and optically-forbidden 1B u or 3A

Pump-probe spectroscopy after selective excitation of all-trans Cars (n = 9-13) in nonpolar solvent identified a symmetry selection rule of diabatic electronic mixing and diabatic internal conversion, i.e., '1B(u)(+)-to-1B(u)(-) is allowed but 1B(u)(+)-to-3A(g)(-) is forbidden'. Kerr-gate fluorescence spectroscopy showed that this selection rule breaks down, due to the symmetry degradation when the Car molecules are being excited, and, as a result, the 1B(u)(+)-to-3A(g)(-) diabatic electronic mixing and internal conversion become allowed. On the other hand, pump-probe spectroscopy after coherent excitation of the same set of Cars in polar solvent identified three stimulated-emission components (generated by the quantum-beat mechanism), consisting of the long-lived coherent cross term from the 1B(u)(+) + 1B(u)(-) or 1B(u)(+) + 3A(g)(-) diabatic pair and incoherent short-lived 1B(u)(+) and 1B(u)(-) or 3A(g)(-) split incoherent terms. The same type of stimulated-emission components were identified in Cars bound to LH2 complexes, their lifetimes being substantially shortened by the Car-to-BChl singlet-energy transfer. Each diabatic pair and its split components appeared with high intensities in the first component. The low-energy shifts of the 1B(u)(+)(0), 1B(u)(-)(0) and 3A(g)(-)(0) levels and efficient triplet generation were also found.

Here, attention was focused on the overlap of 1B u + -to-1B u -and 1B u + -to-3A g -vibronic levels, shown in Fig. 1b.Then, experiments were designed to excite more than two different vibronic levels coherently (in phase) and to find out what kind of excited-state dynamics could be obtained.
In the Figure, we assumed sets of vibrational ladders with a spacing of ~1400 cm -1 (collectively considering the C=C and C-C stretchings and other vibrational modes).Then, the overlap of the vibrational ladders solely depended on the υ = 0 vibrational origins of the 1B u + , 3A g -, 1B u -and 2A g -singlet states shown in the linear relations in Fig. 1a.The energy gap of vibrational ladders in Car (n = 11) was the largest (300 cm -1 ), whereas that in Car (n = 10) was practically negligible (0 cm -1 ).
To change the conditions of excitation, two different pulse durations, i.e., 100 fs and 30 fs, were used.Figure 2 shows correlation between the pulse durations and the spectral widths.Here, the energy gap of 300 cm -1 in Car (n = 11) is an example.Then, the 100 fs pulse with a 200 cm -1 spectral width tends to selectively and incoherently excite the 1B u + (0) level, whereas the 30 fs pulse with a 700 cm -1 spectral width tends to simultaneously and coherently excites both the 1B u + (0) and 3A g -(1) levels.This is an extreme case but the situation can be more or less similar when the energy gap is smaller.

SELECTIvE, InCOHEREnT ExCITATIOn By 100 fs PuLSES (a) Pump-probe stimulated-emission spectroscopy:
Excitation to the 1B u + (0) and 1B u + (1) levels of Cars (n = 9-13) in nonpolar solvents (Zuo et al., 2007;Sutresno et al., 2007) Here, the Car molecules were excited to the 1B u + (0) and 1B u + (1) vibronic levels with 100 fs pulses with a high photon density from the A g toward the B u state.Then, the Pariser's ± signs lose their implication.(However, we will keep using the signs as formality.)Here, attention was focused on the patterns of the initial stimulated emission spectra.It turned out that the stimulated emission of the shorter-chain Cars (n = 9 and 10) consisted of two components, i.e., from the 1B u + and 1B u -vibronic levels, whereas the stimulated emission of the longer-chain Cars (n = 11-13), only one component, i.e., from the 1B u + vibronic level.
Longer-chain Cars (n = 11-13): After 0 ← 0 excitation, only the 1B u + (0) stimulated emission was observed, whereas after the 1 ← 0 excitation, only the 1B u + (1) stimulated emission, instead.Neither the contribution of the 3A g -counterpart nor the vibrational relaxation in the 1B u + manifold was observed at all.Thus, in both excitations, the direct 1B u + to 1B u -internal conversion took place, skipping the 3A g -state inbetween.This is due to the absence of electronic mixing between the 1B u + + 3A g -diabatic pair and the presence of strong electronic interaction between the 1B u + and 1B u -vibronic pair.Thus, the reason why we did not see the 3A g -signal at all was explained.The above set of results lead us to a symmetry selection rule concerning the diabatic electronic mixing and internal conversion: '1B u +to-1B u -is allowed but 1B u + -to-3A g -is forbidden.'(Kakitani et al., 2009) We tried to excite a set of Cars (n = 9-12) to the higher 1B u + vibronic levels to examine the effect of twisting of the conjugated chain upon excitation and the resultant breakdown of the above-mentioned symmetry selection rule due to symmetry degradation from C 2h to C i .

