Benchmarking two-photon absorption cross sections: performance of CC2 and CAM-B3LYP

Two-photon absorption of BODIPY, BIDIPY, GADIPY, and SBDIPY

Substituted boron-dipyrromethene compounds (BODIPYs) have gained significant attention due to their tunable photophysical properties, including two-photon absorption (2PA), a nonlinear optical process where two photons are absorbed simultaneously. The tuning of BODIPY's photophysical properties has recently led to the synthesis of pnictogen-containing derivatives, such as SBDIPY and BIDIPY, where boron is replaced by antimony (Sb) or bismuth (Bi), respectively, as well as other analogues like GADIPY, which contain gallium (Ga). This study presents a computational investigation into their 2PA properties, exploring the impact of various substitutions across these systems. The 2PA cross-sections (σ2PA), electronic excitation energies (ΔE), and dipole moments (μ00, μ11, μ01, Δμ) were computed for 18 DIPY chromophores in the gas-phase with time-dependent density-functional theory (TD-DFT) using several functionals (CAM-B3LYP, ωB97X, M06-2X, M11, and MN15), and then compared to second-order approximate coupled-cluster with the resolution-of-identity approximation (RI-CC2) results. The computed mean absolute errors were small, with the MN15, CAM-B3LYP, and M06-2X functionals being among the best-performing for the properties analyzed. In general, for the parent (unsubstituted) compounds, replacing the core atom in DIPY chromophores results in negligible changes to their σ2PA. However, extending the conjugation through the addition of phenyl substituents significantly increases σ2PA values, and the nature of the core atom impacts the magnitude of this enhancement.

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.

Two-Photon Absorption Strengths of Small Molecules: Reference CC3 Values and Benchmarks

We present a large dataset of highly accurate two-photon transition strengths (δTPA) determined for standard small molecules. Our reference values have been calculated using the quadratic response implementation of the third-order coupled cluster method including iterative triples (Q-CC3). The aug-cc-pVTZ atomic basis set is used for molecules with up to five non-hydrogen atoms, while larger molecules are assessed with aug-cc-pVDZ; the differences due to the basis sets are discussed. This dataset, encompassing 82 singlet transitions of various characters (Rydberg, valence, and double excitations), enables a comprehensive benchmark of smaller basis sets and alternative wavefunction methods when Q-CC3 calculations become beyond reach as well as time-dependent density functional theory (TD-DFT) approaches. The evaluated wavefunction methods include quadratic response and equation-of-motion CCSD approximations, Q-CC2, and second-order algebraic diagrammatic construction in its intermediate state representation (I-ADC2). In the TD-DFT framework, a set of five commonly used exchange-correlation functionals are evaluted. This extensive analysis provides a quantitative assessment of these methods, revealing how different system sizes, response intensities, and types of transitions affect their performances.

Elucidating the Photophysics and Nonlinear Optical Properties of a Novel Azo Prototype for Possible Photonic Applications: A Quantum Chemical Analysis

The photophysics and nonlinear optical responses of a novel nitrothiazol-methoxyphenol molecule were investigated using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) methods with the polarizable continuum model to take the solvent effect into account. Special attention is paid to the description of the lowest absorption band, characterized as a strong π → π* state in the visible region of the spectrum. The TD-DFT emission spectrum analysis reveals a significant Stokes shift of more than 120 nm for the π → π* state in gas phase condition. The results show a great influence of the solvent polarity on the nonlinear optical (NLO) response of the molecule. Specifically, the second harmonic generation hyperpolarizability β(-2ω; ω, ω) shows a large variation from gas to aqueous solvent (82 × 10-30 to 162 × 10-30 esu), exhibiting notably higher values than those reported for standard compounds such as urea (0.34 × 10-30 esu) and p-nitroaniline (6.42 × 10-30 esu). Furthermore, a two-photon absorption analysis indicates a large cross-section (δ2PA = 77 GM) with superior performance compared to several dyes. These results make the molecule quite interesting for nonlinear optics.

Theoretical insights into a turn-on fluorescence probe based on naphthalimide for peroxynitrite detection

Compared with other reactive oxygen species, peroxynitrite (ONOO-) has diversified reactions and transformations in organisms, and its specific action mechanism is not very clear. The study of reactive oxygen species is of great significance in the field of physiology and pathology. Recently an effective on/off fluorescent probe HCA-OH was designed by Liu et al. through tethering p-aminophenol to 1,8-naphthalimide directly. The probe HCA-OH could release the fluorophore HCA-NH2 with good photostability and high fluorescence quantum yield under oxidation of ONOO- via dearylation process. In this work, the sensing mechanism and spectrum character of probe HCA-OH were studied in detail under quantum chemistry calculation. The electronic structures, reaction sites and fluorescent properties of the probe were theoretically analyzed to benefit us for in-depth understanding the principle of detection on reactive oxygen species (ONOO-) with the fluorescent probe HCA-OH. These theoretical results could inspire the medical research community to design and synthesize highly efficient fluorescent probe for reactive oxygen species detection.

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.

