2PA Cross Section Research Articles

Tuning Two-Photon Absorption in Rhodopsin Chromophore via Backbone Modification: The Story Told by CC2 and TD-DFT.

We investigate here a systematic way to tune two-photon transition strengths (δ2PA) and two-photon absorption (2PA) cross sections (σ2PA) of the rhodopsin's chromophore 11-cis-retinal protonated Schiff base (RPSB) via the modulation of the methyl groups pattern along its polyene chain. Our team employed the resolution of identity, coupled cluster approximate second order (RI-CC2) method with Dunning's aug-cc-pVDZ basis set, to determine the structural impact on δ2PA, as well as its correlation to both transition dipole moments and permanent electric dipole moments. Seven structures were probed in vacuo, including five-double-bond-conjugated model of the native chromophore, shortened by the β-ionone ring (RPSB5), and its de/methylated analogues: 9-methyl, 13-methyl, planar and twisted models of 9,10-dimethyl and 9,10,13-trimethyl. Our results demonstrate that the magnitude of δ2PA is dictated by both the position and number of methylated groups attached to its polyene chain as well as the degree of dihedral twist that is introduced due to the de/methylation. In fact, a strong correlation between δ2PA enhancement and the presence of a C13-methyl group in the planar RPSB5 species is found. Trends in δ2PA values follow the trends observed in their corresponding changes in the permanent dipole moment upon the S0-S1 excitation nearly exactly. The assessment of four DFT functionals, i.e., M11, MN15, CAM-B3LYP, and BHandHLYP, previously found most successful in predicting 2PA properties in biological chromophores, points to a long-range-corrected hybrid meta-GGA M11 as the top-performing functional, albeit still delivering underestimated δ2PA and σ2PA values by a factor of 3.3-5.3 with respect to the CC2 results. In the case of global-hybrid meta-NGA (MN15), as well as CAM-B3LYP and BHandHLYP functionals, this factor deteriorates significantly to 6.7-20.9 and is mostly related to significantly lower quality of the ground- and excited-state dipole moments.

Non-Degenerate Two-Photon Absorption of Fluorescent Protein Chromophores.

Two-photon absorption (2PA), where a pair of photons are absorbed simultaneously, is recognized as a potent bioimaging technique, which depends on the quantified 2PA probability, defined as cross-section (σ2PA). The absorbed photons either have equivalent (ω1 = ω2) or different frequencies (ω1 ≠ ω2), where the former is degenerate 2PA (D-2PA) and the latter is nondegenerate 2PA (ND-2PA). ND-2PA is of particular interest since it is a promising imaging technology with flexibility of photon frequencies and enhanced cross sections, however, it remains a relatively unexplored area compared to D-2PA. This work utilizes time-dependent density functional theory (TD-DFT) and second-order approximate coupled-cluster with the resolution-of-identity approximation (RI-CC2), for the excitation from S0 to S1, to investigate σD-2PA and σND-2PA of FP chromophore models. Interestingly, comparing CAM-B3LYP with the RI-CC2 computations shows qualitative and, in fact, near quantitative agreement in the computed improvements of σND-2PA for comparable (relative) frequency detunings, despite the known underestimations of 2PA cross sections, for TD-DFT results relative to RI-CC2 values. As expected from the 2-state model, the computed values of σND-2PA are quantitatively larger than σD-2PA, where chromophores with the largest values of σD-2PA show greater potential for σND-2PA improvement. Anionic chromophores demonstrated improvements up to 14%, while substantial enhancements were observed in neutral chromophores with some achieving a 30% increase. This work investigates the ND-2PA photophysical characteristics of FP chromophores and identifies qualitative patterns in the computed properties of ND-2PA relative to D-2PA.

A Single-Shot Technique for Measuring Broadband Two-Photon Absorption Spectra in Solution.

