TDDFT Study of One- and Two-Photon Absorption Properties: Donor−π−Acceptor Chromophores

Two-photon absorption behavior of conjugated oligomers suitable for low colour temperature LEDs

Light emitting diodes (LEDs) with low colour temperatures (CTs) have been proved to be physiologically-friendly light sources. However, there are few reports on the photophysical properties of luminescent materials with CTs lower than candlelight. Herein, one- and two-photon optical properties of four fluorenone-based conjugated oligomers have been systemically investigated. By using a sum-over-essential states (SOS) approach, we obtained the transition dipole moments and two-photon absorption (TPA) cross sections. The triphenylamine end-capped oligomer exhibits reddish orange luminescence with extremely low colour temperature of 1686 K, which is much lower than that of candlelight. Fluorene-ethylene units serving as π-spacers could weaken the role of electron-donating units and effectively enhance the TPA performance of oligomers. Our results provide an effective way for the design and optimization of universal light-emitting material candidates in optoelectronic devices.

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

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

Controlling Aggregation-Induced Two-Photon Absorption Enhancement via Intermolecular Interactions

Historically, two-photon absorption (2PA) cross sections reported in the literature have been derived from solution-phase measurements. However, such techniques fail to grasp the implications of how these cross sections can be impacted by varying degrees of aggregation or in the condensed phase as bulk solids or thin films. For a precise determination of how aggregation impacts 2PA at a molecular level, computational methods present themselves as ideal. Herein, a series of quadrupolar π-conjugated dyes were simulated by molecular dynamics (MD) in the gas phase and condensed phase. In the condensed phase, their intermolecular interactions and electronic coupling behavior were fully characterized, both quantitatively and qualitatively. Using quadratic-response time-dependent density functional theory, 2PA cross sections of structures derived from MD trajectories were calculated. Comparisons are made between gas-phase and condensed-phase results, and enhancement factors are defined to show how certain dyes may experience changes in their respective 2PA cross sections as a function of aggregation. It was found that these cross sections depend heavily on conformational locking in the condensed phase and relative stacking arrangements. J-aggregates were associated with enhanced 2PA and H-aggregates with quenched 2PA activity. However, in a highly disordered aggregate, the effects of these stacking arrangements are averaged out of the bulk result, and the effects of conformational locking dominate.

Diradical Character of Neutral Heteroleptic Bis(1,2-dithiolene) Metal Complexes: Case Study of [Pd(Me2timdt)(mnt)] (Me2timdt = 1,3-Dimethyl-2,4,5-trithioxoimidazolidine; mnt2- = 1,2-Dicyano-1,2-ethylenedithiolate)

The reaction of the bis(1,2-dithiolene) complex [Pd(Me₂timdt)₂] (1; Me₂timdt^•– = monoreduced 1,3-dimethyl-2,4,5-trithioxoimidazolidine) with Br₂ yielded the complex [Pd(Me₂timdt)Br₂] (2), which was reacted with Na₂mnt (mnt^2– = 1,2-dicyano-1,2-ethylenedithiolate) to give the neutral mixed-ligand complex [Pd(Me₂timdt)(mnt)] (3). Complex 3 shows an intense solvatochromic near-infrared (NIR) absorption band falling between 955 nm in DMF and 1060 nm in CHCl₃ (ε = 10700 M^–1 cm^–1 in CHCl₃). DFT calculations were used to elucidate the electronic structure of complex 3 and to compare it with those of the corresponding homoleptic complexes 1 and [Pd(mnt)₂] (4). An in-depth comparison of calculated and experimental structural and vis–NIR spectroscopic properties, supported by IEF-PCM TD-DFT and NBO calculations, clearly points to a description of 3 as a dithione-dithiolato complex. For the first time, a broken-symmetry (BS) procedure for the evaluation of the singlet diradical character (DC) of heteroleptic bis(1,2-dithiolene) complexes has been developed and applied to complex 3. The DC, predominant for 1 (n_DC = 55.4%), provides a remarkable contribution to the electronic structures of the ground states of both 3 and 4, showing a diradicaloid nature (n_DC = 24.9% and 27.5%, respectively). The computational approach developed here clearly shows that a rational design of the DC of bis(1,2-ditiolene) metal complexes, and hence their linear and nonlinear optical properties, can be achieved by a proper choice of the 1,2-dithiolene ligands based on their electronic structure.

