Electronic Supplementary Information for : Ultrafast Action Chemistry in Slow Motion : Atomistic Description of the Excitation and Fluorescence Processes in an Archetypal Fluorescent Protein

We report quantum mechanical/molecular mechanical non-adiabatic molecular dynamics simulations on the electronically excited state of green fluorescent protein mutant S65T/H148D. We examine the driving force of the ultrafast (τ < 50 fs) excited-state proton transfer unleashed by absorption in the A band at 415 nm and propose an atomistic description of the two dynamical regimes experimentally observed [Stoner Ma et al., J. Am. Chem. Soc., 2008, 130, 1227]. These regimes are explained in terms of two sets of successive dynamical events: first the proton transfers quickly from the chromophore to the acceptor Asp148. Thereafter, on a slower time scale, there are geometrical changes in the cavity of the chromophore that involve the distance between the chromophore and Asp148, the planarity of the excited-state chromophore, and the distance between the chromophore and Tyr145. We find two different non-radiative relaxation channels that are operative for structures in the reactant region and that can explain the mismatch between the decay of the emission of A* and the rise of the emission of I*, as well as the temperature dependence of the non-radiative decay rate.


Time Evolution of Selected Geometrical Parameters
The main article describes the time evolution of several parameters to show how the structure of the fluorescent protein accommodates to the photoexcitation.
Here we address the time evolution of the entire swarm of more than 300 individual QM/MM MD simulations (more precisely, of those that are still in the photoexcited state at a given instant).Fig. S1 to S3 show 2-dimensional histograms that indicate how many of these individual trajectories of the swarm have a specific value of each geometric parameter at a given time, and they also provide the root-mean-square (RMS) value of the distribution at each time frame.
The distances between donor and acceptor, as well as the position of the transferred proton, follow the general behavior described in the main text.The spread of the distributions increases in a natural way with increasing time (Fig. S1).As stated in the main text, the average distance between the phenolic oxygen and the oxygen of Tyr145 decreases during the dynamics after photoexcitation.In the ground state this distance obeys a bimodal distribution with two maxima, one around 3.0 Å and another less pronounced one around 4.5 Å. 1 Panel (c) in Fig. S1 shows that this decrease is actually due to the depletion of the outer maximum since most of the population shifts to fill the inner maximum: Tyr145 does not only move on average closer to the chromophore, but it actually vacates the configuration in which it was farthest away.
We have also checked the distribution of the dihedrals that define the planarity of the two rings of the chromophore (or the lack thereof).The average value of the dihedral τ (defined in the main text) changes upon photoexcitation by about 40 • away from planarity.Analysis of the distribution (Panel (a) in Fig. S2) shows the existence of two populations, one close to planarity (the larger one) and another at ∼240 • , with an almost perpendicular conformation of the imidazolinone ring, which is populated after 0.1 ps.For the other angular parameters in Fig. S2 normal distributions are observed throughout.
Finally, Fig. S3 shows the distribution of the two angles that have been used to indicate the proximity to the two conical intersections, T-like or P-like.In both cases the color histogram shows that the corresponding dihedral develops two different populations (becomes bimodal) for times of 0.1 ps and beyond.The distribution of the dihedral characterizing a T-type CI (θ, panel (a) in Fig. S3) shows that most systems are found around θ ∼ 180 • , but a certain population appears around 270 • at times over 0.1 ps.This is the part of the swarm of trajectories that is moving close to the T CI and decays to the ground state as time increases.For the P-type CI, panel (b) in Fig. S3 shows a small population that peaks at ρ ∼ 120

Molecular Orbitals Involved in the Photoexcitation
Fig. S4 shows a picture of the (local) π molecular orbitals that are involved in the photoexcitation.The determinant with the largest weight in the CI expansion corresponds to the π-HOMO → π-LUMO single excitation.These orbitals are analogous to those already published for the same system. 2Among the changes unleashed by the photoexcitation, we note here the creation of a nodal surface across the bond between C 4 and C 6 in the LUMO (which is absent in the HOMO).This helps to understand why during the dynamics many systems undergo a torsion around this bond, which loses its double bond character upon photoexcitation.

Charge Redistribution Caused by Photoexcitation
A natural bond orbital (NBO) analysis has been carried out on a single snapshot of the QM/MM MD simulation to assess the changes caused in the electronic distribution upon photoexcitation.Fig. S5 shows the corresponding overall variation of charges, computed as the difference between the NBO charges of each fragment in the photoactive and the ground electronic state.Table S1 lists the values of the NBO charges in the ground and the photoactive state for each moiety.
The net effect of the photoexcitation, in terms of gross charge redistribution, is a displacement of about 0.2 electrons from the phenolic moiety, mainly to the methine bridge.

