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

Degenerate two-photon absorption in all-trans retinal: nonlinear spectrum and theoretical calculations

In this work we investigate the degenerate two-photon absorption spectrum of all-trans retinal in ethanol employing the Z-scan technique with femtosecond pulses. The two-photon absorption (2PA) spectrum presents a monotonous increase as the excitation wavelength approaches the one-photon absorption band and a peak at 790 nm. We attribute the 2PA band to the mixing of states (1)B(u)(+)-like and |S(1)>, which are strongly allowed by one- and two-photon, respectively. We modeled the 2PA spectrum by using the sum-over-states approach and obtained spectroscopic parameters of the electronic transitions to |S(1)>, |S(2)> ("(1)B(u)(+)"), |S(3)>, and |S(4)> singlet-excited states. The results were compared with theoretical predictions of one- and two-photon transition calculations using the response functions formalism within the density functional theory framework with the aid of the CAM-B3LYP functional.

Theoretical study of one- and two-photon absorption spectra of azoaromatic compounds

In this study, the one- and two-photon absorption spectra of seven azoaromatic compounds (five pseudostilbenes-type and two aminoazobenzenes) were theoretically investigated using the density functional theory combined with the response functions formalism. The equilibrium molecular structure of each compound was obtained at three different levels of theory: Hartree-Fock, density functional theory (DFT), and Møller-Plesset 2. The effect of solvent on the equilibrium structure and the electronic transitions of the compounds were investigated using the polarizable continuum model. For the one-photon absorption, the allowed pi-->pi(*) transition energy showed to be dependent on the molecular structures and the effect of solvent, while the n-->pi(*) and pi-->pi(*)(n) transition energies exhibited only a slight dependence. An inversion between the bands corresponding to the pi-->pi(*) and n-->pi(*) states due to the effect of solvent was observed for the pseudostilbene-type compounds. To characterize the allowed two-photon absorption transitions for azoaromatic compounds, the response functions formalism combined with DFT using the hybrid B3LYP and PBE0 functionals and the long-range corrected CAM-B3LYP functional was employed. The theoretical results support the previous findings based on the three-state model. The model takes into account the ground and two electronic excited states and has already been used to describe and interpret the two-photon absorption spectrum of azoaromatic compounds. The highest energy two-photon allowed transition for the pseudostilbene-type compounds shows to be more effectively affected (approximately 20%) by the torsion of the molecular structure than the lowest allowed transition (approximately 10%). In order to elucidate the effect of the solvent on the two-photon absorption spectra, the lowest allowed two-photon transition (dipolar transition) for each compound was analyzed using a two-state approximation and the polarizable continuum model. The results obtained reveal that the effect of solvent increases drastically the two-photon cross-section of the dipolar transition of the pseudostilbene-type compounds. In general, the features of both one- and two-photon absorption spectra of the azoaromatic compounds are well reproduced by the theoretical calculations.

DFT study of linear and nonlinear optical properties of donor-acceptor substituted stilbenes, azobenzenes and benzilideneanilines

A theoretical analysis of the linear and nonlinear optical properties of six push-pull pi-conjugated molecules with stilbene, azobenzene and benzilideneaniline as a backbone is presented. The photophysical properties of the investigated systems were determined by using response functions combined with density functional theory (DFT). Several different exchange-correlation potentials were applied in order to determine parameters describing the one- and two-photon spectra of the studied molecules. In particular, the recently proposed Coulomb-attenuated model (CAM-B3LYP) was used to describe charge-transfer (CT) excited states. In order to compare theoretical predictions with available experimental data, calculations with inclusion of solvent effects were performed. The BLYP and the CAM-B3LYP functionals were found to yield values of two-photon absorption (TPA) probabilities closer to experimental values than the B3LYP functional or the HF wavefunction. Moreover, molecular static hyperpolarisabilities were determined using both DFT and second-order Møller-Plesset perturbation (MP2) theory. Likewise, the CAM-B3LYP functional was found to outperform other applied exchange-correlation potentials in determining first hyperpolarisability (beta). Moreover, it was confirmed on a purely theoretical basis that the presence of a -C=C- bridge between the phenyl rings leads to a much larger nonlinear optical response in comparison with a -N=N- bridge.

