Two-photon absorption in solution by means of time-dependent density-functional theory and the polarizable continuum model

Enhancing Efficiency of Dye Sensitized Solar Cells by Coinage Metal Doping of Cyanidin-Silver Trimer Hybrids at TiO2 Support Based on Theoretical Study

Identification of a natural-based sensitizer with optimal stability and efficiency for dye-sensitized solar cell (DSSC) application remains a challenging task. Previously, we proposed a new class of sensitizers based on bio-nano hybrids. These systems composed of natural cyanidin dyes interacting with silver nanoclusters (NCs) have demonstrated enhanced opto-electronic and photovoltaic properties. In this study, we explore the doping of silver nanocluster within a cyanidin-Ag3 hybrid employing Density Functional Theory (DFT) and its time-dependent counterpart (TDDFT). Specifically, we investigate the influence of coinage metal atoms (Au and Cu) on the properties of the cyanidin-Ag3 system. Our findings suggest that cyanidin-Ag2Au and cyanidin-AgAuCu emerge as the most promising candidates for improved light harvesting efficiency, increased two-photon absorption, and strong coupling to the TiO2 surface. These theoretical predictions suggest the viability of replacing larger silver NCs with heterometallic trimers such as Ag2Au or AgAuCu, presenting new avenues for utilizing bio-nano hybrids at the surface for DSSC application.

Frequency-Dependent Quadratic Response Properties and Two-Photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory

We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing comprehensive insights into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross sections of transition [ns1S0 → (n + 1)s1S0] of Ga+ and In+, which are suggested as candidates for new ion clocks. As our implementation allows for the use of nonrelativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code and show that the differences between CC and EOMCC response are in general smaller than 5% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models, such as density functional theory for higher-order properties.

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.

Model systems for dye-sensitized solar cells: cyanidin-silver nanocluster hybrids at TiO2 support

Theoretical study of structural, optical, and photovoltaic properties of novel bio-nano hybrids (dye-nanocluster), as well as at TiO2 surface model support is presented in the context of the application for dye-sensitized solar cells (DSSC). A group of anthocyanidin dyes (pelargonidin, cyanidin, delphinidin, peonidin, petunidin, and malvidin) represented by cyanidin covalently bound to silver nanoclusters (NCs) with even or odd number of valence electrons have been investigated using DFT and TDDFT approach. The key role of nanoclusters as acceptors in hybrids cyanidin-NC has been shown. The nanoclusters with an even number of valence electrons are suitable as acceptors in hybrids. The interaction of bio-nano (cyanidin-NC) hybrid with the TiO2 surface model has been investigated in the context of absorption in near-infrared (NIR) and charge separation due to donor and acceptor subunits. Altogether, the theoretical concept serves to identify the key steps in the design of novel solar cells based on bio-nano hybrids at TiO2 surface for DSSC application.

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.

Theoretical study and application of 2-phenyl-1,3,4-thiadiazole derivatives with optical and inhibitory activity against SHP1

Src homology-2 domain-containing protein tyrosine phosphatase 1 (SHP1) is mainly restricted to hematopoietic and epithelial cells and widely accepted as a convergent node for oncogenic cell-signaling cascades. The development of efficient methods for rapidly tracing and inhibiting the SHP1 activity in complex biological systems is of considerable significance for advancing the integration of diagnosis and treatment of the related disease. With this aim, we designed and synthesized five 2-phenyl-1,3,4-thiadiazole derivatives (PT2, PT5, PT8, PT9 and PT10) here based on the reported SHP1 inhibitors (PT1, PT3, PT4, PT6 and PT7). The photophysical properties and inhibitory activities of these 2-phenyl-1,3,4-thiadiazole derivatives (PT1-PT10) against SHP1 were thoroughly studied from the theoretical simulation and experimental application aspects. The representative compound PT10 exhibited a larger quantum yield than the other molecules because of the smaller geometric relaxation and reorganization energy of the excited state, which was consistent with the results from the fluorescence experiments in organic solvents. In addition, PT10 showed a selective fluorescence response for SHP1 activity and low cytotoxicity in HeLa cells. Lastly, it indicated the potential application in two-photon cell fluorescence imaging in the future according to the calculated excellent two-photon absorption properties. In this contribution, firstly, we offered the fluorescent and activated molecule PT10 against SHP1, which achieved the integration of visualization and inhibitory activity of SHP1 preliminarily at the enzyme molecular level.

