Bacteriochlorophyll a Franck−Condon Factors for the S0 → S1(Qy

12410

J. Phys. Chem. B 2001, 105, 12410-12417

Bacteriochlorophyll a Franck-Condon Factors for the S0 f S1(Qy) Transition V. Zazubovich, I. Tibe, and G. J. Small* Ames Laboratory-U.S. Department of Energy, and Department of Chemistry, Iowa State UniVersity, Ames, Iowa 50011 ReceiVed: July 23, 2001

Pseudovibronic satellite hole-burning spectroscopy of bacteriochlorophyll a (BChl a) in two glasses at 5 K was used to determine the Franck-Condon (FC) factors for 56 one-quantum (0 f 1) vibrational transitions that lie between 160 and 1600 cm-1. As in the case of Chl a (Pieper, J.; et al. J. Phys. Chem. B 1999, 103, 2319), the FC factors are small, ranging between 0.05 and 0.0007 (uncertainty ≈ (20%). The FC factors, together with the experimentally determined inhomogeneous site excitation distribution function for the zerophonon line and linear electron-phonon coupling parameters, account well for the S0 f Qy absorption spectra. Thus, the FC factors are accurate enough to be used in quantum mechanical calculations of excitation energy transfer rates in photosynthetic antenna complexes (with their intrinsic structural heterogeneity) exhibiting excitonic coupling that ranges between weak and strong. The BChl a FC factors determined by hole burning are compared with those obtained by fluorescence line narrowing spectroscopy (Wendling, M.; et al. J. Phys. Chem. B 2000, 104, 5825). The latter, which are about a factor of 5 smaller than those determined by hole burning, are too small to account for the vibronic contribution to the S0 f Qy absorption spectrum. The discrepancy between the two sets of FC factors is discussed.

1. Introduction Chlorophyll (Chl) molecules play a critically important role in solar energy absorption and excitation energy transfer (EET) within and between photosynthetic antenna complexes and in the eventual transfer of energy to the reaction center by proximal antenna complexes. The cyclic light-harvesting (LH) LH1 and LH2 complexes of purple bacteria such as Rhodopseudomonas acidophila and Rhodospirillum molischianum are but one (splendid) example of how nature has designed an antenna system that is optimized for light harvesting and efficient EET to the reaction center, as recently reviewed in.1 A firm understanding of EET in photosynthetic complexes requires several types of information,1-5 including (i) Chl-Chl excitonic coupling energies (Coulombic, electron-exchange), (ii) S0 f S1(Qy) site excitation energies of the Chls in the absence of excitonic interactions, (iii) the site excitation energy distributions functions (SDF) that stem from intrinsic protein structural heterogeneity, (iv) the extent to which the SDF of different Chls are correlated, and (v) the spectral density due to phonons and intramolecular vibrations that enters into rate expressions. The calculation of electron-exchange coupling energies still remains as a challenging theoretic problem. This coupling can introduce charge-transfer character to the Qy states. Concerning condition ii, there is currently no reliable method for calculating site excitation energies. Thus, simulations of several types of optical spectra, e.g., absorption, linear dichroism, circular dichroism, and triplet minus singlet, with known excitonic coupling energies, are necessary to determine the site energies. The Fenna-Matthews-Olson antenna complex of green sulfur bacteria with its seven symmetry inequivalent BChl a molecules serves as a good example of this.6-8 From such simulations, one determines the extent to which the Qy states are delocalized in the static lattice approximation and in the absence of energy *

Corresponding author. E-mail: [email protected].

disorder. When the excitonic couplings V are considerably larger than the energy gaps obtained from the site energies, the Qy states exhibit significant delocalization (strong coupling limit). With the static lattice approximation and neglect of energy disorder, the wave functions would be perfectly delocalized for complexes in which the Chls are symmetry equivalent and, therefore, energetically equivalent, the B850 and B875 BChl a rings of LH2 and LH1 being good examples. With an understanding of excitonic structure in the static lattice and “perfect” protein approximations, one can then examine how energy disorder (diagonal, off-diagonal) from protein structural heterogeneity leads to excitonic localization and static inhomogeneous broadening of optical transitions (∼50-200 cm-1 at low temperatures). Energy disorder renders symmetry-equivalent Chls energetically inequivalent but, it is also important for symmetry inequivalent Chls. A key finding from spectral hole-burning9 and fluorescence line-narrowing10,11 studies is that the SDFs of Qy states are uncorrelated, as recently confirmed by spectroscopic studies of single photosynthetic complexes.12 With reference to item iv, this means that the SDFs of site energies are uncorrelated. Gaussians for these SDFs have generally been used. When their standard deviations (σ˜ ) are considerably larger than the excitonic coupling energies, excitonic localization is pronounced.1,2 Strong excitonic coupling, which leads to motional narrowing of the inhomogeneous broadening contribution to optical bandwidths, is roughly defined by V > σ˜ . A comparison of the effects of diagonal and off-diagonal energy disorder in the LH2 complex is given in ref 13 (see also refs 14,15). An absence of correlation between SDFs leads to a distribution of values for the electronic energy gap between the donor (D) and acceptor (A) states. With ΓD2 and ΓA2, the variances for inhomogeneous broadening, the variance for the energy gap is ΓD2 + ΓA2 ≡ Γ2. When 2Γ is greater than the width of the homogeneous spectral density, dispersive kinetics for EET is

10.1021/jp012804m CCC: $20.00 © 2001 American Chemical Society Published on Web 11/08/2001