Applications involving two-photon activation, including two-photon fluorescence imaging, photodynamic therapy, and 3D data storage, require precise knowledge of the two-photon absorption (2PA) spectra of target chromophores. Broadband pump-probe spectroscopy using femtosecond laser pulses provides wavelength-dependent 2PA spectra with absolute cross sections, but the measurements are sometimes complicated by cross-phase modulation effects and dispersion of the broadband probe. Here, we introduce a single-shot approach that eliminates artifacts from cross-phase modulation and enables more rapid measurements by avoiding the need to scan the time delay between the pump and the probe pulses. The approach uses counterpropagating beams to automatically integrate over the full interaction between the two pulses as they cross. We demonstrate this single-shot approach for a common 2PA reference, coumarin 153 (C153), in three different solvents using the output from a Yb:KGW laser. This approach provides accurate 2PA cross sections that are more reliable and easier to obtain compared with scanning pump-probe methods using copropagating laser beams. The single-shot method for broadband two-photon absorption (BB-2PA) spectroscopy also has significant advantages compared with single-wavelength measurements, such as z-scan and two-photon fluorescence.

Rational design and investigation of nonlinear optical response properties of pyrrolopyrrole aza-BODIPY-based novel push-pull chromophores.

Intramolecular charge transfer (ICT)-based chromophores are highly sought after for designing near-infrared (NIR) absorbing and emitting dyes as well as for designing materials for nonlinear optical (NLO) applications. The properties of these 'push-pull' molecules can easily be modified by varying the electronic donor (D) and acceptor (A) groups as well as the π-conjugation linker. This study presents a methodical approach and employs quantum chemical analysis to explore the relationship between the structural features, electro-optical properties, and the NLO characteristics of molecules with D-π-A framework. The one- and two-photon absorption (2PA), linear polarizability (α), and first hyperpolarizability (β) of some novel chromophores, consisting of a dimeric aza-Boron Dipyrromethene (aza-BODIPY) analogue, called, pyrrolopyrrole aza-BODIPY (PPAB), serving as the acceptor, have been investigated. The electronic donors used in this study are triphenylamine (TPA) and diphenylamine (DPA), and they are conjugated to the acceptor via thienyl or phenylene π-linkers. Additionally, the Hyper-Rayleigh Scattering (βHRS), which enables direct estimation of the second-order NLO properties, is calculated for the studied chromophores with 1064 nm excitation in acetonitrile. The β value shows a significant increase with increasing solvent polarity, indicating that the ICT plays a crucial role in shaping the NLO response of the studied molecules. The enhancement of the 2PA cross-section of the investigated molecules can also be achieved by modulating the combinations of donors and linkers. The results of our study indicate that the novel D-π-A molecules designed in this work demonstrate considerably higher hyperpolarizability values than the standard p-nitroaniline, making them promising candidates for future NLO applications.

Beyond Explored Functionals: A Computational Journey of Two-Photon Absorption.

We present a thorough investigation into the efficacy of 19 density functional theory (DFT) functionals, relative to RI-CC2 results, for computing two-photon absorption (2PA) cross sections (σ2PA) and key dipole moments (|μ00|, |μ11|, |Δμ|, |μ01|) for a series of coumarin dyes in the gas-phase. The functionals include different categories, including local density approximation (LDA), generalized gradient approximation (GGA), hybrid-GGA (H-GGA), range-separated hybrid-GGA (RSH-GGA), meta-GGA (M-GGA), and hybrid M-GGA (HM-GGA), with 14 of them being subjected to analysis for the first time with respect to predicting σ2PA values. Analysis reveals that functionals integrating both short-range (SR) and long-range (LR) corrections, particularly those within the RSH-GGA and HM-GGA classes, outperform the others. Furthermore, the range-separation approach was found more impactful compared to the varying percentages of Hartree-Fock exchange (HF Ex) within different functionals. The functionals traditionally recommended for 2PA do not appear among the top 9 in our study, which is particularly interesting, as these top-performing functionals have not been previously investigated in this context. This list is dominated by M11, QTP variants, ωB97X, ωB97X-V, and M06-2X, surpassing the performance of other functionals, including the commonly used CAM-B3LYP.

Giant Star-shaped meso-substituted Fluorescent Porphyrins with Fluorenyl-containing Arms Designed for Two-photon Oxygen Photosensitization.

