Solvent induced channel interference in the two-photon absorption process--a theoretical study with a generalized few-state-model in three dimensions

Effect of meso-pentafluorophenyl group on two-photon absorption in heterocorroles and heterocorrins

Owing to their high reactivity, the meso-positions of corroles and corrins are usually protected by some bulky groups. These groups in addition to the said purpose may also affect the photophysical properties of such systems. However, there is no systematic study in the literature exploring this effect. In this work, we target to answer how the meso-substitution affects the photophysical properties in some heterocorroles and heterocorrins. We considered one of the commonly used substitutions, i.e., pentafluorophenyl (-PFPh), at meso positions of 26 heterocorroles and heterocorrins. We employed the state-of-the-art CC2 method in conjunction with resolution-of-identity approximation to study the charge-transfer and one- and two-photon absorption in these systems. It is further explored using a four-state model that helps in understanding the contribution of various transition dipole moments and their relative orientation. At the end, we also investigated the effect of other substitutions such as -CH3, -CF3, -C2H3, -OMe, -phenyl, and -tolyl on two-photon activity.

Theoretical Investigation of Novel Nitrogen-Heterocyclic Iridium(III) Polypyridyl Complexes as Photosensitizers for Two-Photon Photodynamic Therapy

Two-photon photodynamic therapy (TP-PDT) has become a major cancer treatment due to its larger tissue penetration depth, good spatial selectivity, and less damage to normal cells. In this contribution, a series of novel photosensitizer molecules (Ir-2, Ir-2-1∼Ir-2-4) have been designed based on the experimentally demonstrated photosensitizer [Ir(ppy)2(osip)] (PF6) by fine tuning the π-conjugated structure and introducing different nitrogen-heterocyclic substituents. The electronic structures, one- and two-photon absorption spectra, triplet excited state lifetime, solvation-free energy, and photosensitizing performance were evaluated by means of density functional theory (DFT) and time-dependent density functional theory (TDDFT). The results suggested that the molecule Ir-2, incorporating thiophene as the π-connecting group, exhibits a higher probability of triplet state formation, enhanced two-photon absorption cross-section, and prolonged triplet state lifetime. Furthermore, the four designed nitrogen-heterocyclic complexes Ir-2-1∼Ir-2-4 demonstrate favorable photosensitizing properties, with two-photon absorption cross-sections reaching up to 110 GM and triplet excited state lifetimes exceeding 1000 μs for Ir-2-4.

Rational design of anthocyanidins-directed near-infrared two-photon fluorescent probes

Recently, two-photon fluorescent probes based on anthocyanidin molecules have attracted extensive attention due to their outstanding photophysical properties. However, there are only a few two-photon excited fluorescent probes that really meet the requirements of relatively long emission wavelengths (>600 nm), large two-photon absorption (TPA) cross-sections (300 GM), significant Stokes shift (>80 nm), and high fluorescence intensity. Herein, the photophysical properties of a series of anthocyanidins with the same substituents but different fluorophore skeletons are investigated in detail. Compared with b-series molecules, a-series molecules with a six-membered ring in the backbone have a slightly higher reorganization energy. This results in more energy loss upon light excitation, enabling the reaction products to detect NTR through a larger Stokes shift. More importantly, there is very little decrease in fluorescence intensity as the Stokes shift increases. These features are extremely valuable for high-resolution NTR detection. In light of this, novel 2a-n (n = 1-5) compounds are designed, which are accomplished by inhibiting the twisted intramolecular charge transfer (TICT) effect through alkyl cyclization, azetidine ring and extending π conjugation. Among them, 2a-3 gains a long emission spectrum (λem = 691.4 nm), noticeable TPA cross-section (957 GM), and large Stokes shift (110 nm), indicating that it serves as a promising candidate for two-photon fluorescent dyes. It is hoped that this work will offer some insightful theoretical direction for the development of novel high performance anthocyanin fluorescent materials.

A Curious Case of Two-Photon Absorption in n-Helicene and n-Phenylene, n=6-10: Why n=7 is Different?

n-Helicenes and n-Phenylenes are interesting examples of twisted molecules, where although the atoms are connected through conjugated π ${\pi }$ -bonds, the π ${\pi }$ -conjugation is largely hindered by the twisted nature of the bonds. Such structures provide a unique opportunity to study the effect of twisted π ${\pi }$ -system on non-linear optical properties. In this work, we studied the two-photon absorption in donor-acceptor substituted n-helicenes and n-phenylenes employing the state-of-the-art RI-CC2 method and reported a unique feature we observed in n=7 systems. We found that both 7-helicene and 7-phenylene systems exhibit largest two-photon absorption than other members in their respective classes. Furthermore, using generalized few-state model, we provided a detailed microscopic mechanism of this unique observation involving participation of different transition dipole moment vectors and their relative orientations.