Two- and three-photon processes during photopolymerization in 3D laser printing

The performance of a photoinitiator is key to control efficiency and resolution in 3D laser nanoprinting. Upon light absorption, a cascade of competing photophysical processes leads to photochemical reactions toward radical formation that initiates free radical polymerization (FRP). Here, we investigate 7-diethylamino-3-thenoylcoumarin (DETC), belonging to an efficient and frequently used class of photoinitiators in 3D laser printing, and explain the molecular bases of FRP initiation upon DETC photoactivation. Depending on the presence of a co-initiator, DETC causes radical generation either upon two-photon- or three-photon excitation, but the mechanism for these processes is not well understood so far. Here, we show that the unique three-photon based radical formation by DETC, in the absence of a co-initiator, results from its excitation to highly excited triplet states. They allow a hydrogen-atom transfer reaction from the pentaerythritol triacrylate (PETA) monomer to DETC, enabling the formation of the reactive PETA alkyl radical, which initiates FRP. The formation of active DETC radicals is demonstrated to be less spontaneous. In contrast, photoinitiation in the presence of an onium salt co-initiator proceeds via intermolecular electron transfer after the photosensitization of the photoinitiator to the lowest triplet excited state. Our quantum mechanical calculations demonstrate photophysical processes upon the multiphoton activation of DETC and explain different reactions for the radical formation upon DETC photoactivation. This investigation for the first time describes possible pathways of FRP initiation in 3D laser nanoprinting and permits further rational design of efficient photoinitiators to increase the speed and sensitivity of 3D laser nanoprinting.

Tuning the optoelectronic properties of selenophene-diketopyrrolopyrrole-based non-fullerene acceptor to obtain efficient organic solar cells through end-capped modification

With the goal of developing a high-performance organic solar cell, nine molecules of A2-D-A1-D-A2 type are originated in the current investigation. The optoelectronic properties of all the proposed compounds are examined by employing the DFT approach and the B3LYP functional with a 6-31G (d, p) basis set. By substituting the terminal moieties of reference molecule with newly proposed acceptor groups, several optoelectronic and photovoltaic characteristics of OSCs have been studied, which are improved to a significant level when compared with reference molecule, i.e., absorption properties, excitation energy, exciton binding energy, band gap, oscillator strength, electrostatic potential, light-harvesting efficiency, transition density matrix, open-circuit voltage, fill factor, density of states and interaction coefficient. All the newly developed molecules (P1-P9) have improved λmax, small band gap, high oscillator strengths, and low excitation energies compared to the reference molecule. Among all the studied compounds, P9 possesses the least binding energy (0.24 eV), P8 has high interaction coefficient (0.70842), P3 has improved electron mobility due to the least electron reorganization energy (λe = 0.009182 eV), and P5 illustrates high light-harvesting efficiency (0.7180). P8 and P9 displayed better Voc results (1.32 eV and 1.33 eV, respectively) and FF (0.9049 and 0.9055, respectively). Likewise, the phenomenon of charge transfer in the PTB7-Th/P1 blend seems to be a marvelous attempt to introduce them in organic photovoltaics. Consequently, the outcomes of these parameters demonstrate that adding new acceptors to reference molecule is substantial for the breakthrough development of organic solar cells (OSCs).

The eXact integral simplified time-dependent density functional theory (XsTD-DFT)

In the framework of simplified quantum chemistry methods, we introduce the eXact integral simplified time-dependent density functional theory (XsTD-DFT). This method is based on the simplified time-dependent density functional theory (sTD-DFT), where all semi-empirical two-electron integrals are replaced by exact one- and two-center two-electron integrals, while other approximations from sTD-DFT are kept. The performance of this new parameter-free XsTD-DFT method was benchmarked on excited state and (non)linear response properties, including ultra-violet/visible absorption, first hyperpolarizability, and two-photon absorption (2PA). For a set of 77 molecules, the results from the XsTDA approach were compared to the TDA data. XsTDA/B3LYP excitation energies only deviate on average by 0.14 eV from TDA while drastically cutting computational costs by a factor of 20 or more depending on the energy threshold chosen. The absolute deviations of excitation energies with respect to the full scheme are decreasing with increasing system size, showing the suitability of XsTDA/XsTD-DFT to treat large systems. Comparing XsTDA and its predecessor sTDA, the new scheme generally improves excitation energies and oscillator strengths, in particular, for charge transfer states. TD-DFT first hyperpolarizability frequency dispersions for a set of push-pull π-conjugated molecules are faithfully reproduced by XsTD-DFT, while the previous sTD-DFT method provides redshifted resonance energy positions. Excellent performance with respect to the experiment is observed for the 2PA spectrum of the enhanced green fluorescent protein. The obtained robust accuracy similar to TD-DFT at a fraction of the computational cost opens the way for a plethora of applications for large systems and in high throughput screening studies.

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.