Theoretical study of the two-photon absorption properties of several asymmetrically substituted stilbenoid molecules

Two-photon absorption (TPA) properties of noncentrosymmetric pi-conjugated stilbenoid molecules with D-pi-A structures, TPA spectra of which have been reported [L. Antonov et al., Phys. Chem. Chem. Phys. 5, 1193 (2003)], have been investigated theoretically by ab initio molecular orbital methods. The difference in the observed one-photon absorption and TPA spectra among compounds with the same donor (D) and acceptor (A) units is well reproduced by the present calculations, although the calculated excitation energies are overestimated by the configuration interaction with single excitation method used. It was found that the spectral differences among the compounds were mainly due to the deviation from the planar structure by intramolecular rotation around the N[Single Bond]C (phenyl) bond of the N-benzilideneanilines having the C[Double Bond]N linkage as the central pi bridge. Substitution of the end donor or acceptor groups with weaker ones leads to a decrease in the TPA intensity of the lowest pi-pi(*) TPA states, resulting mainly from the decrease in the dipole moment of the excited states. The total TPA cross section spectra have been separated into contributions of the dipolar term, which appear only in noncentrosymmetric systems, and the three-state term, which appear in any systems irrespective of symmetry. The dipolar term predominates only for the lowest pi-pi(*) state, while for the higher excited states the three-state terms become predominant. An analysis employing the index R(f) defined with the transition polarizability shows that the TPA properties of the higher excited states are well described by the three-state approximation mediated by the lowest pi-pi(*) state. The differences found between the centrosymmetric and dipolar molecules in the enhancement mechanism of the TPA intensity by substituting the end groups with strong donors are discussed by comparison with the TPA properties of azobenzenes symmetrically substituted with the same donors.

Structure to property relationships for multiphoton absorption in covalently linked porphyrin dimers: a correction vector INDO/MRDCI study

The correction vector method has been used to investigate structure to property relationships for multiphoton absorption properties in covalently linked porphyrin dimers. The electronic structure of the system is described within the multireference single and double configuration interaction (MRDCI) method coupled with the intermediate neglect of differential overlap (INDO) Hamiltonian. We find a strong increase in the two-photon absorption (2PA) and three-photon absorption (3PA) cross sections when going from an isolated porphyrin to the dimers. The nature of the 2PA and 3PA active states as well as the cross sections show a strong but not straightforward dependence on the length of the bridge between the two porphyrins. Our theoretical results are in very good agreement with experimental data for 2PA. The resulting structure to property relationships are analyzed on the basis of essential-state models, where it turns out that a three-state model considering only the Q(x) intermediate state proposed in literature does not provide a full description of the actual situation.

Effects of Donor/Acceptor Strengths on the Multiphoton Absorption: An EOM-CCSD Correction Vector Study

We have developed a correction method (CV) to calculate the single- and multiphoton absorption (MPA) spectra of organic pi-conjugated systems within the equation of motion coupled-cluster method with single and double excitations (EOM-CCSD). The effects of donor/acceptor strengths on the multiphoton absorption in a series of symmetrically substituted stilbene derivatives have been reinvestigated at both the ab initio and the semiempirical intermediate neglect of differential overlap (INDO) Hamiltonian levels. Both ab initio and INDO calculations show that the electron-donating or electron-withdrawing substituents lead to enhancements of two- and three-photon absorption cross sections, more pronounced for two-photon absorption than for three-photon absorption. The ab initio calculations usually produce larger excitation energies than the semiempirical, which lead to lower MPA cross sections.