Research and Design of Aggregation-Regulated Thermally Activated Delayed Fluorescence Materials for Time-Resolved Two-Photon Excited Fluorescence Imaging and Biological Monitoring

Exploring the nature of aggregation-regulated thermally activated delayed fluorescence (TADF) and proposing effective design strategies for two-photon excited TADF materials for time-resolved biological imaging and monitoring are urgent and encouraging. In this work, it is found that the aggregation effect not only plays an important role in decreasing the internal conversion decay rate but also strongly influences the singlet-triplet excited-state energy difference as well as the intersystem crossing rate. It is proposed that the transformation from prompt fluorescence materials to long lifetime TADF or phosphorescence materials can be accomplished by regulating the position of substituent groups, which provides an effective method to design and develop long afterglow materials. Then, a high-performance TADF compound with a large two-photon absorption cross section in the biological window (112 GM/775 nm), high TADF efficiency (nearly 100%), and long fluorescence lifetime (50.75 μs) has been designed, which demonstrates the potential application in time-resolved two-photon excited fluorescence imaging and biological detection.

Molecular Design of Highly Efficient Heavy-Atom-free NpImidazole Derivatives for Two-Photon Photodynamic Therapy and ClO- Detection

Two-photon photodynamic therapy (TP-PDT), as a treatment technology with deep penetration and less damage, provides a broad prospect for cancer treatment. Nowadays, the development of TP-PDT suffers from the low two-photon absorption (TPA) intensity and short triplet state lifetime of photosensitizers (PSs) used in TP-PDT. Herein, we propose some novel modification strategies based on the thionated NpImidazole (the combination of naphthalimide and imidazole) derivatives to make efforts on those issues and obtain corresponding fluorescent probes for detecting ClO- and excellent PSs for TP-PDT. Density functional theory (DFT) and time-dependent DFT (TD-DFT) are used to help us characterize the photophysical properties and TP-PDT process of the newly designed compounds. Our results show that the introduction of different electron-donating groups at the position 4 of NpImidazole can effectively improve their TPA and emission properties. Specifically, 3s with a N,N-dimethylamino group has a large triplet state lifetime (τ = 699 μs) and TPA cross section value (δTPA = 314 GM), which can effectively achieve TP-PDT; additionally, 4s (with electron-donating group 2-oxa-6-azaspiro[3.3]heptane in NpImidazole) effectively realizes the dual-function of a PS for TP-PDT (τ = 25,122 μs, δTPA = 351 GM) and a fluorescent probe for detecting ClO- (Φf = 29% of the product 4o). Moreover, an important problem is clarified from a microscopic perspective, that is, why the transition property of 3s and 4s (1π-π*) from S1 to S0 is different from that of 1s and 2s (1n-π*). It is hoped that our work can provides valuable theoretical clues for the design and synthesis of heavy-atom-free NpImidazole-based PSs and fluorescent probes for the detection of hypochlorite.

Impact of the Protein Environment on Two-Photon Absorption Cross-Sections of the GFP Chromophore Anion Resolved at the XMCQDPT2 Level of Theory

The search for fluorescent proteins with large two-photon absorption (TPA) cross-sections and improved brightness is required for their efficient use in bioimaging. Here, we explored the impact of a single-point mutation close to the anionic form of the GFP chromophore on its TPA activity. We considered the lowest-energy transition of EGFP and its modification EGFP T203I. We focused on a methodology for obtaining reliable TPA cross-sections for mutated proteins, based on conformational sampling using molecular dynamics simulations and a high-level XMCQDPT2-based QM/MM approach. We also studied the numerical convergence of the sum-over-states formalism and provide direct evidence for the applicability of the two-level model for calculating TPA cross-sections in EGFP. The calculated values were found to be very sensitive to changes in the permanent dipole moments between the ground and excited states and highly tunable by internal electric field of the protein environment. In the case of the GFP chromophore anion, even a single hydrogen bond was shown to be capable of drastically increasing the TPA cross-section. Such high tunability of the nonlinear photophysical properties of the chromophore anions can be used for the rational design of brighter fluorescent proteins for bioimaging using two-photon laser scanning microscopy.