In the continuation of previous studies on carbon-rich meso-tetraarylporphyrins featuring 2,7-fluorene units at their periphery, the effect of changing the peripheral dendritic arms for linear arms on their oxygen-photosensitizing ability, their fluorescence and their two-photon absorption (2PA) properties is now analyzed. Thus, starburst porphyrins possessing up to twenty conjugated fluorenyl units were isolated and studied. More precisely, a series of five new free-base porphyrins featuring fully conjugated arms incorporating an increasing number of fluorenyl groups connected via 1,2-alkenyl spacers were synthesized, along with their Zn(II) complexes. Upon excitation in the arm-centred π-π* absorption band, an efficient energy transfer takes place from the peripheral fluorenyl units to the central porphyrin core, leading to intense red-light emission and oxygen photosensitization by the latter. More interestingly, while the linear optical properties of these porphyrins were only slightly improved compared to those of their dendrimer analogues for photodynamic therapy (PDT) or fluorescence imaging, their 2PA cross-sections were much more significantly boosted, evidencing the key role played by different structures on nonlinear optical properties. Finally, by comparison with other porphyrin-based two-photon photosensitizers reported in the literature, we show that these new "semi-disconnected" starburst systems exhibit a remarkable trade-off between intrinsic 2PA, fluorescence and oxygen photosensitization.

Structure-activity relationships of aniline-based squaraines for distinguishable staining and bright two-photon fluorescence bioimaging in plant cells.

An organelle-selective vision provides insights into the physiological response of plants and crops to environmental stresses in sustainable agriculture ecosystems. Biological applications often require two-photon excited fluorophores with low phototoxicity, high brightness, deep penetration, and tuneable cell entry. We obtained three aniline-based squaraines (SQs) tuned from hydrophobic to hydrophilic characteristics by modifying terminal pendant groups and substituents, and investigated their steady-state absorption and far-red-emitting fluorescence properties. The SQs exhibited two-photon absorption (2PA) ranging from 750 to 870 nm within the first biological spectral window; their structure-property relationships, corresponding to the 2PA cross sections (δ2PA), and structure differences were demonstrated. The maximum δ2PA value was ∼1220 GM at 800 nm for hydrophilic SQ3. Distinct biological staining efficiency and selective SQ bioimaging were evaluated utilizing the onion epidermal cell model. Contrary to the hydrophobic SQ1 results in the onion epidermal cell wall, amphiphilic SQ2 tagged the vacuole and nucleus and SQ3 tagged the vacuole. Distinguishable staining profiles in the roots and leaves were achieved. We believe that this study is the first to demonstrate distinct visualisation efficiency induced by the structure differences of two-photon excited SQs. Our results can help establish the versatile roles of novel near-infrared-emitting SQs in biological applications.

Insights into nonlinear absorption transitions in a silver-incorporated reduced graphene oxide-molybdenum disulfide (Ag-rGO-MoS2) hybrid.

Optical nonlinearity in a silver-decorated reduced graphene oxide-molybdenum disulfide (Ag-rGO-MoS2) nanocomposite was experimentally investigated via the Z-scan technique using a Q-switched Nd:YAG nanopulsed green laser. An interesting switching behaviour from saturable to reverse saturable absorption with varying input on-axis intensity of the laser was demonstrated. Under low-intensity laser excitation, Ag-rGO-MoS2 displayed ground-state bleaching, which resulted in saturable absorption (SA) behaviour. Here, the prominent SPR phenomenon of Ag enforced plasmon absorption and is assigned to the SA process. Interestingly at higher intensity, the material switched its nonlinearity to reverse saturable absorption (RSA), attributed to two different mechanisms of two-photon absorption (2PA). At moderate laser pulse energies, the sample underwent sequential 2PA, which is underpinned by calculated varying nonlinear optical parameters and excited-state absorption cross-sections. However, at higher intensities, nonlinear absorption coefficients and excited-state absorption cross-sections remained constant, indicating the occurrence of genuine 2PA. In addition, theoretical estimation of the 2PA cross-section validates the observed transition. Thus, experimental evidence for the validity of nonlinear absorption theory (intensity-dependent transition from linear to nonlinear SA to nonlinear RSA to genuine 2PA via sequential 2PA) is provided for the first time in the literature.