Two-Photon Absorption Dependence on the Temperature for Azoaromatic Compounds: Effect of Molecular Conformation

This work reports on the effect of temperature on the two-photon absorption cross section of azoaromatic chromophores. A linear decrease in the two-photon absorption cross section with the temperature was observed for several azochromophores. This process was characterized by introducing a two-photon absorption thermal coefficient (ddelta/dT), whose typical values are approximately 2GM/degrees C for all the azochromophores studied here. Such an effect was attributed to thermal induced molecular conformation changes, described by the sum-over-states model and semiempirical calculations, which affect the molecular dipole moments. The characterization of the phenomenon reported here for other nonlinear materials can help in the design of specific applications using two-photon absorption.

Effects of solvation on one- and two-photon spectra of coumarin derivatives: A time-dependent density functional theory study

We report one- and two-photon absorption excitation energies and cross sections for a series of 7-aminocoumarins using time-dependent density functional theory with various basis sets and functionals, including exchange-correlation functionals using the Coulomb-attenuating method, to evaluate their performance in the gas phase and in solvents. Except for the results of one functional, the computed one-photon excitation energies and transition dipole moments are in good agreement with experiment. The range of errors obtained from various functionals is discussed in detail. The relationship of donor and acceptor groups with the one- and two-photon resonances and intensities is also discussed.

Insight into the Nonlinear Absorbance of Two Related Series of Two-Photon Absorbing Chromophores

A comprehensive photophysical study of the linear and nonlinear absorption properties has been carried out on two series of two-photon absorbing dyes to gain insight into how structure-property relationships influence observed nonlinear absorption. The materials studied consist of an electron accepting benzothiazole group connected to an electron donating diphenylamine via a fluorene bridging group. Two series differ from each other by the addition of one phenyl group and for each series one-arm (dipolar, AF240 and AF270), two-arm (quadrupolar, AF287 and AF295), and three-arm (octupolar, AF350 and AF380) versions were studied. Overall the AF240 series exhibits higher intrinsic two-photon absorption (TPA) cross-sections than the AF270 series as well as enhanced nanosecond nonlinear absorption, with an increase with number of branches. The enhanced nanosecond nonlinearity is understood by taking into account the contribution from the singlet and triplet excited states and was verified by a two-photon assisted excited-state absorption model that satisfactorily predicts the nonlinear absorption of the chromophores.

Effects of Conjugation in Length and Dimension on Spectroscopic Properties of Fluorene-Based Chromophores from Experiment and Theory

A series of one-photon absorption spectra for fluorene-based donor-pi-acceptor molecules is presented and spectroscopically assigned, based upon the results obtained from time-dependent density functional theory. The computed excitation energies were generally shown to be in good agreement with experiment, particularly when compared to results from measurements carried out in a nonpolar solvent, which were available for some molecules. The computed oscillator strengths may resolve discordant experimental values in some cases, for example, for AF-380, AF-270, and AF-295. However, a quantitative comparison between computed and observed oscillator strengths is complicated by band overlapping. Thus, the computed extinction coefficients obtained by summing over the Gaussian bands are useful in such cases.

Nonlinear Optical Properties and Excited-State Dynamics of Highly Symmetric Expanded Porphyrins

A strong correlation among calculated Nucleus-Independent Chemical Shift (NICS) values, molecular planarity, and the observed two-photon absorption (TPA) values was found for a series of closely matched expanded porphyrins. The expanded porphyrins in question consisted of [26]hexaphyrin, [28]hexaphyrin, rubyrin, amethyrin, cyclo[6]pyrrole, cyclo[7]pyrrole, and cyclo[8]pyrrole containing 22, 24, 26, 28, and 30 pi-electrons. Two of the systems, [28]hexaphyrin and amethyrin, were considered to be antiaromatic as judged from a simple application of Hückel's [4n + 2] rule. These systems displayed positive NICS(0) values (+43.5 and +17.1 ppm, respectively) and gave rise to TPA values of 2600 and 3100 GM, respectively. By contrast, a set of congeners containing 22, 26, and 30 pi-electrons (cyclo[n]pyrrole, n = 6, 7, and 8, respectively) were characterized by a linear correlation between the NICS and TPA values. In the case of the oligopyrrolic macrocycles containing 26 pi-electron systems, a further correlation between the molecular structure and various markers associated with aromaticity was seen. In particular, a decrease in the excited state lifetimes and an increase in the TPA values were seen as the flexibility of the systems increased. Based on the findings presented here, it is proposed that various readily measurable optical properties, including the two-photon absorption cross-section, can provide a quantitative experimental measure of aromaticity in macrocyclic pi-conjugated systems.

