Resonance Raman Spectroscopy of Helical Porphyrin Nanotubes

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Resonance Raman Spectroscopy of Helical Porphyrin Nanotubes Benjamin A. Friesen, Christopher C. Rich, Ursula Mazur, and Jeanne L. McHale* Department of Chemistry, Washington State UniVersity, Pullman, Washington 99164-4630 ReceiVed: July 14, 2010; ReVised Manuscript ReceiVed: August 18, 2010

We report polarized resonance Raman data of tetrakis(4-sulfonato)phenyl porphyrin (TSPP) aggregates in solution and deposited on Au(111) at wavelengths resonant with the red-shifted (J-band) and blue-shifted (H-band) components of the split Soret (B) band. We also report scanning tunneling microscopy (STM) images which reveal that the aggregate on Au(111) is a nanotube with a 2 nm wall thickness which tends to flatten on the substrate. Relative Raman intensities and their dependence on polarization of the incident and scattered light are found to vary greatly for H- and J-band excitation, revealing a much greater degree of coherence for the J-band, in agreement with the resonance light scattering spectrum. The J-band transition is found to have transition moment components both parallel and perpendicular to the long axis of the nanotube, consistent with a helical nanotube structure. The intensity increase of the Q-band on aggregation and the weak intensity of the H-band in both the absorption and the resonance light scattering spectra are explained by vibronic B-Q coupling, which is permitted in the lowered site symmetry of the aggregate. The resonance Raman data presented here provide insight into the molecular basis for the hierarchal structure of the aggregate. Introduction Aggregates of tetrakis(4-sulfonato)phenyl porphyrin (TSPP) are well-known to form in aqueous solution at low pH and high ionic strength and show evidence of strong coupling of the Soret band transition moments.1-5 This excitonic coupling is revealed by the sharp, red-shifted J-band at about 490 nm and by intense resonance light scattering5 in the vicinity of this band, both of which evidence a delocalized excited electronic state. Various techniques such as X-ray scattering6 and light scattering7,8 have been used to probe the solution phase aggregate, often suggesting a fractal9 or otherwise hierarchal mesoscale structure. Interpretations of the optical spectroscopy of the aggregate, however, tend to fall back on the conventional staircase structure of a linear J-aggregate in which the near-neighbor arrangement of the porphyrins optimizes the electrostatic interaction of the peripheral negative charges on the sulfonato groups with the protonated porphyrin core. While this model tends to support some of the optical data, such as flow-induced linear dichroism,3 it does not account for the reported AFM images of the aggregates deposited on various surfaces.10,11 These images reveal apparent nanorods about 4 nm in height and 25 to 27 nm in width, dimensions which are larger than the ∼2 nm size of the TSPP molecule. Another failure of the staircase model is that the coupling of the degenerate Soret-band (B-band) transition moments parallel and perpendicular to the aggregation direction should lead respectively to red-shifted (J-band) and blue-shifted (H-band) transitions of equal intensity. The intensity of the H-band at ∼420 nm is much less than that of the J-band, as shown below. The H-band does not appear to be exchangenarrowed, does not give rise to an appreciable resonance light scattering (RLS) signal (vide infra) and is not appreciably polarized in a flow-induced linear dichroism experiment.3 Perhaps related to this is the large increase in Q-band intensity that accompanies aggregation. This apparent intensity borrowing might result from excitonic coupling with the split B-band12 * To whom correspondence should be addressed. E-mail: jmchale@ wsu.edu.

SCHEME 1: Presumed Zwitterionic Structure of the TSPP Diacid Monomer

and nonplanar distortions that influence the mixing of excited configurations that contribute to both the B- and Q-bands.13 It is well-established that the precursor to aggregation is the diacid monomer of TSPP formed by protonation of the pyrrole nitrogens at pH values below about 514 (see Scheme 1). This protonation is accompanied by significant structural and spectroscopic changes. Similar to unsubstituted tetraphenylporphyrin,14 both the B- and Q-bands of TSPP red-shift on protonation of the pyrrole nitrogens, with a significant increase in intensity of the Q-band. This red-shift might reasonably be assumed to result from the more-coplanar arrangement of the phenyl groups in the diacid,15,16 but at the same time, steric hindrance of the hydrogens in the porphyrin core leads to puckering and increase in Q-band intensity at the expense of the B-band. As shown by Gouterman, nonplanar distortions corresponding to saddling are the correct symmetry to cause B-Q mixing and intensity perturbations. The question remains, however, as to the basis

