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Abstract
As one kind of the most useful organic molecules, diketopyrrolopyrrole (DPP) derivatives are very promising in nonlinear optics due to their excellent thermal resistance and light stability. In this work, for the first time, we report the MPA properties of three chiral DPP derivatives by the modern analytical response theory. The calculated results demonstrate that all of the three molecules show superior two- and three-photon absorption (2 and 3PA) in the near-infrared window I and II, respectively, which are promising materials for deep tissue imaging applications. More importantly, they show excellent two-photon circular dichroism (2PCD) spectra. And, the calculations of orbital transitions elucidate that the intramolecular charge transfer contributes to the molecular strong MPA and 2PCD.
© 2017 Optical Society of America
1. Introduction
In recent decades, organic materials with strong optical nonlinearities in the near-infrared window I and II have attracted tremendous attention for their wide applications, such as optical power limiting, frequency upconversion photoluminescence and lasing as well as medical applications [1–7]. Therefore, increasing enthusiasm to design and develop more promising organic materials with good nonlinear optical behavior is triggered [8]. Furthermore, chiral control of nonlinear optical functions, constituting the field of chiral photonics, can be utilized for a variety of important applications including all-optical switching and biolabelling [9]. Chiralities include the difference in absorption, photoluminescence and scattering as well as in refractive index with respect to the two opposite circularly polarized components of a linearly polarized input light beam. Corresponding to one-photon circular dichroism (1PCD), multiphoton circular dichroism (MPCD) means MPA cross-sections are different for left and right circular polarization of excitation light, both of which can be used as fingerprinting tools. MPCD in chiral molecules will help us to obtain structural and conformational information that cannot be accessed by 1PCD. So far, there has been a lack of MPA characterization of chiral materials due to the limited development of related materials. Only a few MPA chiral molecules have been investigated by experimental measurements and theoretical computations [10–12]. For saving the time and vigor of experiments, the molecular synthetic procedures are always guided by theoretical computations. It is well known that MPA processes, such as two- and three-photon absorption (2 and 3PA), can be simulated by time-dependent density functional theory (TDDFT)-based response theory [13–15]. Uniquely, an alternative method called origin-independent formulation [16] is available to calculate the MPCD spectra. Therefore, novel chiral organic molecules can be dealt with the molecular structure theory to evaluate the nonlinear chiroptical activities with the aim to facilitate their following experimental studies.
As one of the most recently discovered groups of small organic dyes, diketopyrrolopyrrole (DPP) derivatives have distinctive advantages relative to other organic dyes, including high fluorescence quantum yields, and good light and thermal stability. Significant advances have been made in the development of various DPP-based optoelectronic devices in recent years [17–20]. However, the MPA properties of DPP derivatives are still largely unexplored and the studies on their chiral derivatives are even absent, which will seriously hinder their applications [17–19]. Therefore, we choose DPP core as the parent unit to design and modify its chiral derivatives through the chiral perturbation of pendants. Considering the intrinsic chirality of amino acid analogues, it will be greatly interesting to decorate the DPP core with them to obtain chiral DPP derivatives, which may show newly fascinating nonlinear chiroptical properties. In the present work, based on this design strategy, three chiral structures of DPP derivatives are proposed and they are investigated by theoretical tools. Simulated results indicate that the chiral DPP derivatives demonstrate excellent 2PA, two-photon CD (2PCD) and 3PA in the near-infrared window I and II. Additionally, the corresponding intramolecular charge transfer (ICT) is calculated to elaborate the nature of those nonlinear optical spectra [21]. Herein, we elucidate the relationship between the molecular structure of chiral DPP derivatives and their MPA properties, which may speed up the development of more excellent optoelectronic materials [22–24].
2. Theory formulas
Three amino acid pendants (alanine, proline and phenylalanine) are used to modify the DPP core and three DPP derivatives are then obtained as shown in Fig. 1, which are abbreviated as DPP-A, -B and -C and are expected to show large MPA and MPCD.
Actually, there are no commercial products available for the DPP derivatives displayed in Fig. 1, and the asymmetrical synthesis of them has not been reported yet. However, based on other DPP derivatives reported in previous work [25–27], a referable synthetic route was designed by us and corresponding experiments are well ongoing. The potential synthetic route for DPP-C is suggested as follows (Fig. 2).