Franck-Condon Factors for S0 f S1(Qy) Transition expected. Intramolecular vibrations and phonons (protein, pseudolocalized) active in EET determine the spectral density. The temperature dependence of the spectral density is often dominated by the low-frequency phonons (electron-phonon coupling) and pure electronic dephasing. Thus, a density matrix treatment is required for a rigorous treatment of EET.3 We report here ν′′ ) 0 f ν′ ) 1 Franck-Condon (FC) factors for 56 BChl a vibrations (160-1600 cm-1), where the double- and single-prime quantum numbers indicate the ground and S1(Qy) electronic states. As in the case of Chl a,16,17 the FC factors are small, ranging between 0.05 and 0.0007. The availability of accurate intramolecular FC factors is essential for calculation of EET rates in photosynthetic complexes where energy disorder is always important and the excitonic couplings range from weak to strong. Fo¨rster18,19 or Dexter20 theory applies when the resonant couplings are weak and the donor and acceptor emission and absorption spectra are homogeneously broadened. Thus, they are not applicable to photosynthetic complexes exhibiting weak coupling because of the significant inhomogeneous broadening of optical transitions. It is instructive to consider the following (approximate) weak coupling expression for the average EET rate between chemically identical but energetically inequivalent Chl molecules in a bulk sample:

〈kDA〉(T) ) 2πV2(1 - e- S˜ ph)2e-2St[4π(Γ2 + Σ2)]-1/2

∑i

2(FCF)i exp-{[(Ω0 - ωi - 2Sphωm)2/4(Γ2 + Σ2)]} (1) which follows from the results in.21 It takes into account acceptor modes that are phonons (ph) and Chl modes (subscript i) as well as the distribution of values for the D-A electronic energy gap with average angular frequency Ω0. The variance of the gap is Γ2. As in Fo¨rster theory, eq 1 is based on the Condon approximation (V is the electronic coupling in the static lattice approximation), the assumption that the donor and acceptor Chl molecules are far enough apart so that the vibrations and phonons are localized on either the donor or acceptor molecule and that thermal equilibration occurs prior to energy transfer. Equation 1 is valid for temperatures (T) low enough to satisfy pωi . kT, where ωi is the frequency of the ith Chl vibration. Since most antenna Qy-transitions exhibit weak electronphonon coupling (Huang-Rhys factor Sph j 0.5) and a dominant single one-phonon profile peaked at ωm ∼ 20-30 cm-1,22-24 a Gaussian with variance σ2 was used for the onephonon profile. Typical values for 2σ are ∼20-40 cm-1. S˜ ph ) Sph coth(pωm/2kT), and (1 - exp(-Sph)) is the FC factor for phonon transitions. Σ2(T) is the variance of the homogeneous spectral density and is given by ∼S˜ ph(σ2 + ωm2) + (Γh/2)2, where Γh represents homogeneous broadening other than that due to linear electron-phonon coupling, e.g., pure electronic dephasing. When Γ2 > Σ2, the kinetics are expected to be dispersive.21 In eq 1, (FCF)i is the FC factor of mode i. The simple way in which it enters the rate expression is a consequence of the smallness of the FC factors, which renders EET involving overtone and combination vibrations highly improbable. That is, only EET pathways for downward transfer involving creation of one quantum of a Chl vibration need be considered. The factor of 2 multiplying (FCF)i is a consequence of the fundamental acceptor mode being able to reside on either the acceptor or donor molecule. St is the total Huang-Rhys factor for the Chl vibrations, ΣiSi. When frequency changes associated with the absorption transition are j10%, which appears to be the case for Chls (see last subsection of section 4), (FCF)i ) Si exp(-Si) ∼ Si for (FCF)i j 0.05. Although eq

J. Phys. Chem. B, Vol. 105, No. 49, 2001 12411 1 is approximate, it conveys the essential physics of EET for weak excitonic coupling in systems exhibiting energy disorder and linear electron-phonon coupling as well as the importance of having available accurate FC factors. Knowing the values of the parameters in eq 1, one can calculate the Fo¨rster spectral overlap between the D and A fluorescence and absorption spectra of single D-A pairs in an ensemble characterized by a distribution of D-A energy gap values.25 Averaging of the kDA values would give 〈kDA〉. Franck-Condon factors for phonons and Chl vibrations are also important for EET in systems exhibiting strong excitonic coupling. In the case of symmetry-equivalent Chls, e.g., the B850 and B875 BChl a rings, such coupling needs to be considered when the excitonic splittings, as calculated in the static lattice approximation, are large relative to the pure dephasing frequencies of the levels. In the absence of nuclear motion, the excitonic states are stationary. Thus, for interexciton level relaxation one must go beyond the Condon approximation and consider promoting modes (e.g., librations) that modulate the excitonic couplings. (We recall that it is the static intermolecular potential that governs the electronic coupling in Fo¨rster theory.) Such relaxation has been well-studied in molecular crystals26-31 but not in antenna complexes. A further and difficult complication arises when the excitonic couplings (V) are comparable to or larger than Chl vibrational or phonon frequencies (ω), as discussed, for example, in refs 32-34. The vibronic energy level diagram for V J ω is very different from that for V , ω, and furthermore, two-particle excitations enter the picture. They correspond to the electronic and vibrational excitations being on different molecules. The FC factors reported here can be used to calculate such vibronic energy level diagrams. To the best of our knowledge, this has not been done for an antenna complex where V J ω. 2. Experimental Section Glycerol:water (1:1 by volume) with 0.5% LDAO (lauryldimethylamine oxide) detergent and neat triethyamine (TEA, Aldrich) were used as glass-forming solvents for BChl a, which was kindly provided by R. J. Cogdell. BChl a was extracted from Rhodobacter sphaeroides. The cells were extracted with methanol. The extract was transferred into 40-60 bp Pet Ether and chromatographed on alumina, eluted in methanol. Samples were contained in polypropylene tubes (9 mm i.d.) and the BChl a concentration adjusted so that the absorbance at the maximum of the absorption origin band was ∼1. Samples were cooled to 5.0 K in a Janis 8-DT liquid helium optical cryostat. Temperature was stabilized and measured with a Lake Shore model 330 temperature controller. The laser used for hole burning was a Coherent CR 899-21 Ti:sapphire laser (operated with a 0.07 cm-1 line width) pumped by a 15 W Coherent Innova 200 Ar ion laser. Burn wavelengths ranged between ∼700 and 800 nm. At each wavelength, several burn fluences from 3.7 to 140 J/cm2 were used with the glycerol:water/LDAO glass. Fluences as high as 500 J/cm2 were used with the TEA glass due to lower burning efficiency. Hole spectra (post-burn minus pre-burn absorption) were measured with a Bruker IFS 120 Fourier transform spectrometer operating at a resolution of 1.0 cm-1. Zero-phonon hole (ZPH) action spectra, which determine the site excitation frequency distribution function (SDF), were obtained under constant burn fluence conditions with the same laser and spectrometer (resolution of 0.5 cm-1). For the glycerol: water/LDAO and TEA glasses, the burn intensity was 25 mW/ cm2, and burn times were 10 and 15 s, respectively. Maximum fractional ZPH depths for the two glasses were ∼0.2 and 0.1, respectively.