10.1021/jp106514g  2010 American Chemical Society Published on Web 09/13/2010

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for further red-shift and intensity increase in the Q-band when the diacid monomers self-assemble. We have recently reported STM images of the TSPP aggregate deposited on Au(111), which provide evidence that the conventional staircase model of the J-aggregate is not valid.17 Instead, the images reveal flattened helical nanotubes about 50 nm in circumference that appear to be built up from 6 nm disks. We have postulated that the 6 nm disks shown in ref 17 are circular 16-mers of protonated TSPP molecules, reminiscent of BChl-850 rings in light harvesting complexes of purple photosynthetic bacteria.18 In effect, the circular aggregate results from a 16-member strand of the staircase model which forms a closed loop. We have proposed that the protonated porphyrins are driven to assemble by near-neighbor electrostatic and pistacking forces, as in the staircase model, but nonplanar distortions by an angle (∼21°) that is an integral divisor of 360° lead to a circular aggregate. Note that we do not resolve the number of porphyrins that contribute to the 6 nm disks of ref 17; the assumption of a 16-mer is a working hypothesis that is consistent with a reasonable degree of nonplanarity for a tetraphenylporphyrin diacid. Our images could be accounted for by a model in which the putative cyclic 16-mers are further assembled into a helical nanotube in which the porphyrin planes and the planes of the circular aggregate are respectively perpendicular and parallel to the nanotube surface. This hierarchal model of the aggregate would explain the ∼4 nm height of the flattened nanotubes imaged in STM and AFM (approximately twice the dimension of the TSPP molecule) and the consistent ∼26 nm width of the flattened tubes could be accounted for by a nanotube radius on the order of 8 nm and helical angle of about 42° between neighboring 16-mers. The ∼2 nm wall thickness of the nanotubes that results from this model is consistent with our images as well as the cryo-electron microscopy images reported by Vlaming et al.19 and the analysis of small-angle X-ray scattering reported in ref 6. Similarly, Micali et al. in ref 9 interpreted their dynamic light scattering data for the TSPP aggregate in terms of large (1-1.5 µm), medium (100-200 nm), and small (3-6 nm) aggregates, the latter having an aggregation number between 6 and 32. However, because the 6-nm disks are not resolved in all our nanotube images, perhaps owing to the coherent coupling among the putative N-mers, we wish to subject the model to further experimental exploration. In the present work, we examine the ability of a helical nanotube model to account for polarized resonance Raman data for the aggregate in solution and deposited on Au(111). We have also recently reported STM images of single molecules of the TSPP diacid monomer on HOPG, which evidence a saddled geometry.20 Such a nonplanar distortion inspired our model for the circular aggregates, which we proposed to account for the 6 nm disks seen in STM images of the aggregate deposited on gold. The previously reported enhancement of low-frequency vibrations associated with outof-plane motion in the aggregate excited within the J-band could in part derive from the nonplanar distortions of the monomers that comprise the aggregate. However, enhancement of lowfrequency vibrations is a common feature in the resonance Raman spectra of coherently coupled chromophore aggregates. This enhancement results from the strong coupling of vibrations that modulate the interchromophore separation to the delocalized excited electronic state. Using an exciting radiation resonant with both the H- and J-bands of the aggregate, we find that the activity of low-frequency vibrations assigned to out-of-plane porphyrin vibrations is very different for excitation at 488 (J-