Nonlinear absorption and optical limiting performance of broad-band multi-branched aniline derivatives in the near-infrared region

A thorough investigation was conducted into the impact of π-linker and acceptor group modifications on the nonlinear absorption coefficient and optical limiting (OL) capabilities of multi-branched aniline derivatives. In the experiment, the femtosecond Z-scan technology and the OL experiment were used to detect the nonlinear optical (NLO) response of the samples dissolved in DMF solution at different wavelengths and energies. The femtosecond Z-scan experiments show that all samples exhibit reverse saturable absorption (RSA) caused by excited state absorption (ESA) induced by two-photon absorption (2PA) at specific wavelengths. NBTT still exhibits strong RSA properties at the near-infrared wavelengths, and the 2PA cross-section can reach 293 GM and 289 GM under the incident laser at the wavelength of 900 nm and 1030 nm, while maintaining strong two-photon-induced ESA. Furthermore, the femtosecond OL experiments reveal the commendable OL property of NBTT, and the limiting thresholds reach 0.0026 J/cm2 (at 800 nm) and 0.0033 J/cm2 (at 1030 nm). Quantum chemistry calculations utilizing density functional theory (DFT) show thatπ electrons contribute differently to the bond order on different branches of multi-branched molecules, and the value of Branch 1 is greater than or equal to that of the other two branches at the same position. This leads to the charge transfer (CT) of the molecules NBC and NBTC predominantly concentrated on Branch 1 during the 2PA process, while the addition of conjugate units and cyano-groups in the acceptor groups makes the CT of NBTT not only concentrated on Branch 1, but also extended to Branches 2 and 3. This research seeks to develop the structural design and practical application of multi-branched aniline derivatives to achieve high nonlinear absorption capacity, while maintain a low OL threshold in the near-infrared spectral range.

BF2-Functionalized Benzothiazole Amyloid Markers: Effect of Donor Substituents on One- and Two-Photon Properties.

Investigation of amyloids with the aid of fluorescence microscopy provides crucial insights into the development of numerous diseases associated with the formation of aggregates. Here, we present a series of BF2-functionalized benzothiazoles with electron-donating methoxy group(s), which are tested as amyloid fluorescent markers. We evaluate how the position of donor functional group(s) influences optical properties (fluorescence lifetime (τ) and fluorescence quantum yield (FQY)) in a solution and upon binding to amyloids. We elucidate the importance of surrounding environmental factors (hydrogen-bonding network, polarity, and viscosity) on the observed changes in FQY and evaluate how the localization of a donor influences radiative and nonradiative decay pathways. We conclude that a donor attached to the benzothiazole ring contributes to the increment of radiative decay pathways upon binding to amyloids (kr), while the donor attached to the flexible part of a molecule (with rotational freedom) contributes to a decrease in nonradiative decay pathways (knr). We find that the donor-acceptor-donor architecture allows us to obtain 58 times higher FQY of the dye upon binding to bovine insulin amyloids. Finally, we measure two-photon absorption (2PA) cross sections (σ2) of the dyes and their change upon binding by the two-photon excited fluorescence (2PEF) technique. Measurements reveal that dyes that exhibit the increase/decrease of σ2 values when transferred from highly polar solvents to CHCl3 present a similar behavior upon amyloid binding. Our 2PA experimental values are supported by quantum mechanics/molecular mechanics (QM/MM) simulations. Despite this trend, the values of σ2 are not the same, which points out the importance of two-photon absorption measurements of amyloid-dye complexes in order to understand the performance of 2P probes upon binding.

Influence of peripherical modifications in linear and nonlinear photophysical properties of imidazo[4,5-b]pyridine derivatives

This study reports a wide study on linear and nonlinear optical properties of six imidazo[4,5-b]pyridines derivates. The compounds are coupled with a series of peripheral groups forming different dipolar structures (D-π-A and A-π-A). Photophysical parameters such as the anisotropy coefficient, transition dipole moment, and permanent dipole moment difference were determined using spectroscopic techniques. The two-photon absorption (2PA) cross-section spectra were obtained by the tunable femtosecond Z-scan technique. In addition, quantum chemical calculations and the Sum Over States (SOS) model for two energy levels were applied to support the experimental data. A single 2PA band, with 2PA cross-section varying from 70 to 110 GM, was observed in the 2PA cross-section spectra in the molecules with only acceptor groups. In addition, the presence of a second band around 660 nm and an increase in 2PA cross-section values (around 110 to 130 GM in the principal band) was observed for the molecules with a combination of the methoxy radical (OMe) with halogen groups (D-π-A structure). These results indicate that the non-centrosymetric A-Imp-D structures facilitate the polarizability and internal charge transfer processes, resulting in photophysical and two-photon absorption properties enhancement compared to A-Imp-A structures.

