Assignment of the Q-Bands of the Chlorophylls: Coherence Loss via Qx − Qy Mixing

We provide a new and definitive spectral assignment for the absorption, emission, high-resolution fluorescence excitation, linear dichroism, and/or magnetic circular dichroism spectra of 32 chlorophyllides in various environments. This encompases all data used to justify previous assignments and provides a simple interpretation of unexplained complex decoherence phenomena associated with Qx → Qy relaxation. Whilst most chlorophylls conform to the Gouterman model and display two independent transitions Qx (S2) and Qy (S1), strong vibronic coupling inseparably mixes these states in chlorophyll-a. This spreads x-polarized absorption intensity over the entire Q-band system to influence all exciton-transport, relaxation and coherence properties of chlorophyll-based photosystems. The fraction of the total absorption intensity attributed to Qx ranges between 7% and 33%, depending on chlorophyllide and coordination, and is between 10% and 25% for chlorophyll-a. CAM-B3LYP density-functional-theory calculations of the band origins, relative intensities, vibrational Huang-Rhys factors, and vibronic coupling strengths fully support this new assignment.


S2. Extraction of high-resolution properties of the Q y state of Chl-a in ether at 4.2 K from observed FE (and other) data.
The observed high-resolution FE spectrum of Chl-a in ether at 4.2 K 1 contains data in the range of ν ∆ = 60-2300 cm -1 from the Q y origin. As the origin region itself is not accessible by FE, the shapes of the zero-phonon line (ZPL) and its associated phonon side-band (PSB) are not fully discernible from this experiment, features required for the determination of the absolute magnitudes of the vibrational Huang-Rhys factors S i . To determine absolute values, we inhomogeneously broaden the deduced high-resolution lines, normalizing the total S value to reproduce the observed lowresolution contours observed in ABS for Chl-a in ether over the range 120 K to 295 K (see Sect. S4). However, the unobserved ZPL+PSB absorption shape is complex (see e.g. Fig. 2 insert) and requires much more detailed information to correctly reproduce. We use a standard analytical form for the ZPL and PSB shapes, expressing them as 2 The observed FE contains not only high-resolution features attributed to individual y-polarized vibrational lines of Q y but also low-resolution data attributed to the inhomogeneously broadened Q x state and its associated vibronic coupling. Note that this inhomogeneity broadens the would-be sharp Q y vibrational bands as the vibronic coupling lowers their energy by of order 2 / ( ) vc E α ν ∆ − , accessing the inhomogeneous broadening of the Q x state. We subtract the low-resolution x-polarized intensity, deduced by the MCD/ABS fit, from the observed FE before fitting the Q y Huang-Rhys factors.
An additional complication is that the sample measured by FE contained an unquantified mixture of 5CO and 6CO species (we have identified the 6CO species as being associated with water contamination 3 ). By monitoring emission at 660 nm in the far high-frequency tail of the spectrum, Avarmaa and Rebane 1 aimed at measuring the spectrum of primarily the higher-energy 5CO species, having determined that its prominence increases rapidly as the monitored emission wavelength is decreased. 1,4 Given the inhomogeneous broadening at 4.2 K, the likely composition ratio, and that our fitting of the temperature dependence of the ABS and MCD spectra of Chl-a in ether indicate that the 6CO Q y origin lies 130 cm -1 below the 5CO one (see Sect. S4), of order 5-10% of the FE signal is expected to arise from the 6CO species. As this estimate is too imprecise in nature and the expected contribution too low to fit to the experimental data, we chose to ignore any 6CO contribution to the spectrum.
The fit to the identified y-polarized non-ZPL contribution to the observed FE is then performed using m n = 236 individual vibrational modes (see Fig. 2). A maximum of q n =3 quanta of excitation in any individual mode is allowed (convergence of calculated spectra occurs at just 2 such quanta) an a convolution technique is used to calculate the full Franck-Condon allowed spectrum involving all possible multi-mode overtones of these individual-mode levels. This requires computer time of the order ( 1) m q n n + , taking for Chl-a of order 1 s to complete on a laptop computer. During this procedure, every line associated with single and multi-quanta excitations is given the same intrinsic lineshape, that of the ZPL+PSB. This procedure works by first representing the ZPL+PSB spectrum on a finite grid of points j ν ∆ as iteratively convolving in the Franck-Condon factors which is only valid in the limit of 1 S  , a limit that in general does not accurately apply for chlorophylls.