Friesen et al. band) and 413 (H-band) nm. Analysis of the polarizationdependent Raman data for the aggregate on Au(111) provides insight into the basis for the weak maximum intensity of the H-band and its apparent lack of coherence. Excitonic coupling within helical aggregates of molecules has been considered by several authors.21-23 In the limit of infinite length, the component of the molecular transition dipole moment parallel to the axis of the nanotube gives rise to a nondegenerate transition polarized along this axis, while the component perpendicular to the axis results in a transition to a doubly degenerate excited state polarized in the perpendicular direction. These transitions are, respectively, red- and blue-shifted relative to the monomer and thus become the J and H bands of the helical aggregate. In our helical “super-aggregate”, the situation is somewhat more complex, as the model would predict strong excitonic coupling of monomers within the cyclic N-mers followed by further weak coupling among the N-mers within the helical aggregate. Within the N-mers, the monomer transition dipoles could couple to give rise to H-band (nondegenerate, polarized perpendicular to the plane of the cyclic N-mer) and J-band (doubly degenerate, polarized in the plane) type excitons. After assembly in the helical nanotube, the transition moments for these excitons are no longer mutually orthogonal and further mixing of the excitons can take place, altering the energies, degeneracies, and transition moments of delocalized excited states. Resonance Raman scattering in solution provides insight into the degeneracies and couplings of excited electronic states. Application of surface selection rules to the polarized Raman spectra of the aggregate adsorbed on Au(111), the same substrate used to obtain STM images, provides additional information about the form of the Raman tensor and the excited states on which it depends. Because excitonic coupling of the monomer B- and Q-band transition moments can also redistribute the oscillator strength on assembly into the aggregate, we investigated the concentration-dependent resonance light scattering spectrum to reveal the extent of coherence in the H-, J-, and Q-band regions. We also report concentration-dependent integrated absorbance data, which reveals the B-Q intensity borrowing that accompanies aggregation. Experimental Section Materials. TSPP was obtained as the hydrochloride salt from Porphyrin Products and used as received. Solutions were prepared by dissolving the porphyrin salt in Millipore (18 MΩ) water degassed by boiling for 1 h. Aggregate solutions were prepared by employing porphyrin concentrations ranging from 0.74 to 50 µM in 0.75 M HCl. All solutions were allowed to age for 1 h prior to deposition to allow equilibration. STM substrates were prepared by depositing epitaxial Au(111) films on mica. These films had well-defined terraces and single atomic steps on mica by previously described methods.24,25 Gold substrates were freshly flame-annealed just before use. UV-Vis Spectra. Electronic absorption spectra were obtained in 1 cm path length quartz cuvettes on a Perkin-Elmer 330 dual-beam spectrometer. Solutions were allowed to stand for sufficient time to allow the spectral intensities of the aggregates to become constant. RLS Spectra. Spectra were measured with a PTI Quanta Master Fluorimeter using a 1.00 cm quartz fluorescence cell and slit widths of 0.125 and 2.00 nm for excitation and emission, respectively. RLS intensities were recorded by scanning simultaneously the excitation and emission monochromators (∆λ ) 10 nm) from 200 to 800 nm. A porphyrin concentration range of 0.74 to 5.9 µM in 0.75 M HCl was used.

Raman Spectroscopy of Helical Porphyrin Nanotubes

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Figure 1. Large scale constant current STM images of TSPP nanorods on Au(111) acquired under ambient conditions: (a) double layer structures of totally collapsed rods; (b) partially collapsed and fractured TSPP nanotube. A high resolution image of an intact nanotube is displayed in the inset in (b). The set point equals 1.6 V and 1 pA for all images shown.

Raman Spectra. Resonance Raman (RR) spectra of aggregates in solution and deposited on Au(111) were acquired with previously described instrumentation.17 Solution phase spectra were obtained at a 90° scattering geometry using a quartz flow cell and vertically polarized light, detecting the polarized (vertical) and depolarized (horizontal) components of the Raman spectrum. Absorption spectra were recorded before and after acquisition of the Raman spectra to confirm sample integrity. For the sample adsorbed on Au(111), Raman spectra were excited with both vertically and horizontally polarized light by using a half-wave plate to rotate the polarization of the incident light, followed by detection of both the vertical and the horizontal components of the scattered light to generate SS, SP, PS, and PP spectra, as described below. To achieve resonance with both the red-shifted (J-band) and blue-shifted (H-band) transitions of the aggregate, two laser wavelengths were used: the 488 nm line (at 15 mW power) of a Lexel Model 95 Ar ion laser and the 413.1 nm line (at 50 mW power) of a Spectra Physics Beamlock 2060 Kr ion laser. The displayed data were collected with a 2 cm-1 integration interval. Porphyrin solutions (50 µM) in 0.75 M HCl were used to acquire the solution phase RR spectra. Aggregate samples on Au(111) were prepared by deposition from a 5 µM solution of TSPP in 0.75 M HCl when using 488 nm excitation and from a 50 µM solution in 0.75 M HCl for measurements at the 413 nm line. Raman samples were prepared by placing a drop of the 5 µM porphyrin solution on Au(111) substrate (same as for the STM samples) for 1 h followed by spinning for 30 s at 4000 rpm. Higher porphyrin concentration for surface Raman samples were made by allowing a drop of the 50 µM solution to completely evaporate from the Au(111) surface. The gold substrates were mounted in a spinner rotating at 3000 rpm oriented such that the angle between the propagation direction and the surface normal was fixed at 66 and 24° for the incident and scattered beams, respectively. STM Images. Samples for imaging were prepared using freshly made solution of 5 µM porphyrin in 0.75 M HCl. A drop of solution was placed on the Au(111) substrate for 1 h and then the solution was spun at 4000 rpm for 30 s. Imaging experiments were performed in an ambient environment at 21 °C using the Molecular Imaging Pico Plus STM equipped with a 10 µ head. Constant current images were collected and are

