Two-photon absorption spectroscopy of trans-stilbene, cis-stilbene, and phenanthrene: Theory and experiment

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.

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.

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.

Two- and one-photon absorption spectra of aqueous thiocyanate anion highlight the role of symmetry in the condensed phase

We present the two-photon absorption (2PA) spectrum of aqueous thiocyanate calculated using high-level quantum-chemistry methods. The 2PA spectrum is compared to the one-photon absorption (1PA) spectrum computed using the same computational protocol. Although the two spectra probe the same set of electronic states, the intensity patterns are different, leading to an apparent red-shift of the 2PA spectrum relative to the 1PA spectrum. The presented analysis explains the intensity patterns and attributes the differences between the 1PA and 2PA spectra to the native symmetry of isolated SCN  - , which influences the spectra in the low-symmetry solvated environment. The native symmetry also manifests itself in variations of the polarization ratio (e.g., parallel vs. perpendicular cross sections) across the spectrum. The presented results highlight the potential of 2PA spectroscopy and high-level quantum-chemistry methods in studies of condensed-phase phenomena.

4a,4b-Dihydrophenanthrene → cis-stilbene photoconversion: TD-DFT/DFT study

CONTEXT

DHP → CS photoconversion was analyzed in terms of electron density redistribution for the first time. The following explanation for the non-recovery of the C4a-C4b bond upon CS relaxation is proposed: during this process, the Coulomb repulsion energy between these pairs of atoms increases by almost one and a half times, and their bonding by an electron at LUMO is insufficient to recover the C4a-C4b bond. According to calculations, upon CS relaxation, the linker connecting the benzene rings undergoes significant structural changes. In this case, the distance between the C4a and C4b atoms increases from 3.00 Å to 3.28 Å. Calculations showed that the C4a-C4b vibration of the DHP bond has a very low intensity. Therefore, thermal motion does not contribute to the rupture of this bond.

METHODS

All calculations were performed using the Gaussian16 software package at the B3LYP/6-311 +  + G(d,p)/IEFPCM theory level. B3LYP was the only hybrid functional supported by Gaussian16, which ensured the cleavage of the C4a-C4b bond of DHP while optimizing its S1 excited state. A quantitative description of the redistribution of electron density in the studied conformers was carried out using the analysis of the NPA of atomic charges. Cyclohexane was used as an implicitly specified non-polar solvent. Visualization of molecular orbitals, and electron densities, as well as plotting of calculated IR spectra, were performed using the Gaussview6 software package.

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

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

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.

Pressure induced modification of the electronic properties of stilbene by two-photon spectroscopy

Carbon nanothreads are the most exciting carbon based nanomaterials recently discovered. Obtained by compressing aromatics around 20 GPa, they are characterized by potentially exceptional mechanical properties. The reaction mechanisms have been partly elucidated through computational studies and x-ray diffraction experiments. However, in all these studies, the electronic modifications to which the molecule is subjected with increasing pressure are neglected as also if, and to which extent, the electronic excited states are involved in the high-pressure reactivity. In fact, the pressure increase induces remarkable changes in the electronic properties of molecular crystals, which are often directly related to the reaction's onset and path. We report the pressure evolution of the two-photon induced emission spectrum of crystalline stilbene, the archetype of a class of molecules from which double-core nanothreads are obtained, with the twofold purpose of gaining insight into the reaction mechanism and monitoring if the structural changes observed in x-ray diffraction studies have a detectable counterpart in the electronic properties of the system. The freezing of the spectral diffusion observed on rising pressure is ascribed to a hampered conformational rearrangement because of the larger stiffness of the local environment. The transition to the high pressure phase where the nanothreads form is revealed by the slope change of the pressure shift of all spectral components, while the progressive intensification with pressure of the 0-0 transition suggests a strengthening of the ethylenic bond favoring the charge delocalization on the benzene moieties, which is likely the trigger of the chemical instability.