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

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

The Challenge of Accurate Computation of Two-Photon Absorption Properties of Organic Chromophores in the Condensed Phase

Two strategies are applied to evaluate the effect of the environment on the two-photon absorption (TPA) cross sections for two characteristic excited states of C₂H₄ upon complexation with H₂O. The supermolecular strategy provides the reference complexation-induced shifts and uses either the EOM-CCSD or ADC(2) method. The embedding strategy is based on frozen-density-embedding theory (FDET) and uses only fundamental constants. The TPA cross sections from high-level supermolecular calculations are extremely basis-set-sensitive. Literature data and the present study indicate that accuracy of the absolute TPA cross sections below 100 atomic units and their shifts below 10 atomic units remains a challenge. The obtained FDET results show a similar basis-set behavior. For the largest basis set (d-aug-cc-pVQZ), TPA cross sections obtained from these two strategies are in excellent agreement. The complexation-induced shifts have the correct sign of the effect and a small (12-33%) relative error in magnitude. The deviations of the FDET-derived shifts from the reference are of similar magnitude as the reliability threshold of the reference shifts.

Responsive mechanism of 2-fluoro-5-nitrobenzoate based two-photon fluorescent probes for H2Sn detection: A theoretical perspective

Two-photon fluorescent probes with large two-photon absorption (TPA) cross sections have shown wide applications in biomedical domain. However, both the species and amounts of high efficient probes are far from meeting the requirements, one main reason is that the relationship between the molecular structures and the responsive mechanisms are not clear and theoretical framework in this field is not perfect. In this work, the photophysical properties including one- and two-photon absorption and emission of three newly synthesized fluorescent probes for hydrogen polysulfide (H₂S_n) detection are investigated by density functional theory and time-dependent density functional theory with the polarizable continuum model in different solvents. Results indicate that the enhanced fluorescent intensity and enlarged TPA cross section can be found when the probes reacted with H₂S_n. Moreover, the OPA intensity is largest and its fluorescent intensity is largely enhanced when detecting H₂S_n for Pro2, this verifies its superior performance in the detection of H₂S_n than Pro1 and Pro 3. Furthermore, the inner mechanism for the increase of TPA cross section is revealed, the responsive mechanisms for photo induced electron transfer (PET) and fluorescence resonance energy transfer (FRET) processes are revealed through analyzing the energies and distributions of frontier orbitals. Our calculations provide theoretical perspectives for experimental measurements and could sever as a useful reference for developing advanced probes in biomedical fields.

Enhancement of one- and two-photon absorption and visualization of intramolecular charge transfer of pyrenyl-contained derivatives

To further improve the pyrenyl-contained derivatives two-photon absorption (TPA) and third-order nonlinear optical (NLO) properties, three steps of optimization are employed based on experimental molecule PCVS-B: heteroatomic substitution, exchanging the position of double bonds and adding a branch. The contributions of π electrons to localized orbital locators and Mayer bond orders (LOL-π and I_AB^π) show that the second step can enhance the chemical interaction between pyrenyl and the branched-chain. Two visual methods of charge density difference (CDD) and transition density matrix (TDM) are combined to intuitively analyze the intramolecular charge transfer (ICT) process of one (two) photon absorption; results show that both following two steps can increase the degree of ICT on the conjugated plane of the pyrenyl. The sum over state (SOS) model was used to find out the dominant two-photon transition process. The difference between the dipole moments obtained by the McRae equation is applied to the three-state model, revealing the inherent law of the second static hyperpolarizability.