The theoretical formulas of their MPA processes including 2PA, 2PCD and 3PA are briefly presented as follows. 2PA means that the molecule simultaneously absorbs two low-energy photons transferring from the ground state to the excited state. The corresponding 2PA cross-section is expressed as follows:
where is Bohr radius, is the fine structure constant, is the speed of light in vacuum, is the normalized line shape, is the frequency of radiation, is the energy difference between initial state and final state, is the 2PA transition probability [28].2PCD () can be derived as follows:
where , is the 2PCD rotatory strength [20]. The parameters in the rotatory strength are set to be 6, 2, −2, which are determined by the polarization and propagation status of the beam. In the equation, is Avogadro’s number,is the vacuum permittivity. are the functions of the frequency of radiation.3PA cross-section can be calculated according to
where is the 3PA transition probability [29]. MPA spectra can be achieved in DALTON [30]. The geometries optimization of the three modified molecules and the corresponding orbital transitions are completed in G09 with DFT [31]. All of the calculations employ two different exchange–correlation functionals (B3LYP and CAM-B3LYP) and two basis sets (6-31G* and 6-311 + + G**).3. Results and discussion
For 2PA and 2PCD spectra, the small basis set (6-31G*) can take fifteen lowest excited states into consideration. For the fifth-order nonlinear process (3PA), six lowest excited states are involved. The bigger basis set (6-311 + + G**) can only involve six lowest excited states for 2PA and 2PCD and three lowest excited states for 3PA. For better comparing the effects of basis sets, both of them take the same less lowest excited states into account. As shown in Figs. 3(a) and 3(b), even though the relative 2PA intensities of the three molecules are some different, 2PCD and 3PA spectra calculated from the small basis (Fig. 3(c) and 3(e)) are in good agreement with those obtained from the big basis set (Figs. 3(d) and 3(f)), respectively. Therefore, the simulated spectra slightly depend on the basis set. In order to unravel more information about the molecular structures, the MPA spectra containing more lowest excited states obtained by the small basis set will be demonstrated.
Fig. 3 The 2PA, 2PCD, 3PA spectra of the three chiral DPP derivatives simulated by B3LYP with two different basis sets. (The right column corresponds to the small basis while the left column corresponds to the big basis set.)
The 2PA spectra of the three molecules dealt with B3LYP and CAM-B3LYP are shown in Figs. 4(a) and 4(b), respectively. For better analyzing the spectrum profile, the intensity is displayed in arbitrary unit and normalized in Fig. 4. Obviously, the spectrum profiles of DPP-A and DPP-B in Fig. 4(a) are similar with those in Fig. 4(b). Moreover, the 2PA peaks of the two molecules located at the higher energy region are stronger than the peaks located at the low energy region due to near resonance effect. Even though the spectra profiles of DPP-C in both figures are different, there are two 2PA bands (500~750 nm and 750~1000 nm) no matter what functional is used. Particularly, the maximum 2PA intensities of two bands are nearly equal. All the spectra in Fig. 4(b) are blue-shifted compared with those in Fig. 4(a) since the functional CAM-B3LYP overestimates the vertical excitation energies. From the insets in both of the figures, the relative intensity of 2PA spectra can be obtained. The spectra intensity of DPP-B is always the strongest while that of DPP-C is always the weakest. Therefore, the influences of the functional we used is not very obvious. It is noted that the 2PA of the three molecules mainly locate in the near-infrared window I, which may play an important role in the applications of biomedicine and bioimaging.
Fig. 4 2PA spectra of the three chiral DPP derivatives calculated by 6-31G* with different functionals. (a) B3LYP; (b) CAM-B3LYP. Red line signifies DPP-A; Blue line represents DPP-B; Green line is DPP-C.
Based on the 2PA process, 2PCD is also calculated and presented in Fig. 5. Again, the spectra calculated by CAM-B3LYP are blue-shifted compared with those obtained by B3LYP. The 2PCD signals of DPP-B and DPP-C in Fig. 5(a) are stronger than corresponding signals in Fig. 5(b). Moreover, the 2PCD signals of DPP-A are always the strongest among the three molecules. As to the profiles of 2PCD spectra, DPP-B and DPP-C show different features when different functions are used, while DPP-A exhibits the similar spectrum shapes in the two figures. It is also noted that all the three molecules display strong 2PCD signals in the short wavelength region. Even so, it can be concluded that all of the three molecules exhibit distinct nonlinear chiroptical behaviors, which may possess potential chirality-based applications. As is expected, the molecular 2PCD spectra also locate at the near-infrared window I.