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.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S₀/T₁ minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S₀/S₁ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

E/Z Molecular Photoswitches Activated by Two-Photon Absorption: Comparison between Different Families

Nonlinear optical techniques as two-photon absorption (TPA) have raised relevant interest within the last years due to the capability to excite chromophores with photons of wavelength equal to only half of the corresponding one-photon absorption energy. At the same time, its probability being proportional to the square of the light source intensity, it allows a better spatial control of the light-induced phenomenon. Although a consistent number of experimental studies focus on increasing the TPA cross section, very few of them are devoted to the study of photochemical phenomena induced by TPA. Here, we show a design strategy to find suitable E/Z photoswitches that can be activated by TPA. A theoretical approach is followed to predict the TPA cross sections related to different excited states of various photoswitches’ families, finally concluding that protonated Schiff-bases (retinal)-like photoswitches outperform compared to the others. The donor-acceptor substitution effect is therefore rationalized for the successful TPA activatable photoswitch, in order to maximize its properties, finally also forecasting a possible application in optogenetics. Some experimental measurements are also carried out to support our conclusions.

Molecular photoswitches in aqueous environments

Molecular photoswitches enable dynamic control of processes with high spatiotemporal precision, using light as external stimulus, and hence are ideal tools for different research areas spanning from chemical biology to smart materials. Photoswitches are typically organic molecules that feature extended aromatic systems to make them responsive to (visible) light. However, this renders them inherently lipophilic, while water-solubility is of crucial importance to apply photoswitchable organic molecules in biological systems, like in the rapidly emerging field of photopharmacology. Several strategies for solubilizing organic molecules in water are known, but there are not yet clear rules for applying them to photoswitchable molecules. Importantly, rendering photoswitches water-soluble has a serious impact on both their photophysical and biological properties, which must be taken into consideration when designing new systems. Altogether, these aspects pose considerable challenges for successfully applying molecular photoswitches in aqueous systems, and in particular in biologically relevant media. In this review, we focus on fully water-soluble photoswitches, such as those used in biological environments, in both in vitro and in vivo studies. We discuss the design principles and prospects for water-soluble photoswitches to inspire and enable their future applications.

Electronic Structure of Liquid Alkanes: A Representative Case of Liquid Hexanes and Cyclohexane Studied Using Polarization-Dependent Two-Photon Absorption Spectroscopy

Two-photon absorption (2PA) spectra of liquid cyclohexane and hexanes are reported for the energy range 6.4-8.5 eV (177-145 nm), providing detailed information about their electronic structures in bulk liquid. Using a broadband pump-probe fashion, we measured the continuous 2PA spectra by simultaneous absorption of a 266 nm (4.6 eV) pump photon and one UV-vis probe photon from the white-light continuum (1.8-3.9 eV). Theoretical one-photon absorption (1PA) and 2PA cross sections of isolated gas phase molecules are computed by the equation of motion coupled-cluster method with single and double substitutions (EOM-CCSD) to substantiate the assignment of the experimental spectra, and the natural transition orbital (NTO) analysis provides visualization of the participating orbitals in a transition. Our analysis suggests that upon solvation transitions at the lowest excitation energy involving promotion of electron to the 3s Rydberg orbitals are blue-shifted (∼0.55 eV for cyclohexane and ∼0.18 eV for hexanes) to a greater extent as compared to those involving other Rydberg orbitals, which is similar to the behavior observed for water and alcohols. All other transitions experience negligible (cyclohexane) or minor red-shift by ∼0.15-0.2 eV (hexane) upon solvation. In both alkanes, the spectra are entirely dominated by Rydberg transitions: the most intense bands in 1PA and 2PA spectra are due to the excitation of electrons to the Rydberg "p" and "d" type orbitals, respectively, although one transition terminating in the 3s Rydberg has significant 2PA strength. This work demonstrates that the gas phase electronic transition properties in alkanes are not significantly altered upon solvation. In addition, electronic structure calculations using an isolated-molecule framework appear to provide a reasonable starting point for a semiquantitative picture for spectral assignment and also to analyze the solvatochromic shifts for liquid phase absorption spectra.

