utilizing ab initio calculations that have been carried out on a broad set of compounds to unravel the role of the substituent. With respect to acceptor groups, oxazines bearing donor groups are characterized not only by larger βHRS and βHRS contrast ratios but also by smaller excitation energies, larger opening-induced charge transfer, and reduction of the bond length alternation, as well as smaller Gibbs energies of the opening reaction. Compared to protonated open forms (b(+)), calculations on the zwitterionic open forms (b) have pointed out similarities in the long-wavelength UV/vis absorption spectra, whereas their βHRS values might differ strongly as a function of the substituent. Indeed, the open forms present two NLOphores, the indoleninium-substituent entity and the nitrophenol (present in the protonated open form, b(+)) or nitrophenolate (present in the zwitterionic open form, b) moiety. Then, nitrophenolate displays a larger first hyperpolarizability than nitrophenol and the β tensor of the two entities might reinforce or cancel each other.

First-order hyperpolarizabilities of chiral, polymer-wrapped single-walled carbon nanotubes.

We report the first-order hyperpolarizabilities (βHRS values) of individualized, length-sorted (700 ± 50 nm long) (6,5) SWNTs and corresponding polymer-wrapped (6,5) SWNT superstructures. These SWNT-based nanohybrids feature semiconducting polymers that wrap the SWNT surface in an exclusive left-handed helical fashion. Manipulation of the polymer electronic structures in these well-defined nanoscale objects provides a new avenue to modulate the magnitude of βHRS at long wavelength (1280 nm).

Interpreting the First-Order Electronic Hyperpolarizability for a Series of Octupolar Push–Pull Triarylamine Molecules Containing Trifluoromethyl

In this present paper, we investigate the relationship between the dynamic first-order hyperpolarizability (DFH, or βHRS) of a triarylamine core bearing two 3,3′-bis(trifluoromethyl)phenyl arms and the nature of a third group containing distinct electron-withdrawing strength (H < CN < CHO < NO2 < Cyet < Vin). For that, we have combined hyper-Rayleigh scattering (HRS) experiments with picosecond pulse train at 1064 nm and quantum chemical calculations at the density functional theory (DFT) level. The βHRS values exhibited pronounced enhancement from 56 × 10–30 cm5/esu (EWG = CN) up to ∼400 × 10–30 cm5/esu (EWG = Vin) due to the increase in the degree of donor–acceptor charge transfer concomitant with the intensification of the resonance enhancement effect observed when the scattered photon (2ω = 532 nm) approaches, in energy, the lowest energy band of chromophores. Furthermore, our experimental results suggest that the CF3 group has a significant effect on the βHRS, since we observed a considerable increas...

Optimizing calculations of electronic excitations and relative hyperpolarizabilities of electrooptic chromophores.

CONSPECTUS: Organic glasses containing chromophores with large first hyperpolarizabilities (β) are promising for compact, high-bandwidth, and energy-efficient electro-optic devices. Systematic optimization of device performance requires development of materials with high acentric order and enhanced hyperpolarizability at operating wavelengths. One essential component of the design process is the accurate calculation of optical transition frequencies and hyperpolarizability. These properties can be computed with a wide range of electronic structure methods implemented within commercial and open-source software packages. A wide variety of methods, especially hybrid density-functional theory (DFT) variants have been used for this purpose. However, in order to provide predictions useful to chromophore designers, a method must be able to consistently predict the relative ordering of standard and novel materials. Moreover, it is important to distinguish between the resonant and nonresonant contribution to the hyperpolarizabiliy and be able to estimate the trade-off between improved β and unwanted absorbance (optical loss) at the target device's operating wavelength. Therefore, we have surveyed a large variety of common methods for computing the properties of modern high-performance chromophores and compared these results with prior experimental hyper-Rayleigh scattering (HRS) and absorbance data. We focused on hybrid DFT methods, supplemented by more computationally intensive Møller-Plesset (MP2) calculations, to determine the relative accuracy of these methods. Our work compares computed hyperpolarizabilities in chloroform relative to standard chromophore EZ-FTC against HRS data versus the same reference. We categorized DFT methods used by the amount of Hartree-Fock (HF) exchange energy incorporated into each functional. Our results suggest that the relationship between percentage of long-range HF exchange and both βHRS and λmax is nearly linear, decreasing as the fraction of long-range HF exchange increases. Mild hybrid DFT methods are satisfactory for prediction of λmax. However, mild hybrid methods provided qualitatively incorrect predictions of the relative hyperpolarizabilities of three high-performance chromophores. DFT methods with approximately 50% HF exchange, and especially the Truhlar M062X functional, provide superior predictions of relative βHRS values but poorer predictions of λmax. The observed trends for these functionals, as well as range-separated hybrids, are similar to MP2, though predicting smaller absolute magnitudes for βHRS. Frequency dependence for βHRS can be calculated using time-dependent DFT and HF methods. However, calculation quality is sensitive not only to a method's ability to predict static hyperpolarizability but also to its prediction of optical resonances. Due to the apparent trade-off in accuracy of prediction of these two properties and the need to use static finite-field methods for MP2 and higher-level hyperpolarizability calculations in most codes, we suggest that composite methods could greatly improve the accuracy of calculations of β and λmax.