Time Evolution of the Average Emission Energy
Fig. S6 shows the time evolution of the excitation energy vs. the classical proton position.It is possible to discern at a glance the displacement of the cloud of points from top left to bottom right, implying that along the average motion of the proton from donor to acceptor, the computed excitation energies shift to lower values.
Moiety  S1: NBO charges of different fragments of the chromophore-Asp148 unit in the ground electronic state and the photoactive excited electronic state, and net change of these charges upon photoexcitation (see also Fig. S5).The charges have been computed for the atoms shown, including the corresponding hydrogens where applicable.The given net charges in S 0 and S 1 do not add up to -1 because the side chains of the residues Phe64, Val68 and Asp148 have not been considered in this analysis.: Relationship between the position of the proton on the proton transfer reaction coordinate (Eq 5) and the emission energy in the early stages (up to 50 fs).The upper panels depicts this relationship for specific snapshots at ∆t= 0, 10, 30 and 50 fs, respectively.The bottom panel presents all data together, plus the path followed by the average excitation energy as a function of the average proton position (red dots and path).The red dot for ∆t = 0 is at the top-left, and that for ∆t = 50 fs is at the bottom-right.

Barriers on the Way from FC region to T-and P-type CIs
The ultrafast non-radiative decay indicates an exaggerated accessibility of the CI region at the QM(OM2/MRCI)/MM level.To check this further, we computed a relaxed potential energy profile in the S 1 state to generate a minimum-energy path from the Franck-Condon region to the T-type CI region taking the dihedral θ as the reaction coordinate (running the computations in forward and backward direction until convergence to overcome hysteresis problems).The left panel of Fig. S7 shows the resulting stable potential energy profile obtained at the QM(OM2/MRCI)/MM level (same as in the MD simulations): the potential energy profile is downhill and barrierless.For comparison, the right panel of the same Figure presents an S 1 -relaxed potential energy profile computed at the QM(TDDFT)/MM level in a single pass (without going back and forth): it has a small barrier, consistent with previous ab initio QM/MM results; 3 we have also computed a second such QM(TDDFT)/MM profile which reaches the CI region on an uphill path in the S 1 state (data not shown).Apparently the QM(OM2/MRCI)/MM method, with the choice of active space used presently, affords an excited-state surface on which the approach to the CI region is too facile, compared with higher-level electronic structure methods.Hence, the QM(OM2/MRCI)/MM simulations will overestimate the rate of decay through the T-type conical intersection.The corresponding path to the P-type CI has been explored at OM2/MRCI level taking the dihedral ρ as the reaction coordinate.A relaxed potential energy profile is shown in Fig. S8.In this case, the potential energy profile has a small potential energy barrier in the S 1 state.This agrees with the observation that the decay through the P-type CI occurs much less frequently in our simulations than the decay through the T-type CI.The reason why OM2/MRCI might perform worse in describing the region surrounding the CIs is unknown.Nevertheless, one possibility is the choice of MOs used in the description of the active space.This choice, set forth in the main text, was conceived to provide a good description of the π system during the main chemical event (the proton transfer).However, the approach of the CI regions involves areas of configurational space with a strongly twisted chromophore moiety, and thus it is possible that the corresponding out-of-plane torsions require of a different choice of MOs to be described appropriately.Of course, to describe at the same time proton transfer and CI transit with a single active space, the latter should consist of the union of the sets of MOs adequate for each process, which is probably too large to be practical.

P-type CI in the Isolated Chromophore
Fig. S9 shows unrelaxed potential energy profiles determined for the isolated chromophore at the DFT/TDDFT level (methodology as described in the main text).ρ is the angle C 4 C 2 O 3 N 1 .Structures were generated by keeping both rings of the chromophore coplanar at the ground-state equilibrium positions while moving the oxygen atom of the imidazolinone moiety out of plane.DFT/TDDFT was used to compute the ground state/excitation energy, using the CAM-B3LYP functional and the 6-31G(d,p) basis set.Structures with all atoms of the chromophore rings in a plane, except for the oxygen in the imidazolinone moiety (see text).

Figure S1 :Figure S2 :Figure S3 :Figure S4 :
Figure S1: Time evolution of (a) the donor-acceptor distance, (b) the proton position according to Eq 5, and (c) the distance between the oxygens of Tyr66 (in the chromophore) and Tyr145, for the full swarm of trajectories.Left column: 2-dimensional histogram depicting with darker colors the regions with higher structure count; right column: time evolution of the average values of the distances.The vertical bars represent one standard deviation in each case.

Figure S5 :
Figure S5: Changes in fragment charges due to photoexcitation.Red (blue) figures indicate a net increase (decrease) of negative charge.
FigureS6: Relationship between the position of the proton on the proton transfer reaction coordinate (Eq 5) and the emission energy in the early stages (up to 50 fs).The upper panels depicts this relationship for specific snapshots at ∆t= 0, 10, 30 and 50 fs, respectively.The bottom panel presents all data together, plus the path followed by the average excitation energy as a function of the average proton position (red dots and path).The red dot for ∆t = 0 is at the top-left, and that for ∆t = 50 fs is at the bottom-right.

Figure
Figure S7: S 1 -relaxed potential energy profile leading from the Franck-Condon region (FC) to the T-type CI region (CI) computed at the QM/MM level; red: optimized S 1 energies; blue: single-point S 0 energies.Left panel: QM = OM2/MRCI; right panel: QM = TDDFT.

Figure S9 :
FigureS9: Energy (relative to the P-type CI) of structures of the gas-phase chromophore as a function of angle ρ.Structures with all atoms of the chromophore rings in a plane, except for the oxygen in the imidazolinone moiety (see text).