(b) Kerr-gate fluorescence spectroscopy: Excitation to the 1B u + (3) or 1B u + (4) levels of Cars (n = 9-12) in nonpolar solvents
(1) In shorter-chain Cars (n = 9 and 10), the fluorescence patterns of components I and II (hereafter, abbreviated as 'fluorescence patterns I and II') consisted of fluorescence from the relevant 1B u + and 1B u -vibronic levels, although the fluorescence pattern II of Car (n = 10) contained fluorescence from the 3A g -vibronic levels, originating from the 3A g -state overlapped with the 1B u + state in the energy diagram (see Fig. 1a), and its splitting into two peaks was ascribable to a pair of molecules in the unit cell of an aggregate.Fluorescence pattern III was predominated by fluorescence from the 1B u + (0), because the 1B u -optically-forbidden component internallyconverted to the isoenergetic 2A g -vibronic level.Figure 2. Correlation between pulse-duration and spectralwidth.Optically-allowed 1B u + and optically-forbidden 1B u -or 3A g -vibronic levels of carotenoids (2) In longer-chain Cars (n = 11 and 12), slightly-shaped, broad profiles of fluorescence patterns I, II and III could be simulated partially by fluorescence from the 1B u + (2), 1B u + (1) and 1B u + (0) vibronic levels but predominantly by a pair of fluorescence progressions from the 3A g -vibronic levels.The relative contributions of the above three fluorescence components exhibited no systematic changes at all.
Most importantly, we observed not only the 1B u + -to-1B u - diabatic electronic mixing in the shorter-chain Cars (n = 9 and 10) but also the 1B u + -to-3A g -diabatic electronic mixing in the longer-chain Cars (n = 11 and 12).The results indicated that symmetry degradation took place while the Car molecules were being vibronically excited, presumably due to the twisting of the conjugated chain around the C=C bonds.Then, the symmetry selection rule concerning the diabatic mixing broke down, and it became 'both the B u -to-B u and B u -to-A g mixing are allowed' (See, for the details, the reference listed in the title).

SImuLTAnEOuS, COHEREnT ExCITATIOn By ~30 fs PuLSES
The key results obtained here was the generation of quantum beat, consisting of the coherent cross term of the diabatic pair and the split incoherent terms of the diabatic counterparts.In the following subsections, descriptions will be made in the order, the split incoherent terms of the optically-forbidden counterparts and, then, the coherent cross term of the diabatic pair.
Here, we examine whether the excited-state dynamics of the same set of Cars free in solution (Fig. 3) are similar to, or different from, those bound to LH complexes (Fig. 4).In this and the next subsections, we are going to compare the excited-state dynamics between Cars free in solution and those bound to the LH2 complexes.This is the reason why we specifically choose Cars (n = 9-11).
The time-resolved stimulated-emission and transientabsorption spectra (Fig. 3) can be characterized in terms of relaxation schemes shown in Fig. 5.This Figure explains a quantum-beat mechanism as follows: Emission from the split counterparts.Weak stimulated-emission peaks labeled 1B u -(blue) and 3A g -(green) have been found to have energies which fit the linear relations of the 1B u -  (0) and 3A g -( 0) levels as shown in Fig. 1a.Thus, they are ascribable to the results of splitting from the 1B u + (0) + X -(υ) diabatic pair followed by vibrational relaxation.Weak emission peaks which are labeled '1B u + (red)' can be ascribed to the transitions of the optically-allowed split counterpart, accompanying the optically-forbidden 1B u -(blue) or 3A g -(green) emission.
Emission from the diabatic pair.Immediately after excitation ('0.02 ps' in Fig. 3), a weak peak appears at the (0 ← 0) peak position of the ground-state absorption (the top panels).This indicates that the 1B u + (0) counterpart is initially excited as a precursor.Subsequently, much stronger and broader peaks ascribable to the 1B u + (0) + X -(υ) diabatic pairs grow and stay for a long time.Intuitively, backand-forth transformation between the optically-allowed (1B u + ) and optically-forbidden (1B u -or 3A g -) diabatic vibronic levels gives rise to such a long-lived emission peak (called 'persistent peak').

