184
6 Charge and Energy Transfer Processes
6.3 Electronic Energy Transfers
When a collision in gas phase or an encounter in solution occurs, we can consider
the system made up by the two molecules as one “supermolecule” and investigate its
dynamics with the same tools we developed in the previous chapters for unimolecular
processes. If the supermolecule splits again to yield the same molecules as before the
collision/encounter or new ones, the quantum state of the products will depend on the
transitions occurred during the interaction time. The supermolecule approach is then
suitable to treat energy and charge transfer processes as electronic transitions between
well-defined initial and final states. Note that, while the internal degrees of freedom
of a molecule (vibrational and electronic) are not or only weakly coupled with the
overall translation and rotation, for two interacting molecules the mutual translational
and orientational coordinates become internal coordinates of the supermolecule that
can exchange energy with the other degrees of freedom (see the discussion at the end
of Sect. 6.1 concerning vibrational energy).
Starting from an electronically excited molecule X
∗ , two kinds of energy transfer
processes can occur. In one, the species X
∗ goes back to the ground state because of
the interaction with Y, and the latter, although normally accepting a certain amount
of energy, remains in the electronic ground state:
X
∗
+ Y −→ X + Y .
(6.16)
This is a mere quenching of X
∗ . If instead Y is promoted to an excited state, we talk
about electronic excitation transfer or “sensitization”:
X
∗
+ Y −→ X + Y
∗
.
(6.17)
In both cases, as in other nonadiabatic processes, part of the initially available energy
is converted into vibrational, rotational, and translational energy shared by the two
partners and eventually lost to the medium as depicted in the two Jablonski diagrams
of Fig. 6.2. For the excitation transfer to occur, the Y
∗ state must be lower in energy
than X
∗ or at most slightly higher. In the latter case, Y and/or X
∗ must possess some
extra vibrational energy, possibly supplied by the exciting photon or due to thermal
fluctuations.
The nature of the processes (6.16) and (6.17) allows to define a set of diabatic
electronic states based on the localization of the excitation and suitable to describe
the energy transfer dynamics [1–4]. The initial state is
|η i ≡ |ϕ X ∗ ϕ Y
(6.18)
where on the RHS we have antisymmetrized products of the wavefunctions representing X in the excited state and Y in the ground state. We are here assuming the
orbitals of X and Y to be orthogonal, which is not compatible with perfect localization on either molecule (see Appendix E). An approximate localization of the ϕ
6 Charge and Energy Transfer Processes
6.3 Electronic Energy Transfers
When a collision in gas phase or an encounter in solution occurs, we can consider
the system made up by the two molecules as one “supermolecule” and investigate its
dynamics with the same tools we developed in the previous chapters for unimolecular
processes. If the supermolecule splits again to yield the same molecules as before the
collision/encounter or new ones, the quantum state of the products will depend on the
transitions occurred during the interaction time. The supermolecule approach is then
suitable to treat energy and charge transfer processes as electronic transitions between
well-defined initial and final states. Note that, while the internal degrees of freedom
of a molecule (vibrational and electronic) are not or only weakly coupled with the
overall translation and rotation, for two interacting molecules the mutual translational
and orientational coordinates become internal coordinates of the supermolecule that
can exchange energy with the other degrees of freedom (see the discussion at the end
of Sect. 6.1 concerning vibrational energy).
Starting from an electronically excited molecule X
∗ , two kinds of energy transfer
processes can occur. In one, the species X
∗ goes back to the ground state because of
the interaction with Y, and the latter, although normally accepting a certain amount
of energy, remains in the electronic ground state:
X
∗
+ Y −→ X + Y .
(6.16)
This is a mere quenching of X
∗ . If instead Y is promoted to an excited state, we talk
about electronic excitation transfer or “sensitization”:
X
∗
+ Y −→ X + Y
∗
.
(6.17)
In both cases, as in other nonadiabatic processes, part of the initially available energy
is converted into vibrational, rotational, and translational energy shared by the two
partners and eventually lost to the medium as depicted in the two Jablonski diagrams
of Fig. 6.2. For the excitation transfer to occur, the Y
∗ state must be lower in energy
than X
∗ or at most slightly higher. In the latter case, Y and/or X
∗ must possess some
extra vibrational energy, possibly supplied by the exciting photon or due to thermal
fluctuations.
The nature of the processes (6.16) and (6.17) allows to define a set of diabatic
electronic states based on the localization of the excitation and suitable to describe
the energy transfer dynamics [1–4]. The initial state is
|η i ≡ |ϕ X ∗ ϕ Y
(6.18)
where on the RHS we have antisymmetrized products of the wavefunctions representing X in the excited state and Y in the ground state. We are here assuming the
orbitals of X and Y to be orthogonal, which is not compatible with perfect localization on either molecule (see Appendix E). An approximate localization of the ϕ