How a Single 5 eV Electron Can Induce Double-Strand Breaks in DNA: A Time-Dependent Density Functional Theory Study

Low-energy (<20 eV) electrons (LEEs) can resonantly interact with DNA to form transient anions (TAs) of fundamental units, inducing single-strand breaks (SSBs), and cluster damage, such as double-strand breaks (DSBs). Shape resonances, which arise from electron capture in a previously unfilled orbital, can induce only a SSB, whereas a single core-excited resonance (i.e., two electrons in excited orbitals of the field of a hole) has been shown experimentally to cause cluster lesions. Herein, we show from time-dependent density functional theory (TDDFT) that a core-excited resonance can produce a DSB, i.e., a single 5 eV electron can induce two close lesions in DNA. We considered the nucleotide with the G-C base pair (ds[5'-G-3']) as a model for electron localization in the DNA double helix and calculated the potential energy surfaces (PESs) of excited states of the ground-state TA of ds[5'-G-3'], which correspond to shape and core-excited resonances. The calculations show that shape TAs start at ca. 1 eV, while core-excited TAs occur only above 4 eV. The energy profile of each excited state and the corresponding PES are obtained by simultaneously stretching both C5'-O5' bonds of ds[5'-G-3']. From the nature of the PES, we find two dissociative (σ*) states localized on the PO4 groups at the C5' sites of ds[5'-G-3']. The first σ* state at 1 eV is due to a shape resonance, while the second σ* state is induced by a core-excited resonance at 5.4 eV. As the bond of the latter state stretches and arrives close to the dissociation limit, the added electron on C transfers to C5' phosphate, thus demonstrating the possibility of producing a DSB with only one electron of ca. 5 eV.

Intramolecular charge transfer enhanced optical limiting in novel hydrazone derivatives with a D1-D-Ai-π-A structure

The present paper investigates one of the hydrazone derivatives (BTH with a D-π-A structure) based on density functional theory. With the computation results of ground state absorption (GSA), excited-state absorption (ESA) and multi-photon absorption (MPA), the optical limiting effect observed in the experiment for the BTH molecule can be well predicted and elucidated by the MPA-ESA mechanism. The analysis of the hole-electron and the electron density differences between two transition states reveal that the main transitions involved in the GSA and ESA of BTH could be recognized as local excitation. Based on these observations, four novel hydrazone derivatives based on the BTH unit with a D1-D-Ai-π-A structure were designed to promote intramolecular charge transfer (ICT). It shows that the ICT effect is well improved by adding the D1 and Ai units. Compared with the original BTH molecule, the main bands of GSA and ESA of D1-D-Ai-π-A molecules are both red-shifted. In addition, GSA, ESA and MPA probabilities are all improved because the obvious charge transfer character results in the transition dipole moment change from localized to delocalized. Accordingly, the optical limiting effect in these hydrazone derivatives is well enhanced. These observations provide guidance for designing novel optical limiting materials based on the hydrazone derivatives.

Theoretical study on photoinduced charge transfer in one-photon and two-photon absorption of branching oligofluorenes

Oligofluorenes have been identified as very promising two-photon absorption (TPA) materials and present great application potential for the fabrication of nonlinear optical devices, but the TPA mechanism and corresponding electron excitation properties have not been studied. Here, the photoinduced charge transfer characteristics of V-shaped and Y-shaped branching oligofluorenes that consist of two and three fluorene units in each branch during one-photon absorption (OPA) and TPA processes are analyzed theoretically using the density functional theory and visualization sum-over-states model. The calculated results show that the OPA intensity and TPA cross-section are significantly enhanced by increasing the branch length or changing the structure from V-shaped to Y-shaped. The long-distance charge transfer only occurs on the second transition of TPA at high excited states. Compared to Y-shaped molecules, V-shaped structures exhibit a stronger cooperative effect among the different branches.

End-capped engineering of Quinoxaline core-based non-fullerene acceptor materials with improved power conversion efficiency

Improving the light-harvesting efficiency and boosting open circuit voltage are crucial challenges for enhancing the efficiency of organic solar cells. This work introduces seven new molecules (SA1-SA7) to upgrade the optoelectronic and photovoltaic properties of Q-C-F molecule-based solar cells. All recently designed molecules have the same alkyl-substituted Quinoxaline core and CPDT donor but vary in the end-capped acceptor subunits. All the investigated molecules have revealed superior properties than the model (R) by having absorbance ranging from 681 nm to 782 nm in the gaseous medium while 726 nm-861 nm in chloroform solvent, with the lowest band gap ranging from 1.91 to 2.19 eV SA1 molecule demonstrated the highest λmax (861 nm) in chloroform solvent and the lowest band gap (1.91 eV). SA2 molecule has manifested highest dipole moment (4.5089 D), lower exciton binding energy in gaseous (0.33 eV) and chloroform solvent (0.47 eV), and lower charge mobility of hole (0.0077693) and electron (0.0042470). At the same time, SA7 showed the highest open circuit voltage (1.56 eV) and fill factor (0.9166) due to solid electron-pulling acceptor moieties. From these supportive outcomes, it is inferred that our computationally investigated molecules may be promising candidates to be used in advanced versions of OSCs in the upcoming period.

