Evripidis
Michail
,
Maximilian H.
Schreck
,
Marco
Holzapfel
and
Christoph
Lambert
*
Institut für Organische Chemie and Center for Nanosystems Chemistry, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany. E-mail: christoph.lambert@uni-wuerzburg.de
First published on 5th August 2020
We explored a series of squaraine homodimers with varying π-bridging centres to probe the relationship between the chemical structure and the two-photon absorption (2PA) characteristics. To this end, we designed and synthesised six linear homodimers based on two indolenine squaraine dyes with transoid configuration (SQA) which are connected by diverse bridges. In this regard, we investigated the effect of exciton coupling in these dimeric systems where the variation of the bridging units affects the magnitude of exciton coupling and leads to an alteration of their linear optical properties. Using two-photon absorption induced fluorescence measurements we determined the two-photon absorption cross section in this series of homodimers and found sizable values up to 5700 GM at ca. 11000 cm^{−1} and 12000 GM at 12500 cm^{−1}. The 2PA strength roughly follows the exciton coupling interaction between the squaraine chromophores which therefore may be used as design criteria to achieve high 2PA cross sections. The results were substantiated by polarization dependent linear and nonlinear optical measurements and by density functional theory calculations based on time dependent and quadratic response theory.
Recently, we investigated the cooperative enhancement versus additivity of the 2PA cross section in linear and branched squaraine superchromophores.^{18} There, we could show that excitonic interactions lead to an enhancement of 2PA. In the present work we focus on engineering the exciton interaction by varying the spacer unit in a series of dimeric squaraine systems and probe the influence on the linear and non-linear photophysical properties. To this end, we have studied a series of six compounds built up from the well-investigated trans-squaraine parent chromophore SQA using a systematic length variation of the bridging unit, i.e. from a single bond in dSQA-1, over an acetylene bridge in dSQA-2, and a butadiyne-bridge in dSQA-3, to a tolan bridge in dSQA-5. But we also considered different conjugation pathways in e.g.dSQA-4vs.dSQA-3, and in dSQA-6vs.dSQA-1, as shown in Fig. 1.
Because of the flexible bridging units, in solution different conformers (rotamers) of the dimers exist, with exception of dSQA-6. The π-conjugated bridges allow us to consider essentially only two different stretched orientations, as indicated in Fig. 1. The arrangement where the long axes of the squaraine chromophores are parallel is called Type I and the one where they possess an angle of ca. 120° is called Type II. While for both conformers of all squaraine dimers besides dSQA-1, the two squaraine chromophores lie in the same plane, the biaryl dihedral angle in dSQA-1 leads to an out-of-plane arrangement of the two conformers. In fact, the two conformers of dSQA-1 possess C_{2} symmetry as the highest point group for Type I while that of all other dimers is higher (disregarding the symmetry lowering racemic alkyl chains R): D_{2h} for dSQA-2, dSQA-3, and dSQA-6, C_{i} for dSQA-4 and dSQA-5. However, electronically all homodimers exhibit “pseudo centrosymmetric” symmetry, thus in the following discussion we treat all dimers as they belonged to the D_{2h} point group and, for simplicity, we will use the symmetry assignments of states accordingly. Thus, considering the selection rules of 1PA and 2PA we assume that the one-photon states belong to the irreducible representation B_{u} and the two-photon allowed states belong to the A_{g} irreducible representation in all cases. Furthermore, Spano et al.^{19} recently investigated the optical properties of dSQA-1 by theoretical methods in detail and showed that the optical properties of the two conformers are rather similar. Thus, for most aspects, we do not further discriminate between these two conformers in this paper.
The linear optical absorption properties of this series of compounds were investigated by UV/vis absorption and emission spectroscopy and the 2PA spectra were determined by the two-photon induced fluorescence technique. One-photon fluorescence excitation anisotropy (1P-FEA) and two-photon fluorescence excitation anisotropy (2P-FEA) measurements were performed in viscous media (poly-THF) in order to assign the spectral positions of transitions and to determine the mutual orientation of transition dipoles, respectively. Experimental verification of the excited state symmetry has been carried out using two-photon polarization dependent spectroscopy with linear and circular polarised light. To gain a deeper insight into the evolution of the 2PA cross section as a function of the transition dipole moment as the exciton coupling decreases, transition dipole moment calculations were performed applying a three-state model.
