6.3 Electronic Energy Transfers
187
This process is also called triplet sensitization and is exploited to populate the
triplet state of a molecule Y that does not undergo ISC efficiently, by using a
“sensitizer” X which has instead a high triplet yield (see Sect. 1.6.2).
• Triplet quenching by oxygen:
X(T 1 ) + O 2 (
3
−
g ) −→ X(S 0 ) + O 2 (
1
Δ g ,
1
+
g ) .
(6.25)
The ground state of the oxygen molecule is a triplet, but there are two low-lying
singlet states,
1
Δ g ,
1
+
g , so O 2 can accept energy from most organic molecules in
their excited triplet states. Oxygen is therefore an efficient triplet quencher. The
singlet oxygen state
1
Δ g is long-lived and cytotoxic.
• Triplet–triplet annihilation:
X(T 1 ) + X(T 1 ) −→ X(S 1 ) + X(S 0 ) .
(6.26)
This is an “energy pooling” process where the energy of two lower-lying triplets
is used to populate a higher-lying singlet. The X(S 1 ) species may fluoresce, with a
lifetime equal to half of that of the triplet [6, 7]. This kind of delayed fluorescence
is labeled as “type P” because it was first studied in pyrene.
• Singlet fission:
X(S 1 ) + X(S 0 ) −→ X(T 1 ) + X(T 1 ) .
(6.27)
This process is the reverse of the previous one. A singlet with sufficiently high
energy donates part of it to a neighboring molecule, so producing two molecules in
the triplet state. This process may be used to improve photovoltaics yields, because
it can exploit short wavelength photons to produce two electron/hole pairs instead
of one.
Besides the interaction matrix element H i, f =
η i
ˆ
H el
η f
, the cross section σ bim
and the probability P bim for any of these processes also depend on how close to each
other the potential energy surfaces of η i and η f can get, during the interaction of the
two molecules. If the diabatic PESs do cross, giving place to adiabatically avoided
crossings or conical intersections, the transition probability can be large, whereas
two PESs that are well separated at all geometries make the radiationless transitions
unlikely. For instance, electronic quenching by collisions with rare gas atoms has
small cross sections because their interaction with most molecules is repulsive both
for the ground and for the excited state and gives place to approximately parallel PESs.
This is due to the closed shell configuration of the rare gas atoms and to their lack
of low-lying antibonding orbitals that could mix with the molecular orbital hosting
the excited electron. A much studied example are the alkali-rare gas interaction
potentials, such as those originating from the
2 S and
2 P 1/2,3/2 states of Na, with one
electron in the 3s or 3 p orbitals, and the ground state of Xe, as shown in Fig. 6.3
[8]. Rare gases are used as solid matrices or nanodroplets, as well as in gas phase, to
cool the translational, rotational, and vibrational degrees of freedom of molecules,
without quenching their electronic excitation.
187
This process is also called triplet sensitization and is exploited to populate the
triplet state of a molecule Y that does not undergo ISC efficiently, by using a
“sensitizer” X which has instead a high triplet yield (see Sect. 1.6.2).
• Triplet quenching by oxygen:
X(T 1 ) + O 2 (
3
−
g ) −→ X(S 0 ) + O 2 (
1
Δ g ,
1
+
g ) .
(6.25)
The ground state of the oxygen molecule is a triplet, but there are two low-lying
singlet states,
1
Δ g ,
1
+
g , so O 2 can accept energy from most organic molecules in
their excited triplet states. Oxygen is therefore an efficient triplet quencher. The
singlet oxygen state
1
Δ g is long-lived and cytotoxic.
• Triplet–triplet annihilation:
X(T 1 ) + X(T 1 ) −→ X(S 1 ) + X(S 0 ) .
(6.26)
This is an “energy pooling” process where the energy of two lower-lying triplets
is used to populate a higher-lying singlet. The X(S 1 ) species may fluoresce, with a
lifetime equal to half of that of the triplet [6, 7]. This kind of delayed fluorescence
is labeled as “type P” because it was first studied in pyrene.
• Singlet fission:
X(S 1 ) + X(S 0 ) −→ X(T 1 ) + X(T 1 ) .
(6.27)
This process is the reverse of the previous one. A singlet with sufficiently high
energy donates part of it to a neighboring molecule, so producing two molecules in
the triplet state. This process may be used to improve photovoltaics yields, because
it can exploit short wavelength photons to produce two electron/hole pairs instead
of one.
Besides the interaction matrix element H i, f =
η i
ˆ
H el
η f
, the cross section σ bim
and the probability P bim for any of these processes also depend on how close to each
other the potential energy surfaces of η i and η f can get, during the interaction of the
two molecules. If the diabatic PESs do cross, giving place to adiabatically avoided
crossings or conical intersections, the transition probability can be large, whereas
two PESs that are well separated at all geometries make the radiationless transitions
unlikely. For instance, electronic quenching by collisions with rare gas atoms has
small cross sections because their interaction with most molecules is repulsive both
for the ground and for the excited state and gives place to approximately parallel PESs.
This is due to the closed shell configuration of the rare gas atoms and to their lack
of low-lying antibonding orbitals that could mix with the molecular orbital hosting
the excited electron. A much studied example are the alkali-rare gas interaction
potentials, such as those originating from the
2 S and
2 P 1/2,3/2 states of Na, with one
electron in the 3s or 3 p orbitals, and the ground state of Xe, as shown in Fig. 6.3
[8]. Rare gases are used as solid matrices or nanodroplets, as well as in gas phase, to
cool the translational, rotational, and vibrational degrees of freedom of molecules,
without quenching their electronic excitation.