6.5 Charge or Electron Transfer
207
Light absorption can also populate a local excited state of X, S n , higher in energy
than the charge transfer one or close to it. This is the beginning of the photoinitiated
mechanism (blue pathway in Fig. 6.9). The next step is internal conversion from S n
to the charge transfer state, driven by the coupling
Ψ X,S n Ψ Y,D 0
ˆ
H el
Ψ X,D 0 Ψ Y,S 0
,
Eq. (6.72). Again this coupling can be very small if X and Y are too far apart, so this
transition may suffer the competition of other quenching mechanisms of X. Once on
the X
+
+Y PES, the dynamics is similar to that of the optical mechanism.
6.6 Computational Note: Diabatic States for ET and CT
Studies
As we have seen in this chapter, the diabatic representation based on localization
of charge and excitation is a quite natural choice for the analysis of ET and CT
phenomena. However, when tackling the computational problem, one finds once
again that practically all quantum chemistry methods are devoted to approximate the
energies and properties of adiabatic eigenstates. Yet there are also some important
technical reasons to switch to a (quasi-)diabatic basis in this context.
A first good reason is that the size of many molecular systems under study, especially the multichromophoric ones, calls for “divide and conquer” strategies [1–4,
20, 22, 23]. So, instead of computing the adiabatic states of the whole system, one
determines the state energies of each molecular unit or subunit and the interactions
between pairs of such units. More often the DFT and TD-DFT methods are applied,
but also wavefunction approaches such as coupled cluster and CASSCF plus perturbation. In so doing, the strategy is intrinsically diabatic. For excitation transfer,
the state η i can be defined as the ground state for all chromophores except for the
ith chromophore, which is excited. For charge transfer, the diabatic states differ
according to where the exchanged electron is localized. The adiabatic eigenstates
are obtained by diagonalizing the Hamiltonian matrix H, the elements of which are
H i j =
η i
ˆ
H el
η j
. For spatially well-separated chromophores that interact through
Förster’s mechanism, the diabatic states can be assumed to be orthogonal. In other
cases, as in Dexter’s ET and generally in CT, the diabatic basis is nonorthogonal. In
this case, the effective interaction between two centers i and j, taking into account
the overlap S i j =
η i
η j
, is
V i j =
2H i j − S i j (H ii + H j j )
2(1 − S
2
i j )
.
(6.76)
Nonorthogonal CI methods can also be applied to the whole system, using the
nonorthogonal local orbitals [24].
All the state energies and interaction matrix elements are subject to important
environmental effects. Obvious static effects are the different stabilization of ground
and excited states of the various chromophores and, even more important, of oxidized/reduced species. Electrostatic interactions between chromophores and between
207
Light absorption can also populate a local excited state of X, S n , higher in energy
than the charge transfer one or close to it. This is the beginning of the photoinitiated
mechanism (blue pathway in Fig. 6.9). The next step is internal conversion from S n
to the charge transfer state, driven by the coupling
Ψ X,S n Ψ Y,D 0
ˆ
H el
Ψ X,D 0 Ψ Y,S 0
,
Eq. (6.72). Again this coupling can be very small if X and Y are too far apart, so this
transition may suffer the competition of other quenching mechanisms of X. Once on
the X
+
+Y PES, the dynamics is similar to that of the optical mechanism.
6.6 Computational Note: Diabatic States for ET and CT
Studies
As we have seen in this chapter, the diabatic representation based on localization
of charge and excitation is a quite natural choice for the analysis of ET and CT
phenomena. However, when tackling the computational problem, one finds once
again that practically all quantum chemistry methods are devoted to approximate the
energies and properties of adiabatic eigenstates. Yet there are also some important
technical reasons to switch to a (quasi-)diabatic basis in this context.
A first good reason is that the size of many molecular systems under study, especially the multichromophoric ones, calls for “divide and conquer” strategies [1–4,
20, 22, 23]. So, instead of computing the adiabatic states of the whole system, one
determines the state energies of each molecular unit or subunit and the interactions
between pairs of such units. More often the DFT and TD-DFT methods are applied,
but also wavefunction approaches such as coupled cluster and CASSCF plus perturbation. In so doing, the strategy is intrinsically diabatic. For excitation transfer,
the state η i can be defined as the ground state for all chromophores except for the
ith chromophore, which is excited. For charge transfer, the diabatic states differ
according to where the exchanged electron is localized. The adiabatic eigenstates
are obtained by diagonalizing the Hamiltonian matrix H, the elements of which are
H i j =
η i
ˆ
H el
η j
. For spatially well-separated chromophores that interact through
Förster’s mechanism, the diabatic states can be assumed to be orthogonal. In other
cases, as in Dexter’s ET and generally in CT, the diabatic basis is nonorthogonal. In
this case, the effective interaction between two centers i and j, taking into account
the overlap S i j =
η i
η j
, is
V i j =
2H i j − S i j (H ii + H j j )
2(1 − S
2
i j )
.
(6.76)
Nonorthogonal CI methods can also be applied to the whole system, using the
nonorthogonal local orbitals [24].
All the state energies and interaction matrix elements are subject to important
environmental effects. Obvious static effects are the different stabilization of ground
and excited states of the various chromophores and, even more important, of oxidized/reduced species. Electrostatic interactions between chromophores and between