12412 J. Phys. Chem. B, Vol. 105, No. 49, 2001

Figure 1. Absorption spectra for bacteriochlorophyll a in (a) a glycerol: water/LDAO (0.5%) glass and (b) a neat triethylamine (TEA) glass at 5 K. The dashed curve in spectrum a is the vibronic absorption expected for a pure BChl a sample, see text.

Figure 2. Absorption (solid curve), fluorescence (dot-dash curve), and zero-phonon hole action spectrum (triangles) of BChl a in a glycerol:water/LDAO (0.5%) glass. The action spectrum is multiplied by a factor of 6. The fluorescence band at 700 nm is due to an impurity (see text). T ) 5 K. The insert shows the T ) 77 K absorption spectra of BChl a in a glycerol:water/LDAO (0.5%) glass (a) and glycerol: water glass without LDAO (b).

The excitation source for the non-line-narrowed fluorescence experiments was a Lambda Physik LEXTRA excimer laser (308 nm) or excimer-pumped Lambda Physik FL 2002 dye laser operating at 416 nm. Fluorescence was dispersed by a McPherson 2061 1 m focal length monochromator (with slit width set for 0.8 nm resolution) and detected with a Princeton Instruments IRY 1024/G/G intensified diode array. Samples were contained in 2 mm i.d. quartz tubes. The concentration of BChl a was kept sufficiently low to avoid reabsorption effects. 3. Results The 5 K S0 f S1(Qy) absorption spectra of BChl a in a glycerol:water/LDAO and TEA glass are shown in Figure 1, curves a and b, respectively. The former exhibits a lowest energy (origin) band at 777.7 nm (12860 cm-1), with a width (fwhm) of 760 cm-1 and a weaker feature at 697.6 nm (14335 cm-1). The origin band in TEA is at 775.2 nm (12900 cm-1) and carries a width of only 360 cm-1. The two higher energy and weak features lie at 684 and 708 nm. It will become apparent that the widths of the origin bands are mainly determined by inhomogeneous broadening. Figure 2 shows the absorption (solid curve), non-linenarrowed fluorescence (dash-dot curve) and ZPH action spectra (triangles) of BChl a in a glycerol:water/LDAO glass. The fluorescence spectrum exhibits two bands at 12 810 cm-1 (780.6

Zazubovich et al. nm) and 14345 cm-1 (697.7 nm), with the former being the origin of BChl a. The latter is the fluorescence origin of an impurity which is most likely the BChl a photooxidation product 2-desvinyl-2-acetylchlorophyll a that absorbs at ∼700 nm.35,36 No attempt was made to remove it since it does not contribute to the pseudovibronic hole spectra whose ZPH are located in the absorption origin band of BChl a. It is such spectra that were used to determine the FC factors (vide infra). The dashed curve in spectrum a of Figure 1 indicates the vibronic intensity expected in the vicinity of 700 nm for a pure BChl a sample. It was determined using the BChl a origin band of spectrum a and the spectrum of pure BChl a from refs 37 and 38. As will be seen, however, there are several vibrational modes of BChl a that absorb near 700 nm. Returning to the action spectrum (triangles) of Figure 2, we note that the increase in its intensity at energies J 14 000 cm-1 is consistent with the onset of impurity absorption near 700 nm. The width of the action spectrum at 786.2 nm (12 720 cm-1) is 545 cm-1, which is narrower by 215 cm-1 than the width of the absorption band. The action spectrum, which has a Gaussian shape, is the site excitation frequency distribution function (SDF). That it lies 140 cm-1 lower in energy than the absorption maximum might suggest that the electron-phonon coupling and coupling to low-frequency BChl a modes is quite strong, with a predicted Stokes shift of ∼2 × 140 cm-1. However, the fluorescence maximum at 12 810 cm-1 leads to a Stokes shift of only 48 cm-1. Thus, such an explanation is untenable. An alternative explanation is that BChl a in the glycerol:water/ LDAO glass exists in two grossly different environments, with one of them responsible for the above SDF located on the lowenergy side of the absorption origin band. This is supported by the absorption spectra shown in the inset of Figure 2. The solid and dash-dot curves are for a glycerol:water/LDAO (0.5%) and glycerol:water glass devoid of LDAO, respectively. The absorption origin of the latter is red-shifted to 12 730 cm-1, which, within experimental uncertainty, is equal to the position of the maximum of the above SDF at 12 720 cm-1. It appears, therefore, that in the glass with LDAO BChl a inside the micelle might exist in equilibrium with BChl a outside the micelle. (LDAO concentrations higher than 0.5% led to no further shifting of the absorption band.) The SDF for the internal environment would have to be located on the high-energy side of the absorption origin band, and furthermore, the NPHB efficiency for the internal environment would have to be significantly lower than that of the external environment. We emphasize that although both SDFs are important in simulating the absorption spectrum, only the SDF shown in Figure 2 is important for determination of the FC factors since the ZPHs in the pseudovibronic hole spectra used are located on the low energy side of that SDF (vide infra). We also considered the possibility that the lower energy SDF may be due to BChl a dimers. Dimer formation of Chl molecules leads to red-shifting of the Qy absorption spectrum.39-41 However, the energy difference between the two SDF in the glycerol:water/LDAO glass is much smaller than the monomer-dimer shifts reported in.39-41 Furthermore, we did not observe a dependence of the 777.7 nm absorption band on concentration of BChl a. Concentration was varied from 2 times higher to 10 times lower than that used for determination of FC factors. Thus, we consider dimer formation to be unlikely. For the TEA glass, only one SDF was required in the fitting of the absorption origin band (cf. section 4). As will be seen, the FC factors for most of the modes of BChl a in the TEA and glycerol:water/LDAO glasses are in reasonable agreement.