The reaction of [Pd(Me₂timdt)₂] (1; Me₂timdt^•− = monoreduced 1,3-dimethyl-2,4,5-trithioxoimidazolidine) with Br₂ yielded [Pd(Me₂timdt)Br₂] (2), which was reacted with Na₂mnt (mnt²⁻ = 1,2-dicyano-1,2-ethylenedithiolate) to give [Pd(Me₂timdt)(mnt)] (3), showing an intense solvatochromic near-infrared (NIR) absorption band. The singlet diradical character (DC), predominant for 1, provides a remarkable contribution to the ground states of 3 and 4. A rational design of the DC of bis(1,2-dithiolene) complexes can be achieved by a proper choice of the 1,2-dithiolene ligands.

Heteroleptic Ir(iii) complexes with varied π-conjugated diimine ligands: synthesis, tunable triplet states and nonlinear absorption properties

Four heteroleptic Ir(iii) complexes (Ir-1-Ir-4) with varied π-conjugated diimine ligands were synthesized. Their optical properties were investigated systematically via spectroscopic methods, in order to elucidate the influence of the extended π-conjugation on the singlet and triplet states of the molecules. All these Ir(iii) complexes exhibit ligand localized ¹π,π* transitions below 370 nm, and broad metal-to-ligand and ligand-to-ligand charge transfer (MLCT/LLCT) absorption bands in the visible region. Extending the π-conjugation in diimine ligands influences the electron distribution of the triplet state. The ³π,π* dominated Ir(iii) complexes (Ir-3 and Ir-4) exhibit long-lived triplet states and low phosphorescence quantum yields, compared with the charge transfer dominated Ir(iii) complexes (Ir-1 and Ir-2). Complexes Ir-3 and Ir-4 exhibit broadband transient absorption spectra from 420 to 750 nm, between which the nonlinear absorption could be observed by virtue of reverse saturable absorption. The results of nonlinear transmission measurements using 532 nm laser pulses further elucidate that selected complexes Ir-3 and Ir-4 are promising candidates for optical limiting applications.

Nonlinear Optical Study in a Set of Dibenzylideneacetone Derivatives with Potential for Optical Frequency Conversion

The search for advanced optical materials, in particular, materials with nonlinear optical responses, has, in the last years, experienced substantial growth due to their vast applications in the photonics field. One of those applications is ultra-fast optical frequency conversion, in the optics communications field. Organic compounds have emerged as promising candidates for raw materials to develop nonlinear optical devices, such as optical converters, due to their intrinsic ultra-fast electronic responses. Also, the easy tailoring of organic molecular structures makes organic materials much more appealing than the inorganic ones. In this work, we have performed a linear and nonlinear optical characterization of a set of dibenzylideneacetone derivatives. The nonlinear optical responses investigated correspond to second- and third-order nonlinear processes, namely, first electronic molecular hyperpolarizability and two-photon absorption cross-section, respectively. The value of the first electronic molecular hyperpolarizability, up to 52 cm4·statvolt−1, could be considered a robust value when compared to the short-sized π-electron backbone length of the studied compounds. Such results suggest that these compounds exhibit the potential to be used as optical frequency converters. Quantum chemical calculations were used to predict the theoretical value of the first molecular hyperpolarizability, as well as to simulate the one- and two-photon absorption spectra for all compounds.

The effects of extended π-conjugation in bipyridyl ligands on the tunable photophysics, triplet excited state and optical limiting properties of Pt(ii) naphthalimidyl acetylide complexes

Pt(ii) complexes that exhibit long-lived triplet excited state lifetimes are promising for optical power limiting materials. The introduction of large π-conjugated substituents can switch the triplet excited state to a long-lived 3π,π* state. Herein, we report four Pt(ii) diimine complexes with high π-conjugation via inserting an aryl group on the diimine ligand. Their photophysical properties were investigated using spectroscopic techniques. All the complexes exhibit strong ground absorption bands in their UV-Vis absorption spectra (maximum peaks ranging from 370 to 530 nm) and long-lived emission and triplet excited states. The insertion of π-conjugated substituents induces a pronounced red-shift in the ground state absorption and longer emission lifetime. Broadband transient absorption spectra in the visible-NIR region and Z-scan properties under 532 nm were carried out on the Pt(ii) diimine complexes, resulting in a remarkably strong reverse saturable absorption at 532 nm for nanosecond laser pulses. Otherwise, the high π-conjugation in the bipyridyl ligand increases the reverse saturable absorption. Therefore, these Pt(ii) diimine complexes with high π-conjugation are excellent candidates for devices that require strong reverse saturable absorption.