Full results for the fit to the FE data 1 for Chl-a in ether at 4.2 K are given in Table S1. This data is collapsed into 51 clearly resolved bands in Table S2, conserving the reorganization energy partitioned into each band; this process does not significantly affect the calculated low-resolution spectra. The resultant total Huang-Rhys factor is 0.278 whilst the total reorganization energy is 262 cm -1 .  The hole burning spectra obtained for Chl-a in various photosystems differ significantly from each other, 5 indicating significant dependence of both the total magnitude of the Huang-Rhys factor and its vibrational distribution upon local environment. Large differences between chlorophyll in situ and in solvents has also been noted. 2 For example, in Table S3 high-resolution data for Chl-a in ether (this work, from FE) is compared to that obtained from hole burning experiments on the WSCP 5 and PSI-200 6 photosystems, with the total Huang-Rhys factors being S= 0.278 in ether, 0.79 in WSCP, and 0.57 in PS1-200; more crudely estimated values in other solvents (Table S4) are S= 0.28 in pyridine, 0.42 in 1-propanol (0.39 previously 2 using a similar scaling method), and 0.38 in 2-propanol. These results suggest that this effect in not controlled primarily by magnesium coordination, and indeed a large difference is also found between the Huang-Rhys factor of 0.45 deduced for Pheo-a in EtOH/MeOH and 0.20 deduced for its methylated derivative methylpheophorbide-a in dioxane (Table  S4). S4. Fits to MCD and/or ABS spectra obtained by fitting vibronically coupled full Q x and Q y Franck-Condon-allowed band shapes.
The potential-energy surfaces of the Q y and Q x states, respectively, are represented in terms of n m = 51 dimensionless normal coordinates of the Q y state q i , coupled by a single vibronically active mode q vc as 2 where Qx i δ are the coordinate displacements between the minima of the Q y and Q x states; many alternate forms of expressing this equation are available 9-16 but they are all equivalent. 17 This electronic matrix is then expressed in terms of a vibronic basis set formed as a product of harmonicoscillator wavefunctions containing k i quanta of excitation Simple diagonalization of this Hamiltonian matrix would yield the eigenstates of the vibronically coupled band system and hence the ABS spectrum given the unperturbed Q y and Q x transition moment matrices: where x  and y  are orthogonal unit vectors in the molecular coordinate frame and GS i δ are the differences in geometry between the Q y state and the ground state (GS) , with the total Huang-Rhys factor of the Q y state given by (S12) However, such an approach is very computationally intensive and instead a numerically equivalent time-dependent procedure is utilized. Initial wavefunctions representing Franck-Condon absorption from the zero-point level of the ground state to the Q y and Q x states are then written from Eqn. (S11) as These non-stationary states are then propagated forward in time t using the appropriate time-dependent Schrödinger equations d ( ) ( ) and operations that require only repeated matrix-vector products to evaluate. From these, the autocorrelation functions ( ) (0) | ( ) and are deduced and converted to ABS spectra by Fourier-Laplace transform where ( ) w t is the Fourier Transform of the spectral lineshape function comprising the inhomogeneous broadening of the Q y state, the zero-phonon lineshape, and the phonon-side band, multiplied by the Fourier transform of the Gaussian inhomogeneous-broadening function. Only this function is used to include thermal effects on the spectrum, but this method can be readily extended to include explicitly thermally populated vibrational levels if necessary. 18 This procedure automatically includes the inhomogeneous broadening of the Q y state but that for Q x is much larger owing to the stronger interaction of Q x with its environment. This additional contribution is included by integrating over the associated inhomogeneity E′ implemented by just adding E′ ∆ to E ∆ in Eqn. S9, etc.; here Qy σ and Qx σ are the inhomogeneous broadenings of Q y and Q x , respectively. In the program FITMCD, these integrations are performed using an 11-point Simpson's Rule quadrature, but the averaging is actually performed for the autocorrelation functions rather than for the final spectra. A total of 22 2912×2912 matrices H are thus constructed per molecular component, but the spectra are determined quickly enough to facilitate interactive mouse-driven adjustment of the model parameters by our program FITMCD.