reported after a flattening procedure. Electrochemically etched Pt0.8Ir0.2 tips were employed. Results and Discussion Scanning Tunneling Microscopy. As previously reported,17 scanning probe microscopy of TSPP aggregates deposited on Au(111) reveals flattened nanotubes about 25-27 nm in width, 4 nm in height, and a variable length up to several micrometers. Figure 1b shows an intact nanotube. The ∼2 nm wall thickness of TSPP nanotubes detected by cryo-electron microscopy and reported in ref 19 is in good agreement with the 4 nm thickness of the flattened tubes imaged by STM and AFM in our work and by AFM in refs 10 and 11. Absorption and Resonance Light Scattering. Figure 2 shows the absorption and resonance light scattering (RLS) spectra of TSPP aggregates in acidic aqueous solution. The Hand J-bands at about 420 and 490 nm can be compared to the absorption band of the monomer diacid at 434 nm.17 RLS signal strength depends on the coherence number, Nc, and not the physical size of the aggregate.5,8 Nc, which also influences the absorption line width and the radiative decay rate, represents the number of molecules that share the delocalized excited state. Consistent with the apparent exchange narrowing of the J-band in the absorption spectrum, there is a strong RLS feature in the vicinity of this band. The weaker and broader H-band, which is overlapped by the absorbance of residual monomer, does not result in a strong RLS signal. The apparent weak RLS intensity in the vicinity of the Q-band is assigned to fluorescence from the residual monomer. When the data shown in Figure 2a are scaled by the total porphyrin concentration, apparent isosbestic points are seen at 424 ( 1, 453 ( 0.5, and 660 ( 1 nm (see Supporting Information). Akins et al. also reported isosbestic points in the spectra of the TSPP aggregate obtained at fixed porphyrin concentration and variable ionic strength.14 (Note that in both cases the spectra were uncorrected for scattering.) The existence of such isosbestic points suggests the occurrence of only two absorbing species, that is, monomer and aggregate, and would not be expected to occur in the case of stepwise assembly of aggregates of increasing size. In our previous work on aggregates of tetra(p-carboxyphenyl)porphyrin,27 the crossing points observed in absorption spectra as a function of ionic

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Figure 2. Absorption (left) and resonance light scattering (right) spectra of the TSPP aggregate in acidic aqueous solution (0.75 M HCl) as a function of TSPP concentration in order of increasing intensity of the J-band at 490 nm: 0.74 (black), 1.50 (red), 3.0 (green), 3.8 (blue), 4.5 (cyan), and 5.9 µM (magenta).