Non-linear light-matter interactions from the Bethe-Salpeter equation

A route to assess non-linear light-matter interactions from the increasingly popular GW-Bethe-Salpeter equation (GW-BSE) method is outlined. In the present work, the necessary analytic expressions within the static-screened exchange approximation of the BSE are derived. This enables a straightforward implementation of the computation of the first hyperpolarizability as well as two-photon absorption processes for molecular systems. Benchmark calculations on small molecular systems reveal that the GW-BSE method is intriguingly accurate for predicting both first hyperpolarizabilities and two-photon absorption strengths. Using state-of-the-art Kohn-Sham references as a starting point, the accuracy of the GW-BSE method rivals that of the coupled-cluster singles-and-doubles method, outperforming both second-order coupled-cluster and time-dependent density-functional theory.

Designing Thieno[3,4-c]pyrrole-4,6-dione Core-Based, A2-D-A1-D-A2-Type Acceptor Molecules for Promising Photovoltaic Parameters in Organic Photovoltaic Cells

Nonfullerene-based organic solar cells can be utilized as favorable photovoltaic and optoelectronic devices due to their enhanced life span and efficiency. In this research, seven new molecules were designed to improve the working efficiency of organic solar cells by utilizing a terminal acceptor modification approach. The perceived A2-D-A1-D-A2 configuration-based molecules possess a lower band gap ranging from 1.95 to 2.21 eV compared to the pre-existing reference molecule (RW), which has a band gap of 2.23 eV. The modified molecules also exhibit higher λmax values ranging from 672 to 768 nm in the gaseous and 715-839 nm in solvent phases, respectively, as compared to the (RW) molecule, which has λmax values at 673 and 719 nm in gas and chloroform medium, respectively. The ground state geometries, molecular planarity parameter, and span of deviation from the plane were analyzed to study the planarity of all of the molecules. The natural transition orbitals, the density of state, molecular electrostatic potential, noncovalent interactions, frontier molecular orbitals, and transition density matrix analysis of all studied molecules were executed to validate the optoelectronic properties of these molecules. Improved charge mobilities and dipole moments were observed, as newly designed molecules possessed lower internal reorganization energies. The open circuit voltage (Voc) of W4, W5, W6, and W7 among newly designed molecules was improved as compared to the reference molecule. These results elaborate on the superiority of these novel-designed molecules over the pre-existing (RW) molecule as potential blocks for better organic solar cell applications.

Toward Accurate Two-Photon Absorption Spectrum Simulations: Exploring the Landscape beyond the Generalized Gradient Approximation

In this Letter, we present a pioneering analysis of the density functional approximations (DFAs) beyond the generalized gradient approximation (GGA) for predicting two-photon absorption (2PA) strengths of a set of push-pull π-conjugated molecules. In more detail, we have employed a variety of meta-generalized gradient approximation (meta-GGA) functionals, including SCAN, MN15, and M06-2X, to assess their accuracy in describing the 2PA properties of a chosen set of 48 organic molecules. Analytic quadratic response theory is employed for these functionals, and their performance is compared against the previously studied DFAs and reference data obtained at the coupled-cluster CC2 level combined with the resolution-of-identity approximation (RI-CC2). A detailed analysis of the meta-GGA functional performance is provided, demonstrating that they improve upon their predecessors in capturing the key electronic features of the π-conjugated two-photon absorbers. In particular, the Minnesota functional MN15 shows very promising results as it delivers pleasingly accurate chemical rankings for two-photon transition strengths and excited-state dipole moments.

Two-photon chemistry of tetrahydrofuran in clathrate hydrates

High-lying electronic states hold the potential for new and unusual photochemical reactions. However, for conventional single-photon excitation in the condensed phase, reaching these states is often not possible because the vacuum-ultraviolet (VUV) light required is competitively absorbed by the surrounding matrix rather than the molecule of interest. Here, this hurdle is overcome by leveraging nonresonant two-photon absorption (2PA) at 265 nm to achieve preferential photolysis of tetrahydrofuran (THF) trapped within a clathrate hydrate network at 77 K. Electron spin resonance (ESR) spectroscopy enables direct observation and identification of otherwise short-lived organic radicals stabilized by the clathrate cages, providing clues into the rapid dynamics that immediately follow photoexcitation. 2PA induces extensive fragmentation of enclathrated THF yielding 1-alkyl, acyl, allyl and methyl radicals-a stark departure from the reactive motifs commonly reported in γ-irradiated hydrates. We speculate on the undetected transient dynamics and explore the potential role of trapped electrons generated from water and THF. This demonstration of nonresonant two-photon chemistry presents an alternative approach to targeted condensed phase photochemistry in the VUV energy range.