Franck-Condon Factors for S0 f S1(Qy) Transition

J. Phys. Chem. B, Vol. 105, No. 49, 2001 12413 TABLE 1: Vibrational Frequencies and Franck-Condon Factors for BChl a and Chl a ω′ (cm-1), FCFa

ω′ (cm-1), FCFb

ω′′ (cm-1), FCFc

ω′ (cm-1), FCFd (Chl a)

161 ( 3, 0.015 ( 0.007 164, 0.020 ( 0.010 195 ( 2, 0.040 ( 0.020 192, 0.050 ( 0.015 238, 0.016 236, 0.016 260, 0.012 285, 0.020 286, 0.010 341, 0.023

Figure 3. Pseudovibronic satellite hole spectra of BChl a in a glycerol: water/LDAO glass for seven burn wavelengths (λB) between 710 and 777 nm; burn fluence ) 140 J/cm2 and T ) 5 K. The arrows in the two top spectra locate the ZPH at λB. To their immediate left is the pseudophonon sideband hole displaced by 26 cm-1. The asterisks locate the 565 cm-1 BChl a vibration. See text for discussion of the rectangular boxes and the normalization procedure used to obtain the FC factors. Also shown is the absorption origin band (short dashed curve) and zerophonon hole action spectrum from Figure 2 fitted with a Gaussian (long dashed curve).

Pseudovibronic hole spectra of BChl a in a glycerol:water/ LDAO glass are shown in Figure 3 for seven burn wavelengths (λB) between 777 and 710 nm and a burn fluence of 140 J/cm-2, one of several used (see section 2). Use of different burn fluences is important for arriving at reliable FC factors. As is evident, the hole spectra are rich in excited-state vibrational structure. Intramolecular mode frequencies are obtained as the differences between the frequency of the ZPH at λB and the frequencies of the pseudovibronic ZPHs.16,42 Thus, the latter ZPHs track the burn frequency. In the top spectrum, the ZPH at λB ) 777 nm is indicated by the solid arrow. To its immediate left is the intense pseudophonon sideband hole (PSBH)42,43 with a maximum that is displaced by 26 cm-1 to the red of the ZPH. That the integrated intensity of the pseudo-PSBH is much greater than that of the ZPH at λB is the result of the burn fluence used being far greater than required to saturate the ZPH (for a detailed discussion see refs 44,43). In separate experiments (see section 4), we determined that the Huang-Rhys factor (Sph) of the phonons peaked at 26 cm-1 is only 0.3. Thus, the FC factor for the zero-phonon line associated with the ZPH is43 exp(-Sph) ) 0.74. This, along with the fact that the FC factors of BChl a modes are no greater than 0.05 (vide infra), qualitatively explains why the low energy satellite ZPHs are not accompanied by observable pseudo-PSBHs. That is, the satellite ZPHs are far from being saturated. The hole spectra shown in Figure 3 and others identified 56 excited-state BChl a modes whose energies lie between 161 and 1598 cm-1 (first column of Table 1). The uncertainty in the energies is (1 cm-1. The spectrum a of Figure 4 is an expanded version of the λB ) 777 nm spectrum of Figure 3. The satellite holes are labeled with the excited-state mode energies (cm-1). The first column of Table 1 also lists the FC factors. They were obtained as follows: (1) The observed hole-burned spectra (pre-burn absorption minus post-burn absorption) were divided by the SDF profile shown in Figure 2 so that the integrated intensities of the satellite ZPHs are normalized to the same absorbance value. The resulting spectra are those shown in Figure 3 and can be directly used to determine the relative values of the FC factors. The division by the SDF is mandated by the theory of hole spectra.43 (2) The well-isolated 565 cm-1 mode

373, 0.010 383, 0.007 402, 0.006 420, 0.003 453, 0.002 483, 0.002 531, 0.004 565, 0.017 592, 0.007

173, 0.008 185, 0.008 195, 0.011 237, 0.005 285, 0.005 327, 0.0015

341, 0.025 353, 0.010 379, 0.010* 395, 0.0035 421, 0.003 454, 0.004

350, 0.02 365, 0.002 381, 0.002

390, 0.015 425, 0.007

479, 0.001

564, 0.016 589, 0.006

262, 0.012 283, 0.004

541, 0.001 565, 0.002 580, 0.001

469, 0.019 501, 0.007 521, 0.017 541, 0.009 574, 0.025 588, 0.005 607, 0.012

635, 0.003 676, 0.010 711, 0.006 724, 0.025

676, 0.009

742, 0.010 ( 0.005 760, 0.006 772, 0.012

744, 0.006 760, 0.005 774, 0.012

787, 0.0026 799, 0.0036

787, 0.0025

839, 0.012 864, 0.005 886, 0.003

836, 0.012 858, 0.007 882, 0.003

915, 0.013 932, 0.0068 953, 0.0040 977, 0.0007 993, 0.0017 1008, 0.0024 1031, 0.0007 1047, 0.0007 1062, 0.004 1099, 0.012 1115, 0.009 1141, 0.002 1154, 0.010 1175, 0.016 1185, 0.009 1223, 0.013 1257, 0.010 1287, 0.002 1335, 0.010 1351, 0.012 1377, 0.0076 1388, 0.010 1418, 0.0012 1442, 0.0026 1456, 0.0052 1484, 0.0087 1501, 0.0104 1541, 0.0075 1584, 0.0044 1598, 0.0044