Ligand shell size effects on one- and two-photon excitation fluorescence of zwitterion functionalized gold nanoclusters

Gold nanoclusters (Au NCs) are an emerging class of luminescent nanomaterials but still suffer from moderate photoluminescence quantum yields. Recent efforts have focused on tailoring their emission properties. Introducing zwitterionic ligands to cap the metallic kernel is an efficient approach to enhance their one-photon excitation fluorescence intensity. In this work, we extend this concept to the nonlinear optical regime, i.e., two-photon excitation fluorescence. For a proper comparison between theory and experiment, both ligand and solvent effects should be considered. The effects of ligand shell size and of aqueous solvent on the optical properties of zwitterion functionalized gold nanoclusters have been studied by performing quantum mechanics/molecular mechanics (QM/MM) simulations.

Enhanced two-photon absorption of ligated silver and gold nanoclusters: theoretical and experimental assessments

Ligated silver and gold nanoclusters belonging to a non-scalable size regime with molecular-like discrete electronic states represent an emerging class of extremely interesting optical materials. Nonlinear optical (NLO) characteristics of such quantum clusters have revealed remarkable features. The two-photon absorption (TPA) cross section of ligated noble metal nanoclusters is several orders of magnitude larger than that of commercially-available dyes. Several such case studies on NLO properties of ligated silver and gold nanoclusters have been reported, making them promising candidates for various bio-imaging techniques such as multiphoton-excited fluorescence microscopy. However, the structure-property relationship is of great importance and needs to be properly addressed in order to design new nonlinear optical materials. Using small ligated silver nanoclusters as test systems, we illustrate how theoretical approaches together with experimental findings can contribute to the understanding of structure-property relationships that might ultimately guide nanocluster synthesis.

The Diradical-Dication Strategy for BODIPY- and Porphyrin-Based Dyes with Near-Infrared Absorption Maxima from 1070 to 2040 nm

Four stable boron dipyrromethene (BODIPY)- and porphyrin-based bis-arylamine diradical dications were synthesized by two-electron oxidation of their neutral molecules. The two BODIPY-based dications have open-shell singlet ground states. UV/Vis absorption spectra of all four dications showed large redshifts in the NIR region compared to their neutral precursors with absorption maxima at 1274 and 1068 nm for the two BODIPY-based dications and 1746 and 2037 nm for the two porphyrin-based dications. Thus, two new types of NIR dyes with longer wavelengths are provided by the diradical-dication strategy, which can be applied for the generation of other NIR dyes with a range of different chromophores and auxochromes.

Why Do Silver Trimers Intercalated in DNA Exhibit Unique Nonlinear Properties That Are Promising for Applications?

Our investigation of one-photon absorption (OPA) and nonlinear optical (NLO) properties such as two-photon absorption (TPA) of silver trimer intercalated in DNA based on TDDFT approach allowed us to propose a mechanism responsible for large TPA cross sections of such NLO-phores. We present a concept that illustrates the key role of quantum cluster as well as of nucleotide bases from the immediate neighborhood. For this purpose, different surroundings consisting of guanine-cytosine and adenine-thymine such as (GCGC) and (ATAT) have been investigated that are exhibiting substantially different values of TPA cross sections. This has been confirmed by extending the immediate surroundings as well as using the two-layer quantum mechanics/molecular mechanics (QM/MM) approach. We focus on the cationic closed-shell system and illustrate that the neutral open-shell system shifts OPA spectra into the NIR regime, which is suitable for applications. Thus, in this contribution, we propose novel NLO-phores inducing large TPA cross sections, opening the route for multiphoton imaging.