Direct Observation of Different One- and Two-Photon Fluorescent States in a Pyrrolo[3,2-b]pyrrole Fluorophore

Two-photon fluorophores are frequently employed to obtain superior spatial resolution in optical microscopy applications. To guide the rational design of these molecules, a detailed understanding of their excited-state deactivation pathways after two-photon excitation is beneficial, especially to assess the often-assumed presumption that the one- and two-photon excited-state dynamics are similar after excitation. Here, we showcase the breakdown of this assumption for one- and two-photon excitation of a centrosymmetric pyrrolo[3,2-b]pyrrole chromophore by combining time-resolved fluorescence and broadband femtosecond transient absorption spectroscopy. Compared to one-photon excitation, where radiative decay dominates the photodynamics, two-photon excitation leads to dynamics arising from increased nonradiative decay pathways. These different photodynamics are manifest to different quantum yields, thus highlighting the types of time-resolved studies described here to be valuable guideposts in the design of two-photon fluorophores for imaging applications.

How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core–valence separation

We present a novel approach with robust convergence of the response equations for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework.

Multistate Multiconfiguration Quantum Chemical Computation of the Two-Photon Absorption Spectra of Bovine Rhodopsin

Recently, progress in IR sources has led to the discovery that humans can detect infrared (IR) light. This is hypothesized to be due to the two-photon absorption (TPA) events promoting the retina dim-light rod photoreceptor rhodopsin to the same excited state populated via one-photon absorption (OPA). Here, we combine quantum mechanics/molecular mechanics and extended multiconfiguration quasi-degenerate perturbation theory calculations to simulate the TPA spectrum of bovine rhodopsin (Rh) as a model for the human photoreceptor. The results show that the TPA spectrum of Rh has an intense S₀ → S₁ band but shows also S₀ → S₂ and S₀ → S₃ transitions whose intensities, relative to the S₀ → S₁ band, are significantly increased when compared to the corresponding bands of the OPA spectrum. In conclusion, we show that IR light in the 950 nm region can be perceived by rod photoreceptors, thus supporting the two-photon origin of the IR perception. We also found that the same photoreceptor can perceive red (i.e., close to 680 nm) light provided that TPA induces population of S₂.

Quantum cutting using organic molecules

Ab initio based study of organic molecular based quantum cutting with predicted efficiency of 1.2, and proposition of design criteria.

Pyridinium Analogues of Green Fluorescent Protein Chromophore: Fluorogenic Dyes with Large Solvent-Dependent Stokes Shift

Novel fluorogenic dyes based on the GFP chromophore are developed. The compounds contain a pyridinium ring instead of phenolate and feature large Stokes shifts and solvent-dependent variations in the fluorescence quantum yield. Electronic structure calculations explain the trends in solvatochromic behavior in terms of the increase of the dipole moment upon excited-state relaxation in polar solvents associated with the changes in bonding pattern in the excited state. A unique combination of such optical characteristics and lipophilic properties enables using one of the new dyes for imaging the membrane structure of endoplasmic reticulum. An extremely high photostability (due to a dynamic exchange between the free and absorbed states) and selectivity make this compound a promising label for this type of cellular organelles.

Revisiting absorption and electronic circular dichroism spectra of cholesterol in solution: a joint experimental and theoretical study

Cholesterol is doubtless one of the most studied bio-molecules, which unfortunately features low emitting properties, precluding its in vivo study by fluorescence experiments. The design of fluorescent analogues of cholesterol is thus an appealing challenge in biochemistry, which simultaneously requires minor changes in its chemical structure (to retain main biological properties) and considerable enhancement of light emission. To this aim, the photochemical behaviour of the native molecule has to be deeply understood. In this work, we focused our attention on the electronic absorption of cholesterol in several common organic solutions, combining experimental (through ultraviolet-visible and electronic circular dichroism spectroscopy) and theoretical approaches (at the time-dependent density functional theory level) in order to solve the important discrepancies previously reported in the literature on the maximum absorption wavelengths and on the nature (Rydberg and/or π → π*) of the associated electronic transition.