Ultrafast Anisotropy Decay Reveals Structure and Energy Transfer in Supramolecular Aggregates

Chlorosomes from green bacteria perform the most efficient light capture and energy transfer, as observed among natural light-harvesting antennae. Hence, their unique functional properties inspire developments in artificial light-harvesting and molecular optoelectronics. We examine two distinct organizations of the molecular building blocks as proposed in the literature, demonstrating how these organizations alter light capture and energy transfer, which can serve as a mechanism that the bacteria utilize to adapt to changes in light conditions. Spectral simulations of polarization-resolved two-dimensional electronic spectra unravel how changes in the helicity of chlorosomal aggregates alter energy transfer. We show that ultrafast anisotropy decay presents a spectral signature that reveals contrasting energy pathways in different chlorosomes.


Initial structure
Initial structures of chlorosome model systems are created by rolling up a 2D sheet structure into cylinders.Lattice parameters such as vectors ⃗ a and ⃗ b and the angle between them γ giving information on the unit cell are obtained from solid state NMR studies 1   We used the software CTubeGen 6 to generate the two model systems represented as three concentric cylinders, that are defined by their radius R and the chiral angle δ.Three cylinders will be referred to as inner, middle and outer cylinder.Parameters describing two model systems are summarized in Table S1.

Transition dipole moments of exciton states
In the main text, we discussed the impact of the molecular packing within chlorosomes, with a focus on the angle β, the angle between the molecular transition dipole moment µ and the cylinder axis of the chlorosome, on the optical response of the system.This angle will dictate the orientation of the transition dipole moments of exciton states, µ exciton .A large number of the optically active excitons in cylindrical aggregates arise due to the presence of structural disorder included in our model.In Fig. S2 we give the angles that individual exciton transition dipole moments, µ exciton , form with the respective coordinate axes z (θ), x (ϕ x ), and y(ϕ y ).
Since we are mostly interested in optically active, superradiant, excitons: we show the dependence of the oscillator strength µ 2 exciton on these angles.While in System 1 the transition dipole moments clearly preferentially orient in the direction of the cylinder axis, a clear preferential direction is absent in System 2. In line with the discussion in the main text, we thus see that the bright exciton states in System 1, are predominantly almost parallel to the long z axis.In contrast, in System 2, the distribution of orientations of the exciton transition dipole moments, µ exciton , is much broader.This is the fundamental background leading to the ultrafast anisotropy decay that we report for this system.

Comparison of simulated to experimental linear absorption spectra
In Fig. S3 we compare our simulated linear absorption spectra of System 1 and System 2 with the experimentally measured spectra for Chloroflexus aurantiacus 7 and Chlorobaculum tepidium. 8For the most direct comparison with the experiment, we included effects of homogeneous and inhomogeneous broadening, caused by the presence of mesoscale disorder 9 on the linear absorption and 2D ES spectra by weighting simulated response functions with exponential (τ homo = 300 fs) and Gaussian (τ inhomo = 166 fs) apodization functions, 10 as reported previously in Ref. 11.We note that local structural disorder and bath fluctuations, as included in our model, are responsible for the resulting spectral width, while the convolution procedure leads to smoother spectra, but no significant additional broadening.All spectra are normalized to the maximal peak height.The spectra of System 1 and System 2 are red-shifted by 1150 cm −1 and 1350 cm −1 , respectively.The required red-shift may be explained by a combination of the choice of the frequency of the isolated chromophores 3,11 and the size of the couplings predicted by the transition dipole coupling model. 3,11The low intensity absorption band centered around 12500 cm −1 in the spectrum of Chloroflexus aurantiacus comes from BChl a of the baseplate.Likewise there is a contribution of the baseplate absorption in the same frequency region in the spectrum of Chlorobaculum tepidium effectively broadening the spectrum.Our model systems do not include baseplate and, thus, do not include these features.The comparisons confirm that System 1 and System 2 are good models of chlorosomes from Chloroflexus aurantiacus and Chlorobaculum tepidium, respectively.Table S2: Characterization of the linear absorption spectra of a small model system for which simulation of 2D ES are performed.The peak positions and FWHM were extracted directly from the spectra presented in Fig. S4, which were calculated using a quantum-classical simulation procedure 12 based on the exciton model including the structural disorder predicted from the molecular dynamics simulations as well as the discussed mesoscopic disorder.
Linear absorption spectra Number of molecules ⟨ω⟩ (cm −1 ) FWHM (cm We observed that the absorption spectrum of the small model of System 2 is additionally shifted towards the red compared to the spectra of the full system.The decomposition of these spectra on components which define intensity in the direction parallel and perpendicular to the long axis of the cylinder is shown in Figure S5.Based on this we correlate the additional shift to the shift of high energy (perpendicularly polarized) exciton states, which strongly depend on the radius of the tube. 13Information on peak positions and fullwidth-half-maximum of two spectral components estimated for the small model representing System 2 are given in the Table S3.Presented information is useful for better understanding of peak positions in calculated 2D spectra shown in Figure 3. and anisotropy spectrum in  Table S3: Parameters describing positions and widths of parallel and perpendicular spectral component of the small model representing System 2.

Figure S1 :
Figure S1: Schematic representation of a 2D sheet which is rolled along the chiral vector C into the tube, following the procedure explained in Refs.2-5.

Figure S2 :
Figure S2: Characterization of the orientation of the transition dipole moments µ exciton in System 1 (left panel) and System 2 (right panel).a) Representation of the coordinate system where z is chosen as a long axis of the chlorosome cylinder, while x and y define the xy plane perpendicular to z. Transition dipole moment vectors of exciton states enclose angle θ with the long axis and angles ϕ x and ϕ y with the x and y, respectively.b), c), d) show the dependence of the oscillator strength µ 2exciton on the angle that transition dipole moments enclose with respective coordinates z, x, y: cos θ (in orange), cos ϕ x (in red) and cos ϕ y (in green), respectively.

Figure S3 :
Figure S3: Comparison of the simulated linear absorption spectra of System 1 (red) and System 2 (black) with experimental spectra of Chloroflexus aurantiacus 7 (red dashed) and Chlorobaculum tepidium 8 (black dashed).The experimental spectra for chlorosomes for the two bacterial species are digitized from Refs. 7 and 8.

Figure S4 :
Figure S4: Comparison of linear absorption spectra calculated for small cylindrical systems, used for calculations of 2D ES of the two chlorosome models System 1 (red) and System 2 (green).

Figure 4 .
Figure 4. that are given in the main text.

Figure S5 :
Figure S5: Decomposition of linear absorption spectra calculated for the small chlorosome model systems representing System 1 (left panel) and System 2 (right panel) on parallel I ∥ and perpendicular components I ⊥ .

Table S1 :
Characterization of the linear absorption spectra of small model system for which simulations of 2D electronic spectra are performed.