6.3 Electronic Energy Transfers
189
An attractive interaction is instead established between Na(3 p) and atoms with a
smaller energy gap between occupied and virtual orbitals, such as Cd (see Fig. 6.3).
The lowest potential energy curves in this case are those of
2
states, with a small
energy difference due to spin–orbit coupling between the
2
3/2 and
2
1/2 states
(parallel and antiparallel orientation of spin and orbital angular momenta, respectively) [9]. A system which is bound in an excited state but not in the ground state is
called an exciplex or excimer. When the excited state is sufficiently long-lived, one
can observe light emission at longer wavelengths with respect to the isolated excited
species. Similarly, aromatic molecules in solution can form fluorescent excimers.
For instance, at low concentrations, pyrene shows a fluorescence band with a clear
vibrational structure between 370 and 430 nm, while by increasing the concentration
one observes a structureless band between 420 and 550 nm, with λ max = 480 nm,
due to excimer formation.
If the interaction is strongly attractive in the excited state and repulsive in the
ground state, the two potential energy curves tend to cross. Such is the case of Na
approaching collinearly CO, because binding interactions are established between
the electron of Na in a 3p orbital perpendicular to the CO axis and the empty π
∗
orbital of CO, as well as between the empty 3s orbital of Na and the lone pairs of
CO. The charge transfer configuration Na
+ CO
− also contributes to strengthen the
attractive interaction in the excited state. On the contrary, in the Na ground state
the 3s electron and the lone pairs of CO repel each other. In Fig. 6.3 we show the
crossing of the
2
+ and
2
curves for the collinear approach of Na and CO [10].
When considering bent geometries, the
2
+ state becomes
2 A
and the
2
state
originates a pair of
2 A
and a
2 A
states. The two
2 A
states therefore give place to a
conical intersection, near which the exciplex switches very easily to the ground state
and dissociates. The quenching of Na(2 p) by CO molecules is very efficient, with
cross sections of the order of 20–50 Å
2 , and the same happens with other molecules
containing π bonds, such as nitrogen and ethylene.
6.4 Localized Excitations and Energy Transfer
Mechanisms
We shall consider two subsystems X and Y, such as two molecules or two distinct
chromophores in the same molecule. Each subsystem can be the seat of electronic
excitation, but in the adiabatic eigenstates of the whole system the excitation may be
delocalized, i.e., distributed over both centers. As already observed in the previous
section, the localized description is a good starting point to describe energy transfer phenomena, especially when the initial and final states are definitely localized
because of the physical separation of X and Y. The localized states provide a sound
physical example of diabatic states, and their interaction matrix elements determine
the transition cross sections or probabilities.
189
An attractive interaction is instead established between Na(3 p) and atoms with a
smaller energy gap between occupied and virtual orbitals, such as Cd (see Fig. 6.3).
The lowest potential energy curves in this case are those of
2
states, with a small
energy difference due to spin–orbit coupling between the
2
3/2 and
2
1/2 states
(parallel and antiparallel orientation of spin and orbital angular momenta, respectively) [9]. A system which is bound in an excited state but not in the ground state is
called an exciplex or excimer. When the excited state is sufficiently long-lived, one
can observe light emission at longer wavelengths with respect to the isolated excited
species. Similarly, aromatic molecules in solution can form fluorescent excimers.
For instance, at low concentrations, pyrene shows a fluorescence band with a clear
vibrational structure between 370 and 430 nm, while by increasing the concentration
one observes a structureless band between 420 and 550 nm, with λ max = 480 nm,
due to excimer formation.
If the interaction is strongly attractive in the excited state and repulsive in the
ground state, the two potential energy curves tend to cross. Such is the case of Na
approaching collinearly CO, because binding interactions are established between
the electron of Na in a 3p orbital perpendicular to the CO axis and the empty π
∗
orbital of CO, as well as between the empty 3s orbital of Na and the lone pairs of
CO. The charge transfer configuration Na
+ CO
− also contributes to strengthen the
attractive interaction in the excited state. On the contrary, in the Na ground state
the 3s electron and the lone pairs of CO repel each other. In Fig. 6.3 we show the
crossing of the
2
+ and
2
curves for the collinear approach of Na and CO [10].
When considering bent geometries, the
2
+ state becomes
2 A
and the
2
state
originates a pair of
2 A
and a
2 A
states. The two
2 A
states therefore give place to a
conical intersection, near which the exciplex switches very easily to the ground state
and dissociates. The quenching of Na(2 p) by CO molecules is very efficient, with
cross sections of the order of 20–50 Å
2 , and the same happens with other molecules
containing π bonds, such as nitrogen and ethylene.
6.4 Localized Excitations and Energy Transfer
Mechanisms
We shall consider two subsystems X and Y, such as two molecules or two distinct
chromophores in the same molecule. Each subsystem can be the seat of electronic
excitation, but in the adiabatic eigenstates of the whole system the excitation may be
delocalized, i.e., distributed over both centers. As already observed in the previous
section, the localized description is a good starting point to describe energy transfer phenomena, especially when the initial and final states are definitely localized
because of the physical separation of X and Y. The localized states provide a sound
physical example of diabatic states, and their interaction matrix elements determine
the transition cross sections or probabilities.