Hyper-Rayleigh scattering and two-photon luminescence of phenylamine- indandione chromophores

Based on results of quantum chemical (QC) screening, we put under research several phenylamine indane-1,3-dione derivatives including octupolar NLO chromophore A3BI. According to these calculations, molecular first hyperpolarizability (βHRS) should be enhanced upon replacement of methyl substituents with phenyl groups. Surprisingly, βHRS values obtained in our measurements by hyper-Rayleigh scattering (HRS) are much higher than one could expect from QC. Bearing in mind that two-photon luminescence (TPL) is usual cause for overestimation of βHRS in HRS measurements, we have accomplished investigations of TPL properties of these compounds. All investigated triphenylamine derivatives exhibit strong TPL. In case of DANS and DMABI captured simultaneously, TPL spectra and HRS signal, reveal the least as clearly distinct on TPL background, thus TPL-free βHRS values can be defined. Concurrently, sharp HRS signal of DPABI is sinking in TPL and background noise along with increase in concentration. Due to fairly intensive TPL for other investigated triphenylamino compounds, the HRS signal was rather indistinguishable and therefore correct βHRS values could not be extracted.

The Roles of Molecular Structure and Effective Optical Symmetry in Evolving Dipolar Chromophoric Building Blocks to Potent Octopolar Nonlinear Optical Chromophores

A series of mono-, bis-, tris-, and tetrakis(porphinato)zinc(II) (PZn)-elaborated ruthenium(II) bis(terpyridine) (Ru) complexes have been synthesized in which an ethyne unit connects the macrocycle meso carbon atom to terpyridyl (tpy) 4-, 4'-, and 4''-positions. These supermolecular chromophores, based on the ruthenium(II) [5-(4'-ethynyl-(2,2';6',2''-terpyridinyl))-10,20-bis(2',6'-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-(2,2';6',2''-terpyridine)(2+) bis-hexafluorophosphate (RuPZn) archetype, evince strong mixing of the PZn-based oscillator strength with ruthenium terpyridyl charge resonance bands. Potentiometric and linear absorption spectroscopic data indicate that for structures in which multiple PZn moieties are linked via ethynes to a [Ru(tpy)(2)](2+) core, little electronic coupling is manifest between PZn units, regardless of whether they are located on the same or opposite tpy ligand. Congruent with these experiments, pump-probe transient absorption studies suggest that the individual RuPZn fragments of these structures exhibit, at best, only modest excited-state electronic interactions that derive from factors other than the dipole-dipole interactions of these strong oscillators; this approximate independent character of the component RuPZn oscillators enables fabrication of nonlinear optical (NLO) multipoles with extraordinary hyperpolarizabilities. Dynamic hyperpolarizability (β(λ)) values and depolarization ratios (ρ) were determined from hyper-Rayleigh light scattering (HRS) measurements carried out at an incident irradiation wavelength (λ(inc)) of 1300 nm. The depolarization ratio data provide an experimental measure of chromophore optical symmetry; appropriate coupling of multiple charge-transfer oscillators produces structures having enormous averaged hyperpolarizabilities (β(HRS) values), while evolving the effective chromophore symmetry from purely dipolar (e.g., Ru(tpy)[4-(Zn-porphyrin)ethynyl-tpy](PF(6))(2), β(HRS) = 1280 × 10(-30) esu, ρ = 3.8; Ru(tpy)[4'-(Zn-porphyrin)ethynyl-tpy](PF(6))(2), β(HRS) = 2100 × 10(-30) esu, ρ = 3.8) to octopolar (e.g., Ru[4,4''-bis(Zn-porphyrin)ethynyl-tpy](2)(PF(6))(2), β(HRS) = 1040 × 10(-30) esu, ρ = 1.46) via structural motifs that possess intermediate values of the depolarization ratio. The chromophore design roadmap provided herein gives rise to octopolar supermolecules that feature by far the largest off-diagonal octopolar first hyperpolarizability tensor components ever reported, with the effectively octopolar Ru[4,4''-bis(Zn-porphyrin)ethynyl-tpy](2)(PF(6))(2) possessing a β(HRS) value at 1300 nm more than a factor of 3 larger than that determined for any chromophore having octopolar symmetry examined to date. Because NLO octopoles possess omnidirectional NLO responses while circumventing the electrostatic interactions that drive bulk-phase centrosymmetry for NLO dipoles at high chromophore concentrations, the advent of octopolar NLO chromophores having vastly superior β(HRS) values at technologically important wavelengths will motivate new experimental approaches to achieve acentric order in both bulk-phase and thin film structures.

Second harmonic generation of a series of axially substituted titanium(IV) and gallium(III) tetra-tert-butylphthalocyanines

Electric Field Induced Second-Harmonic (EFISH) Generation and Hyper Raleigh Scattering (HRS) measurements were performed on a representative series of axially substituted titanium(IV) and gallium(III) tetra-tert-butylphthalocyanines. The comparison of γEFISH and βHRS values within the series and in particular in the case of the dimeric species shows the influence of both the reduction of symmetry of the phthalocyanine ring and the intramolecular stacking on the second order nonlinear optical properties.