Relaxation Processes and Fluorescence Dynamics

Excited states can relax along different channels (see Figure 8). These relaxation channels are often visualized by a so-called “Jablonski diagram” which contains the energetic scheme of the relevant molecule’s states. The absorption process occurs instantaneously, i.e. it is faster than the resolution limit of the applied optical setup. In the literature there is still discussion about the duration of an absorption process, assumed times for absorption range from the time light needs to cross a molecule (i.e. about 10_17 s = 0.01 fs) up to the time that the electron needs to cross the molecule (i.e. about 10_14 s = 10 fs). The (one electron) excited states of molecules typically exhibit spin multiplicity 1 (singlet states) or 3 (triplet states). We distinguish this by the notation Sl for the excited singlet state and T for the ith excited triplet state.

According to the Franck Condon principle the absorption process does not excite the vibronic ground state of an electronically excited singlet state S г v0 but a higher vibronic level S^j. Due to the shift of the energy parabola between ground and exited state along the reaction coordinate, the overlap between the wave functions of the vibronic ground states (j = 0) of the electronic ground and first excited state (S0v0 and S3v0, respectively) is smaller than the overlap between S0v„ and Stvk (k > 0) (see inset of Figure 8).

Jablonski diagram for chlorophyll coupled to a neighbouring molecule

Figure 8. Jablonski diagram for chlorophyll coupled to a neighbouring molecule. The shown energetic states of chlorophyll are the singlet states S0, S1, S2, S3 and Sn and exemplarily the triplet states T3 and Tn with vibronic niveaus that are denoted as vj. The indicated transitions are explained in the text. The inset is showing the parabola for the ground state and the first excited state with the most probable transitions for absorption and fluorescence according to the Franck-Condon principle.

This energetic picture can be explained by the fact that the molecular configuration of the nuclei is different between the electron in the ground state and in the first excited state. Therefore the nuclei start to move if one electron is excited and the lattice takes up a phonon.

The relaxation by light emission (luminescence) cannot emit the same amount of energy as was absorbed before. Therefore, the fluorescence must be red shifted with respect to the absorption. This red shift of the fluorescence light is called a “Stokes shift”.

With typical rate constants kIC1—1012 s 1 the electrons relax

IC

from SjV. into the state S^0 due to internal conversion (phonon emission). The subsequent radiative relaxation to the electronic ground state terminates again in a higher vibronic level S0vk due to the Franck-Condon principle.

The electronic relaxation from St> S1 into S1 occurs with kIC> 1011 s_1 and therefore much faster than the intrinsic fluorescence decay which is about kP & 6.7-107 s"*. From S1 to S0 the vibrational relaxation kIC is improbable for chlorophyll and therefore fluorescence can be observed especially from S1 with wavelengths Я > 680 nm for Chl a. The improbable kCC from S1 to S0 is correlated with the rigid structure of the porphyrin ring system. Therefore the vibrational modes are energetically separated and the wave functions overlap only slightly.

The highest occupied molecule orbital of the ground state of chlorophyll contains two electrons. Due to the internal spin-orbit (LS)-coupling it should be improbable that a spin flip occurs during the transition from S0 to Sj when the chlorophyll molecule is excited. But there exist intramolecular aberrations of the potential which lead to high probabilities for the spin flip which is called “Inter-System Crossing” (ISC) and has a probability of kISC& 1,5-108 in chlorophyll. The spin flip results in an electronically excited triplet state, which is most probable T3 or T4 (Renger et al., 2009). The rate constants for kF , kIC and kISC are in detail investigated for Chl a and Chl b. Due to the Pauli principle spontaneous emission from the triplet states to the singlet ground state can occur only after a further spin flip. Therefore at least the lowest triplet state T1 is long-lived with typical decay rates of kph »1000.

The fast relaxation from excited singlet states is called “fluorescence” whereas the long-lived emission from the triplet states is called “phosphorescence”.

For photosynthetic organisms, the existence of long-lived triplet states formed from excited Chl singlet states 1Chl * is a disadvantage because Chl triplet states 3 Chl * tend to interact with environmental oxygen which is found in the triplet ground state 3 02 forming highly reactive singlet oxygen 02* which afterwards quickly converts to other ROS (Schmitt et al., 2014a):

The singlet oxygen oxidizes neighbouring molecules and cell structures. The rate constant for the formation of singlet oxygen via triplet- triplet interaction is denoted with kO^ in Figure 8.

There exist several other relaxation channels for excited singlet states. The Sj can for instance interact with other singlet states of coupled pigments and lead to a strong fluorescence quenching via singlet-singlet annihilation (kAnnlha). This process is a nonlinear relaxation that depends quadratically on the concentration of excited singlet states ^S^ in the sample.

Efficient photosynthesis occurs via the excitation energy transfer (EET) from the antenna pigments to the photochemically active reaction center (see Figure 5). To achieve quantum efficiencies for charge separation in the RC after light absorption up to 99% big EET rate constants in the order of kET «1010 are necessary. This process of EET and the subsequent electron transfer (ET) determines the dynamics of the excited states and therefore the fluorescence dynamics.

In spite of the concurrence of the efficient EET, the photosynthetic active organisms exhibit a small amount of fluorescence of about 1% of the absorbed light energy. Triplet states of the Chl molecules are efficiently quenched by the reaction with carotenoid triplets (kCarot in Figure 8). Carotenoids are very flexible molecules that dissipate their excitation energy fast via internal conversion. It is well known that carotenoids also act as quenchers for excited Chl singlet states (see Belyaeva et al., 2008, 2011, 2014, 2015, and references therein).

The relaxation of an excited singlet state population probability ^S^ occurs with the sum of all decay rates according to the formulation of eq. 33 (see Figure 8):

Eq. 33 can be integrated and the solution (i.e. the excited state dynamics) is an exponential decay:

with the average apparent fluorescence lifetime

The fluorescence dynamics depends on all possible relaxation channels. The observable fluorescence F(t) is proportional to the actual population probability of the excited state (Sj):

The quantum efficiency of the fluorescence C>F is defined as the relation between the emitted fluorescence photons per time unit and the overall number of relaxing excited states in the same time interval:

with the intrinsic fluorescence lifetime r0 1—«15 ns for chlorophyll.

-Flour

As mentioned above the radiative relaxation of excited Chl molecules 1 Chl*:= (St) happens with kFlour = (15 ns) = 6.7-107s_1 for Chl a and somewhat slower fluorescence relaxation -Flour = (23 ns) = 4.3-107s_1

for Chl b (see Renger et al., 2009) and kISC = (6.7ns) = 1.5-108 s_1 for both species at room temperature. In Chl b an additional thermally activated ISC channel might exist that enhances kISC at higher temperatures (Renger et al., 2009). Therefore the apparent fluorescence lifetime of Chl a calculates to {knour + kISC ) 1 = 4.6 ns while a slightly faster relaxation is expected for Chl b at room temperature, but a slightly slower relaxation in comparison to Chl a at 10 K (see Schmitt et al., 2008).

The resulting fluorescence quantum yield calculates to (?>FCh,a =1»

  • *0
  • -F°L —«31% for Chl a at room temperature.

k 4-k 15

Flour ISC

 
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