Broadband Two-Photon Absorption Spectroscopy with Stimulated Raman Scattering as an Internal Standard.

Two-photon absorption (2PA) spectroscopy provides valuable information about the nonlinear properties of molecules. In contrast with single-wavelength methods, broadband 2PA spectroscopy using a pump-probe approach gives a continuous 2PA spectrum across a wide range of transition energies without tuning the excitation laser. This contribution shows how stimulated Raman scattering from the solvent can be used as a convenient and robust internal standard for obtaining accurate absolute 2PA cross sections using the broadband approach. Stimulated Raman scattering has the same pump-probe overlap dependence as 2PA, thus eliminating the need to measure the intensity-dependent overlap of the pump and probe directly. Eliminating the overlap represents an important improvement because intensity profiles are typically the largest source of uncertainty in the measurement of absolute 2PA cross sections using any method. Raman scattering cross sections are a fundamental property of the solvent and therefore provide a universal standard that can be applied any time the 2PA and Raman signals are present within the same probe wavelength range. We demonstrate this approach using sample solutions of coumarin 153 in methanol, DMSO, and toluene, as well as fluorescein in water.

New Fluorescent Porphyrins with High Two-Photon Absorption Cross-Sections Designed for Oxygen-Sensitization: Impact of Changing the Connectors in the Peripheral Arms

In the continuation of our sustained interest in porphyrin-based dendrimers and their use as luminescent photosensitizers for two-photon photodynamic therapy (2P-PDT), we wondered about the effect of changing the connectors in our macromolecular structures. We also wanted to initiate preliminary studies on meso-tetraarylporphyrins decorated with more electron-releasing arms. Thus, various meso-tetrafluorenylporphyrin-cored star-shaped and dendrimeric derivatives have been synthesized and characterized, as well as their zinc(II) complexes. In the new dendrimeric derivatives, the peripheral fluorenyl units of the dendrons are linked to the inner core either by N-phenylcarbazole (CCbz) or triphenylamine (CTpa) connectors instead of the more classic 1,3,5-phenylene (CPh) linkers previously used by us. Selected linear and non-linear optical (LO and NLO) properties were then determined for these compounds via absorption or emission studies and by two-photon excited fluorescence (TPEF) measurements. It was found that the CCbz-containing dendrimer, which has the most rigid structure, exhibits a significantly lower two-photon absorption (2PA) cross-section than its CTpa analog, presenting a more flexible structure while rather similar luminescence and singlet oxygen activation quantum yields are found for both. The origin of this unexpected discrepancy is briefly discussed based on our photophysical data. It is then demonstrated that the latter dendrimer also outperforms several closely related dendrimers in terms of 2PA action cross-section and 2PA-oxygen sensitization, making its molecular architecture quite appealing for developing new 2PA photosensitizers suited to theranostic uses.

Beyond Universal Volume Scaling: Tailoring Two-Photon Absorption in Nanomaterials by Heterostructure Design.

Colloidal semiconductor nanomaterials present broadband, with large cross-section, two-photon absorption (2PA) spectra, which turn them into an important platform for applications that benefit from a high nonlinear optical response. Despite that, to date, the only means to control the magnitude of the 2PA cross-section is by changing the nanoparticle volume, as it follows a universal volume scale, independent of the material composition. As the emission spectrum is connected utterly to the nanomaterial dimensions, for a given material, the magnitude of the nonlinear optical response is also coupled to the emission spectra. Here, we demonstrate a means to decouple both effects by exploring the 2PA response of different types of heterostructures, tailoring the volume dependence of the 2PA cross-section due to the different dependence of the density of final states on the nanoparticle volume. By heterostructure engineering, one can obtain 1 order of magnitude enhancement of the 2PA cross-section with minimum emission spectra shift.