We also performed theoretical calculations using time-dependent and quadratic response density functional theory (TD-DFT and QR-DFT) using the BHandHLYP hybrid functional for the optical properties and the B3LYP functional for optimisation of the geometries and the 6-31G* basis set. The calculations were carried out using the Gaussian and the DALTON program packages.^{20–22}
A detailed description of the syntheses of all compounds and the experimental methodology of this photophysical study is presented in the ESI.†
The steady state linear absorption and normalised fluorescence spectra of the monomer and the homodimers in toluene are shown in Fig. 2, a logarithmic plot can be found in the ESI† (Fig. S4). All the compounds investigated exhibit typical spectroscopic characteristics of squaraine dyes. The linear absorption spectrum of the monomer shows an intense sharp absorption peak at ca. 15500 cm^{−1} together with a weak vibronic shoulder on the high-energy side. The fluorescence spectrum behaves like a mirror image of the monomer absorption accompanied with a small Stokes shift.
Fig. 2 Linear absorption (top) and normalised fluorescence (bottom) spectra of monomer SQA, and homodimers dSQA-1–dSQA-6 in toluene. |
The absorption spectra of the homodimers are more complex, they are generally red shifted compared to the monomer and show higher molar extinction coefficients compared to the parent monomer. Moreover, in the case of the dSQA-1 to dSQA-4 homodimers, additional absorption bands on the high energy side of the main absorption peak are observed. The most intense absorption peak (14500–15200 cm^{−1}) originates from the lowest exciton state S_{1} which is bathochromically shifted with respect to the SQA monomer. In addition, two shoulders located at higher energies are attributed to the subsidiary vibronic progression and to a second electronic transition. The latter electronic transition is assigned to the upper exciton state S_{2}. We interpret the presence of this S_{2} state within the series of squaraine dimers as being caused by exciton coupling of monomer localised transitions. This coupling produces a so-called Davydov splitting of the first excited state of the two coupled parent monomer states.^{23,24} According to exciton coupling theory the S_{1} excited state of the SQA monomer splits in two excited states (S_{1}, S_{2}) in the homodimers and the splitting energy refers to twice the electronic exciton coupling energy, J.^{25}
The squaraine homodimer dSQA-6 with a rigid bridge was also investigated. Taking the advantage of its rigidity, the dimer cannot form rotamers and exhibits the features of a “J-type” dimer (i.e. head-to-tail arrangement of transition moments) exclusively. In this case, the upper exciton state vanishes, and the full transition strength is concentrated in the lower exciton state. The linear absorption spectra of the dSQA-6 in toluene shows an 1.5 times higher extinction coefficient (858000 M^{−1} cm^{−1} at 15100 cm^{−1}) than the other homodimers.
The squared transition dipole moments (μ^{2} = dipole strength) between the ground state S_{0} and the two exciton states were determined by integration of these bands^{26} (see eqn (S7) in the ESI†) and are summarised in Table 1. According to the Thomas–Reiche–Kuhn sum rule^{27} the square of the transition dipole moments shows nearly additive behaviour with respect to the SQA monomer, which gives similar values for all the homodimers (μ^{2} = 245–269 D^{2}) proving that no other states besides the two exciton states are located in this energy range.