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

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

Ligand-core NLO-phores: a combined experimental and theoretical approach to the two-photon absorption and two-photon excited emission properties of small-ligated silver nanoclusters

We report a combined experimental and theoretical study of the two-photon absorption and excited emission properties of monodisperse ligand stabilized Ag₁₁, Ag₁₅ and Ag₃₁ nanoclusters in aqueous solutions. The nanoclusters were synthesized using a cyclic reduction under oxidative conditions and separated by vertical gel electrophoresis. The two-photon absorption cross-sections of these protected noble metal nanoclusters measured within the biologically attractive 750-900 nm window are several orders of magnitude larger than that reported for commercially available standard organic dyes. The two-photon excited fluorescence spectra are also presented for excitation wavelengths within the same excitation spectral window. They exhibit size-tunability. Because the fundamental photophysical mechanisms underlying these multiphoton processes in ligand protected clusters with only a few metal atoms are not fully understood yet, a theoretical model is proposed to identify the key driving elements. Elements that regulate the dipole moments and the nonlinear optical properties are the nanocluster size, its structure and the charge distribution on both the metal core and the bound ligands. We coined this new class of NLO materials as "Ligand-Core" NLO-phores.

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

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

Two-photon absorption of fluorescent protein chromophores incorporating non-canonical amino acids: TD-DFT screening and classical dynamics

Two-photon spectroscopy of fluorescent proteins is a powerful bio-imaging tool characterized by deep tissue penetration and little damage. However, two-photon spectroscopy has lower sensitivity than one-photon microscopy alternatives and hence a protein with a large two-photon absorption cross-section is needed. We use time-dependent density functional theory (TD-DFT) at the B3LYP/6-31+G(d,p) level of theory to screen twenty-two possible chromophores that can be formed upon replacing the amino-acid Tyr66 that forms the green fluorescent protein (GFP) chromophore with a non-canonical amino acid. A proposed chromophore with a nitro substituent was found to have a large two-photon absorption cross-section (29 GM) compared to other fluorescent protein chromophores as determined at the same level of theory. Classical molecular dynamics are then performed on a nitro-modified fluorescent protein to test its stability and study the effect of the conformational flexibility of the chromophore on its two-photon absorption cross-section. The theoretical results show that the large cross-section is primarily due to the difference between the permanent dipole moments of the excited and ground states of the nitro-modified chromophore. This large difference is maintained through the various conformations assumed by the chromophore in the protein cavity. The nitro-derived protein appears to be very promising as a two-photon absorption probe.

Two-photon absorption of ligand-protected Ag15 nanoclusters. Towards a new class of nonlinear optics nanomaterials

Theoretical and experimental two-photon absorption cross sections of thiolated small silver cluster Ag₁₅L₁₁ exhibiting extraordinary large TPA.

Theoretical investigation on the one- and two-photon responsive behavior of fluoride ion probes based on diketopyrrolopyrrole and its π-expanded derivatives

The intrinsic two-photon absorption properties of the studied fluoride anion probes and their corresponding reaction products are systematically investigated.

Calculation of One-Photon and Two-Photon Absorption Spectra of Porphyrins Using Time-Dependent Density Functional Theory

Time-dependent density functional theory has been used to calculate the one-photon and two-photon absorption spectra of free-base porphyrin, a substituted zinc porphyrin, and a zinc porphyrin dimer, in order to assess the validity of the method to reproduce the large increase in the two-photon absorption (TPA) cross-section for the dimer. Three hybrid functionals with varying amounts of exact exchange were tested, and the calculated one-photon absorption spectra for each of the molecular systems were shown to be in qualitative agreement with the measured spectra. All three functionals predict a large enhancement in the TPA cross-section for the dimer relative to the monomer, in agreement with experimental results. However, because of the sensitivity of the resonance enhancement factor to small differences in the relevant state energies, quantitative prediction of the TPA cross-section by this method is still a challenge.