Difluoroborate-based bichromophores: Symmetry relaxation and two-photon absorption

Given potential applications of multiphoton absorbers, in the present work we have studied the symmetry-relaxation effects in one- and two-photon absorption spectra in two bichromophore systems based on difluoroborate core linked by biphenylene or bianthracene moieties. We have employed a palette of experimental methods (synthesis, one- and two-photon spectroscopy, X-ray crystallography) and state-of-the-art computational methods to shed light on how symmetry relaxation, a result of twisting of building blocks, affects one- and two-photon absorption of the two studied fluorescent dyes. Electronic-structure calculations revealed that the planarity of central biphenyl moiety, as well as deviations from planarity up to 30-40 deg., ensure maximum values of two-photon transition strengths. Perpendicular arrangement of phenylene units in biphenylene moiety leads to 20% drop in the two-photon transition strengths. More detailed studies demonstrated that equilibrium structures of both compounds in chloroform solution show very different values of two-photon absorption cross sections at absorption band maxima, i.e. 224 GM for and 134 GM for biphenyle and bianthracene linkers, respectively. The latter value is in good agreement with experimental value obtained using Z-scan method. The difference in two-photon absorption cross section between both compounds can be rationalized based on equilibrium geometry differences, i.e. interplanar angle is 35 deg and 91 deg in the case of biphenylene and bianthracene moiety, respectively. It is thus not beneficial to introduce conformationally locked central linker based on bianthracene moiety.

Computational Investigations into Two-Photon Fibril Imaging Using the DANIR-2c Probe

The design of novel fibril imaging molecules for medical diagnosis requires the simultaneous optimization of fibril-specific optical properties and binding specificity toward amyloid fibrils. Because of the possibility to monitor internal organs and deep tissues, the two-photon probes that can absorb in the infrared (IR) and near-IR (NIR) region with a significant two-photon absorption cross section are of immense interest. To contribute to this exploration of chemical compounds suitable for two-photon fibril imaging, we have computationally studied the one- and two-photon properties of a donor-acceptor-substituted DANIR-2c probe, which was used for in vivo detection of β-amyloid deposits using fluorescence spectroscopy. In particular, a multiscale computational approach was employed involving molecular docking, molecular dynamics, hybrid QM/MM molecular dynamics, and coupled-cluster/MM to study the binding of the studied probe to amyloid fibril and its one- and two-photon absorption properties in the fibrillar environment. Multiple binding sites are available for this probe in amyloid fibril, and the one corresponding to the largest binding affinity exhibits also the largest and experimentally meaningful two-photon absorption cross section, thus demonstrating the potential of the studied probe in two-photon microscopy.

Theoretical Investigation of Ru(II) Complexes with Long Lifetime and a Large Two-Photon Absorption Cross-Section in Photodynamic Therapy

Two-photon photodynamic therapy (TP-PDT), as a new method for cancer, has shown unique advantages in tumors. A low two-photon absorption cross-section (δ) in the biologic spectral window and a short triplet state lifetime are the important issues faced by the current photosensitizers (PSs) in TP-PDT. In this paper, the photophysical properties of a series of Ru(II) complexes were studied by density functional theory and time-dependent density functional theory methods. The electronic structure, one- and two-photon absorption properties, type I/II mechanisms, triplet state lifetime, and solvation free energy were calculated. The results showed that the substitution of methoxyls by pyrene groups greatly improved the lifetime of the complex. Furthermore, the addition of acetylenyl groups subtly enhanced δ. Overall, complex 3b possess a large δ(1376 GM), a long lifetime (136 μs), and better solvation free energy. It is hoped that it can provide valuable theoretical guidance for the design and synthesis of efficient two-photon PSs in the experiment.

Research and Design of Aggregation-Induced Phosphorescent Materials for Time-Resolved Two-Photon Excited Luminescence Imaging

Pure organic two-photon excited room temperature phosphorescent (RTP) materials have attracted great attention for time-resolved imaging due to their long emission lifetime and high resolution. The materials with an aromatic carbonyl group exhibit aggregation-induced emission (AIE) and RTP characteristics simultaneously. Here, we deeply explored the nature of aggregation-induced phosphorescence (AIP), especially the relationship between molecular configuration and optical properties. It was found that aggregation effect can suppress geometrical vibrations and regulate energy difference between S₁ and T₁. The aromatic carbonyl group plays significant roles in changing electronic configuration, resulting in large Stokes shift and spin-orbit coupling. It also leads to small transition dipole moment, decreasing two-photon absorption cross section and radiative decay rate. To improve two-photon absorption properties, we further designed a π-conjugated compound with large two-photon absorption cross section in the biological window (36.40 GM/656 nm) and AIP characteristics, which is a potential material in the application of time-resolved two-photon excited imaging.