A DFT study for improving the photovoltaic performance of organic solar cells by designing symmetric non-fullerene acceptors by quantum chemical modification on pre-existed LC81 molecule

Minimizing the energy loss and improving the open circuit voltage of organic solar cells is still a primary concern for scientists working in this field. With the aim to enhance the photovoltaic performance of organic solar cells by minimizing energy loss and improving open circuit voltage, seven new acceptor molecules (LC1-LC7) are presented in this work. These molecules are designed by modifying the terminal acceptors of pre-existed "LC81" molecule based on an indacinodithiophene (IDT) fused core. The end-group modification approach is very fruitful in ameliorating the efficacy and optoelectric behavior of OSCs. The newly developed molecules presented remarkable improvements in performance-related parameters and optoelectronic properties. Among all designed molecules, LC7 exhibited the highest absorption maxima (λmax = 869 nm) with the lowest band-gap (1.79 eV), lowest excitation energy (Ex = 1.42 eV), lowest binding energy, and highest excited state lifetime (0.41 ns). The newly designed molecules LC2, LC3, and LC4 exhibited remarkably improved Voc that was 1.84 eV, 1.82 eV, and 1.79 eV accordingly, compared to the LC81 molecule with Voc of 1.74 eV LC2 molecule showed significant improvement in fill factor compared to the previously presented LC81 molecule. LC2, LC6, and LC7 showed a remarkable reduction in energy loss by showing Eloss values of 0.26 eV, 0.18 eV, and 0.25 eV than LC81 molecule (0.37 eV). These findings validate the supremacy of these developed molecules (especially LC2) as potential components of future OSCs.

Accuracy of One- and Two-Photon Intensities with the Extended Polarizable Density Embedding Model

The recently developed extended polarizable density embedding (PDE-X) model is evaluated for the spectroscopic properties of organic chromophores solvated in water, including both one- and two-photon absorption properties. The PDE-X embedding model systematically improves vertical excitation energies over the preceding polarizable density embedding model (PDE). PDE-X shows more modest improvements over existing embedding models for oscillator strengths and two-photon absorption cross-sections, which are more sensitive properties. We argue that the origin of these discrepancies is related to the description of polarization effects, suggesting directions for future development of the embedding model.

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.

A Single Organic Fluorescent Probe for the Discrimination of Dual Spontaneous ROS in Living Organisms: Theoretical Approach

Single-organic-molecule fluorescent probes with double-lock or even multi-lock response modes have attracted the attention of a wide range of researchers. The number of corresponding reports has rapidly increased in recent years. The effective application of the multi-lock response mode single-molecule fluorescent probe has improved the comprehensive understanding of the related targets' functions or influences in pathologic processes. Building a highly efficient functional single-molecule fluorescent probe would benefit the diagnosis and treatment of corresponding diseases. Here, we conducted a theoretical analysis of the synthesizing and sensing mechanism of this kind of functional single-molecule fluorescent probe, thereby guiding the design and building of new efficient probes. In this work, we discuss in detail the electronic structure, electron excitation, and fluorescent character of a recently developed single-molecule fluorescent probe, which could achieve the discrimination and profiling of spontaneous reactive oxygen species (ROS, •OH, and HClO) simultaneously. The theoretical results provide insights that will help develop new tools for fluorescent diagnosis in biological and medical fields.

Photophysical Exploration of Alectinib and Rilpivirine: Insights from Theory and Experiment

Due to the excellent characteristics of fluorescence-based imaging, such as non-invasive detection of biomarkers in vitro and in vivo with high sensitivity, good spatio-temporal resolution and fast response times, it has shown significant prospects in various applications. Compounds with both biological activities and fluorescent properties have the potential for integrated diagnosis and treatment application. Alectinib and Rilpivirine are two excellent drugs on sale that represent a clinically approved targeted therapy for ALK-rearranged NSCLC and have exhibited more favorable safety and tolerance profiles in Phase III clinical trials, ECHO and THRIVE, respectively. The optical properties of these two drugs, Alectinib and Rilpivirine, were deeply explored, firstly through the simulation of molecular structures, electrostatic potential, OPA/TPA and emission spectral properties and experiments on UV-vis spectra, fluorescence and cell imaging. It was found that Alectinib exhibited 7.8% of fluorescence quantum yield at the 450 nm excited wavelength, due to a larger electronic transition dipole moment (8.41 Debye), bigger charge transition quantity (0.682 e) and smaller reorganization energy (2821.6 cm-1). The stronger UV-vis spectra of Rilpivirine were due to a larger electron-hole overlap index (Sr: 0.733) and were also seen in CDD plots. Furthermore, Alectinib possessed obvious active two-photon absorption properties (δmaxTPA* ϕ = 201.75 GM), which have potential TPA imaging applications in bio-systems. Lastly, Alectinib and Rilpivirine displayed green fluorescence in HeLa cells, suggesting the potential ability for biological imaging. Investigation using theoretical and experimental methods is certainly encouraged, given the particular significance of developing integrated diagnosis and treatment.

