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 1B +-like and |S , 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 |S1, |S2 (“1B +”), |S3, and |S4 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.
1. Introduction
All-trans retinal (ATR) is a polyene chromophore of foremost relevance in the light transduction process in nervous impulses. Its charge redistribution is associated with a significant change in dipole moment.1-3 In the last few decades, ATR was exhaustingly studied for applications in optoelectronic devices due to its ultrafast isomerization in bacteriorhodopsin.4-7 However, there is still a small number of studies on the third- order nonlinear optical properties of ATR, in particular, those that allow the direct measurement of the nonlinear absorption coefficient, such as the Z-scan technique,8 for instance.
Pioneering studies of nanosecond up-conversion fluorescence and theoretical analysis carried out by Birge1,3 revealed that the three low-lying excited singlet states of ATR are of nu*, 1A — like (uu*), and 1B +-like (uu*) characters, respectively. Excited- state ordering is important to define the photochemical properties of the ATR chromophore in solution. Nevertheless, so far there is no consensus on the order of the electronic states involved in one- and two-photon transitions of ATR, mainly because of the distinct molecular conformation and polarity exhibited by ATR in different solvents.9,10 Two-photon induced fluorescence results1 revealed a red shift between the two-photon and the linear absorption band, indicating the presence of a two-photon allowed state near “1B +”. Ultrafast transient absorption9 and To help the understanding of the electronic states of ATR, we study its degenerate two-photon absorption spectrum in ethanol, using the open aperture Z-scan technique with femto- second pulse excitation. In an effort to further comprehend the two-photon absorption spectrum of ATR, we carried out theoretical calculations using the quadratic response function formalism within the density functional theory (DFT) frame- work, which allowed the determination of the lowest two-photon allowed states of the chromophore.
2. Experimental Section
We prepared ATR/ethanol solutions with concentrations of 1.65 × 10-3 and 3.5 × 10-2 mol L-1, for linear and nonlinear optical measurements, respectively. ATR was purchased from Sigma-Aldrich. The ATR molecular structure is presented in femtosecond fluorescence up-conversion spectroscopy have contributed to the understanding of the electronic states involved in the photophysics of ATR. More recently, Yamaguchi and Tahara11 have used femtosecond pump-probe technique to measure the 2PA spectrum of ATR in hexane. A red shift was also observed in the 2PA peak with respect to the one-photon absorption, which was attributed to an allowed 2PA state. Hence, the study of ATR using different experimental approaches seems to be of foremost importance to comprehend its photophysical processes.
3. Results
The one-photon absorption spectrum of ATR in ethanol is presented in Figure 2a (gray line). Such a linear absorption spectrum can be decomposed (Gaussian decomposition) in three bands (dashed line in Figure 2a), corresponding to three uu* transitions, with absorption maxima at 250, 300, and 385 nm. The circles in Figure 2a represent the two-photon absorption spectrum of ATR determined by performing open-aperture Z-scan measurements similar to the ones presented in Figure 3a at three distinct wavelengths. The decrease observed in the normalized transmittance as a function of the z position in Figure 3a indicates a 2PA process, since excitation took place in nonresonant conditions. In Figure 3, the solid lines represent the theoretical fitting obtained with eq 1, from which we were able to determine the 2PA cross-section (b) as a function of the excitation wavelength. In Figure 3b, we show the linear dependence observed for the transmittance change (∆T) as a function of the excitation laser irradiance at 790 nm. Such behavior is typical of a two-photon absorption process12 and it was observed for all excitation wavelengths investigated (from 530 to 900 nm).
The 2PA spectrum (Figure 2a, circles) presents a monotonous increase as the excitation wavelength approaches the one-photon absorption band and a peak in 790 nm. Figure 2b shows a comparison between the one- and two-photon absorption spectra (the two-photon absorption data were plotted as a function of half-excitation wavelength). One can clearly observe that the two-photon absorption band is red-shifted by about 10 nm in comparison to the one-photon absorption band, indicating that the state accessed by the absorption of two-photons does not correspond, necessarily, to the state accessed by one photon. Moreover, the line width of the two-photon spectrum is smaller, in energy, than the one-photon spectrum, corroborating the previous hypothesis.