Solvent-Dependent Non-Linear Optical Properties of 5,5′-Disubstituted-2,2′-bipyridine Complexes of Ruthenium(II): A Quantum Chemical Perspective

In this research article, we reported solvent effects on non-linear optical (NLO) properties of 5,5′-disubstituted-2,2′-bipyridine complexes of ruthenium. The polarizability (α) and hyperpolarizability (β) were calculated in the gas phase. Benzene (ϵ (dielectric constant) = 2.3), THF (ϵ = 7.52), dichloromethane (ϵ = 8.93), acetone (ϵ = 21.01), methanol (ϵ = 33.00), and water (ϵ = 80.10) were used by density functional theory. These solvents cover a wide range of polarities. The results of theoretical investigation showed that the non-linear optical properties were significantly increased with the increase in solvent polarity. The results of this study also showed that similarly to structural modifications, polarity of the medium may play a significant role in modulating the NLO properties.

Assessment of mode-mixing and Herzberg-Teller effects on two-photon absorption and resonance hyper-Raman spectra from a time-dependent approach

A time-dependent approach is presented to simulate the two-photon absorption (TPA) and resonance hyper-Raman scattering (RHRS) spectra including Duschinsky rotation (mode-mixing) and Herzberg-Teller (HT) vibronic coupling effects. The computational obstacles for the excited-state geometries, vibrational frequencies, and nuclear derivatives of transition dipole moments, which enter the expressions of TPA and RHRS cross sections, are further overcome by the recently developed analytical excited-state energy derivative approaches in the framework of time-dependent density functional theory. The excited-state potential curvatures are evaluated at different levels of approximation to inspect the effects of frequency differences, mode-mixing and HT on TPA and RHRS spectra. Two types of molecules, one with high symmetry (formaldehyde, p-difluorobenzene, and benzotrifluoride) and the other with non-centrosymmetry (cis-hydroxybenzylidene-2,3-dimethylimidazolinone in the deprotonated anion state (HDBI(-))), are used as test systems. The calculated results reveal that it is crucial to adopt the exact excited-state potential curvatures in the calculations of TPA and RHRS spectra even for the high-symmetric molecules, and that the vertical gradient approximation leads to a large deviation. Furthermore, it is found that the HT contribution is evident in the TPA and RHRS spectra of HDBI(-) although its one- and two-photon transitions are strongly allowed, and its effect results in an obvious blueshift of the TPA maximum with respect to the one-photon absorption maximum. With the HT and solvent effects getting involved, the simulated blueshift of 1291 cm(-1) agrees well with the experimental measurement.

Two-Photon Absorption in Fluorescent Protein Chromophores: TDDFT and CC2 Results

Two-photon spectroscopy of fluorescent proteins is a powerful bioimaging tool. Considerable effort has been made to measure absolute two-photon absorption (TPA) for the available fluorescent proteins. Being a technically involved procedure, there is significant variation in the published experimental measurements even for the same protein. In this work, we present a time-dependent density functional theory (TDDFT) study on isolated chromophores comparing the ability of four functionals (PBE0, B3LYP, CAM-B3LYP, and LC-BLYP) combined with the 6-31+G(d,p) basis set to reproduce averaged experimental TPA energies and cross sections. The TDDFT energies and TPA cross sections are also compared to corresponding CC2/6-31+G(d,p) results for excitation to S1 for the five smallest chromophores. In general, the computed TPA energies are less functional dependent than the TPA cross sections. The variation between functionals is more pronounced when higher-energy transitions are studied. Changes to the conformation of a chromophore are shown to change the TPA cross-section considerably. This adds to the difficulty of comparing an isolated chromophore to the one embedded in the protein environment. All functionals considered give moderate agreement with the corresponding CC2 results; in general, the TPA cross sections determined by TDDFT are 1.5-10 times smaller than the corresponding CC2 values for excitation to S1. LC-BLYP and CAM-B3LYP give erroneously large TPA cross sections in the higher-energy regions. On the other hand, B3LYP and PBE0 yield values that are of the same order of magnitude and in some cases very close to the averaged experimental data. Thus, based on the results reported here, B3LYP and PBE0 are the preferred functionals for screening chromphores for TPA. However, at best, TDDFT can be used to semiquantitatively scan chromophores for potential TPA probes and highlight spectroscopic peaks that could be present in the mature protein.