915, 0.013

725, 0.030**

714, 0.002 723, 0.003 730, 0.001 747, 0.002 759, 0.002 768, 0.004 777, 0.0015 819, 0.002 859, 0.0025 896, 0.002

714, 0.010 746, 0.044 771, 0.007 791, 0.014 805, 0.012 819, 0.005 855, 0.009 864, 0.007 874, 0.007 896, 0.013 932, 0.025 994, 0.028 1009, 0.005

1075, 0.012 1114, 0.009 1158, 0.004 1176, 0.003 1216, 0.002

1178, 0.018 1203, 0.012 1259, 0.041 1285, 0.011 1340, 0.011 1364, 0.032 1390, 0.018 1411, 0.005 1433, 0.009 1455, 0.006 1465, 0.006 1504, 0.010 1524, 0.032

a This work for BChl a in a glycerol:water/LDAO glass. b This work for BChl a in a neat TEA glass. c Frequencies and Franck-Condon factors (FCF) for BChl a determined by fluorescence line narrowing spectroscopy; ref 11. d Frequencies and FC factors for Chl a; refs 16 and 17. Double- and single-prime superscripts indicate the ground and S1(Qy) states, respectively. In the second column, * indicates that there is a poorly resolved 373 cm-1 mode; ** indicates that there is a poorly resolved 711 cm-1 mode.

12414 J. Phys. Chem. B, Vol. 105, No. 49, 2001

Zazubovich et al. Spectrum b of Figure 4 is the TEA hole spectrum obtained with λB ) 755 nm. The vibronic holes are labeled with their excited-state vibrational energies (cm-1). The similarity between the vibronic hole structure in the 164-592 cm-1 range of spectra a and b should be noted. The positive increase in absorption to the right of λB in spectra a and b is the blue-shifted antihole associated with NPHB of 1ππ* states.45,46 Also listed in Table 1 (third column) are the BChl a frequencies and FC factors determined by Wendling et al.11 using origin band-excited fluorescence line-narrowed spectra. The fourth column of Table 1 lists the frequencies and FC factors of Chl a from Gillie et al.16 as determined by pseudovibronic hole-burning spectroscopy. 4. Discussion

Figure 4. Pseudovibronic satellite hole spectra for BChl a in a glycerol: water/LDAO (0.5%) glass (a) and neat triethylamine glass (b) obtained with burn wavelengths (λB) 777 and 755 nm, respectively. The asterisks locate the pseudophonon sideband holes. The positive absorption to the right of the resonant ZPH at λB is the antihole associated with nonphotochemical hole burning.

indicated by the asterisks in Figure 3 was used to set a value for a FC factor that can be used to determine the values of the FC factors for all other BChl a modes. The value obtained for the 565 cm-1 mode is 0.017 (Table 1). It was determined using the λB ) 777 and 765 nm hole spectra and the relationships that the FC factors for the 0- and 1-quantum transitions are given by exp(-S565) and S565 exp(-S565), respectively, which are valid in the harmonic approximation and when the difference between the ground and excited-state frequencies is small (j10%). When S is j0.05, the fundamental FC factor is, to a good approximation, equal to S. The integrated intensity of the 0-quantum transition includes the ZPH at λB and its pseudoPSBH. Regardless of the burn fluence, the FC factor of the 565 cm-1 mode remained the same to within 15%. And (3) a multistep scaling process was used. For example, the FC factors of the modes in the rectangular box of the λB ) 765 nm spectrum in Figure 3 (energies in the ∼700-800 cm-1 range) were determined by ratioing their integrated ZPH intensities to that of the 565 cm-1 ZPH. In the λB ) 750 nm spectrum, the FC factors of the ∼700-800 cm-1 modes were used to determine the FC factors of several higher energy modes, etc. The same procedure was used to determine the FC factors of BChl a in a TEA glass. For the sake of brevity, the pseudovibronic hole spectra obtained with λB ) 775, 765, 755, 745, and 735 cm-1 are not shown. Their quality is comparable to those of the spectra in Figure 3. Rather than using the FC factor of the 565 cm-1 mode as the reference, the combined FC factors of the 341 and 353 cm-1 modes were used. This led to the same value for the FC factor of the 565 cm-1 mode for the glycerol: water/LDAO glass (Table 1). The Gaussian SDF for the TEA glass obtained from the ZPH action spectrum is centered at 12 847 cm-1 (778.4 nm) and carries a width of 310 cm-1, 50 cm-1 narrower than the width of the absorption origin band. The small difference in width is consistent with weak electronphonon and -vibration coupling. The frequencies and FC factors for the TEA glass are listed in the second column of Table 1. No attempt was made to study BChl a modes with energies greater than 915 cm-1.