strength were more blurred than those observed for TSPP aggregates. This suggests that in the case of TSPP aggregates there is a precursor to formation of the overall aggregate, which dominates the spectral perturbations, followed by smaller spectral perturbations on assembly of the precursor. Integrated absorbance data for the monomer and for the aggregate in acidic solution as a function of concentration were used to determine the oscillator strengths f and transition dipole moments of the B and Q bands of the monomer and the H, J, and Q bands of the aggregate (see Supporting Information). Note that the total oscillator strength of the aggregate exceeds the sum of fB and fQ for the monomer, no doubt because of the contribution of resonance light scattering to the total extinction in the vicinity of the J-band.8 The B-band of the diacid monomer was found to have an integrated absorbance of 19500 L mol-1 cm-1, a transition dipole moment of 11.6 D, and an oscillator strength f of 1.47. The corresponding values for the monomer Q-band are 2890 L mol-1 cm-1, 4.5 D, and f ) 0.14. Based on oscillator strength, the monomer B-band is more intense that the Q-band by a factor of 10. While we calculate fJ ∼ 0.75 for the aggregate J-band and a transition dipole moment of about 8.3 D, these values are quite uncertain: neglect of light-scattering contribution to the extinction would overestimate these quantities, while calculating the molar absorptivity based on total porphyrin concentration tends to underestimate them. Thus, we focus on the Q- and H/B-band regions where scattering corrections are minimal. Integrated intensities of the Q-band in acidic aqueous solution containing the aggregate in equilibrium with residual monomer tend toward a value of about 7700 L mol-1 cm-1 at the highest concentration (5.94 µM). This molar absorptivity, calculated per mole of porphyrin monomer, corresponds to a transition dipole moment of 7.3 D and an oscillator strength of 0.37, which is larger than the monomer Q-band oscillator strength by a factor of 2.5. This should be considered a weighted average of the Q-band oscillator strengths for monomer and aggregate. Similarly, the overlapping aggregate H-band and the residual monomer B-band gives a total oscillator strength of about 0.74, which is also a weighted average. If x is the fraction of monomeric porphyrin in the 5.94 µM solution, then

fQ(total) ) 0.37 ) 0.14x + (1 - x)fQa

(1)

Figure 3. Polarized and depolarized resonance Raman spectra of 50 µM TSPP in 1.5 M aqueous HCl excited at 488 nm. The spectra have been background subtracted, and the depolarized spectrum was multiplied by 3.

fH/B(total) ) 0.74 ) 1.47x + (1 - x)fH

(2)

where fQa is the oscillator strength of the Q-band of the aggregate. Values of x in the range 0.2 to 0.3, estimated from the absorbance at 434 nm, result in fQa on the order of 0.43 to 0.47 and fH on the order of 0.43 to 0.56. The total intensity of the H-band is less than half that of the monomer Soret band and intensity has apparently been stolen by the aggregate Q-band. Despite the uncertainties that result from J-band scattering and overlap of the H-band with residual monomer, the expected splitting of the Soret band into equal intensity Hand J-bands of the aggregate is clearly not realized. Resonance Raman Spectra with J-Band Excitation. Figure 3 shows the polarized and depolarized Raman spectra of the solution-phase TSPP aggregate excited within the J-band. The depolarization ratio F is defined by IVH/IVV, the ratio of the intensities of scattered light polarized, respectively, perpendicular (H, horizontal) and parallel (V, vertical) to the electric field of the incident light, which is vertically polarized relative to the scattering plane. Consistent with our previous work, we find depolarization ratios equal to 1/3 for all but the strongly enhanced low-frequency vibrations at 241 and 314 cm-1. A value of F ) 1/3 indicates resonance enhancement via a single nondegenerate excited electronic state, while



Figure 4. Raman spectra of TSPP aggregates on Au(111) excited at 488 nm obtained with PP, SS, PS, and SP polarization in order of decreasing intensity. Shown in (a) is a survey scan, while the data in (b) were obtained as an average of three scans over the 200-400 cm-1 range. Relative to the SP intensity, the PP, SS, and PS intensities in (b) are 4.9, 3.0, and 2.0, respectively.

the value F ) 1/8 is diagnostic of resonance with a doubly degenerate excited state. The Raman bands at 241 and 314 cm-1, however, have F on the order of 0.5. Intensity enhancement of low-frequency modes is a common feature in the resonance Raman spectra of chromophore aggregates, including natural light-harvesting complexes.26-28 Though the 241 and 314 cm-1 bands have been referred to as “ruffling” and “doming” modes of the porphyrin core, respectively, their precise assignment is uncertain. The reported red-shift by several cm-1 of both bands in D2O is evidence that N-H (N-D) motion contributes to this mode.4 Thus, it is reasonable to assume they are out-of-plane vibrations that are strongly coupled to the delocalized electronic transition via perturbation of the interchromophore separation. Theory predicts the J-band of the circular aggregate, which arises from coupling of B-band transition moments that are parallel to the plane of the ring, to be doubly degenerate.29 This conflicts with the observed Raman depolarization ratios, which deviate from 1/8 for all the bands shown in Figure 3. On the other hand, a nondegenerate J-band polarized along the nanotube axis can not account for the values F ) 0.5 observed for the low-frequency modes. Further insight is provided by Raman spectra of the TSPP aggregates deposited on Au(111). These were obtained as a function of polarization (PP, SS, PS, and SP) with J-band excitation and are shown in Figure 4. The first and second letters denote the polarization of the incident and scattered light, respectively, which is either parallel (P) or perpendicular (S) to the plane defined by the incident and scattered beams. As in solution, the modes at 241 and 314 cm-1 are the most intense. The average intensity ratios PP/SS/PS/SP of these two low-frequency modes are 4.9:3.0:2.0:1.0. To interpret this data, we use the surface Raman selection rules given by Moskovits:30,31 SS ∝ |RXX(1 + rs)(1 + r's)| 2 PS ∝ |RXY(-1 + rp)(1 + r's)cos φ + RXZ(1 + rp)(1 + r's)sin φ| 2 SP ∝ |RYX(1 + rs)(1 - r'p)cos φ′ + RZX(1 + rs)(1 + r'p)sin φ′| 2 PP ∝ |[RYY(1 - rp)cos φ + RYZ(1 + rp)sin φ](1 - r'p)cos φ′+ [RZY(-1 + rp)cos φ + RZZ(1 + rp)sin φ](1 + r'p)sin φ′| 2

