Another paper to report on (open-access link available here). This work examines excitation energy transport in LH2, a supramolecular photosynthetic complex which is found in the cell membranes of purple bacteria. Lots of people have gotten interested in LH2 ever since Graham Fleming’s group published a paper in 2007 reporting on fancy 2d spectroscopy which observed coherent quantum “beating” between initially prepared electronic states. Beating patterns of this sort are certainly of fundamental interest, and the experiments used to observe it were very nice; however, the consensus which seems to be emerging is that the “beating” is in fact not so important for explaining the efficiency at which photosynthetic systems transport electronic energy across their membranes.

So why did I decide to get involved in LH2? Well, a few reasons. First, my colleague Dr. Tom Oliver has had a longstanding interest in this system. And second, I’ve been extremely confused by the LH2 modelling literature. When we think about excited state and non-adiabatic dynamics in small and medium sized molecules, we think about topological features like conical intersections, avoided crossings, near degeneracies, non-adiabatic coupling vectors, etc. For small molecules, we know that fluctuations in vibrational degrees of freedom are often responsible for bringing electronic states into near-degeneracy, and transferring amplitude between states.

Despite the fact that all of these concepts are extremely mature owing to developments over the years within the small molecule excited state dynamics community, they are nowhere to be found when one reads the LH2 literature. Instead, we read about master equation treatments where every single vibration is anonymised, and folded into a linearly coupled “spectral density function”. Conical intersections? Avoided crossings? Near degeneracies? Non-adiabatic coupling vectors? Entirely absent. It’s almost like LH2 is linked to an entirely different discipline with an entirely different vocabulary.

So my aim with the LH2 work was full representation of vibrations! No more nameless vibrations folded into some anonymous spectral density function. Full representation of each and every vibration, capturing the fullness of its unique dynamical anharmonic identity. It’s the kind of sentiment that seems particularly well aligned with the current populist zeitgeist sweeping the globe.

But LH2 is big, and it has has lots of excited states, so a full representation of all of its vibrations in atomistic detail is a non-trivial challenge. To do it, we built a multi-tiered parallel computational framework (using TDDFT parallelized across GPUs within nodes, and MPI to scale across nodes) for calculating atomic cartesian gradients on each and every excited state. We also introduced some approximations for how to treat cartesian gradients of the excited state dipole moments and the transition dipole moments. This builds on some work we published a couple years ago. Once all that was stabilised, we were then able to run surface-hopping simulations to treat the explicit dynamics of both the atoms and also the electronic degrees of freedom. The picture that emerges is shown in the movie. The key thing which this movie highlights (compared to previous simulations) is the fact that the atomic motion is explicitly being accounted for, along with the electronic motion (which is shown as diffuse blue clouds). In fact, you need to speed up the frame-rate to see the atoms moving, because your eyes are more attuned to the flashing blue electronic amplitude than to the subtleties of the atomic motion. But it’s definitely all in there – check out the video below!

The dynamical picture of electronic energy transport which emerges from this work is one of excited states which fluctuate rapidly as a result of the underlying vibrational dynamics of the atoms which make up the constituent LH2 chromophores. The excited states are delocalized over multiple chromophores and undergo frequent crossing on a femtosecond timescale, as depicted in Fig 4A of the paper. Every crossing offers an opportunity to transfer amplitude from one excited state to another. The result is a sort of highly connected excited state network: the frequent crossings combine to create scenario where the states are in a sort of constant “communication” with one another, allowing excitation localized in any one state to travel far and fast. The take-home message?* It’s all about the vibrations!*