Comparison of the Franck-Condon Factors for the Glycerol:Water/LDAO and TEA Glasses as Determined by Hole Burning. The BChl a mode energies (cm-1) and FC factors for the glycerol:water/LDAO and TEA glasses are given in the first and second columns of Table 1, respectively. The uncertainty in the mode energies is ( 1 cm-1. Unless otherwise indicated, the estimated uncertainty in the FC factors is ( 20%. (As mentioned, no attempt was made to measure modes of energy greater than 915 cm-1 with the TEA glass.) Given that uncertainty, the agreement between the FC factors for the two glasses is good for most of the modes. As a result, we are confident in the FC factors for BChl a modes with energies greater than 915 cm-1 obtained with the glycerol:water/LDAO glass. It appears that the FC factors are not very sensitive to the solvent. We hasten to add that not all of the modes are necessarily fundamental vibrations since, with the quite dense fundamental mode spacings, anharmonic and Duschinsky mixing is to be expected. Such mixing may explain why a number of weaker modes observed with the glycerol:water/LDAO glass are not observed with the TEA glass. Simulation of the S0 f S1(Qy) Absorption Spectrum. A stringent test for Chl FC factors is that they, along with data on inhomogeneous broadening and electron-phonon coupling, be able to reproduce the experimental absorption spectrum. Figure 5 shows the end results of simulations of the BChl a absorption spectrum for the glycerol:water/LDAO glass. The dark solid line spectrum (a) is experimental. Spectrum d is the calculated spectrum. The procedure used to obtain it was guided by the experimental absorption and fluorescence “origin” bands shown in Figure 2, the linear electron-phonon coupling parameters determined from hole-burning experiments and the FC factors of lower frequency BChl a modes that contribute to absorption in the origin region. The electron-phonon coupling is characterized by Sph ) 0.3 and a one-phonon profile peaked at 26 cm-1 that is well described by a Gaussian with a half-width of 10 cm-1 at its low energy side and a Lorentzian with a halfwidth of 25 cm-1 on the high side. Sph was determined from the saturated fractional depth of ZPH burned at the red edge of the absorption origin band. To a good approximation, the depth is given by exp(-Sph). The one-phonon profile was determined from the pseudo-PSBH in spectra obtained in the low burn fluence limit (results not shown). The long-dashed curve (b) in Figure 5 is the effective SDF for the origin band dressed only with phonons. The effective SDF, which accounts for the two SDFs associated with the external and internal environments of BChl a, was taken to be a Gaussian whose position and width were adjustable parameters. Dressing with phonons was performed using the above electron-phonon coupling parameters with the hole profile theory of Hayes et al.43 It was found that

Franck-Condon Factors for S0 f S1(Qy) Transition

Figure 5. Calculated absorption spectrum of BChl a in a glycerol: water/LDAO (0.5%) glass at 5 K (d). The experimental spectrum is the dark solid curve (a). Profile b is the site excitation distribution function (SDF) dressed with phonons. Curve c is the contribution to the absorption due to BChl a vibrations dressed with SDF. The calculated spectrum (d) is the sum of curves b and c. The calculated spectrum and curve c are indistinguishable at energies J 14 000 cm-1. The discrepancy between the experimental and calculated spectrum is due to impurity absorption; see text. The inset shows the experimental (a) and calculated (b) spectrum for the triethylamine glass. The discrepancy at energies J 14 250 cm-1 is due to impurity absorption.

a position and width of 12833 and 630 cm-1 for the effective SDF led to the best fit of the absorption band upon inclusion of the BChl a modes. That the effective SDF dressed with phonons is nearly symmetric is a consequence of weak electron-phonon and -vibration coupling. The same SDF was used for the BChl a vibrations since in the harmonic approximation the electron-phonon coupling is independent of vibrational level and the inhomogeneous broadening associated with vibrational frequencies is typically only several cm-1, as evidenced by the widths of the vibronic satellite holes (Figure 4). The inhomogeneously broadened spectral density due to BChl a modes is curve c in Figure 5. The calculated absorption spectrum (d) is the sum of curves c and b. At energies greater than ∼13 800 cm-1, curve c is indistinguishable from spectrum d. Comparison of spectra a and d reveals a reasonable fit to the origin band. The poor fit at energies J 14 000 cm-1 is due to the aforementioned impurity. The shape and intensity (relative to the origin band) of the calculated spectrum (d) in this region are in reasonable agreement with the spectrum reported in refs 37 and 38 (see also dashed curve in Figure 1). The inset of Figure 5 compares the experimental (a) and calculated (b) spectra for the TEA glass. For clarity, the SDF and the inhomogeneously broadened vibrational spectral density are not shown. The SDF used, which was determined by ZPH action spectroscopy, is defined in section 3. Hole spectra (not shown) obtained at suitable low burn fluences were also used to assess the electron-phonon coupling. The coupling is characterized by Sph ) 0.45 and a one-phonon profile peaked at 18 cm-1 that is well described by a Gaussian with a halfwidth of 5 cm-1 on the low energy side and a Lorentzian with a half-width of 10 cm-1 on the high energy side. As before, the theory of Hayes et al. was used to dress the SDF with phonons. Since the highest-energy BChl a mode studied with the TEA glass was at 915 cm-1, the FC factors for higher energy modes used were those for the glycerol:water/LDAO glass (Table 1). The agreement between spectra a and b in the inset of Figure 5 is reasonable for energies lower than about 14 200 cm-1. The poor fit at higher energies is, again, due to impurity absorption.