Designing a Propellane-based Nonlinear Optically Active System Absorbing in Three Different Wavelength Regions

The aim of this work is to demonstrate the possibility of using propellane in designing a molecule that can absorb in three different wavelength regions and their nonlinear optical (NLO) activity can be fine-tuned by varying the three wings. We considered 22 tailor-made propellane derivatives consisting of phenyl, naphthyl, and biphenyl wings for this purpose. Using the state-of-the-art linear and quadratic response methods within TD-DFT and RI-CC2 theories and a suitable generalized few-state model that quantifies the effect of orientation of different transition moments on NLO properties, we discussed how and why the linear and nonlinear optical activity of propellane vary when the three wings are assembled successively to construct a full-propellane.

Persistent and Efficient Multimodal Imaging for Tyrosinase Based on Two-Photon Excited Fluorescent and Room-Temperature Phosphorescent Probes

Tyrosinase is crucial to regulate the metabolism of phenol derivatives, playing an important role in the biosynthesis of melanin pigments, whereas an abnormal level of tyrosinase would lead to severe diseases. It is rather necessary to develop a sensitive and selective imaging tool to assess the level of tyrosinase in vivo. We thoroughly researched the luminous mechanism of the existing TPTYR probe and provided design strategies to improve its two-photon excited fluorescence properties. The designed probes benza2-TPTYR and product benza2-TPTYR-coumarin have large two-photon absorption cross sections at the NIR spectral region (41 GM/706 nm, 71 GM/852 nm), while benza2-TPTYR-coumarin possesses easily distinguishable spectrum in the visible region and a high fluorescence efficiency (Φ_F = 0.27). What is more, novel two-photon excited multimodal imaging based on the pure organic small molecule benza1-TPTYR-coumarin (61 GM/936 nm) is proposed first, simultaneously possessing strong instantaneous fluorescent (563.79 nm) and persistent room-temperature phosphorescent emissions (767.68 nm, 0.54 ms).

Much of a Muchness: On the Origins of Two- and Three-Photon Absorption Activity of Dipolar Y-Shaped Chromophores

The molecular origin of two- (2PA) and three-photon absorption (3PA) activity in three experimentally studied chromophores, prototypical dipolar systems, is investigated. To that end, a generalized few-state model (GFSM) formula is derived for the 3PA transition strength for nonhermitian theories and employed at the coupled-cluster level of theory. Using various computational techniques such as molecular dynamics, linear and quadratic response theories, and GFSM, an in-depth analysis of various optical channels involved in 2PA and 3PA processes is presented. It is found that the four-state model involving the second and third excited singlet states as intermediates is the smallest model among all considered few-state approximations that produces 2PA and 3PA transition strengths (for S₀ → S₁ transition) close to the reference results. By analyzing various optical channels appearing in these models and involved in studied multiphoton processes, we found that the 2PA and 3PA activities in all the three chromophores are dominated and hence controlled by the dipole moment of the final excited state. The similar origins of the 2PA and the 3PA in these prototypical dipolar chromophores suggest transferability of structure–property relations from the 2PA to the 3PA domain.

Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths Based on Popular Density Functional Approximations

We present a benchmark study of density functional approximation (DFA) performances in predicting the two-photon-absorption strengths in π-conjugated molecules containing electron-donating/-accepting moieties. A set of 48 organic molecules is chosen for this purpose, for which the two-photon-absorption (2PA) parameters are evaluated using different DFAs, including BLYP, PBE, B3LYP, PBE0, CAM-B3LYP, LC-BLYP, and optimally tuned LC-BLYP. Minnesota functionals and ωB97X-D are also used, applying the two-state approximation, for a subset of molecules. The efficient resolution-of-identity implementation of the coupled-cluster CC2 model (RI-CC2) is used as a reference for the assessment of the DFAs. Two-state models within the framework of both DFAs and RI-CC2 are used to gain a deeper insight into the performance of different DFAs. Our results give a clear picture of the performance of the density functionals in describing the two-photon activity in dipolar π-conjugated systems. The results show that global hybrids are best suited to reproduce the absolute values of 2PA strengths of donor–acceptor molecules. The range-separated functionals CAM-B3LYP and optimally tuned LC-BLYP, however, show the highest linear correlations with the reference RI-CC2 results. Hence, we recommend the latter DFAs for structure–property studies across large series of dipolar compounds.