The ABS and MCD spectra in terms of these normalized bandshape functions are then expressed as respectively, where H is the applied magnetic-field strength, D are absorption dipole strengths, and B and MCD susceptibilities (only this MCD "B" term 19 is usually included in the analysis of chlorophyllides).
For spectra arising from just a single molecular component, 12 adjustable parameters naturally arise in our vibronic coupling model: the two vibronic-coupling parameters vc ν and α, the two unperturbed origin frequencies, the two ABS dipole strengths D x and D y , the associated MCD sensitivities B x and B y , the associated inhomogeneous-broadening FWHM, and two parameters associated with the Franck-Condon Huang-Rhys factors S of Q x and Q y . Other parameters in the model such as those specifying the zero-phonon-line shape and the phonon-side-band are not adjusted.
The relative Huang-Rhys factors for each of the 51 vibrational lines of the Q y state relative to the ground state are frozen and only its total magnitude S that is adjusted for each chlorophyllide. This is a somewhat crude approximation but one which exposes the intrinsic similarities of the properties of the different chlorophyllides as well as the important feature that the geometry change between the ground state and Q y is quite sensitive to both the nature of the chlorophyllide and the solvation environment. Replacing this approximation by a more realistic one requires the measurement and accurate interpretation of high-resolution spectra for each individual chlorophyllide in each solvation environment.
For most chlorophyllides, it is assumed that the Franck-Condon factors for the Q x state are the same as those for Q y . This is a much poorer approximation than the previous one as the two states are expected to have significantly different geometries. As Eqns. S11 and S13 indicate, (unsigned) Huang-Rhys factors alone are insufficient to describe the spectral properties of two vibronically coupled states, the actual (signed) displacements δ being required instead. Even if high-resolution spectra for Q x were available, the determination of this sign information would be a seriously difficult task. As it stands, only information concerning the Q x band contour is available, but this highly inhomogeneously broadened band contour must also be extracted from underneath the much more intense Q y band for many chlorophyllides. For those molecules for which Q x is well resolved, the Huang-Rhys factors for Q x appear similar to those for Q y and so it appears reasonable to take them as being equal. For Chl-a and its close analogues like Chl-d, BChl-c and BChl-d, the observed MCD signal shows much more intensity in the region of Q x + 500 cm -1 than does Q y , however, so we introduce an arbitrary rescaling of the displacements for these modes, leading to the prescription The same molecular vibration frequencies are used for all states of all molecules. The effect of the above rescaling is to increase the spectral reorganization energy associated with absorption from the ground state from 262 cm -1 for Q y to 380 cm -1 for Q x .
In practical terms, fitting the vibronic coupling model to the observed ABS and MCD spectra involves the determination of 7 non-trivial parameters: the unperturbed Q x -Q y gap E ∆ , the fraction of absorption / ( ) has historically played a significant role in the justification of the "modern" assignment for the spectrum of Chl-a. 20 However, this result is only expected if the Q x transition is formally forbidden (i.e., f x = 0), and the related constraints affecting / x x B D are rarely considered. In a more general approach we introduce the quantities to represent the fitted MCD susceptibilities.