J. Phys. Chem. B, Vol. 105, No. 49, 2001 12415 In summary, the BChl a FC factors and other relevant data determined by hole burning provide an acceptable description of the S0 f S1(Qy) absorption spectrum. Comparison of the FC Factors of BChl a Determined by Hole-Burning and Fluorescence Line-Narrowing Spectroscopies. The former and latter FC factors are listed in columns 1 and 3 of Table 1. On average, the FC factors determined by FLNS are a factor of 4-5 times smaller than those determined by hole burning. Furthermore, no vibronic activity in the FLN spectra was observed at vibrational energies higher than 1216 cm-1. Given the FLN FC factors in Table 1, one can infer that the FC factors for modes with energies > 1216 cm-1 are j0.001. Noting that hole burning identified 15 modes with energies > 1216 cm-1, with 6 carrying FC factors J 0.01, it is apparent that the FLN FC factors cannot account for the BChl a absorption that appears as a shoulder near 14 000 cm-1 (see spectrum d of Figure 5 and the spectra of pure BChl a given in refs 37 and 38). It is also the case that the FLN FC factors of lower frequency modes are too small to account for the high energy side of the origin band. The question of why the FC factors determined by FLN are significantly smaller than those determined by hole burning is important since they enter into EET rate expressions. It is unlikely that the differences are due to non-Condon effects, e.g., Herzberg-Teller vibronic coupling, since the S0 f Qy transition is strongly allowed. Breakdown of intensity mirror symmetry between a vibronic absorption transition and the corresponding fluorescence transition can occur due to constructive and destructive interference between the Herzberg-Teller and Condon transition dipoles as has been observed for phenanthrene.47 However, when there are a large number of modes involved in such interference, one expects that the constructive and destructive interferences should average out. That is, one expects ΣiSi′ ∼ ΣiSi′′, where Si′ and Si′′ are the effective HuangRhys factors determined by hole burning and FLNS, respectively. From Table 1, these sums equal 0.47 and 0.08, respectively. (We recall that since the FC factors are j 0.05, the FC factors are, to a good approximation, given by S.) The optical reorganization energies, ΣiSi′ωi′ and ΣiSi′′ωi′′, are also very different, 378 and 44 cm-1, respectively. It is apparent that an alternative explanation is required. We are led to consider that the procedure used in11 to determine the BChl a FC factors resulted in their underestimation. In that work, the ZPL resonant with the laser excitation frequency could not be measured due to light scatter. (Note that this is not a problem in hole burning since the resonant ZPL and its pseudoPSBH are measured.) The intensity of the resonant ZPL relative to the intensities of the vibronic ZPLs would lead directly to the FC factors. A quite involved procedure was used to determine a value of S ) 0.3 for phonons peaked at 20 cm-1 as well as the shape of the one-phonon profile that governs the phonon sideband (PSB) in absorption. This PSB, often referred to as the real-PSB because it builds in a FC sense on the ZPL, was used to construct FLN spectra that include the PSB and BChl a vibronic structure. It was assumed, however, that only the real-PSB contributes to the observed PSB associated with the resonant ZPL. Neglected were two other important contributions to the PSB. They are discussed in detail in ref 48. One is due to sites (off-resonant) that absorb via their phonon wing. Following rapid relaxation to their zero-point levels, the sites emit to produce a broad distribution of ZPLs that interferes with the PSB of interest in the FLN spectrum. The second contribution is the phonon wing that builds on the just-mentioned distribution of ZPLs. The two contributions together are referred

12416 J. Phys. Chem. B, Vol. 105, No. 49, 2001 to as the pseudo-PSB. It is analogous to the pseudo-PSBH. Note, however, that the pseudo-PSBH and real-PSBH lie on opposite sides of the ZPH whereas both the real- and pseudo-PSB lie to lower energy of the ZPL. Thus, analysis of phonon structure in hole spectra is more straightforward. Neglect of the pseudoPSB results in overestimation of the intensity of the real-PSB and, as a consequence, an underestimation of the BChl a FC factors when they are determined by ratioing the intensities of the vibronic ZPLs against the intensity of the observed PSB. It is unclear, however, whether the neglect of the pseudo-PSB can account for the significant differences between the two sets of FC factors. Nevertheless, the FLN FC factors are too small to account for the vibronic structure in the absorption spectrum of BChl a. The excited-state energies and FC factors of 40 Chl a vibrations determined by Gillie et al.16 are given in column 4 of Table 1. Pseudo-vibronic hole burning was also used in that work. Overall, the FC factors are comparable to those of BChl a in the glycerol:water/LDAO. For Chl a, ΣiSi′ and ΣiSi′ωi′ ) 0.56 and 532 cm-1, which are quite similar to the BChl a values of 0.47 and 378 cm-1. Given the large number of modes, it is not possible to correlate the Chl a and BChl a vibrations. Franck-Condon factors for Chl a have also been determined by FLNS.10 They are 10-20 times smaller than the values in Table 1. As pointed out in,17 the FLN FC factors are far too small to account for the vibronic structure in the non-linenarrowed fluorescence spectrum while the FC factors determined by hole burning do. It was also suggested that the problem in obtaining reliable FC factors by FLNS when the resonant ZPL cannot be measured is linked to modeling of the PSB associated with the resonant ZPL, which could not be measured due to laser light scatter. Comparison of BChl a Vibrational Frequencies and Intensities with Those from Raman, Line-Narrowed Fluorescence Excitation and Fluorescence Line Narrowing Studies. Table 2 compares the excited-state BChl a vibrational frequencies (ω′) and FC factors from this work (first column) with results of Renge et al.49 for BChl a in a TEA glass containing 30% pyridine at 5 K. Their excited state frequencies, which were determined by line-narrowed fluorescence excitation spectroscopy, are listed in the second column along with estimated relative intensities of the vibronic bands (numbers in parentheses). Comparison of the first and second columns reveals a significant number of mode frequencies that are closely correlated. Also, for example, modes in the second column with relative intensities g 2 correlate quite well with the strongest modes in the first column (FC factor factors J 0.01). It is not possible to be more precise here since the relative intensities in the second column range only from 1 to 5 while in the first column intensities vary by as much as a factor of 60. The third column lists the ground-state frequencies (ω′′) for the TEA/ pyridine glass as determined by Renge et al.49 using fluorescence line narrowing spectroscopy. Relative intensities of the vibronic transitions are indicated by the numbers in parentheses. As emphasized by Renge et al., very considerable mirror symmetry exists between the absorption and fluorescence spectra. (The failure to observe fluorescence bands with vibrational energies > 1159 cm-1 was attributed to inadequate PMT sensitivity at the red end of the spectrum.) Note that the ground and excited state vibrational frequencies differ by only a couple of percent. Thus, the FC factors (FCF)i in the first column of Table 2 are accurately given by Si exp(-Si), as mentioned earlier. The fourth column of Table 2 lists the ground-state BChl a frequencies reported by Diers et al.50 who employed resonance

Zazubovich et al. TABLE 2: Frequencies and Intensities of the Bchl a Vibration Modes Determined with Different Methods ω′ (cm-1), FCFa