Theoretical Study of a Two-Photon Fluorescent Probe Based on Nile Red Derivatives with Controllable Fluorescence Wavelength and Water Solubility

Hypochloric acid (HOCl) plays a vital role in the natural defense system, but abnormal levels of it can cause cell damage, accelerated human aging, and various diseases. It is of great significance to develop new probes for detecting HOCl in biosystems nondestructively and noninvasively. The purpose of this work is to explore new chemical modification strategies of two-photon excitation fluorescence (TPEF) probes to improve the poor water solubility and low efficiency in imaging applications. Nil-OH-6 has a two-photon absorption cross-section value as high as 243 GM and attains a good quantum yield of 0.49. In addition, the modification of terminal groups with different azetidine-heterospirocycles or N,N-dialkyl fused amino groups to Nile Red can effectively improve the fluorescence efficiency as well as increase the solubility to some extent. This study provides some strategies to simultaneously improve the fluorescence performance and solubility of these two-photon probes and, hence, reliable guidance and a foundation for the subsequent synthesis of TPEF probes based on Nile Red.

Two-Photon Absorption Activity of BOPHY Derivatives: Insights from Theory

We present a theoretical study of a two-photon absorption (2PA) process in dipolar and quadrupolar systems containing two BF₂ units. For this purpose, we considered 13 systems studied by Ponce-Vargas et al. [J. Phys. Chem. B2017, 121, 10850−1085829136383] and performed linear and quadratic response theory calculations based on the RI-CC2 method to obtain the 2PA parameters. Furthermore, using the recently developed generalized few-state model, we provided an in-depth view of the changes in 2PA properties in the molecules considered. Our results clearly indicate that suitable electron-donating group substitution to the core BF₂ units results in a large red-shift of the two-photon absorption wavelength, thereby entering into the desired biological window. Furthermore, the corresponding 2PA strength also increases significantly (up to 30-fold). This makes the substituted systems a potential candidate for biological imaging.

Controlling Two-Photon Action Cross Section by Changing a Single Heteroatom Position in Fluorescent Dyes

The optimization of nonlinear optical properties for "real-life" applications remains a key challenge for both experimental and theoretical approaches. In particular, for two-photon processes, maximizing the two-photon action cross section (TPACS), the figure of merit for two-photon bioimaging spectroscopy, requires simultaneously controlling all its components. In the present Letter, a series of difluoroborates presenting various heterocyclic rings as an electron acceptor have been synthesized and their absorption, fluorescence, photoisomerization, and two-photon absorption features have been analyzed using both experimental and theoretical approaches. Our results demonstrate that the TPACS values can be fine-tuned by changing the position of a single heteroatom, which alters the fluorescence quantum yields without changing the intrinsic two-photon absorption cross section. This approach offers a new strategy for optimizing TPACS.

A generalized few-state model for the first hyperpolarizability

The properties of molecules depend on their chemical structure, and thus, structure-property relations help design molecules with desired properties. Few-state models are often used to interpret experimental observations of non-linear optical properties. Not only the magnitude but also the relative orientation of the transition dipole moment vectors is needed for few-state models of the non-linear optical properties. The effect of the relative orientation of the transition dipole moment vectors is called dipole alignment, and this effect has previously been studied for multiphoton absorption properties. However, so far, no such studies are reported for the first hyperpolarizability. Here, we present a generalized few-state model for the static and dynamic first hyperpolarizability β, accounting for the effect of dipole alignment. The formulas derived in this work are general in the sense that they can be used for any few-state model, i.e., a two-state model, a three-state model, or, in general, an n-state model. Based on the formulas, we formulate minimization and maximization criteria for the alignment of transition dipole moment vectors. We demonstrate the importance of dipole alignment by applying the formulas to the static first hyperpolarizability of ortho-, meta-, and para-nitroaniline. The formulas and the analysis provide new ways to understand the structure-property relationship for β and can hence be used to fine-tune the magnitude of β in a molecule.

Predictions of High-Order Electric Properties of Molecules: Can We Benefit from Machine Learning?

There is an exigency of adopting machine learning techniques to screen and discover new materials which could address many societal and technological challenges. In this work, we follow this trend and employ machine learning to study (high-order) electric properties of organic compounds. The results of quantum-chemistry calculations of polarizability and first hyperpolarizability, obtained for more than 50,000 compounds, served as targets for machine learning-based predictions. The studied set of molecular structures encompasses organic push-pull molecules with variable linker lengths. Moreover, the diversified set of linkers, composed of alternating single/double and single/triple carbon-carbon bonds, was considered. This study demonstrates that the applied machine learning strategy allows us to obtain the correlation coefficients, between predicted and reference values of (hyper)polarizabilities, exceeding 0.9 on training, validation, and test set. However, in order to achieve such satisfactory predictive power, one needs to choose the training set appropriately, as the machine learning methods are very sensitive to the linker-type diversity in the training set, yielding catastrophic predictions in certain cases. Furthermore, the dependence of (hyper)polarizability on the length of spacers was studied in detail, allowing for explanation of the appreciably high accuracy of employed approaches.