Our description of the Q-band spectra explicitly assumes that no other spectroscopic transitions are involved. This is a good approximation in that the next highest energy transitions, the Soret band, is well removed from the Q band for all molecules considered. Under such circumstances, standard MCD theory 19,[21][22][23] indicates that x y B B = − (or equivalently x y η η = ). However, interactions with the distant Soret bands invalidate this relationship and hence we assume that these are independent quantities. We have also developed an independent analytical method for analysing the MCD data which verifies this key aspect of our fitting procedure. 24 We analyse many spectra taken from the previous 50 years' literature plus in addition some new measured spectra at low temperature for Chl-a. Magnetic Circular Dichroism and Absorption measurements were made simultaneously using the system as previously described, 25 consisting of a Spex 0.75 monchromator and an Oxford Instruments SM4 superconducting magnet cryostat and a highly stabilized quartz halogen light source. Samples were rapidly quenched in a helium gas environment (30 sec) to 5 K in a 2 mm path-length cylindrical cell having fused quartz windows. The cell windows were bonded to a thin-wall stainless steel or titanium body, similar to designs previously described. 26 This construction minimized strain in the sample and avoided fracturing the quartz windows. Spectra were taken in the absence and presence of a 5 Tesla applied magnetic field, so as to account for CD baselines and artefacts. The concentration of Chl-a (sourced from Anacystis nidulans algae, Aldrich) in the various solvents was adjusted to provide a peak Q y absorption of ~0.2 in a 2 mm cell. This largely eliminated aggregation effects, which would otherwise be obvious from the MCD and CD spectra. [27][28][29] Reagent grade solvents/solvent mixtures were used except diethyl-ether, which was rigorously dried and distilled under vacuum. Dry ether samples were rapidly transferred to the sample cell and immediately quenched to 5 K in the sample cryostat. The wet ether sample was prepared by adding one drop of water to 0.5 ml of the dry diethyl-ether/Chl-a mixture and stirring for 5 minutes. Table S4 gives the 7 non-trivial fitted parameters for the 12 systems discussed in Fig. 1 of the main text, as well as those for 17 other systems shown in Fig. S1. For Chl-a in ether at low temperature, the observed spectra include contributions from both 5CO and 6CO components. For these samples, two sets of 7 parameters are required, along with a 15 th parameter indicating the relative fraction of the absorption attributed to the 6CO species. A 16 th parameter, the difference between the 6CO and 5CO Q y origins also arises, but for all samples we constrain the 6CO origin to be 130 cm -1 lower in energy than that for 5CO. Quantification of this energy difference is difficult as the perceived value is dependent on assumptions made concerning the inhomogeneous broadening, but 130 cm -1 is consistent with a wide range of data including detailed high-resolution FE measurements. 1,4,30 A value of 140 cm -1 results in a less consistent representation of the other parameters while a value much less than this would seem inconsistent with the qualitative picture depicted by the FE. For samples containing mixed species, all parameters except the composition are frozen, allowing the observed temperature and concentration dependence to be represented using just a single sensitive parameter (other parameters such as the overall Q-band band location and intensity do vary slightly as well). Mixed species are also found in 2-propanol at low temperature, and for this system 6CO Q y is fitted to be 95 cm -1 lower in energy that 5CO. Other samples of 2-propanol at low temperature 2 have revealed just a single component (5CO), and it is clear that composition is strongly dependent on formation conditions in these glasses.
From Table S4 we see that the energy-gap scaled MCD susceptibilities can show marked variations amongst the chlorophyllides, with y η ranging from 0.25 T -1 cm -1 for Ni(II)-Chl-a in ether to 2.63 T -1 cm -1 for methylpheophorbide-a in dioxane; hence the expectation 20,31,32 based on the assumption that the magnetic and electronic transition moments that combine to provide the MCD Bterm response 19,20,31,32 are invariant to solvation and to variations in the macrocycle is not valid. However, the variation found between similar species is much less, with for example y η = 0.75−0.9 T -1 cm -1 for Chl-a and BChl-a, ~1.1 T -1 cm -1 for Pheo-a and BChl-c, and ~1.2 T -1 cm -1 for BChl-d. Also, the naïve expectation that y η should be a universal constant also leads 19,[21][22][23] to the approximation x y η η = but from Table S4 we see that for Chl-a and related species x η is 10-20 % larger than y η , for some chlorophyllides it can be up to five times larger. This analysis has been independently verified. 24 The results shown in Fig. 1 of the main text indicate that the vibronic-coupling model depicts the major qualitative effects controlling the observed ABS and MCD spectra of the chlorophyllides.