Fig. 5 The 2PCD spectra of the three chiral DPP derivatives calculated by 6-31G* with different functions (a) B3LYP, (b) CAM-B3LYP.
As a fifth-order nonlinear optical effect, 3PA demands more computational costs than 2PA. However, 3PA owns more advantages compared with 2PA. Therefore, 3PA of three molecules are also calculated by the two different functionals (Figs. 6(a) and 6(b)). Obviously, the three molecules show quite different spectra profiles, which demonstrate that the simulation of 3PA is sensitive to the functional used. The relative intensities of 3PA of the three molecules are presented in the inset. Again, 3PA of DPP-B is the strongest one. Additionally, 3PA of DPP-A and DPP-C keep nearly the same amplitude. In combination with the theoretical results of 2PA, the results of 3PA further confirm that DPP-B may be the most promising nonlinear chiroptical molecule among the three DPP derivatives. It is a remarkable fact that 3PA of the molecules mainly occurs in the biological window II (950-1350 nm), which will provide deeper penetration depth into biological tissues, better image contrast, and reduced phototoxicity and photobleaching [32].
Fig. 6 The 3PA spectra of the three chiral DPP derivatives dealt with by 6-31G* with different functionals (a) B3LYP, (b) CAM-B3LYP. The numbers (1, 3, 4, 5, 6) in the two figures represents the corresponding excited state contributing to the absorption peaks for the three molecules.
In order to unveil the nature of 3PA, the corresponding electronic transitions and relative electronic structure information (e.g. excitation energy, oscillator strength) achieved from the two functionals are provided in Table 1. To be specific, the dominant contributions of the orbital transition to the electronic transition S0→Sn are exhibited, which make the physical process more clearly. Furthermore, we perform an analysis on the involved frontier molecular orbitals, which are presented in Fig. 7. As can be seen, for the molecular orbitals HOMO-2 of DPP-A, HOMO-4 of DPP-C, HOMO-2 of DPP-A and HOMO-6 of DPP-C, the charges are distributed on both sides of the two molecules. However, for their molecular orbitals LUMO, the charges are transferred to the centralized part of the two molecules. As to DPP-B, although the charges are located at both sides and the central part for HOMO-5 and HOMO-3, the electrons are transferred to the main part for the molecular LUMO. Moreover, as shown in the lower part of Fig. 7, the molecular orbitals of DPP-B also exhibit the same features with those of DPP-A and DPP-C. Although different absorption peaks are contributed from different electronic transitions marked in Figs. 6(a) and 6(b), the similar ICT phenomenon for the three molecules with the same transfer direction from the modified part to the DPP core can be obviously observed in Fig. 7. Alternatively, the DPP core tends to withdraw electrons from the chiral pendants. Additionally, the same results achieved from the two functionals further demonstrate that ICT properties of the low-lying excited states play a significant role in the excellent MPA and MPCD.
Table 1. The excitation energy, oscillator strength, configuration weight and orbital transition of the lowest excited states contributing to the strongest 3PA peaks of the three DPP derivatives with B3LYP/6-31G*.
Fig. 7 The molecular orbital transitions of the three chiral DPP derivatives with B3LYP and CAM-B3LYP.
4. Conclusion
In conclusion, we have carried out theoretical studies on the MPA behaviors of three chiral DPP derivatives. The spectra of 2PA, 2PCD and 3PA are simulated by response theory with two basis sets and two functionals. The calculated results elucidate that chiral DPP derivatives show strong MPA and MPCD in the near-infrared window I and II. Among them, the MPA intensity of DPP-B is the strongest, which makes it a potential candidate in the related applications. Particularly, the obvious 2PCD further demonstrates that all the three molecules are nonlinear chiroptical materials, which possess promising abilities in the chirality related applications, such as biolabelling and optoelectronic devices.
Funding
National Natural Science Foundation of China (NSFC) (11404219); Natural Science Foundation of Guangdong Province (2014A030313552); Youth Innovation Talent Project (Nature Science) of the Universities of Guangdong Province (2014KQNCX127); Shenzhen Basic Research Project of Science and Technology under Grant (JCYJ20150324141711613 and JCYJ20130326111836781); The Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province (GD201603).
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