Charge Transfer and Level Lifetime in Molecular Photon-Absorption upon the Quantum Impedance Lorentz Oscillator.

On the strength of the new quantum impedance Lorentz oscillator (QILO) model, a charge-transfer method in molecular photon-absorption is proposed and imaged via the numerical simulations of 1- and 2-photon-absorption (1PA and 2PA) behaviors of the organic compounds LB3 and M4 in this paper. According to the frequencies at the peaks and the full width at half-maximums (FWHMs) of the linear absorptive spectra of the two compounds, we first calculate the effective quantum numbers before and after the electronic transitions. Thus, we obtain the molecular average dipole moments, i.e., 1.8728 × 10-29 C·m (5.6145 D) for LB3 and 1.9626 × 10-29 C·m (5.8838 D) for M4 in the ground state in the tetrahydrofuran (THF) solvent. Then, the molecular 2PA cross sections corresponding to wavelength are theoretically inferred and figured out by QILO. As a result, the theoretical cross sections turn out to be in good agreement with the experimental ones. Our results reveal such a charge-transfer image in 1PA near wavelength 425 nm, where an atomic electron of LB3 jumps from the ground-state ellipse orbit with the semimajor axis ai = 1.2492 × 10-10m = 1.2492 Å and semiminor axis bi = 0.4363 Å to the excited-state circle (aj = bj = 2.5399 Å). In addition, during its 2PA process, the same transitional electron in the ground state is excited to the elliptic orbit with aj = 2.5399 Å and bj =1.3808 Å, in which the molecular dipole moment reaches as high as 3.4109 × 10-29 C·m (10.2256 D). In addition, we obtain a level-lifetime formula with the microparticle collision idea of thermal motion, which indicates that the level lifetime is proportional (not inverse) to the damping coefficient or FWHM of an absorptive spectrum. The lifetimes of the two compounds at some excited states are calculated and presented. This formula may be used as an experimental method to verify 1PA and 2PA transition selection rules. The QILO model exhibits the advantage of simplifying the calculation complexity and reducing the high cost associated with the first principle in dealing with quantum properties of optoelectronic materials.

High-performance two-photon absorption optical limiter and stabilizer based on phase-pure thick-shell CdSe/CdS core/shell quantum dots

To achieve high-sensitivity two-photon absorption (2PA) optical limiters and stabilizers, two-photon active materials need to have large 2PA cross-sections. Phase-pure wurtzite (WZ) CdSe/CdS core/shell quantum dots (QDs) with a shell thickness of 11 CdS monolayers were prepared by a high-temperature pyrolysis method, which possess a large volume and nearly defect-free core/shell interfaces. The 2PA cross-section of QDs is measured to be as large as 1.5 × 105 GM by the nonlinear transmittance method. Due to the large 2PA cross-section of phase-pure thick-shell WZ CdSe/CdS core/shell QDs, we successfully explored their application in the field of optical limiting and stabilization. Finally, we successfully fabricated a high-sensitivity optical stabilizer made of a polymer (polymethylmethacrylate) matrix comprising phase-pure thick-shell WZ CdSe/CdS core/shell QDs, which can reduce the amplitude fluctuation by ∼67%. In addition, the device reduces the input energy by ∼40%, indicating that the device can also be applied as an optical limiter. This work promotes the application of optical limiters and stabilizers based on QDs in practical work to a certain extent.

Nature of Linear Spectral Properties and Fast Relaxations in the Excited States and Two-Photon Absorption Efficiency of 3-Thiazolyl and 3-Phenyltiazolyl Coumarin Derivatives.

