Chapter 7
Of Excited States Again
It has been long known that some photochemical processes require consideration of interactions between excited states, such as delayed fluorescence. These were clearly distinguished in the work by Lewis, Kasha, and Parker [1].
– E-type delayed fluorescence. As defined by the IUPAC Gold book [2], this is the process “in which the first excited singlet state becomes populated by a ther- mally activated radiationless transition from the first excited triplet state. Since in this case the populations of the singlet and triplet states are in thermal equilibrium, the lifetimes of delayed fluorescence and the concomitant phos- phorescence are equal.” This process takes its name from eosin and is typically observed with dyes, where the S1–T1gap is small.
– P-type delayed fluorescence: “The process in which the first excited singlet state is populated by interaction of two molecules in the triplet state (triplet–triplet annihilation), thus producing one molecule in the excited singlet state. In this biphotonic process the lifetime of delayed fluorescence is half the value of the concomitant phosphorescence.” This takes its name from pyrene and is observed from most aromatic molecules, where S1and T1are too far for thermal activation of the latter.
– Recombination fluorescence: The first excited singlet state becomes populated by recombination of radical ions and electrons or by recombination of radical ions of opposite charge (Scheme7.2).
T + T S hn
n hn
Singlet fission
Multiphoton absorption Photochemical upconversion
triplet-triplet annihilation
Scheme 7.1 Nonlinear processes. Two-(or multi-)photon absorption may occur under appropriate conditions (and exploit also low-energy photons. Singlet fission may lead to two triplet states (and thus to more photochemical acts). Two triplets may be annihilated and form a singlet of higher energy (photochemical upconversion). These phenomena must be taken into account because they lead to important applications
184 7 Of Excited States Again
As shown when discussing the state diagram in Chap.3, in a molecule containing a single chromophore, access to the triplet manifold by absorbance is not viable either by direct absorption (forbidden absorption), or indirectly from the singlet manifold (intersystem crossing), since spin prohibition extends also to horizontal transitions. However, the systems considered in practice do not contain a single molecule, or it may be that the molecule considered contains two or more chromo- phores. In such all-important cases, a different path has to be considered and involves the interaction between an organic chromophore in an excited singlet state and a neighboring one (either of the same or a different kind) in the ground state, whereupon both of them are converted into triplet excited states (Scheme7.1).
In such Singlet Fission, the two triplets are generated coupled in a singlet state and the overall path is spin allowed. This transition can be very fast (down to the ps timescale or even below), competing with vibrational relaxation and easily over- coming direct fluorescence. Actually, cases of triplet quantum yield up to 2 have been reported for solid samples or aggregates. More precisely, the three sublevels of each triplet state result in singlet1(TT), triplet3(TT), and quintet5(TT) states, not exactly degenerate. As pointed out by Michl [3], singlet fission has the potential for converting singlets into both triplets and quintets efficiently, thus expandingthe Jablonski diagram as shown in red in Scheme7.3. Generalizations about favorable structural features are available. Thus, two-photon absorption is observed in donor–
acceptor systems and depends on the polarizability of the molecule, the length of the π-conjugated system, the strength of the donating/accepting groups, and the way in which the systems are connected, with a preference for more complex system over simpler analogues. A high fluorescence quantum yield is generally related to the rigidity of the structure and requires avoiding heavy atoms and substituents such as the nitro group that favor ISC to the triplet (and often photochemical reactions).
S1
S0 T0 A F
P ISC
Scheme 7.2 Fluorescence (F) and phosphorescence (P). “Normal” fluorescence (F) arises from S1 (independently from which singlet has been initially reached, and thus its shape is not affected by the energy of the wavelength used, provided that this has been absorbed. This is the Vavilov rule, rationalized by Kasha as due to the fact that internal conversion among states of the same multiplicity is always the fastest process, see Chap.3). Delayed fluorescence may involve triple–
triplet annihilation, in which self-quenching of the triplet leads back to the singlet S1, with the usual fluorescence spectrum but the triplet lifetime
7.1 Expanding the State Diagram 185
The mechanism involved is represented in Scheme 7.4, where both direct process and singlet fission mediated by charge transfer states are presented. The conditions that have to be met for occurring of this phenomenon, which can be considered a sort of internal conversion, are stringent, but it has now been observed in several cases, and appropriate theories that account quantitatively for both singlet fission and the reverse phenomenon, triplet–triplet annihilation, and their role in solids have been put forward [3]. With aromatics, where the singlet–triplet gap is large, the phenomenon is often significant, although the emission may be weak and not easily detected. In particular, molecules, such as tetracene, where the energy of S1is almost exactly twice as much as that of T1have been extensively studied, both on the crystals and on phenylene-linked dimers as covalently blocked models. In crystals, direct evidence for the fission of initial singlet state into a superposition of triplet pair states has been reported. The beat frequencies depend on crystal orientation with respect to the magnetic field, consistent with theoretical predic- tions. The long-time behavior of the fluorescence decay reflects association and separation of triplet pairs and relaxation into different spin states. Similar phenom- ena have been found also with rubrene [4–6]. Most interestingly, singlet fission was observed on ultrathin single crystals, where the expected quantum beats in the delayed fluorescence arising from recombination of spin-coherent triplet pairs were observed. This indicated that singlet fission proceeds through a direct single-step process within 200 ps at room temperature and gives a pair of unperturbed triplets that have negligible interaction with each other [7]. Theory is not simple, and is being still developed, but important advancements have been made and it is now possible to predict which chemical structures are likely to undergo this phenome- non. The relevant models are indicated in Scheme7.5, where different mechanisms for singlet fission are recognized, viz., direct population of S1(red arrow and matrix element) and charge transfer-mediated mechanism (via S2, cyan arrows and matrix elements followed by blue arrows and matrix elements).
S0 S1
T1
S0 S1
T1 (1)
(2)
(2)
Scheme 7.3 Singlet fission: (1) the chromophore on the left undergoes initial excitation to S1. (2) The excited chromophore shares its energy with the chromophore on the right, creating a T1 from each of the initial states. Reprinted with permission from [3]
186 7 Of Excited States Again
Further related processes occur in inorganic materials (quantum cutting) and in quantum dots [8,9].