Squaraine centre-to-centre distance | Absorption maximum of S_{1} | Absorption maximum of S_{2} from 1PA spectra | Exciton coupling energy as | Absorption maximum of S_{2} from 1P-FEA spectra | Exciton coupling energy as | Dipole strengths of the total exciton manifold | Emission maximum | Fluorescence quantum yield | |
---|---|---|---|---|---|---|---|---|---|
L/Å | _{S1}/cm^{−1} [ε/M^{−1} cm^{−1}] | _{S2}/cm^{−1} | J/cm^{−1} | /cm^{−1} | J ^{ r }/cm^{−1} | μ ^{2}/D^{2} | _{em}/cm^{−1} | Φ _{fl} | |
a See also ref. 34. | |||||||||
SQA | 15530 [3.64 × 10^{5}] | 127 | 15360 | 0.62 | |||||
dSQA-1 | 17.1 | 14480 [4.66 × 10^{5}] | 16140 | 830 | 16310 | 920 | 248 | 14240 | 0.80 |
dSQA-2 | 19.6 | 14550 [4.65 × 10^{5}] | 16060 | 760 | 16290 | 870 | 254 | 14360 | 0.78 |
dSQA-3 | 22.0 | 14720 [6.04 × 10^{5}] | 15400 | 340 | 15600 | 440 | 269 | 14530 | 0.74 |
dSQA-4 | 21.2 | 14910 [5.94 × 10^{5}] | 15420 | 260 | 15690 | 390 | 260 | 14730 | 0.77 |
dSQA-5 | 27.7 | 15110 [5.94 × 10^{5}] | — | — | 15280 | 90 | 252 | 14900 | 0.71 |
dSQA-6 ^{ } | 18.7 | 15120 [8.58 × 10^{5}] | — | — | 15900 | 390 | 245 | 15020 | 0.71 |
All homodimers display strong fluorescence with a small Stokes shift. The fluorescence spectra resemble that of SQA monomer but are red-shifted according to the respective absorption spectra. This proves that fluorescence is emitted from the lowest exciton state only. The quantum yield varies with the exciton coupling strength between 0.80 and 0.71 but is in all cases higher than that of the monomer which is the consequence of the coupled transition moments (superradiance).^{28} Likewise, the squared transition moment for the fluorescence as determined from the Strickler–Berg equation (see eqn (S8) in the ESI†) varies between 147–177 D^{2} for the homodimers compared to 114 D^{2} for SQA (see Table S1 in the ESI†). The strong fluorescence allowed the investigation of the 2PA cross section by the two-photon induced fluorescence method, see below.
The estimation of the exciton coupling strength is an important aspect in this study, as we will correlate the nonlinear optical properties with this quantity. Below, we will take symmetry arguments into account in order to assess the energy of the upper excitonic state, S_{2}. Looking at the Type I conformer and assuming D_{2h} symmetry, the first electric dipole allowed transition is S_{1} ← S_{0} (1B_{u} ← 1A_{g}), with 1B_{u} representing the lowest one-photon excitonic level. The next electronic transition is S_{2} ← S_{0} (2A_{g} ← 1A_{g}) which is forbidden by symmetry as a 1PA process. However this state is weakly allowed for two reasons, firstly, the symmetry of the corresponding S_{2} state in the Type II conformer, which is present in presumably equimolar amounts, is lower which breaks the centrosymmetry and, secondly, vibronic coupling of this 2A_{g} state to an asymmetric vibration also makes this transition weakly allowed.^{28,29}
Going from dSQA-1 to dSQA-6 we observe a gradual decrease of the red-shift of the main absorption peak with respect to SQA which leads to an enhanced mixing of electronic and vibronic states.^{30} The conclusion from the latter result is that the exciton coupling strength of the homodimers decreases by changing the bridging units from dSQA-1 to dSQA-6. This interpretation is confirmed by estimation of the effective exciton coupling strength J between the two monomers (see Table 1) taking half of the S_{2}–S_{1} energy as J for dSQA-1 to dSQA-4. For dSQA-5 and dSQA-6 the upper exciton state is hardly visible as a shoulder to the high energy side of the main peak and does not allow to extract J within reasonable accuracy. However, considering the absolute red-shift of the lowest energy absorption of the squaraine dimer vs. the one of the monomer allows to estimate J at least qualitatively. The fluorescence spectra show the same trend. Thereby, J decreases on going from dSQA-1 to dSQA-5 which has the same lowest energy absorption as dSQA-6. Attention is drawn to the fact that the spacer length between the two chromophores (see Table 1) does not completely correlate with the exciton coupling strength which varies from 830 cm^{−1} for dSQA-1 to 260 cm^{−1} for dSQA-4. This shows that the electronic coupling is not only due to dipole–dipole interactions but also depends to some extent on the chemical structure of the π-bridge and conjugative effects play a role.^{31}
