Vibronic mixing enables ultrafast energy flow in light-harvesting complex II

Since the discovery of quantum beats in the two-dimensional electronic spectra of photosynthetic pigment-protein complexes over a decade ago, the origin and mechanistic function of these beats in photosynthetic light-harvesting has been extensively debated. The current consensus is that these long-lived oscillatory features likely result from electronic-vibrational mixing, however, it remains uncertain if such mixing significantly influences energy transport. Here, we examine the interplay between the electronic and nuclear degrees of freedom (DoF) during the excitation energy transfer (EET) dynamics of light-harvesting complex II (LHCII) with two-dimensional electronic-vibrational spectroscopy. Particularly, we show the involvement of the nuclear DoF during EET through the participation of higher-lying vibronic chlorophyll states and assign observed oscillatory features to specific EET pathways, demonstrating a significant step in mapping evolution from energy to physical space. These frequencies correspond to known vibrational modes of chlorophyll, suggesting that electronic-vibrational mixing facilitates rapid EET over moderately size energy gaps.

higher frequency vibrational modes are not anharmonically coupled to the lower frequency modes 4 that are responsible for the appearance of the vibrational coherences in previous work. The result is that the probed modes are completely ignorant of the wavepacket dynamics. Therefore, these dynamics are absent from the CLSs and peak amplitudes. This conclusion has important implications for 2DEV spectroscopy-in the case where the probed vibrational modes are not anharmonically coupled to those that would be responsible for the appearance of vibrational coherences in a 2DES experiment, any observed oscillations in the CLS or peak amplitude in a 2DEV experiment will not be of purely vibrational origin, but rather must be electronic or vibronic in origin. In terms of the current study, the vibrational modes of chlorophyll pigments in the probed region (1525-1715 cm -1 ) are not anharmonically coupled to lower frequency modes (i.e. the frequency region of the observed beats in the current study). 5 Therefore, the observed beats can not be vibrational in origin.

Cresyl Violet: Methods
The same 2DEV experimental setup described in the main text and elsewhere 6 was used for this experiment, however, the excitation and probe frequencies were adjusted accordingly. The visible excitation spectrum was centered at 17390 cm -1 and spanned 16129~18518 cm -1 , while the IR probe spectrum was centered at 1587 cm -1 . The excitation energy was set at 250 nJ and the pump pulse duration was ~8 fs.

Theoretical Modelling
The model presented in the main text features two electronically coupled monomers, each with one electronic degree of freedom (DoF) and one Franck-Condon active vibrational mode. The model parameters (labeled in Supplementary Figure 6) were chosen to be similar to those expected for LHCII and are as follows: − α = 100 cm -1 , J = 100 cm -1 , , = 1650 cm -1 , , = 1560 cm -1 , , = 1660 cm -1 , ω e,β = 1550 cm -1 , and the Huang-Rhys factor, , was set to 0.005 for both vibrational modes. [7][8][9] As in previous work 10,11 , the site basis is spanned by the nine states: �α 0 0 �, �α 1 0 �, �α 0 1 �, �α 0 0 �, �α 0 1 �, �α 1 0 �, �α 0 0 �, �α g 0 β e 1 �, and �α 1 0 �, where the subscript on α or indicates whether or not the electronic DoF is excited (e for excited state or g for ground state) and the superscript indicates whether or not the vibrational DoF on monomer α or is excited (1 for excited state or 0 for ground state). In the site basis, the electronic transition dipole matrix elements were set to α = −5, in order to recover a linear absorption spectrum with reasonable qualitative agreement to LHCII in terms of the intensities of the two main Qy bands, and the vibrational transition dipole matrix elements were all set to unity.
The simulated 2DEV spectra (composed of the rephasing and nonrephasing excited state absorption and ground states bleach pathways 10 ) were calculated using the Full Redfield quantum master equation. 12 The spectral density was taken to be of Drude-Lorentz form 13  reorganization energy, , was set to 35 cm -1 and the cutoff frequency, , was set to ~106 cm -1 ( −1 = 50 fs). These bath parameters were chosen as they are reasonable for pigment-protein complexes. 14,15 For all calculations, the temperature was set at 150 K, rather than 77 K, in order to ease computational demand. As the vibrational modes in this model were assumed to be localized spectators of the dynamics and were not populated until the third light-matter interaction, an electronic bath that induced energy fluctuations and population relaxation was used during the initial coherence time, t 1 , and the waiting time, T, while a vibrational bath that only induced vibrational relaxation was used during the last coherence time, t 3 (note: this would not be the proper treatment in the case where there was substantial electronic-vibrational mixing 16 , however, the separation of the bath into discrete electronic and vibrational portions is valid for the parameter regime inhabited by in this model, which is essentially that of "D1" in Ref. 17). The absorptive 2DEV spectra presented in the text were recovered by Fourier transforming along t 1 and t 3 and combining the total rephasing and nonrephasing pathways. The spectra were calculated as a function of T from 0 to 708 fs in 12 fs steps.
In order to highlight the sensitivity of 2DEV to electronic coupling, the 2DEV spectrum

LHCII: Additional Experimental Details
As mentioned in the Methods section, the experimental data was subjected to a Savitzky-Golay filter 18 for presentation in the main text, in order to emphasize the lower frequency oscillatory signals under discussion. In Supplementary Figure 8, we compare the both the filtered and unfiltered versions of the cross-power spectrum and beat frequency map presented in Figure   5 of the main text. Upon comparison, it is evident that filtering leaves the oscillatory signals under discussion unaltered, rather, as intended, filtering only deemphasizes higher frequency signals.
A more explicit comparison of the beat frequencies versus the noise floor is shown in Supplementary Figure 9. The noise floor was calculated by taking the average power spectrum of the experimental noise.
Supplementary Figure 8. Filtered versus unfiltered center line slope cross-power spectrum and beat frequency map along the excitation axis. a)-b) Filtered (as described in the Methods section) and unfiltered cross power spectrum of the center line slope dynamics of excited state absorptions seven and eight. c)-d) Filtered (again, as described in the Methods section) and unfiltered beat frequency map. Only peaks that survive the noise floor were plotted in c) and d) such that contour levels are drawn in 4% intervals starting from the top of the noise floor. The colormap indicates peak intensity, where intensity is shown to increase from green to red.
The linear absorption spectrum of LHCII at 77 K along with the laser excitation spectrum is presented in Supplementary Figure 10.