Theoretical Prediction of Optical Absorption and Emission in Thiolated Gold Clusters

Although the photoluminescence of gold clusters has been extensively studied so far, there are still questions on the origin of the emission in these materials. In this work, we report time-dependent density functional theory calculations on the absorption and emission spectra of the well-studied Au₂₅(SR)₁₈^- cluster, the lowest energy isomer of the Au₃₈(SR)₂₄ cluster, and five isomers of the Au₂₂(SR)₁₈ cluster. Good agreement between the calculated and measured absorption spectra, as well as with the lowest-energy emission values for these clusters, was demonstrated, verifying the accuracy of the theoretical methods employed. Our results for Au₂₅(SR)₁₈^- explain a newly observed feature in the absorption peak, also rationalizing the optical response in terms of the superatom model. The analysis of the absorption and emission characteristics of the Au₂₅(SR)₁₈^- and Au₃₈(SR)₂₄ clusters provides an estimate of the spectral regions, where fluorescence or phosphorescence is predicted to occur. Interestingly, we find that for Au₂₂(SR)₁₈, one of the five proposed structures could be present at a significant concentration in the sample, even though it is not the lowest in energy structure, which can be explained, in part, by solvent effects.

Spectroscopic and DFT investigation on the photo-chemical properties of a push-pull chromophore: 4-Dimethylamino-4'-nitrostilbene

4-Dimethylamino-4'-nitrostilbene (DANS), a π-conjugated push-pull molecule, has been investigated by means of a combined spectroscopic and computational approach. When the Raman excitation is close to the visible electronic transition of DANS, vibrational bands not belonging to DANS appear in the spectra, increasing with the laser power. These bands are observed at room temperature in the solid phase, but not at low temperature or in solution, and we interpret them as due to a thermally-activated photoreaction occurring under laser irradiation in the visible spectral region. Density-functional calculations correctly reproducing the electronic and vibrational spectra of DANS, describe the charge-transfer process, indicate that an azo-derivative is the product of the photoreaction of DANS and provide a reasonable interpretation of this process.

TD-DFT calculations of one- and two-photon absorption in Coumarin C153 and Prodan: attuning theory to experiment

We use TD-DFT to calculate the one-photon absorption (1PA) and two-photon absorption (2PA) properties of C153 and Prodan in toluene and DMSO, and benchmark different methods relative to accurate experimental data available from the literature on these particular systems. As the first step, we modify the range-separated TD-DFT to provide the best prediction for the peak 1PA wavelength, and then apply the optimized functionals to achieve quantitative predictions of the corresponding two-photon absorption cross section, σ_2PA, with an accuracy ∼10-20% in C153 and ∼20-30% in Prodan. To elucidate the origin of residual discrepancies between the theory and experimental observations, we invoked the two essential states model for σ_2PA, which allows us to verify not only the transition wavelength and the σ_2PA value, but also to quantitatively benchmark the calculation of key molecular parameters such as the transition dipole moment and the change of the permanent dipole moment. Such comprehensive cross-checking indicates that a larger discrepancy in Prodan is most likely caused by a noted failure of DFT to predict the relative intensity and relative ordering of closely lying excited states with different degrees of intramolecular charge transfer, which we further support by analyzing the predictions obtained by high-level coupled-cluster calculations in the gas phase. Our results highlight the utility of benchmarking the calculations not only relative to other theoretical methods, but also in comparison to the experimental measurements, wherever such data are available.

Self-trapping and excited state absorption in fluorene homo-polymer and copolymers with benzothiadiazole and tri-phenylamine

Excited state absorption (ESA) is studied using time-dependent density functional theory and compared with experiments performed in dilute solutions.

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.