Synthesis and Photophysical, Electrochemical, and DFT Studies of Piperidyl and Pyrrolidinyl Chalcones

Small organic molecules with interesting optical and electrochemical properties find applications as organic luminescent materials. In this work, we report the synthesis of novel chalcones with D-A-D and D-A-D-A architecture, followed by their optical, electrochemical, and computational studies. The absorption band of these compounds occurs at 360-480 nm with emission maxima appearing around 513-552 nm. The large Stokes shifts (Δλ) for all compounds (90-132 nm) suggest intramolecular charge transfer (ICT) in the excited states. The molar absorptivity and fluorescence quantum yields were found to be in the range of 1.7-4.26 × 104 M-1 cm-1 and 0.29-0.39, respectively. The electrochemical parameters were determined by using cyclic voltammetry (CV). Density functional theory (DFT) calculations of all compounds were made by using B3LYP/G (d,p) functionals in chloroform and were found to have a good correlation with experimental results. Preliminary studies of absorption, photoluminescence, CV, and their theoretical correlation suggest that these compounds may be optimized for their applications in optoelectronics, sensing, and bioimaging.

Photoswitchable Molecular Units with Tunable Nonlinear Optical Activity: A Theoretical Investigation

The first-, second-, and third-order molecular nonlinear optical properties, including two-photon absorption of a series of derivatives, involving two dithienylethene (DTE) groups connected by several molecular linkers (bis(ethylene-1,2-dithiolato)Ni- (NiBDT), naphthalene, quasilinear oligothiophene chains), are investigated by employing density functional theory (DFT). These properties can be efficiently controlled by DTE switches, in connection with light of appropriate frequency. NiBDT, as a linker, is associated with a greater contrast, in comparison to naphthalene, between the first and second hyperpolarizabilities of the "open-open" and the "closed-closed" isomers. This is explained by invoking the low-lying excited states of NiBDT. It is shown that the second hyperpolarizability can be used as an index, which follows the structural changes induced by photochromism. Assuming a Förster type transfer mechanism, the intramolecular excited-state energy transfer (EET) mechanism is studied. Two important parameters related to this are computed: the electronic coupling (VDA) between the donor and acceptor fragments as well as the overlap between the absorption and emission spectra of the donor and acceptor groups. NiBDT as a linker is associated with a low electronic coupling, VDA, value. We found that VDA is affected by molecular geometry. Our results predict that the linker strongly influences the communication between the open-closed DTE groups. The sensitivity of the molecular nonlinear optical properties could assist with identification of molecular isomers.

Theoretical characterization of two-photon fluorescent probes for nitric oxide detection: sensing mechanism, photophysical properties and protonation effects

Nitric oxide (NO) is an important signal molecule in biological systems and is correlated with many physiological processes and pathological diseases. To date, numerous fluorescent probes based on o-diamino aromatics have been designed and synthesized for NO detection utilizing the principle of photoinduced electron transfer (PET). However, the underlying PET mechanism has rarely been validated, and a systematic computational study on the photophysical properties is urgently desired. In this study, we used a theoretical protocol to comparatively investigate the sensing mechanism, photophysical properties and protonation effects of two emblematic probes NINO and PYSNO in aqueous solution, which combines a polarizable continuum model (PCM), time-dependent density functional theory (TD-DFT) and thermal vibration correlation function formalism (TVCF). Our findings reveal that the weak emission of NINO is due to activated PET with negative driving energy and blocked fluorescence with significant charge separation. In contrast, the poor luminescence of PYSNO is caused by the facilitated non-radiative dissipation, even though the fluorescence emission remains unobstructed. Although NINO has been successfully used in two-photon microscopy for detecting NO, we suggest that PYSNO possesses a superior two-photon absorption (TPA) cross section in the near-infrared region. The protonation effects suggest that both probes can function effectively in practical acidic lysosomal environments. Our study opens a new avenue for understanding the mechanism and predicting the properties of two-photon fluorescent probes for NO detection, thus aiding the rational design of efficient fluorescent sensors.

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.

Degenerate and non-degenerate two-photon absorption of coumarin dyes

Two-photon absorption (2PA) spectroscopy is a robust bioimaging tool that depends on the determined cross-sections (σ^2PA). The absorption of both photons occurs simultaneously with equivalent (degenerate) or different (non-degenerate) photon energies, D-2PA and ND-2PA, respectively. The former has been investigated experimentally and computationally for many systems, while the latter remains relatively unexplored computationally and limited experimentally. In this study, response theory using time-dependent density functional theory (TD-DFT) and the 2-state model (2SM) have been utilized to investigate σ^D-2PA and σ^ND-2PA for the excitation to the lowest energy singlet state (S₁) of coumarin, coumarin 6, coumarin 120, coumarin 307, and coumarin 343. Solvents involved were methanol (MeOH), chloroform (ClForm), and dimethylsulfoxide (DMSO), where the latter leads to the largest σ^2PA. Values of σ^2PA are largest for coumarin 6 and lowest for coumarin, which illustrates the effect of substituents. The 2SM clarifies how the largest cross-sections correspond to molecules with the largest transition dipole moments, μ₀₁. In general, σ^D-2SM computations agree with σ^D-2PA. Moreover, σ^ND-2SM are in qualitative agreement with σ^ND-2PA with comparable enhancement relative to σ^D-2PA. Overall, σ^ND-2PA are larger than σ^D-2PA where the increase is in the range of 22% to 49%, depending on the coumarin as well as the relative energies of the two photons. This work aids in future investigations into various fluorophores to understand their photophysical properties for ND-2PA.