Tuning of hyperpolarizability, and one- and two-photon absorption of donor-acceptor and donor-acceptor-acceptor-type intramolecular charge transfer-based sensors

The present work aims to study the effect of solvent as well as arrangement of donor-acceptor groups on linear and non-linear optical (NLO) response properties of two experimentally studied intramolecular charge-transfer (ICT)-based fluorescent sensors. One of them (molecule 1) is a donor-acceptor (D-A) system with hemicyanine and dimethylanilino as electron withdrawing and donating groups, respectively, while the other one (molecule 3) is molecule 1 fused with a boron-dipyrromethene (BODIPY) moiety. BODIPY acts as the electron acceptor group of molecule 2 that as well consists of dimethylanilino as the electron donor. Density functional theory (DFT) as well as time-dependent DFT has been employed to optimize the geometry of the molecules, followed by computation of dipole moment (μ), static first hyperpolarizability (β_total), and one- and two-photon absorption (TPA) strengths. The results reveal that dipole moment as well as total static first hyperpolarizability (β_total) of the studied molecules is dominated by the respective components in the direction of charge transfer. The ratio of vector component of first hyperpolarizability (β_vec) to β_total also supports the unidirectional charge transfer in the studied systems. In molecule 3, which is a donor-acceptor-acceptor (D-A-A)-type system, the BODIPY moiety is found to play a major role in controlling the NLO response over the other acceptor group. Solvents are also found to play an important role in controlling the linear as well as NLO response of the studied systems. A significant increase in the first hyperpolarizability as well as TPA cross-section of the studied molecules is predicted due to an increase in the dielectric constant of the medium. The results presented are expected to provide a clue in tuning the NLO response of many ICT-based chromophores, especially those with D-A-A arrangements.

Rational design of novel fluorescent analogues of cholesterol: a “step-by-step” computational study

State-of-the-art quantum chemical and molecular dynamics simulations are used as guidelines in design of novel fluorescent analogues of cholesterol.

Excellent benzocoumarin-based ratiometric two-photon fluorescent probe for H2O2 detection

The level of hydrogen peroxide (H2O2) plays an essential role in regulating biological processes. The in vivo or in vitro detection of H2O2 in deep tissues by utilizing two-photon (TP) fluorescent probes can significantly alleviate the detection damage inflicted onto living organisms as well as facilitate high-resolution imaging when compared with one-photon (OP) fluorescent probes. However, few TP fluorescent probes possess both high fluorescence efficiency and easily distinguishable spectra for measuring H2O2. Therefore, an in-depth understanding of the relationship between the electronic structure and TP fluorescent properties and fabricating probes with excellent performance are still challenging. Consequently, we designed a series of benzocoumarin-based ratiometric TP fluorescent probes and corresponding product molecules for H2O2 detection. Thereafter, we theoretically evaluated the TP recognition performance of these compounds and studied the relationship between their molecular structure and TP performance by means of time-dependent density functional theory and quadratic response theory. Moreover, we determined their spectral properties and fluorescence efficiencies. Fortunately, in this study, we were able to propose an excellent TP probe BC-3 and the corresponding product molecule DCCA-3, which exhibit large TPA cross-sections in the NIR region (3420 GM/988 nm; 316 GM/939 nm) and large Stokes (116 nm; 60 nm) and emission (225 nm) shifts. Therefore, this probe enables the simultaneous NIR and TP imaging of H2O2, which is a unique ability and has never been previously reported. Moreover, we comprehensively investigated the effect of the benzene-fused position in the coumarin backbone on the transition dipole moment and nonradiative decay channels, explaining the fluorescence near-quenching mechanism of benzo[f]coumarin derivative DCCA-4 for the first time.

Two-photon absorption of BF2-carrying compounds: insights from theory and experiment

This communication presents a structure-property study of a few novel pyridine-based difluoroborate compounds with a N-BF₂-O core, which exhibit outstanding fluorescence properties. To exploit their potential for two-photon bioimaging, relationships between the two-photon action cross section and systematic structural modifications have been investigated and unravelled.