There are, however, distinct quantitative shortcomings. Form Figs. 1a and 1d for BChl-a, it is clear that the Huang-Rhys factors for this molecule are proportionately larger at Q y (0,0)+500 cm -1 , but the vibronically stolen intensity at +1000 cm -1 is well reproduced, indicating that the magnitude of the vibronic coupling is very similar for Chl-a and BChl-a. For Pheo-a in Fig 1b the strength of the vibronic coupling appears to have increased slightly, while for Chlorin-e6 in Fig S1c the magnitude of the vibronic coupling constant appears to double. Similarly, Zn(II)-Chl-a (Fig. 1e) appears to have similar vibronic coupling to Chl-a whilst it is clearly much larger for Ni(II)-Chl-a (Fig. S1g).
More significantly, the one-mode vibronic-coupling model quantitatively fails to predict the correct magnitude of x-polarization in the +1500 cm -1 region for 5CO Chl-a, BChl-c, and BChl-d, correspondingly also failing to reproduce the correct width of the band at this location for 6CO species (Fig. 1j-l). These deficiencies should be corrected if a full multi-mode treatment of the vibronic coupling is implemented, but at the moment insufficient high-resolution data is available to construct such a model authoritatively.
The spectra of Chl-b and protochlorophyll-a appear to depict dramatically reduced vibronic coupling compared to Chl-a. Further experimental work re-examining the MCD spectra, as well as computational work investigating the vibronic coupling, is warranted.  Fig. 1 of the main text or in Fig. S1, with detailed decompositions provided in the associated file "Detailed_analyses.pdf"; experimental data sources are listed with the figure captions. b: MCD intensities from Nonomura et al. 33 are rescaled to align results for Chl-a with other measurements. *: Q x modes < 700 cm -1 are rescaled, see Eqn. S20. ν =1500 cm -1 and α=750 cm -1 . Solvents are as indicated, measurements were made at room temperature unless otherwise noted. Unperturbed origins are indicated by arrows: black-free-base and 5CO Q y , brownfree-base and 5CO Q x , green-6CO Q y , purple-6CO Q x . Key fitted parameters are listed in Table S4. All spectra are broadened using a Gaussian function of HWHM= 47 cm -1 to reduce noise, obtained from: a-e Briat; 34 f-Razeghifard; 35 g-j-Nonomura; 33 k-Frackowiak; 36 l-q this work; q-Weiss. 37

S5. Conversion of observed LD to fraction Q x absorbance.
Fragata et al. 38,39 observed the LD polarized absorption of Chl-a in an aligned lamellar phase of glycerylmonooctanoate/H 2 O. They found that the Q y transition was polarized at an angle of 70° to that of Q x . As a result, intensity from the Q y band is recorded amongst the Q x absorption. We correct for this effect using which eliminates the x-polarized intensity that tracks the Q y band shape.
Avarmaa and Suisala 4 measured the polarized FE spectrum of Chl-a in ether at 4.2 K by exciting an isotropically aligned sample with linearly polarized light, detecting the resulting polarized emission. The concentrations used are too low to permit exciton energy transfer and so only unimolecular relaxation processes are allowed. Under these conditions, the observed anisotropy r is related to the angle β between the absorbing dipole (which may contain some mixture of Q x and Q y absorption) and the emitting dipole (assumed to be pure Q y ): 40 but under the experimental conditions the observed polarization (Ref. 4 Fig. 1) is related to the anisotropy by 40 3 2 so that the polarization in the x-y plane is given by 7 This quantity, which is unbiased with respect to x and y, is shown in Fig. 4b.
In Fig. 4b, the polarizations extracted from the LD, polarized FE and MCD experiments are qualitatively similar to each other and in particular show the same types of variations in going from 5CO to 6CO species. Monitoring at 665 nm, the polarized FE is most likely to arise from Chl-a molecules with over 80% 5CO, whereas monitoring at 675 nm is likely to sample a more equal proportion of 5CO and 6CO species. Unfortunately, details of the composition cannot be accurately determined as the water content 3 of the sample is unknown and the emission band contour has not been quantitatively apportioned into contributions from 5CO and 6CO species.