In order to estimate the energy of the S_{2} state and of J more accurately, especially for dSQA-5 and dSQA-6, and to assign the symmetry of higher-excited states we performed one-photon fluorescence excitation anisotropy measurements in viscous poly-THF (the 1P-FEA, spectra can be found in the ESI† and the maximal anisotropy in Table 3). The 1PA anisotropy is related to the angle θ_{01} between the absorption and emission transition moment through eqn (1).^{32} Ideally, the lower energy exciton state of all dimers should show an anisotropy of r_{1PA} = 0.4 (i.e. parallel transition moments for absorption and emission of the 1B_{u} state).^{33} In case of Type I conformer, the higher exciton state (2A_{g} symmetry) should possess a vanishing transition moment while that of Type II conformer should have perpendicular transition moments for absorption and emission, that is, r_{1PA} = −0.2. In case of strong exciton coupling, i.e. delocalised excited state over both monomers, the limiting anisotropy of the 1B_{u} state should always be 0.4 even when the solution consists of different conformers of homodimers. Indeed, the 1P-FEA value r_{1PA} for the dSQA-1 homodimer in poly-THF at the 1B_{u} state is 0.36, confirming strong exciton coupling. Even that of dSQA-2 is still pretty high (r_{1PA} = 0.33). However, for weak exciton coupling the excitation becomes increasingly localised within the excited state lifetime because of vibronic coupling.^{34} This leads to a deviation of the angle of the transition moment for delocalised absorption (green transition moments, in Fig. 1) and localised emission (blue transition moments, in Fig. 1) for the Type II conformer. For the extreme case of total localisation of excitation we can estimate the limiting anisotropy as follows: while in Type I conformer the transition moment for absorption and emission are parallel even after localisation, in case of Type II conformer, the transition moments after localisation form an angle of ca. 60° which will lead to an anisotropy of −0.05. Averaging over the two conformers then leads to r_{1PA} = 0.175. Indeed, for dSQA-5 the anisotropy is at the red side of the 1B_{u} band 0.18 which is a distinct hint towards complete exciton localisation after excitation. At the band maximum and the blue side the anisotropy is considerably lower because of band overlap with the 2A_{g} band. The anisotropies of the other dimers are in-between those of dSQA-1 and dSQA-5.
(1) |
For the upper exciton state in case of strong coupling, we find a vanishing transition moment for Type I conformer (2A_{g} state). For the Type II conformer, an anisotropy of −0.2 results (this state is polarised along the C_{2} axis and thus is perpendicular to the emission transition moment). In case of weak exciton coupling, localisation leads to r_{1PA} = 0.4 for Type I but to −0.05 for Type II. Again, averaging yields r_{1PA} = 0.175. For the 2A_{g} state of dSQA-1 the experimental anisotropy is −0.02. The deviation from −0.2 is most likely caused by band overlap with the allowed 1B_{u} state which, if it were exclusively excited, would yield r = 0.4. Nevertheless, this low anisotropy helps to assign the 2A_{g} state to be at 16100 cm^{−1}. The lowest anisotropy for the dSQA-2 homodimer is 0.016 and is at 16100 cm^{−1} which is therefore assigned to the S_{2} state. We therefore used the lowest anisotropy in the suspected S_{2} energy region to assign the energy of the S_{2} state more precisely. These values and the exciton couplings derived from these energies are also given in Table 1. The latter are in good agreement with those estimated from the absorption spectra. dSQA-6 is a special case as it is weakly coupled but cannot form a Type II conformer. Accordingly, the anisotropy is between 0.32–0.38 over the whole exciton state range. The latter finding also supports the interpretation of the anisotropy of the more flexible dimers to be caused by an equimolar mixture of two rotamers. Using the thereby obtained S_{2} energies we can now estimate the exciton coupling energy more accurately which ranges between J^{r} = 920 to 90 cm^{−1} for dSQA-1–dSQA-5 but again increases for dSQA-6 with 390 cm^{−1} (see Table 1).