Chemical control of channel interference in two-photon absorption processes

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

Molecular structure-optical property relationships for a series of non-centrosymmetric two-photon absorbing push-pull triarylamine molecules

This article reports on a comprehensive study of the two-photon absorption (2PA) properties of six novel push-pull octupolar triarylamine compounds as a function of the nature of the electron-withdrawing groups. These compounds present an octupolar structure consisting of a triarylamine core bearing two 3,3′-bis(trifluoromethyl)phenyl arms and a third group with varying electron-withdrawing strength (H < CN < CHO < NO2 < Cyet < Vin). The 2PA cross-sections, measured by using the femtosecond open-aperture Z-scan technique, showed significant enhancement from 45 up to 125 GM for the lowest energy band and from 95 up to 270 GM for the highest energy band. The results were elucidated based on the large changes in the transition and permanent dipole moments and in terms of (i) EWG strength, (ii) degree of donor-acceptor charge transfer and (iii) electronic coupling between the arms. The 2PA results were eventually supported and confronted with theoretical DFT calculations of the two-photon transition oscillator strengths.

25th anniversary article: Design of polymethine dyes for all-optical switching applications: guidance from theoretical and computational studies

All-optical switching--controlling light with light--has the potential to meet the ever-increasing demand for data transmission bandwidth. The development of organic π-conjugated molecular materials with the requisite properties for all-optical switching applications has long proven to be a significant challenge. However, recent advances demonstrate that polymethine dyes have the potential to meet the necessary requirements. In this review, we explore the theoretical underpinnings that guide the design of π-conjugated materials for all-optical switching applications. We underline, from a computational chemistry standpoint, the relationships among chemical structure, electronic structure, and optical properties that make polymethines such promising materials.

Solvent effects on nonlinear optical response of certain tetrammineruthenium(II) complexes of modified 1,10-phenanthrolines

In this research paper, we have reported solvent effects on nonlinear optical properties of tetrammineruthenium(II) complexes of modified 1,10-phenanthrolines. Polarizability and hyperpolarizability were calculated in the gas phase, benzene (ε = 2.3), THF (ε = 7.52), dichloromethane (ε = 8.93), acetone (ε = 21.01), methanol (ε = 33.00), acetonitrile (ε = 36.64), and water (ε = 80.10) using density functional theory. These solvents cover a wide range of polarities. The results of theoretical investigation have shown that nonlinear optical properties significantly increased with the increase of solvent polarity. Solvent strongly affected hyperpolarizability as compared with polarizability. Nonlinear optical properties were also changed by the change of functional. Hyperpolarizability significantly changed with the change of functional as compared with polarizability. The results of this study indicate that like structural modification, polarity of the medium can significantly change the nonlinear optical properties.

The role of molecular conformation and polarizable embedding for one- and two-photon absorption of disperse orange 3 in solution

Solvent effects on the one- and two-photon absorption (1PA and 2PA) of disperse orange 3 (DO3) in dimethyl sulfoxide (DMSO) are studied using a discrete polarizable embedding (PE) response theory. The scheme comprises a quantum region containing the chromophore and an atomically granulated classical region for the solvent accounting for full interactions within and between the two regions. Either classical molecular dynamics (MD) or hybrid Car-Parrinello (CP) quantum/classical (QM/MM) molecular dynamics simulations are employed to describe the solvation of DO3 in DMSO, allowing for an analysis of the effect of the intermolecular short-range repulsion, long-range attraction, and electrostatic interactions on the conformational changes of the chromophore and also the effect of the solute-solvent polarization. PE linear response calculations are performed to verify the character, solvatochromic shift, and overlap of the two lowest energy transitions responsible for the linear absorption spectrum of DO3 in DMSO in the visible spectral region. Results of the PE linear and quadratic response calculations, performed using uncorrelated solute-solvent configurations sampled from either the classical or hybrid CP QM/MM MD simulations, are used to estimate the width of the line shape function of the two electronic lowest energy excited states, which allow a prediction of the 2PA cross-sections without the use of empirical parameters. Appropriate exchange-correlation functionals have been employed in order to describe the charge-transfer process following the electronic transitions of the chromophore in solution.