S6. CAM-B3LYP calculations of the Franck-Condon and Herzberg-Teller spectral envelopes of the Q y band.
The general properties of spectral calculation methods for chlorophyllides and other molecules has recently been extensively reviewed. 41 Here, the Franck-Condon absorption envelope for the Q y band of Chl-a (Fig. 3) was determined from the DFT-optimized structure of the ground state and the TD-DFT optimized structure and normal coordinates of Q y . These calculations were performed by GAUSSIAN-09 42 using the 6-31G* basis set 43 and the CAM-B3LYP 44 density-functional. The fully optimized Cartesian displacements between the two adiabatic minima were projected onto the normal modes using curvilinear internal coordinates using the DUSHIN program 45 and the dimensionless normal-mode displacements GS i δ thus obtained. A similar approach has been shown to quantitatively describe the significant high-resolution asymmetry seen between the ABS and EMI spectra of BChla. 46 The ABS spectrum is synthesized using the convolution techniques described in Sect. S2 but the results obtained are identical to those that would have been obtained by evaluating Eqn. S11 directly.
The corresponding Herzberg-Teller (x-polarized) component of the Q y spectrum shown in with respect to displacements in the normal modes i q of Q y : 14,16 ( ) Always the transition moment was taken to be the geometrical mean of the length-formalism and velocity-formalism transition moments reported by GAUSSIAN. 47 Note that this approach utilizes also the Q x transition-moment vector predicted by CAM-B3LYP as well as the associated energy gap. Once the vibronic-coupling constants are determined, the spectrum is simulated by application of the standard zero-phonon-line and phonon-side-band shapes and expanded to include Franck-Condon progressions based on each Herzberg-Teller origin. The intensity of each Herzberg-Teller origin is obtained from perturbation theory (rather than full solution of H) as The calculated Franck-Condon displacements, Huang-Rhys factors, and reorganization energies, as well as the corresponding Herzberg-teller vibronic-coupling constants, Huang-Rhys factors, and reorganization energies are given in Table S5. For the Franck-Condon term, the calculated reorganization energy is 505 cm -1 , nearly double the observed value (Table S2) of 262 cm -1 , while the Herzberg-Teller term is 615 cm -1 (reducing to 374 cm -1 after damping in a condensed media of modes < 30 cm -1 is included) compared to 750 2 /1500/2= 188 cm -1 used in the vibronic-coupling model fits. While closer agreement for experiment has been found for BChl-a, 46 the values are all actually very small making accurate calculation difficult, with reasonable computational methods often being in error by an order of magnitude. 46 Table S5. CAM-B3LYP/6-31G* calculated Franck-Condon displacements δ, Huang-Rhys factors S, and reorganization energies λ (cm -1 ), as well as the corresponding Herzberg-Teller vibronic-coupling constants α (cm -1 ), Huang-Rhys factors, and reorganization energies (cm -1 ) for Chl-a in the gas phase.  Figure 5 of the main text compares the experimentally deduced unperturbed Q x -Q y energy gaps E ∆ and total fraction of x-polarized Q-band absorptions x f to values calculated by CAM-B3LYP. The calculated values were obtained considering only clusters of chlorophyllides with either one or two solvent molecules ligated to the central metal, or, for free-base molecules, considering only the molecule itself. This treatment ignores long-range solvation effects, but such effects are known to be relatively small for the properties of interest and to vary only slightly with solvent. 48 The B3LYP density-functional 49 was used to optimize all geometries in conjunction with the 6-31G* basis set 43 for C, H, N, O, and Mg and LANL2DZ 50 for Co, Ni, Cu, and Zn, while CAM-B3LYP 44 single-point excited-state energies are reported at these geometries; all calculations were performed using a GAUSSIAN Development Version 47 extended by us 51 to include CAM-B3LYP. The ground-state optimized geometries for the molecules and clusters listed in Table S6 are provided in associated file "Cartersian_Coodrinates.zip".