ω′ (cm-1)b

ω′′ (cm-1)b

ω′′ (cm-1)c

161 ( 3, 0.015 ( 0.007 195 ( 2, 0.040 ( 0.020 238, 0.016 285, 0.020 341, 0.023 373, 0.010 383, 0.007 402, 0.006 420, 0.003 453, 0.002 483, 0.002 531, 0.004 565, 0.017 592, 0.007 676, 0.010 711, 0.006 724, 0.025 742, 0.010 ( 0.005 760, 0.006 772, 0.012 787, 0.0026 799, 0.0036 839, 0.012 864, 0.005 886, 0.003 915, 0.013 932, 0.0068 953, 0.0040 977, 0.0007 993, 0.0017 1008, 0.0024 1031, 0.0007 1047, 0.0007 1062, 0.004 1099, 0.012 1115, 0.009 1141, 0.002 1154, 0.010 1175, 0.016 1185, 0.009 1223, 0.013 1257, 0.010 1287, 0.002 1335, 0.010 1351, 0.012 1377, 0.0076 1388, 0.010 1418, 0.0012 1442, 0.0026 1456, 0.0052 1484, 0.0087 1501, 0.0104 1541, 0.0075 1584, 0.0044 1598, 0.0044

166 (2) 194 (3)

164 (4) 196 (4)

342 (2)

342 (3)

379 (2)

380 (2) 397 (1)

164 190 235 257 340 359 383 396 423

449 (1) 564 (3) 591 (1) 680 (2) 727 (5)

568 (4) 591 (2) 683 (3) 706 (1) 729 (5)

757 (2) 773 (2)

763 (1) 775 (3)

795 (1) 845 (1)

795 (1) 847 (1)

879 (3) 917 (2)

879 (1) 923 (2)

950 (2) 980 (1)

950 (3) 980 (1)

1011 (2) 1033 (2) 1044 (1)

1005 (2) 1026 (3) 1043 (1)

1095 (2) 1104 (2) 1147 (1)

1113 (3) 1135 (3)

1169 (3) 1186 (3)

1159 (1)

536 567 597 685 733 776 843 864 908

1182

1253 (3) 1290 1335 (1) 1350 (2) 1381 (2)

1382

1482 (2) 1508 (2) 1543 (2)

1527

a This work. b Data from ref 49; numbers in parentheses represent relative intensities of the modes. c Raman data from ref 50.

Raman spectroscopy (Qy state excitation) on solid films of BChl a. Almost all of the ground-state frequencies correlate quite well with those in the other three columns. The reader interested in the assignments of the Raman modes to nuclear motions is referred to the recent paper by Ceccarell et al.51 Here we only mention that the intense 195, 565, and 724 modes have been assigned to: out-of-plane MgN bending; in-plane deformations of pyrolle ring III and asymmetric deformations; and symmetric in-plane NCC bending. 5. Concluding Remarks Nonphotochemical hole burning was used to determine the excited-state vibrational frequencies and Franck-Condon factors

Franck-Condon Factors for S0 f S1(Qy) Transition for the S0 f S1(Qy) transition of BChl a in two glasses. Fiftysix intramolecular modes with energies between 161 and 1598 cm-1 were observed using the glycerol:water/LDAO glass. The FC factors are small and range between 0.05 and 0.0007. The total optical reorganization energy, ΣiSi′ωi′, equals 378 cm-1. Experiments with the TEA glass were limited to vibrations with energies e 915 cm-1. The FC factors of the more intense modes for the two glasses were found to be in good agreement. Importantly, the FC factors and other hole-burning results led to calculated absorption spectra for the two glasses that are in acceptable agreement with the experimental spectra. Thus, we are confident that the procedure used, which is based on the well-tested theory of hole spectra, is sound. The procedure involves (i) determination of the ZPH action spectrum of the absorption origin band that is a faithful representation of the site excitation distribution function (SDF), (ii) generation of pseudovibronic hole spectra as a function of burn fluence and with burn frequencies which ensure that the desired range of vibrational energies is covered, and (iii) determination of the Huang-Rhys factor of the low energy phonons (Sph) and the one-phonon profile. Division of the vibronic hole spectra by the SDF is required to normalize the vibronic satellite ZPHs to the same absorbance value. The resulting spectra, which include the resonant ZPH and its pseudophonon sideband hole, can then be used in a straightforward, multistep scaling process to determine the chromophore’s FC factors. Overall, the values of the BChl a FC factors were found to be similar to those of Chl a (40 in total) obtained earlier by hole burning. The large number of active excited state modes, not all of which are necessarily fundamental vibrations, precludes correlating the BChl a and Chl a modes although correlating clumps of modes is possible (Table 1). The BChl a FC factors obtained from origin-excited FLN spectra are, on average, about a factor of 5 smaller than those obtained by hole burning. Furthermore, no vibronic activity of modes with energies > 1216 cm-1 was observed. The FLN FC factors are too small to account for the S0 f Qy absorption spectrum. The same problem (but more severe) exists with Chl a. It appears that the inability to measure the resonant ZPL (due to light scatter) in the FLN spectra leads to underestimation of the FC factors. Nevertheless, the FLN spectra can be used to determine the relative values of FC factors and to assess mirror symmetry breakdown between vibronic absorption and fluorescence spectra. Acknowledgment. Research at the Ames Laboratory was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy. Ames Laboratory is operated for the USDOE by Iowa State University under Contract W-7405-Eng-82. We are indebted to Professor R. J. Cogdell, University of Glasgow, for providing bacteriochlorophyll a and to Dr. Kenneth Roberts for help with fluorescence measurements. References and Notes (1) Sundstro¨m, V.; Pullerits, T.; van Grondelle, R. J. Phys. Chem. B 1999, 103, 2327. (2) van Amerongen, H.; Valkunas, L.; van Grondelle, R. Photosynthetic Excitons; World Scientific: River Edge, NJ, 2000. (3) May, V.; Ku¨hn, O. Charge Transfer and Energy Transfer Dynamics in Molecular Systems; Wiley-VCH: New York, 2000. (4) Ku¨hn, O.; Renger, T.; May, V.; Voigt, J.; Pullerits, T.; Sundstro¨m, V. Trends Photochem. Photobiol. 1997, 4, 213. (5) Renger, T.; May, V.; Ku¨hn, O. Phys. Rep. 2001, 343, 137.

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