Interplay of twist angle and solvents with two-photon optical channel interference in aryl-substituted BODIPY dyes

Channel interference plays a crucial role in understanding the physics behind multiphoton absorption processes. In this work, we study the role of channel interference and solvent effects on the two-photon absorption in aryl-substituted boron dipyrromethene (BODIPY) dyes, a class of intramolecular charge-transfer (ICT) molecules. For this purpose, we consider fourteen dyes of this class with various donor/acceptor substitutions at the para position of the phenyl ring and with or without methyl (-CH₃) substitution on the BODIPY moiety. The presence of a methyl group on the BODIPY moiety affects the dihedral angle significantly, which in turn affects the one- (OPA) and two-photon absorption (TPA) properties of the molecules. Among the molecules studied, the one having the strong electron-donating dimethylamino group and no methyl substitution at the BODIPY moiety is found to have the highest TPA cross section. Our few-state model analysis shows that the large TPA activity of this molecule is due to the all positive contributions from different channel interference terms. Change in dielectric constant of the medium is found to have a profound impact on both the magnitude and sign of the channel interference terms. The magnitude of destructive channel interference gradually decreases with decreasing solvent polarity and becomes constructive in a low-polarity solvent. We also study the effect of rotating the phenyl ring with respect to the BODIPY moiety on the TPA activity. In the gas phase and in different solvents, we found that channel interference is changed from destructive to constructive on twisting the molecule. These results are explained by considering different dipole-, energy- and angle-terms appearing in the expression of a two-state model.

Prediction of two-photon absorption enhancement in red fluorescent protein chromophores made from non-canonical amino acids

Two-photon spectroscopy of fluorescent proteins is a powerful bio-imaging tool known for deep tissue penetration and little cellular damage. Being less sensitive than the one-photon microscopy alternatives, a protein with a large two-photon absorption (TPA) cross-section is needed. Here, we use time-dependent density functional theory (TD-DFT) at the B3LYP and CAM-B3LYP/6-31+G(d,p) levels of theory to screen twenty-two possible chromophores that can be formed upon replacing the amino-acid Tyr66 that forms the red fluorescent protein (RFP) chromophore with a non-canonical amino acid. The two-level model for TPA was used to assess the properties (i.e., transition dipole moment, permanent dipole moment difference, and the angle between them) leading to the TPA cross-sections determined via response theory. Computing TPA cross-sections with B3LYP and CAM-B3LYP yields similar overall trends. Results using both functionals agree that the RFP-derived model of the Gold Fluorescent Protein chromophore (Model 20) has the largest intrinsic TPA cross-section at the optimized geometry. TPA was further computed for selected chromophores following conformational changes: variation of both the dihedral angle of the acylimine moiety and the tilt and twist angles between the rings of the chromophore. The TPA cross-section assumed an oscillatory trend with the rotation of the acylimine dihedral, and the TPA is maximized in the planar conformation for almost all models. Model 21 (a hydroxyquinoline derivative) is shown to be comparable to Model 20 in terms of TPA cross-section. The conformational study on Model 21 shows that the acylimine angle has a much stronger effect on the TPA than its tilt and twist angles. Having an intrinsic TPA ability that is more than 7 times that of the native RFP chromophore, Models 20 and 21 appear to be very promising for future experimental investigation.

Elucidating the Mechanism of Zn(2+) Sensing by a Bipyridine Probe Based on Two-Photon Absorption

In this work, we examine, by means of computational methods, the mechanism of Zn(2+) sensing by a bipyridine-centered, D-π-A-π-D-type ratiometric molecular probe. According to recently published experimental data [Divya, K. P.; Sreejith, S.; Ashokkumar, P.; Yuzhan, K.; Peng, Q.; Maji, S. K.; Tong, Y.; Yu, H.; Zhao, Y.; Ramamurthy, P.; Ajayaghosh, A. A ratiometric fluorescent molecular probe with enhanced two-photon response upon Zn(2+) binding for in vitro and in vivo bioimaging. Chem. Sci. 2014, 5, 3469-3474], after coordination to zinc ions the probe exhibits a large enhancement of the two-photon absorption cross section. The goal of our investigation was to elucidate the mechanism behind this phenomenon. For this purpose, linear and nonlinear optical properties of the unbound (cation-free) and bound probe were calculated, including the influence of solute-solvent interactions, implicitly using a polarizable continuum model and explicitely employing the QM/MM approach. Because the results of the calculations indicate that many conformers of the probe are energetically accessible at room temperature in solution and hence contribute to the signal, structure-property relationships were also taken into account. Results of our simulations demonstrate that the one-photon absorption bands for both the unbound and bound forms correspond to the bright π → π* transition to the first excited state, which, on the other hand, exhibits negligible two-photon activity. On the basis of the results of the quadratic response calculations, we put forward a notion that it is the second excited state that gives the strong signal in the experimental nonlinear spectrum. To explain the differences in the two-photon absorption activity for the two lowest-lying excited states and nonlinear response enhancement upon binding, we employed the generalized few-state model including the ground, first, and second excited states. The analysis of the optical channel suggests that the large two-photon response is due to the coordination-induced increase of the transition moment from the first to the second excited state.