Calculated vertical excitation energy differences (for clusters in the gas phase) E ∆ and observed values (in solution) are compared in Table S7 and graphed in Fig. 5a. Agreement is generally good but a systematic error between free-base and metallated species is apparent. The correlations drawn in Fig. 5a have very similar slopes of 1.27 and 1.24 for free-base and metallated species, but the two lines are offset by 1330 cm -1 .
Note that not all of observed values are taken from our vibronic-coupling assignments, however, with insufficient experimental data being available to facilitate this approach for many important samples. Hence some data taken from observed sub-band maxima in the limit of large E ∆ are also included; application of the vibronic-coupling correction for these systems would increase the deduced experimental value for E ∆ by a small amount. In Fig. 5, raw data is represented by open circles whilst vibronically corrected data is represented by filled circles. An improved vibroniccoupling approach in which individual vibronic-coupling parameters are fitted to every individual chlorophyllide would also result in some small changes to the experimental values.
To improve the comparison between observed and calculated data, comparisons of quantities that negate systematic errors in both sets of data are required. A significant spectroscopic signature of interest is the change from 5CO to 6CO in the induced Q x -Q y gap E ∆∆ , a property that is much less sensitive to both experimental and computational errors. Observed and calculated values are compared in Table S8 and in Fig. 5b, with the observed data presented as either the "traditional" or "modern" assignments based on sub-band maxima or else our full vibronic-coupling assignment. The vibroniccoupling assignment is in excellent agreement with the calculated data while the "traditional" and "modern" assignments agree only for molecules with large E ∆ . This data includes results for 6CO chlorophyllides in ether at low temperature for which an observed signal is only obtained when trace amounts of water are present in the solvent and hence these samples are modelled as water complexes rather than as ether complexes. 3 Also, Table S9 gives the fraction of Q-band intensity apportioned to Q x as calculated by CAM-B3LYP and as deduced from the vibronic-coupling model (this data is graphed in Fig. 5c). The factorof-five variation in Q x intensity deduced from the spectra is paralleled by the calculations. Going from 5CO to 6CO, the largest observed change in Q x intensity is for Chl-a in ether for which the intensity doubles. The calculations for the both the doubly hydrated species Chl-a.water.water and the monohydrate Chl-a.ether.water reproduce the observed effect. 3 Note that the Q x oscillator strength is found to be very sensitive to the angle between the symmetry axis of the water and the Mg-O vector, with results obtained for a tilted angle expected if the water molecule hydrogen-bonded to its environment 3 being used in Fig. 5c. Table S6. Molecules and molecular clusters for which B3LYP/6-31G* optimized gas-phase coordinates are given in SI dataset "Cartesian_Coordinates.xls"; prop= 1-propanol, iprop= 2-propanol. Table S7. CAM-B3LYP calculated gas-phase Q x -Q y energy gaps E ∆ , in 1000 cm -1 , for 5CO and 6CO clusters compared to the "traditional", "modern", and our vibronic-coupling assignments in solution, plus some raw unassigned peak maxima, observed in solution (plotted in Fig. 3a).

Cluster (solution) CAM-B3LYP Trad. Modern Vib. Coup. Raw Peak
Pheo-a (   Table S9. Comparison of CAM-B3LYP calculated fraction of Q-band absorption attributed to Q x , f x for gas-phase clusters and results observed in solution based on the traditional, modern, and vibronic-coupling assignments (plotted in Fig. 3c The method used to estimate the rate of Q x →Q y relaxation follows the general ansatz of Reimers and Hush. 62 Intramolecular relaxation on Q y after transfer of a coherent wavepacket from Q x is modelled using a single parameter ρ representing the Franck-Condon weighted coupled density of states at the energy of the Q y origin plus that of the coupling mode vc ν . An imaginary energy contribution of / i ρ is then added to every level of the Q y state in the vibronic-coupling Hamiltonian H (Eq. S10) that has vibrational excitation in the vibronically coupled mode. The time-dependent Schrodinger equation is then solved for an initial wavefunction representing excitation to the unperturbed Q x origin, yielding ( ) t Ψ . The norm of this wavefunction decays with time owing to the vibrational relaxation that occurs on Q y , and the lifetime for this process is determined as 62