Photodeactivation Channels of Transition Metal Complexes …
277
Fig. 5a, it is shown the TD-PBE UV-Vis is absorption spectrum generated from a
Wigner distribution of ca. 1500 initial geometries. The gray area in Fig. 5a stands for
the energetic excitation window used in the simulations, which mimics the experimental conditions. This energetic window was chosen to account for the possible
variance of the incident wavelength and the inaccuracy in the computed excitation
energies. The GGA functional PBE was chosen to correctly describe singlet–triplet
energy gaps [70]. As shown in Fig. 5a, a high density of bright singlet ESs is found
within this excitation energy range. Therefore, a large number of trajectories starting
from different ESs are needed to mimic the experimental excitation conditions. 101
permissible random trajectories were run for 30 fs, within 15 singlets and 15 triplets
(that means 60 states in total, as the triplet states split into their three spin sublevels). These trajectories were initially distributed in the absorbing states (S 6 –S 14 ),
following their ratio of computed relative intensities. The time evolution of all possible singlet and triplet ES normalized for all trajectories is displayed in panel A of
Fig. 5b, which clearly shows that triplet ESs are rapidly populated from the starting
singlet ES. This is even more clear in panel B of Fig. 5b, where the time evolution of
the summed up triplet and singlet populations is shown. Thus, the triplet population
amounts up to ca. 65% after 30 fs, and the global fitting of this kinetics provides a
time constant of 26 ± 3 fs for ISC, in good agreement with the experimental evidences. Besides the quantitative agreement with the experimental ISC rates, these
TSH simulations provided an in-depth understanding of the ISC processes taking
place in [Ru(bpy) 3 ]
2+ , as it is not a single
1 MLCT and
3 MLCT state that participates
in these processes but instead a manifold of near-degenerate singlet and triplet ES
that are responsible for the ultrafast population transfer between ES. In addition, S 1
and T 1 populations remain well below 3% after 30 fs, implying that ISC processes
occur in an “horizontal” manner between high-lying singlet and triplet ES and thus
breaking Kasha’s rule. The authors further investigated whether it was only the confluence of two important factors: (i) the high density of ESs and (i) the large size
of the SOCs between the involved ES (which amounted up to 350 cm
−1 ) the sole
ingredients to promote rapid ISC in [Ru(bpy) 3 ]
2+ , or contrarily, if other factors also
played an important role. Toward this latter aim, further sets of TSH simulations were
performed, and they are displayed in Panels C-E of Fig. 5b. In Panel C, the results
of freezing the initial Wigner geometries during the dynamics are shown, while in
Panels D and E, the results for the simulations starting both at the FC geometry,
with (D) or without (E) allowing for geometrical relaxation are shown. The frozen
dynamics (C and E) clearly result in a significant decrease of triplet population with
respect to their non-frozen counterparts (e.g., compare 15% in C with 65% in B
after 30 fs). This is because IC is not operative in the frozen dynamics, being the
population transfer only driven by successive spin–orbit-mediated transitions. One
can thus conclude that the ultrafast ISC processes in [Ru(bpy) 3 ]
2+ are not only due
to the high density of ES and the large SOCs, but dynamical molecular relaxation
leads to a substantial enhancement of the ISC rates.
In an effort to identify which are the internal motions that promote ISC in
[Ru(bpy) 3 ]
2+ , time-resolved normal mode (see Fig. 6a) and principal component
analyses of the averaged trajectories were performed. These analyses permitted iden-
277
Fig. 5a, it is shown the TD-PBE UV-Vis is absorption spectrum generated from a
Wigner distribution of ca. 1500 initial geometries. The gray area in Fig. 5a stands for
the energetic excitation window used in the simulations, which mimics the experimental conditions. This energetic window was chosen to account for the possible
variance of the incident wavelength and the inaccuracy in the computed excitation
energies. The GGA functional PBE was chosen to correctly describe singlet–triplet
energy gaps [70]. As shown in Fig. 5a, a high density of bright singlet ESs is found
within this excitation energy range. Therefore, a large number of trajectories starting
from different ESs are needed to mimic the experimental excitation conditions. 101
permissible random trajectories were run for 30 fs, within 15 singlets and 15 triplets
(that means 60 states in total, as the triplet states split into their three spin sublevels). These trajectories were initially distributed in the absorbing states (S 6 –S 14 ),
following their ratio of computed relative intensities. The time evolution of all possible singlet and triplet ES normalized for all trajectories is displayed in panel A of
Fig. 5b, which clearly shows that triplet ESs are rapidly populated from the starting
singlet ES. This is even more clear in panel B of Fig. 5b, where the time evolution of
the summed up triplet and singlet populations is shown. Thus, the triplet population
amounts up to ca. 65% after 30 fs, and the global fitting of this kinetics provides a
time constant of 26 ± 3 fs for ISC, in good agreement with the experimental evidences. Besides the quantitative agreement with the experimental ISC rates, these
TSH simulations provided an in-depth understanding of the ISC processes taking
place in [Ru(bpy) 3 ]
2+ , as it is not a single
1 MLCT and
3 MLCT state that participates
in these processes but instead a manifold of near-degenerate singlet and triplet ES
that are responsible for the ultrafast population transfer between ES. In addition, S 1
and T 1 populations remain well below 3% after 30 fs, implying that ISC processes
occur in an “horizontal” manner between high-lying singlet and triplet ES and thus
breaking Kasha’s rule. The authors further investigated whether it was only the confluence of two important factors: (i) the high density of ESs and (i) the large size
of the SOCs between the involved ES (which amounted up to 350 cm
−1 ) the sole
ingredients to promote rapid ISC in [Ru(bpy) 3 ]
2+ , or contrarily, if other factors also
played an important role. Toward this latter aim, further sets of TSH simulations were
performed, and they are displayed in Panels C-E of Fig. 5b. In Panel C, the results
of freezing the initial Wigner geometries during the dynamics are shown, while in
Panels D and E, the results for the simulations starting both at the FC geometry,
with (D) or without (E) allowing for geometrical relaxation are shown. The frozen
dynamics (C and E) clearly result in a significant decrease of triplet population with
respect to their non-frozen counterparts (e.g., compare 15% in C with 65% in B
after 30 fs). This is because IC is not operative in the frozen dynamics, being the
population transfer only driven by successive spin–orbit-mediated transitions. One
can thus conclude that the ultrafast ISC processes in [Ru(bpy) 3 ]
2+ are not only due
to the high density of ES and the large SOCs, but dynamical molecular relaxation
leads to a substantial enhancement of the ISC rates.
In an effort to identify which are the internal motions that promote ISC in
[Ru(bpy) 3 ]
2+ , time-resolved normal mode (see Fig. 6a) and principal component
analyses of the averaged trajectories were performed. These analyses permitted iden-