Dynamics simulations show 100-fs internal conversion at 0.5-eV gaps.


In brief:

  • We simulated the dynamics of 6- and 7-protonated azaindole (AIH+) after S3 excitation.
  • The  S3 lifetime is 156 fs for 6-AIH+ and 278 fs for 7-AIH+.
  • The S3→S2 hopping happens with a distribution peaked at 0.5 eV.
  • The reason is that although the gap never gets to zero, it is small enough to multiply the number of steps where the transition may occur.

 

The usual interpretation of surface hopping is that the hopping event happens at the state crossing. However, actual hoppings happen at small, non-null energy gaps, usually following an exponential probability distribution function. For example, in the case of ethylene’s surface hopping dynamics, the S1→S0 energy gap at the hopping time is exponentially distributed with a 0.5 eV mean. In fulvene, the S1→S0 energy gap at the hopping time is exponentially distributed with a 0.3 eV mean.

Nevertheless, in 6- and 7-protonated azaindole (AIH+) after S3 excitation, the energy gaps at the S3→S2 hoppings don’t follow an exponential distribution. The distribution peaks at 0.47 eV for both molecules, implying that it should tend to a Gaussian probability function if the statistics are improved.

The reason for such distribution is clear: the S3/S2 state intersection is not energetically accessible after the S3 excitation. The molecules vibrate around the S3 minimum and internally convert from there.

We could expect that such significant gaps would imply a long lifetime. However, we know from experimental results that the lifetime of this state is ultrashort, not more than 200 fs. And surface hopping dynamics simulations confirm that: the simulated S3-state lifetimes of 6- and 7-AIH+ are 156±40 and 278±36 fs, respectively.

How can we reconcile the ultrashort lifetimes and the large energy gaps at the hopping time?

The answer is that although the S3/S2 gaps are large for typical internal conversion cases, they are still small enough during the S3 dynamics to make the hopping probabilities sizable. (The mean S3/S2 energy gap during S3 dynamics is about 0.7±0.2 eV.)

Thus, for 6-AIH+ in the S3 state, the hopping probabilities to S2 (considering only non-null values) are exponentially distributed with a mean value of 3×10-4 per sub-timestep (0.025 fs in our simulations). For 7-AIH+, this value is 2×10-4 per sub-timestep.

These relatively small gaps during S3 dynamics increase the number of time steps where potentially a hopping can occur. For instance, 12% of the sub-timesteps of 7-AIH+ have a hopping probability bigger than 10-5. This situation contrasts with the typical S0/S1 transition through state intersections (like in ethylene or fulvene), where internal conversion can occur only after the gap reduces enough to yield appreciable hopping probabilities.

These results for 6- and 7-AIH+ are reported in our recent publication at PCCP.

MB

Reference

[1] R. Mansour, S. Mukherjee, M. Pinheiro Jr, J. A. Noble, C. Jouvet, and M. Barbatti, Pre-Dewar structure modulates protonated azaindole photodynamics, Phys. Chem. Chem. Phys. (2022). DOI: 10.1039/D2CP01056A


Mario Barbatti

Mario Barbatti is a professor of theoretical chemistry at the Aix Marseille University in France.

1 Comment

Ultrafast internal conversion without energy crossing – Light and Molecules · September 20, 2022 at 7:27 AM

[…] Mansour et al. showed with surface hopping simulations that the S3-state lifetime of protonated azaindole is about 100 fs, even though the energy gap between S3 and S2 is always about 0.5 eV. I discussed this specific example here. […]

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