Solvent effects on static polarizability, static first hyperpolarizability and one- and two-photon absorption properties of functionalized triply twisted Möbius annulenes: a DFT study

Solvent effects on the polarizability (α), static first hyperpolarizability (β) and one- and two-photon absorption (OPA and TPA) properties of triply twisted Möbius annulenes.

Relation between Nonlinear Optical Properties of Push-Pull Molecules and Metric of Charge Transfer Excitations

We establish the relationships between the metric of charge transfer excitation (Δr) for the bright ππ* state and the two-photon absorption probability as well as the first hyperpolarizability for two families of push-pull π-conjugated systems. As previously demonstrated by Guido et al. (J. Chem. Theory Comput. 2013, 9, 3118-3126), Δr is a measure for the average hole-electron distance upon excitation and can be used to discriminate between short- and long-range electronic excitations. We indicate two new benefits from using this metric for the analyses of nonlinear optical properties of push-pull systems. First, the two-photon absorption probability and the first hyperpolarizability are found to be interrelated through Δr; if β ∼ (Δr)(k), then roughly, δ(TPA) ∼ (Δr)(k+1). Second, a simple power relation between Δr and the molecular hyperpolarizabilities of push-pull systems offers the possibility of estimating properties for longer molecular chains without performing calculations of high-order response functions explicitly. We further demonstrate how to link the hyperpolarizabilities with the chain length of the push-pull π-conjugated systems through the metric of charge transfer.

Donor's position-specific channel interference in substituted biphenyl molecules

Changing the relative positions of the donor group can reverse the nature of channel interference in donor–acceptor substituted biphenyls.

New trans-stilbene derivatives with large two-photon absorption cross-section and non-linear optical susceptibility values – a theoretical investigation

In the present study, newly designed TSB derivatives decorated with suitable donor–acceptor groups have large TPA cross-sections and can be used as potential two-photon active materials.

Triply twisted Möbius annulene: a new class of two-photon active material – a computational study

The present study clearly reveals that the triply twisted Möbius annulene molecules decorated with suitable donor–acceptor groups can be used as a potential two-photon active material.

Chemical control of channel interference in two-photon absorption processes

The two-photon absorption (TPA) process is the simplest and hence the most studied nonlinear optical phenomenon, and various aspects of this process have been explored in the past few decades, experimentally as well as theoretically. Previous investigations have shown that the two-photon (TP) activity of a molecular system can be tuned, and at present, performance-tailored TP active materials are easy to develop by monitoring factors such as length of conjugation, dimensionality of charge-transfer network, strength of donor-acceptor groups, polarity of solvents, self-aggregation, H-bonding, and micellar encapsulation to mention but a few. One of the most intriguing phenomena affecting the TP activity of a molecule is channel interference. The phrase "channel interference" implies that if the TP transition from one electronic state to another involves more than one optical pathway or channel, characterized by the corresponding transition dipole moment (TDM) vectors, the channels may interfere with each other depending upon the angles between the TDM vectors and hence can either increase (constructive interference) or decrease (destructive interference) the overall TP activity of a system to a significant extent. This phenomenon was first pointed out by Cronstrand, Luo, and Ågren [Chem. Phys. Lett. 2002, 352, 262-269] in two-dimensional systems (i.e., only involving two components of the transition moment vectors). For three-dimensional molecules, an extended version of this idea was required. In order to fill this gap, we developed a generalized model for describing and exploring channel interference, valid for systems of any dimensionality. We have in particular applied it to through-bond (TB) and through-space (TS) charge-transfer systems both in gas phase and in solvents with different polarities. In this Account, we will, in addition to briefly describing the concept of channel interference, discuss two key findings of our recent work: (1) how to control the channel interference by chemical means, and (2) the role of channel interference in the anomalous solvent dependence of certain TP chromophores. For example, we will show that simple structurally induced changes in certain dihedral angles of the well-known betaine dye (TB type) will help fine-tune the constructive channel interference and hence increase the overall TP activity of molecules with this general TP channel structure. Another intriguing result we will discuss is observed for a tweezer-trinitrofluorinone complex (TS type) where, on moving from polar to essentially nonpolar solvents, the nature of the channel interference switches from destructive to constructive, leading to a net abnormal solvent dependence of the TP activity of the system. The present Account highlights the usefulness of the channel interference effect and establishes it as a new and unique way of controlling the TP transition probability in different types of three-dimensional molecules.