As will be shown below, the above mentioned exciton coupling energies for dSQA-1 to dSQA-4 are supported by quantum chemical time-dependent density functional calculations at BHandHLYP/6-31G* level (see Table 4). While the computed state energies for S_{1} and S_{2} are generally much too high by ca. 4000 cm^{−1}, their energy difference divided by two gives an estimate for the exciton coupling energy. Here, for dSQA-1 to dSQA-4 we obtain values between 786 cm^{−1} and 430 cm^{−1} which are in reasonable agreement with experimental estimates. This gives confidence that the values for dSQA-5 and dSQA-6 are not far off the computed values of 238 and 482 cm^{−1}. Thus, in this work we assume a qualitative order of exciton coupling decreasing from dSQA-1 to dSQA-5.
Fig. 4 Plot of two-photon absorption cross-section spectra versus twice the laser excitation energy of monomer SQA and dSQA-1–dSQA-6 in toluene. |
All the homodimers in toluene solution show significant 2PA in the investigated spectral region between 15000–25000 cm^{−1} (see Fig. 4). We can roughly divide the 2PA spectra into three sections: the first section covers 2PA bands up to 18000 cm^{−1} which comprises the 2PA into the formally 2PA-forbidden lower-energy 1B_{u} exciton state and the 2PA-allowed higher-energy 2A_{g} exciton state. The 2PA cross section reaches maximum values of ca. 400 GM. The second section covers 2PA from roughly 18000 to 24000 cm^{−1}. Here, several peaks are visible which show a distinct spectral evolution on going from dSQA-1 to dSQA-6. The 2PA cross section decreases from ca. 6000 GM for dSQA-1 to ca. 400 GM for dSQA-6, that is, their intensities roughly decrease upon decreasing exciton coupling. DFT computations (see below) yield only one 2PA-allowed transition in this spectral region, thus, the diverse peaks appear to be a vibronic progression of a single electronic transition. The third 2PA section is above 24000 cm^{−1} and shows an extremely high 2PA cross section for all homodimers on the order of 10^{4} GM. A peak maximum cannot be discerned clearly in that case. For the sake of comparison, the 2PA together with linear absorption spectra and 1P-FEA are depicted in Fig. S6 in the ESI.† The optical data are summarised in Table 2.
_{S1}/cm^{−1} | σ ^{2PA}/GM | _{S2}/cm^{−1} | σ ^{2PA}/GM | 〈δ^{2PA}〉^{a}/a.u. | _{S3}/cm^{−1} | σ ^{2PA}/GM | 〈δ^{2PA}〉^{b}/a.u. | |
---|---|---|---|---|---|---|---|---|
a The 2PA strength cover that of the S_{1} and the S_{2} state. Integration limits 14600–17800 cm^{−1} (19300 cm^{−1} for dSQA-6). b Integration limits 17800–24000 cm^{−1} (23200 cm^{−1} for dSQA-6). c The wavenumbers for the assigned states are those with a maximum of 2PA cross section and do not necessarily agree with the wavenumbers in Table 1. | ||||||||
SQA | 15750 | 24 | ||||||
dSQA-1 | 14390 | 47 | 16130 | 397 | 3.42 × 10^{4} | 21980 | 5740 | 4.77 × 10^{5} |
dSQA-2 | 14490 | 44 | 16000 | 360 | 2.53 × 10^{4} | 21980 | 4660 | 3.53 × 10^{5} |
dSQA-3 | 14270 | 121 | 16260 | 405 | 2.68 × 10^{4} | 21980 | 4330 | 3.23 × 10^{5} |
dSQA-4 | 15270 | 99 | 16130 | 397 | 2.07 × 10^{4} | 21980 | 2670 | 2.22 × 10^{5} |
dSQA-5 | 15040 | 36 | 16390 | 239 | 1.52 × 10^{4} | 22470 | 1530 | 9.69 × 10^{4} |
dSQA-6 | 15040 | 13 | 16260 | 269 | 1.58 × 10^{4} | 22222 | 375 | 1.69 × 10^{4} |
(2) |
For the first energy region, a slight decrease of the 2PA strength from about 3.4 × 10^{4} a.u. to 1.5 × 10^{4} a.u. is observed on going from the strongly coupled dSQA-1 to the weakly coupled dSQA-5. In case of centrosymmetric molecules, the 2PA strength can be estimated by a three level model (eqn (3) with all quantities in a.u.)^{40} where μ_{01}^{2} and μ_{12}^{2} are the transition moments between the ground and the first 1PA allowed state (S_{1}) and between first and second excited state (S_{2}). Here, the transition moments are assumed to be parallel (for the general case of arbitrary angle between the transition moments, see eqn (4)). ω_{01} and ω_{02} are the energy differences between these excited states and the ground state. If we deal with excitonically coupled monomers in a dimer, the transition moment between the first and the second exciton state μ_{12} equals the dipole moment difference of ground and excited state of the monomer Δμ. Thus, for a centrosymmetric monomer without CT contribution in the first excited state such as SQA, μ_{12} = Δμ = 0 and for a dimer built from such a monomer the 2PA strength of the S_{2} state should vanish. In practice, because of symmetry breaking small CT contributions will lead to a small 2PA strength as observed in the series of dimers investigated in this work.