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

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

Two-photon absorption in CdSe colloidal quantum dots compared to organic molecules

We discuss fundamental differences in electronic structure as reflected in one- and two-photon absorption spectra of semiconductor quantum dots and organic molecules by performing systematic experimental and theoretical studies of the size-dependent spectra of colloidal quantum dots. Quantum-chemical and effective-mass calculations are used to model the one- and two-photon absorption spectra and compare them with the experimental results. Currently, quantum-chemical calculations are limited to only small-sized quantum dots (nanoclusters) but allow one to study various environmental effects on the optical spectra such as solvation and various surface functionalizations. The effective-mass calculations, on the other hand, are applicable to the larger-sized quantum dots and can, in general, explain the observed trends but are insensitive to solvent and ligand effects. Careful comparison of the experimental and theoretical results allows for quantifying the range of applicability of theoretical methods used in this work. Our study shows that the small clusters can be in principle described in a manner similar to that used for organic molecules. In addition, there are several important factors (quality of passivation, nature of the ligands, and intraband/interband transitions) affecting optical properties of the nanoclusters. The larger-size quantum dots, on the other hand, behave similarly to bulk semiconductors, and can be well described in terms of the effective-mass models.

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.

On the origin of large two-photon activity of DANS molecule

In this work, using the quadratic response theory and two-state model approach, we have explained the origin of high two-photon activity and the corresponding solvent dependence of 4,4'-dimethyl-amino-nitro-stilbene (DANS) molecule. For this purpose, we have made two structural modifications in the DANS molecule (1) at the donor-acceptor part and (2) at the unsaturated bridge between the two rings and calculated the one- and two-photon (OP and TP) absorption parameters of all the systems in gas phase and in three different solvents, viz., MeCN, THF, and toluene. We found that the removal of donor-acceptor groups from the original DANS molecule vanishes the transition moment between the ground and excited states and also the corresponding dipole moment difference, and the saturation of the π-conjugation bridge between the two rings keeping the donor-acceptor groups intact causes a large decrease in the ground to excited state transition moment. These changes, in turn, decrease the overall TP activity of the molecules as compared to DANS. On the basis of our analysis, we have concluded that neither the donor-acceptor pair nor the π-conjugation bridge between the two, rather their cooperative involvement leads to a large overlap between the ground and virtual and also the virtual and charge-transfer states, which are eventually responsible for the very large TP activity of DANS.

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.

Two-photon absorption properties of proquinoidal D-A-D and A-D-A quadrupolar chromophores

We report the synthesis, one- and two-photon absorption spectroscopy, fluorescence, and electrochemical properties of a series of quadrupolar molecules that feature proquinoidal π-aromatic acceptors. These quadrupolar molecules possess either donor-acceptor-donor (D-A-D) or acceptor-donor-acceptor (A-D-A) electronic motifs, and feature 4-N,N-dihexylaminophenyl, 4-dodecyloxyphenyl, 4-(N,N-dihexylamino)benzo[c][1,2,5]thiadiazolyl or 2,5-dioctyloxyphenyl electron donor moieties and benzo[c][1,2,5]thiadiazole (BTD) or 6,7-bis(3',7'-dimethyloctyl)[1,2,5]thiadiazolo[3,4-g]quinoxaline (TDQ) electron acceptor units. These conjugated structures are highly emissive in nonpolar solvents and exhibit large spectral red-shifts of their respective lowest energy absorption bands relative to analogous reference compounds that incorporate phenylene components in place of BTD and TDQ moieties. BTD-based D-A-D and A-D-A chromophores exhibit increasing fluorescence emission red-shifts, and a concomitant decrease of the fluorescence quantum yield (Φ(f)) with increasing solvent polarity; these data indicate that electronic excitation augments benzothiadiazole electron density via an internal charge transfer mechanism. The BTD- and TDQ-containing structures exhibit blue-shifted two-photon absorption (TPA) spectra relative to their corresponding one-photon absorption (OPA) spectra, and display high TPA cross sections (>100 GM) within these spectral windows. D-A-D and A-D-A structures that feature more extensive conjugation within this series of compounds exhibit larger TPA cross sections consistent with computational simulation. Factors governing TPA properties of these quadrupolar chromophores are discussed within the context of a three-state model.