Nonlinear optical properties of zwitterionic merocyanine aggregates: role of intermolecular interaction and solvent polarity

We present a time-dependent quantum-chemical analysis on merocyanine aggregates to understand the insight of the intermolecular interactions and to find the relationship between structural and collective nonlinear optical properties. The first hyperpolarizabilities are evaluated for monomer and aggregates of a series of zwitterionic merocyanine dyes, whose synthesis and formation of H and J type aggregates in solvents are reported recently in the literature (J. Am. Chem. Soc. 2002, 124, 9431). The molecular geometries are obtained via B3LYP/6-31G (hybrid density-functional theory) optimization including PCM approach, while the dynamic NLO properties are calculated with the TD-DFT/SOS and ZINDO/CV method including solvent effects. It has been observed that the first hyperpolarizability changes tremendously as monomers undergo aggregation, and the magnitude of first hyperpolarizabilities highly depends on the nature of the aggregates. It is found that solvents play a remarkable role on the structure and first hyperpolarizabilities of merocyanine monomers and aggregates. Changing the solvent from low to high dielectric causes not only an increase in magnitude of beta but also a change in sign, therefore passing through zero at intermediate dielectric. The importance of our results on the design of electrooptic materials have been discussed.

Calculation of two-photon absorption spectra of donor-π-acceptor compounds in solution using quadratic response time-dependent density functional theory

Linear and quadratic response time-dependent density functional theories have been applied to calculate the photophysical properties of donor-pi-acceptor molecules which are known to have large nonlinear absorption. The linear absorption and two-photon absorption spectra predicted using hybrid functionals, including the Coulomb-attenuated model, with continuum solvation models are reported and compared to experiment and to previous theoretical predictions. While the quadratic response with these functionals overestimated the TPA cross sections relative to experiment when a Gaussian linewidth function was used, a fairly good agreement was obtained when a Lorentzian linewidth function was applied. In addition, the comparison of the TPA cross sections calculated by the sum over states with those calculated by the two-state approximation indicates the importance of the higher energy states in TPA, particularly in nondegenerate experiments.

Two-Photon Excitation of Substituted Enediynes

Electronic spectroscopy of nine benzannelated enediynes and a related fulvene was studied under one-photon and two-photon excitation conditions. We utilize measured absorbance and emission spectra and time-resolved fluorescence decays of these molecules to calculate their radiative lifetimes and fluorescence quantum yields. The fluorescence quantum yields for the other compounds were referenced to the fluorescence quantum yield of compound 3 and used to determine relative two-photon absorption cross-sections. Further insight into experimental studies has been achieved using time-dependent density functional (TD-DFT) computations. The probability of two-photon absorption (TPA) increases noticeably for excitation to the higher excited states. The photophysical properties of benzannelated enediynes are sensitive to substitutions at both the core and the periphery of the enediyne chromophore. Considerably enhanced two-photon absorption is observed in an enediyne with donor substitution in the middle and acceptor substitution at the termini. Excited states with B symmetry are not active in TPA spectra. From a practical point of view, this study extends the range of wavelengths applicable for activation of the enediyne moiety from 350 to 600 nm and provides a rational basis for future studies in this field. Our theoretical computations confirmed that lowest energy TPA in benzannelated enediynes involves different orbitals than lowest energy one-photon absorbance and provided further support to the notion that introduction of donor and acceptor substituents at different ends of a molecule increases TPA.