(3) |
(4) |
(5) |
As the input for eqn (5), the transition moment between S_{0} and S_{1} is known by integration of the S_{1} band (see Table 1). The energy ω_{01} is the S_{1} state energy (see Table 1) and ω_{03} is the S_{3} state energy (see Table 2). The integration of the 2PA allowed S_{3} band yields 〈δ^{2PA}〉 in Table 2. The hitherto unknown angle θ_{13} is related to the 2PA anisotropy r_{2PA}viaeqn (6):^{45}
(6) |
Here, the average angle for Type I and Type II isomer θ_{01} was obtained by 1P anisotropy measurements (see above and Fig. S6, ESI†). The 2PA anisotropy r_{2PA} was determined by measuring the 2PA cross section in viscous poly-THF (see above, Table 3 and Fig. S9, ESI†) which yields the average angle θ_{03} through eqn (6). This angle was inserted in eqn (5) to evaluate μ_{13}^{2} which is listed in Table 3. One can immediately see that μ_{13}^{2} decreases from ca. 64 D^{2} to 3 D^{2} in the series from dSQA-1 to dSQA-6 which is, more or less, with decreasing exciton coupling strength. Here we have to take into account that these numbers are average values referring to an equimolar mixture of Type I and Type II conformers. Therefore, we also give μ_{13}^{2} for the extreme angles θ_{13} = 0° and 90°. Although the thereby evaluated μ_{13}^{2} is smaller/larger than in case of varying angles, they follow the same trend which clearly indicates that the differences in 2PA strength are caused by the difference of exciton coupling in this series of squaraine dimers.
r _{1Pmax} | θ _{01}/deg | r _{2PA} [at /cm^{−1}] | θ _{13}/deg | ω _{01}/cm^{−1} | ω _{03}/cm^{−1} | 〈δ^{2PA}〉/a.u. | μ _{13} ^{2}/D^{2} | μ _{13} ^{2}/D^{2}θ_{13} = 0° | μ _{13} ^{2}/D^{2}θ_{13} = 90° | |
---|---|---|---|---|---|---|---|---|---|---|
a This angle refers to the minimum anisotropy of 0.14. | ||||||||||
dSQA-1 | 0.35 | 16.8 | 0.41 [21 980] | 71 | 14500 | 21980 | 477085 | 63.6 | 25.7 | 77.0 |
dSQA-2 | 0.33 | 20.0 | 0.28 [21 980] | 81 | 14500 | 21980 | 353413 | 53.1 | 18.6 | 55.7 |
dSQA-3 | 0.23 | 32.2 | 0.17 [21 980] | 89 | 14700 | 21980 | 322594 | 53.6 | 17.9 | 53.7 |
dSQA-4 | 0.29 | 25.4 | 0.38 [21 980] | 77 | 14900 | 21980 | 222035 | 38.5 | 14.1 | 42.4 |
dSQA-5 | 0.18 | 37.3 | 0.13 [22 470] | 90^{a} | 15100 | 22470 | 96886 | 18.7 | 6.22 | 18.7 |
dSQA-6 | 0.36 | 15.0 | 0.50 [22 220] | 62 | 15120 | 22220 | 16886 | 2.7 | 1.27 | 3.82 |
S_{1} (1B_{u}) | J = (ΔES_{1}S_{2})/2/cm^{−1} | S_{2} (2A_{g}) | S_{3} (3A_{g}) | S_{4} (2B_{u}) | S_{5} (3B_{u}) | S_{6} (4A_{g}) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
/cm^{−1} | f | /cm^{−1} | 〈δ〉/a.u. | /cm^{−1} | 〈δ〉/a.u. | /cm^{−1} | f | /cm^{−1} | f | /cm^{−1} | 〈δ〉/a.u. | ||