High-Polarity Solvents Decreasing the Two-Photon Transition Probability of Through-Space Charge-Transfer Systems - A Surprising In Silico Observation

In the Letter, we address the question as to why larger two-photon absorption cross sections are observed in nonpolar than in polar solvents for through-space charge-transfer (TSCT) systems such as [2,2]-paracyclophane derivatives. In order to answer this question, we have performed ab initio calculations on two well-known TSCT systems, namely, a [2.2]-paracyclophane derivative and a molecular tweezer-trinitrofluorinone complex, and found that the two-photon transition probability values of these systems decreases with increasing solvent polarity. To rationalize this result, we have analyzed the role of different optical channels associated with the two-photon process and noticed that, in TSCTs, the interference between the optical channels is mostly destructive and that its magnitude increases with increasing solvent polarity. Moreover, it is also found that a destructive interference may sometimes even become a constructive one in a nonpolar solvent, making the two-photon activity of TSCTs in polar solvents less than that in nonpolar solvents.

Exploring control parameters of two photon processes in solutions

Two-photon microscopy depends extensively on the two-photon absorption cross-sections of biologically relevant chromophores. High repetition rate (HRR) lasers are essential in multiphoton microscopy for generating satisfactory signal to noise at low average powers. However, HRR lasers generate thermal distortions in samples even with the slightest single photon absorption. We use an optical chopper with HRR lasers to intermittently 'blank' irradiation and effectively minimize thermal effects to result in a femtosecond z-scan setup that precisely measures the two-photon absorption (TPA) cross-sections of chromophores. Though several experimental factors impact such TPA measurements, a systematic effort to modulate and influence TPA characteristics is yet to evolve. Here, we present the effect of several control parameters on the TPA process that are independent of chromophore characteristics for femtosecond laser pulse based measurements; and demonstrate how the femtosecond laser pulse repetition rate, chromophore environment and incident laser polarization can become effective control parameters for such nonlinear optical properties.

Benzothiazoles with tunable electron-withdrawing strength and reverse polarity: a route to triphenylamine-based chromophores with enhanced two-photon absorption

A series of dipolar and octupolar triphenylamine-derived dyes containing a benzothiazole positioned in the matched or mismatched fashion have been designed and synthesized via palladium-catalyzed Sonogashira cross-coupling reactions. Linear and nonlinear optical properties of the designed molecules were tuned by an additional electron-withdrawing group (EWG) and by changing the relative positions of the donor and acceptor substituents on the heterocyclic ring. This allowed us to examine the effect of positional isomerism and extend the structure-property relationships useful in the engineering of novel heteroaromatic-based systems with enhanced two-photon absorption (TPA). The TPA cross-sections (δ(TPA)) in the target compounds dramatically increased with the branching of the triphenylamine core and with the strength of the auxiliary acceptor. In addition, a change from the commonly used polarity in push-pull benzothiazoles to a reverse one has been revealed as a particularly useful strategy (regioisomeric control) for enhancing TPA cross-sections and shifting the absorption and emission maxima to longer wavelengths. The maximum TPA cross-sections of the star-shaped three-branched triphenylamines are ∼500-2300 GM in the near-infrared region (740-810 nm); thereby the molecular weight normalized δ(TPA)/MW values of the best performing dyes within the series (2.0-2.4 GM·g(-1)·mol) are comparable to those of the most efficient TPA chromophores reported to date. The large TPA cross-sections combined with high emission quantum yields and large Stokes shifts make these compounds excellent candidates for various TPA applications, including two-photon fluorescence microscopy.