Coumarin-based fluorescent agents play an important role in the manifold fundamental scientific and technological areas and need to be carefully studied. In this research, linear photophysics, photochemistry, fast vibronic relaxations, and two-photon absorption (2PA) of the coumarin derivatives, methyl 4-[2-(7-methoxy-2-oxo-chromen-3-yl)thiazol-4-yl]butanoate (1) and methyl 4-[4-[2-(7-methoxy-2-oxo-chromen-3-yl)thiazol-4-yl]phenoxy]butanoate (2), were comprehensively analyzed using stationary and time-resolved spectroscopic techniques, along with quantum-chemical calculations. The steady-state one-photon absorption, fluorescence emission, and excitation anisotropy spectra, as well as 3D fluorescence maps of 3-hetarylcoumarins 1 and 2 were obtained at room temperature in solvents of different polarities. The nature of relatively large Stokes shifts (∼4000-6000 cm-1), specific solvatochromic behavior, weak electronic π → π* transitions, and adherence to Kasha's rule were revealed. The photochemical stability of 1 and 2 was explored quantitatively, and values of photodecomposition quantum yields, on the order of ∼10-4, were determined. A femtosecond transient absorption pump-probe technique was used for the investigation of fast vibronic relaxation and excited-state absorption processes in 1 and 2, while the possibility of efficient optical gain was shown for 1 in acetonitrile. The degenerate 2PA spectra of 1 and 2 were measured by an open aperture z-scan method, and the maximum 2PA cross-sections of ∼300 GM were obtained. The electronic nature of the hetaryl coumarins was analyzed by quantum-chemical calculations using DFT/TD-DFT level of theory and was found to be in good agreement with experimental data.

Theory, implementation, and disappointing results for two-photon absorption cross sections within the doubly electron-attached equation-of-motion coupled-cluster framework.

The equation-of-motion coupled-cluster singles and doubles method with double electron attachment (EOM-DEA-CCSD) is capable of computing reliable energies, wave functions, and first-order properties of excited states in diradicals and polyenes that have a significant doubly excited character with respect to the ground state, without the need for including the computationally expensive triple excitations. Here, we extend the capabilities of the EOM-DEA-CCSD method to the calculations of a multiphoton property, two-photon absorption (2PA) cross sections. Closed-form expressions for the 2PA cross sections are derived within the expectation-value approach using response wave functions. We analyze the performance of this new implementation by comparing the EOM-DEA-CCSD energies and 2PA cross sections with those computed using the CC3 quadratic response theory approach. As benchmark systems, we consider transitions to the states with doubly excited character in twisted ethene and in polyenes, for which EOM-EE-CCSD (EOM-CCSD for excitation energies) performs poorly. The EOM-DEA-CCSD 2PA cross sections are comparable with the CC3 results for twisted ethene; however, the discrepancies between the two methods are large for hexatriene. The observed trends are explained by configurational analysis of the 2PA channels.

Two-photon absorption in imidazo[1,2-a]pyridine derivatives: Study of nonlinear optical response and dipolar properties

Imidazo[1,2-a]pyridine derivatives are versatile molecules with excellent emissive properties, making them interesting for various applications, from fluorescent probes to organic light-emitting diodes (OLEDs). Furthermore, such molecules enable the incorporation of different peripheral groups during the synthesis, which can improve the desired optical properties. However, there is a lack of studies that report this compounds class linear and nonlinear optical characteristics. Here, spectroscopic measurements were performed on seven imidazo[1,2-a]pyridine derivatives with different peripheral groups, to understand their influence on the two-photon absorption (2PA) cross-section. Results showed that the effective increase molecular conjugation, provided by the naphthalene substituent, leads to an increase of approximately seven times in the 2PA cross-section. Furthermore, it was shown that the same result is obtained when groups with a strong electron withdrawing or donating character are linked to the imidazo[1,2-a]pyridine core. Such results indicate a possible route to obtaining considerable nonlinear optical responses in this organic compounds class.

Ultrafast Evaluation of Two-Photon Absorption with Simplified Time-Dependent Density Functional Theory.

This work presents the theoretical background to evaluate two-photon absorption (2PA) cross-sections in the framework of simplified time-dependent density functional theory (sTD-DFT). Our new implementation allows the ultrafast evaluation of 2PA cross-sections for large molecules based on a regular DFT ground-state determinant as well as a variant employing our tight-binding sTD-DFT-xTX flavor for very large systems. The method is benchmarked against higher-level calculations for trans-stilbene and typical fluorescent protein chromophores. For eGFP, a quadrupolar chromophore and its branched version, the flavine mono-nucleotide, and the iLOV protein, we compare sTD-DFT 2PA spectra to experimental ones. This includes extension and testing of our all-atom quantum chemistry methodology for the evaluation of 2PA for a system of ∼2000 atoms, providing striking agreement with the experimental spectrum.