To gain an insight into ATR electronic states and help to interpret its two-photon absorption spectrum, we performed quantum-chemical calculations. Due to the size of the investi- gated system, all computations were carried out using the density functional theory (DFT).13 The Gaussian 03 program14 was used to determine the equilibrium geometry of the molecule with the aid of the Becke’s three-parameter exchange functional in combination with the LYP correlation functional (B3LYP)15 and the standard 6-31G(d) basis set.16 Figure 4 shows the equilibrium geometry of ATR. It is observed that the ATR is not planar, with the polyene chain out of the plane of ß-ionone ring. This conformation is attributed to intramolecular steric repulsion between the hydrogen of the ring and the polyene chain.17
Subsequently, to characterize the lowest allowed 1PA and 2PA states of ATR, the response functions formalism,18 within the DFT framework, was used as implemented in the DALTON program.19 In this approach, the oscillator strengths and two- photon transition probabilities are calculated analytically as single residues of the linear and quadratic response functions of the molecular electronic density, respectively. All electronic transition computations were carried out by employing the recently developed Coulomb-attenuated hybrid functional (CAM- B3LYP)20 and the 6-31+G(d) basis set.16 In particular, the CAM-B3LYP functional used here applies the long-range correction recommend by Tawada et al.21 to better describe long- range charge distribution modifications, an important point for accurately determine the electronic transitions of the investigated.
To further understand the 2PA spectrum and its connection with the molecular properties, we employed the sum-over-states (SOS) approach.23 As a first attempt to model the 2PA spectrum of ATR, we considered a four-level-energy diagram based on the energy states obtained by quantum chemistry calculations and linear absorption data (S2, S3, and S4). Nevertheless, considering only these three states, we were unable to obtain a satisfactory fitting of the 2PA spectrum. However, as indicated by the results presented in Figure 2b, there might be another two-photon allowed state near S2 (“1B +” state) which contrib- utes to the 2PA process.1,6,10 Following this hypothesis, we proposed a five-level-energy diagram (Figure 5), which includes a two-photon allowed S1 state (supposed to be less energetic than S2), to describe the 2PA spectrum under the SOS approach. As reported by Birge et al.,1 the origin of the S1 state is strongly related with the molecular conformation of ATR, which is affected by the solvent environment and temperature. This is the probable reason why it was not observed in the quantum chemical calculations presented here. The n f u* transition (Table 1) was neglected in the SOS model because this transition is extremely weak for both one- and two-photons absorption processes.1 In this case, the SOS expression used to fit the 2PA spectrum is given by 2PA spectrum of ATR (in hexane) using femtosecond time- resolved pump-probe. They observed a red shift of ap- proximately 7 nm in the 2PA band in comparison to the one- photon band, which was also attributed to an allowed 2PA state. In that work, the authors estimated the 2PA cross-section on the order of 200 GM. Such a value is about 3 times higher than the ones reported here, probably due to a resonant enhancement of the nonlinearity achieved in ref 11 when the probe wavelength beam approaches the one-photon absorption of ATR. Therefore, the experimental results we obtained with the degenerate Z-scan technique as well as the interpretation of the 2PA spectrum, assuming a two-photon allowed state below “1B +”, are in agreement with these pioneer studies.1,10,11
The relatively small 2PA cross-section values determined for ATR, experimentally (Figure 2) and theoretically (Table 1), are probably related to the low planarity of the ground-state equilibrium geometry27,28 and the absence of strong electron acceptor or -donnor on the chromophore.29
4. Conclusion
In this paper, we reported the degenerate two-photon absorp- tion cross-section spectrum of ATR, a potential material for development of biophotonic devices, in ethanol by using the open-aperture Z-scan technique with femtosecond pulses. We modeled the nonlinear spectrum by using the sum-over-states approach and obtained spectroscopy parameters of the electronic transitions to |S1, |S2 (“1B +”), |S3, and |S4 singlet-excited states, comparing the results with theoretical predictions for one- and two-photon transition calculations using the response functions formalism within the DFT framework. We associated the 2PA peak (790 nm) with a mixing of the states |S2 (“1B +”) and |S1, strongly allowed by one- and two-photon absorption, respectively. Such interpretation of the 2PA spectrum of ATR is in agreement with previous studies performed with different spectrum (uu* bands located at 385, 300, and 250 nm, respectively), and µ02 estimated from the 1PA peak amplitude.24 The values of Γ02 ) 5530 cm-1 (82 nm), Γ03 ) 6440 cm-1 (58 nm), and Γ04 ) 5760 cm-1 (36 nm) were obtained from the linear absorption spectrum (Figure 2a) through the Gaussian decomposition.25 From the fitting we were able to determine u01 and Γ01, the transition dipole moments µ01, µ23, and µ24, and the dipole moment changes ∆µ01 and ∆µ02. Table 2 summarizes the spectroscopic parameters used/obtained in the SOS model. According to the five-level-energy diagram proposed here, the 2PA band at 790 nm is described by transitions to the states |S2 (“1B +”) and |S1, with the main contribution coming from helps to understand the nature of the nonlinear absorption All trans-Retinal process in ATR.