a ^{ }The symmetry assignments refer to D_{2h} symmetry although the actual symmetry might be different. n–π* excitations with zero oscillator strength and 2PA cross section are omitted. b For dSQA-1 with C_{2} symmetry there are very small oscillator strengths f also for the “pseudo” g state and, vice versa, TPA cross sections for the u states, but these are negligible. c The energetic order of states is reversed concerning symmetry. | |||||||||||||
SQA | 15892 | 1.55 | 29147 | 1.12 × 10^{5} | |||||||||
dSQA-1 ^{ } | 14666 | 3.55 | 786 | 16237 | 1540 | 22337 | 1.63 × 10^{6} | 22613 | 0.01 | 27534 | 0.09 | 28583 | 1.38 × 10^{6} |
dSQA-2 | 14442 | 3.98 | 759 | 15959 | 3880 | 22342 | 3.06 × 10^{6} | 22577 | 0.05 | 26163 | 0.19 | 27454 | 1.64 × 10^{6} |
dSQA-3 | 14460 | 4.21 | 657 | 15773 | 1810 | 22656^{c} | 3.39 × 10^{6} | 22569^{c} | 0.14 | 25195 | 0.34 | 27131 | 2.09 × 10^{6} |
dSQA-4 | 15037 | 3.83 | 430 | 15897 | 500 | 23281 | 7.40 × 10^{5} | 23311 | 0.02 | 27050 | 0.23 | 27776 | 1.61 × 10^{6} |
dSQA-5 | 15156 | 4.11 | 238 | 15632 | 198 | 24011^{c} | 5.30 × 10^{5} | 23924^{c} | 0.14 | 25679 | 1.1 | 27050 | 1.75 × 10^{6} |
dSQA-6 | 15222 | 3.72 | 482 | 16185 | 105 | 23238 | 2.02 × 10^{4} | 23242 | 0 | 28744 | 0.04 | 28825 | 1.29 × 10^{6} |
Exciton coupling of the two squaraine chromophores leads to four excited states in the investigated energy region. While the first exciton state (1B_{u}) is strongly 1PA-allowed, the fourth (2B_{u}) is only weakly allowed. In contrast, the second exciton state (2A_{g}) is only weakly 2PA-allowed but the third (3A_{g}) is strongly 2PA-allowed. This could be rationalised applying a three-level model. Here, the squared transition moment between the first exciton state (1B_{u}) and the 2PA-allowed state plays the dominant role. In case of the weakly 2PA-allowed second exciton state, this transition moment is generally small in the series of squaraine dimers as we deal with chromophores lacking significant local charge-transfer contributions. This leads to overall small 2PA cross sections for the 2A_{g} states which do not vary greatly within the series of homodimers. However, in case of the third exciton state (3A_{g}) this squared transition moment is large and its magnitude follows qualitatively the exciton coupling strength (see Fig. 5). One exception is dSQA-6 which possesses the smallest 2PA cross section although its exciton coupling is quite significant and equals that of dSQA-4. As the homodimer dSQA-6 is the only one where the two squaraines within the investigated series of homodimers are connected by a saturated bridge, we conclude that a lack of conjugation leads to small 2PA cross sections of the 3A_{g} state. Thus, short and conjugated bridging units between the two squaraine chromophores increase the exciton coupling and thereby enhance the 2PA strength in such homodimers. In this way, substantial 2PA cross sections of up to 5700 GM at ca. 11000 cm^{−1} and 12000 GM at 12500 cm^{−1} could be obtained.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0cp03410j |
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