Two-photon isomerization properties of donor-acceptor Stenhouse adducts

Donor-acceptor Stenhouse adducts (DASAs) are important photo-responsive molecules that undergo electrocyclic reactions after light absorption. From these properties, DASAs have received extensive attention as photo-switches with negative photochromism. Meanwhile, several photochemical applications require isomerization events to take place in highly localized volumes at variable depths. Such focused photoreactions can be achieved if the electronic excitation is induced through a non-linear optical process. In this contribution we describe DASAs substituted with extended donor groups which provide them with significant two-photon absorption properties. We characterized the photo-induced transformation of these DASAs from the open polymethinic form to their cyclopentenic isomer with the use of 800 nm femtosecond pulses. These studies verified that the biphotonic excitation produces equivalent photoreactions as linear absorbance. We also determined these DASAs' two-photon absorption cross sections from measurements of their photoconverted yield after biphotonic excitation. As we show, specific donor sections provide these systems with important biphotonic cross-sections as high as 615 GM units. Such properties make these DASAs among the most non-linearly active photo-switchable molecules. Calculations at the TDDFT level with the optimally tuned range-separated functional OT-CAM-B3LYP, together with quadratic response methods indicate that the non-linear photochemical properties in these molecules involve higher lying electronic states above the first excited singlet. This result is consistent with the observed relation between their two-photon chemistry and the onset of their short wavelength absorption features around 400 nm. This is the first report of the non-linear photochemistry of DASAs. The two-photon isomerization properties of DASAs extend their applications to 3D-photocontrol, non-linear lithography, variable depth birefringence, and localized drug delivery schemes.

Synergistic modification of end groups in Quinoxaline fused core-based acceptor molecule to enhance its photovoltaic characteristics for superior organic solar cells

The competence of organic solar cells (OSCs) could be enhanced by improving the light absorption capabilities as well as the open-circuit voltage (V_oc) of utilized molecules. To upgrade overall functionality of OSCs, seven new molecules were designed in this work using an end-cap alteration technique on Quinoxaline fused core-based non-fullerene acceptor (Qx-2) molecule. This technique is known to be quite advantageous in terms of improvement of the effectiveness and optoelectrical behavior of various OSCs. Critical parameters like the absorption maximum, frontier molecular orbitals, excitation energy, exciton binding energy, V_oc, and fill factor of molecules were considered for the molecules thus designed. All newly designed molecules showed outstanding improvement in optoelectronic as well as performance-related properties. Out of all scrutinized molecules, Q1 exhibited highest wavelength of absorption peak (λ_max = 779 nm) with the reduced band gap (1.90 eV), least excitation energy (E_x = 1.59 eV), along with the highest dipole moment (17.982950 D). Additionally, the newly designed compounds Q4, Q5, and Q6 exhibited significantly improved V_ocs that were 1.55, 1.47, and 1.50 eV accordingly, as compared to the 1.37 eV of Qx-2 molecule. These molecules also showed remarkable improvement in fill factor attributed to direct correspondence of V_oc with it. Inclusively, these results support the superiority of these newly developed molecules as prospective constituents of upgraded OSCs.

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.

Benchmarking two-photon absorption strengths of rhodopsin chromophore models with CC3 and CCSD methodologies: An assessment of popular density functional approximations

This work presents the investigations of the impact of an increasing electron correlation in the hierarchy of coupled-cluster methods, i.e., CC2, CCSD, and CC3, on two-photon absorption (2PA) strengths for the lowest excited state of the minimal rhodopsin's chromophore model-cis-penta-2,4-dieniminium cation (PSB3). For a larger chromophore's model [4-cis-hepta-2,4,6-trieniminium cation (PSB4)], CC2 and CCSD calculations of 2PA strengths were performed. Additionally, 2PA strengths predicted by some popular density functional theory (DFT) functionals differing in HF exchange contribution were assessed against the reference CC3/CCSD data. For PSB3, the accuracy of 2PA strengths increases in the following order: CC2 < CCSD < CC3, with the CC2 deviation from both higher-level methods exceeding 10% at 6-31+G* basis sets and 2% at aug-cc-pVDZ basis set. However, for PSB4, this trend is reversed and CC2-based 2PA strength is larger than the corresponding CCSD value. Among the DFT functionals investigated, CAM-B3LYP and BHandHLYP provide 2PA strengths in best compliance with reference data, however, with the error approaching an order of magnitude.

Interpretable Machine Learning of Two-Photon Absorption

Molecules with strong two-photon absorption (TPA) are important in many advanced applications such as upconverted laser and photodynamic therapy, but their design is hampered by the high cost of experimental screening and accurate quantum chemical (QC) calculations. Here a systematic study is performed by collecting an experimental TPA database with ≈900 molecules, analyzing with interpretable machine learning (ML) the key molecular features explaining TPA magnitudes, and building a fast ML model for predictions. The ML model has prediction errors of similar magnitude compared to experimental and affordable QC methods errors and has the potential for high-throughput screening as additionally validated with the new experimental measurements. ML feature analysis is generally consistent with common beliefs which is quantified and rectified. The most important feature is conjugation length followed by features reflecting the effects of donor and acceptor substitution and coplanarity.