(b) Quantum beat and triplet generation in Cars (n = 9-11) bound to the LH2 complexes (Christiana et al., 2009)
As shown in the previous subsection, the coherent excitation of Cars (n = 9-11) in a polar solvent exhibited not only the short-lived stimulated emission from the split and vibrationally-relaxed 1B u + (0) and X -(0) counterparts but also the strongly-coupled, long-lived emission from the 1B u + (0) + X -(υ) diabatic pair, which had been explained in terms of the quantum-beat mechanism.Here, we examine whether the excited-state dynamics of the same set of Cars bound to the LH2 complexes are similar to, or different from, those free in solution.
The time-resolved stimulated-emission and transientabsorption spectra of the set of Cars bound to the LH2 complexes from Rba. sphaeroides G1C, Rba.sphaeroides 2.4.1 and Rsp.molischianum are presented in Fig. 4, which can be characterized as follows: Emission from the split counterparts.When bound to the LH2 complexes, basically the same set of the split counterparts, including 1B u + (0), 1B u -(0) and 3A g -(0), are seen but they appear almost immediately after excitation.It seems that the excited-state dynamics is strongly accelerated.Their energies were compared with those in THF solution (data not shown): All of the 1B u + (0), 1B u -(0) and 3A g -(0) levels were shifted downward in energy when compared with those in solution.Surprisingly, the shifts of the covalent 3A g -and 1B u -levels were larger than that of the ionic 1B u + level.This observation strongly suggests a strong polarization of the conjugated chain.Emission from the diabatic pair.When bound to the LH2 complexes, stimulated emis-  Optically-allowed 1B u + and optically-forbidden 1B u -or 3A g -vibronic levels of carotenoids sion from the diabatic pair becomes much broader or even splits into two peaks, probably due to their strong coupling (Fig. 4).It becomes much stronger and more short-lived, indicating again the accelerated excited-state dynamics.Transient absorptions.Transient absorption from the T 1 state is clearly seen.Importantly, the branching of the 1B u -state into the 2A g -state and the T 1 state is suggested here spectroscopically, which is evidenced in Fig. 6.
The above characterization of the time-resolved spectra leads us to the overall relaxation scheme shown in Fig. 4. The observation of the 1B u + (0) + X -(υ) diabatic pair and the 1B u + (0) and X -(υ) split counterparts evidences the quantum-beat mechanism.The appearance of the 1B u -transient absorption followed by the 2A g -and T 1 transient absorptions indicates the 1B u -→ 2A g -internal conversion plus the 1B u -→ T 1 singlet fission branching processes.The latter process is most probably facilitated by the twisting of the conjugated chain due to the binding of the relevant Car to the apo-complex consisting of peptides and BChls.
The decay of each component, shown below in time profiles, is extremely fast, indicating singlet energytransfer reactions through the three channels.The lightharvesting function of not only the 1B u -state but also the 3A g -state would be evidenced, when the energy-transfer efficiencies had been determined including the excitedstate dynamics of BChl a as the accepter.Obviously, coherent excitation of the diabatic pair, i.e., 1B u + + 1B u -or 1B u + + 3A g -, to generate quantum beat should be another powerful mechanism of enhancing the Car-to-BChl singlet-energy transfer, taking advantage of both the 1B u - and 3A g -optically-forbidden states.

Figure 1 .
Figure 1.(a) Energies of the 1B u + (0), 3A g -(0), 1B u -(0) and 2A g -(0) vibronic levels of Cars (n = 9-13) free in solid and the T 1 state of Cars (n = 9-11) bound to LH2 complexes and the Q x and Q y levels of BChl a bound to LH2 (B800 and B850) and the LH1 (B880) complexes.(b) The vibrational ladder of the 1B u + state overlapped with those of the 1B u -states of Cars (n = 9 and 10) and the 3A g -states of Cars (n = 11-13).