Theoretical framework for achieving high V oc in non-fused non-fullerene terthiophene-based end-capped modified derivatives for potential applications in organic photovoltaics

Non-fused ring-based OSCs are an excellent choice, which is attributed to their low cost and flexibility in applications. However, developing efficient and stable non-fused ring-based OSCs is still a big challenge. In this work, with the intent to increase V _oc for enhanced performance, seven new molecules derived from a pre-existing A-D-A type A3T-5 molecule are proposed. Different important optical, electronic and efficiency-related attributes of molecules are studied using the DFT approach. It is discovered that newly devised molecules possess the optimum features required to construct proficient OSCs. They possess a small band gap ranging from 2.22-2.29 eV and planar geometries. Six of seven newly proposed molecules have less excitation energy, a higher absorption coefficient and higher dipole moment than A3T-5 in both gaseous and solvent phases. The A3T-7 molecule exhibited the maximum improvement in optoelectronic properties showing the highest λ _max at 697 nm and the lowest E _x of 1.77 eV. The proposed molecules have lower ionization potential values, reorganization energies of electrons and interaction coefficients than the A3T-5 molecule. The V _oc of six newly developed molecules is higher (V _oc ranging from 1.46-1.72 eV) than that of A3T-5 (V _oc = 1.55 eV). Similarly, almost all the proposed molecules except W6 exhibited improvement in fill factor compared to the A3T-5 reference. This remarkable improvement in efficiency-associated parameters (V _oc and FF) proves that these molecules can be successfully used as an advanced version of terthiophene-based OSCs in the future.

Vibrationally resolved two-photon electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy with two-photon excitation

Following up on our previous work on vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation [von Cosel et al., J. Chem. Phys. 147, 164116 (2017)], we present a combined theoretical and experimental study of two-photon-induced vibronic transitions in polyatomic molecules that are probed in the VIbrationally Promoted Electronic Resonance experiment using two-photon excitation (2P-VIPER). In order to compute vibronic spectra, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformations of time-domain correlation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method, while the time-dependent approach relies on the analytical evaluation of Gaussian moments within the harmonic approximation, including Duschinsky rotation effects. For the Coumarin 6 dye, two-dimensional 2P-VIPER experiments involving excitation to the lowest-lying singlet excited state (S₁) are presented and compared with corresponding one-photon VIPER spectra. In both cases, coumarin ring modes and a CO stretch mode show VIPER activity, albeit with different relative intensities. Selective pre-excitation of these modes leads to a pronounced redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. Theoretical analysis underscores the role of interference between Franck-Condon and Herzberg-Teller effects in the two-photon experiment, which is at the root of the observed intensity distribution.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

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.

Dissecting conjugation and electronic effects on the linear and non-linear optical properties of rhenium(I) carbonyl complexes

Herein, we report a theoretical and experimental analysis of the conjugation and electronic effects on the one-photon (1PA) and two-photon absorption (2PA) properties of a series of Re(I) carbonyl complexes with terpyridine-based ligands. An excellent agreement was obtained between the calculated and experimental 2PA spectra of the κ2N-terpyridine tricarbonyl complexes (1a-b), with 2PA cross sections reaching up to ca. 40 GM in DMF. By stepwise lowering the conjugation length in the terpy ligand and changing the local symmetry around the metal centre, we show that conjugation and delocalisation play a major role in increasing 2PA cross sections, and that the character of the excited states does not directly enhance the non-linear properties of these complexes-contrary to the results observed in 1PA. Altogether, these results give valuable guidelines towards more efficient two-photon-absorbing coordination complexes of Re(I), with potential applications in photodynamic therapy and two-photon imaging.

Impact of end-capped modification of MO-IDT based non-fullerene small molecule acceptors to improve the photovoltaic properties of organic solar cells

Density functional theory, along with its time dependent computational approach were employed in order to fine tune the photovoltaic attributes along with the efficiency of the MO-IDIC-2F molecule. Thus, five new molecules were designed by substitution of the different notable acceptor fragments in the MO-IDIC-2F molecule, along with the addition of the "[1, 2, 5] thiadiazolo[3,4-d] pyridazine" spacer moieties between donor core and newly substituted acceptor groups. In this research work, various photovoltaic properties, which could affect the efficiency of an organic chromophores, such as bandgap, oscillator strength, dipole moment, binding energy, light-harvesting efficiency, etc. were studied. All the newly proposed molecules demonstrated significantly improved outcomes in comparison to that of the reference molecule, in their absorption spectrum, excitation, as well as binding energy values, etc. In order to confirm the results of optoelectronic properties, density of states, transition density matrix, and electrostatic potential analyses of molecules were also performed, which supported our computational findings. All of the results confirmed the high potential of all the newly proposed molecules for the development of improved OSCs.

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.

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).