(3) where φ (φ′) is the angle between the propagation direction of the incident (scattered) beam and the surface normal. In

Figure 5. Nanotube (xyz) and lab-frame (XYZ) coordinate systems. The nanotube x-axis and the lab-frame Z-axis are both normal to the Au(111) surface.

the present work φ was 66° and φ′ was 24°. The intensity in each case depends on the components of the lab-frame polarizability tensor (RXX, RXY,...) and the Fresnel coefficients for S and P polarization evaluated at the wavelength of the incident (rs, rp) and scattered (r′s, r′p) light (see ref 30 for the relevant formulas). The Fresnel coefficients at the incident (20492 cm-1) and scattered frequencies (20200 cm-1 was chosen as an average for the low-frequency modes) were obtained by interpolation of the real and imaginary parts of the frequency-dependent refractive indices given in ref 32. The resulting Fresnel coefficients (rs ) -0.80 - 0.26i, rp ) -0.11 + 0.50i, r′s ) -0.51 - 0.47i, r′p ) 0.40 + 0.50i) were used to derive the relative intensities of the surface Raman spectra for our experimental configuration:

SS ∝ 0.0502|RXX | 2 PS ∝ 0.112|RXY | 2 + 0.398|RXZ | 2 - 0.127[R* XZ] XYRXZ + RXYR* SP ∝ 0.0551|RYX | 2 + 0.0399|RZX | 2 + 0.0240[R* YXRZX + RYXR* ZX] PP ∝ 0.317|RZZ | 2 + 0.089|RZY | 2 + 0.438|RYZ | 2 + 0.123|RYY | 2 + 0.139[R* YYRYZ + RYYR* YZ] - 0.0750[R* YYRZZ + RYYR* ZZ] R + R R ] + 0.191[R R + R R - 0.101[R* * * * ZY ZZ ZY ZZ YZ ZZ YZ ZZ] - 0.197[R* YZRZY + RYZR* ZY] - 0.0538[R* YYRZY + RYYR* ZY]

(4)

Next, the molecule (nanotube) frame components of the polarizability tensor, Rxx, Rxy,..., were transformed into surface fixed components RXX, RXY,..., using the direction cosines between molecule- and surface-fixed axes, for example, RXY ) ∑F,σRFσ cos(F,X)cos(σ,Y), where F and σ denote directions x, y, and z in the molecule frame and the uppercase letters X, Y, Z are directions in the surface-fixed frame. In accord with AFM and STM images, we assume that the nanotubes lie flat on the gold surface, as depicted in Figure 5, and obtain expressions for the lab-frame polarizabilities in terms of the angle of rotation θ about the surface normal Z, taking z as the long axis of the nanotube and x as the direction normal to the surface. After inserting the molecule-frame polarizabilities in eq 4, taking the squares, and then averaging over the random angle θ, we obtain the polarized Raman intensities in terms of molecule frame polarizability components as follows:

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1 |2R + Rzz | 2 3 xx 2 Σ2 ) |Rxx - Rzz | 2 3

SS ∝ 0.019[|Ryy | 2 + |Rzz | 2] + 0.0063|Ryz + Rzy | 2 + 0.0063[R* yyRzz + RyyR* zz ]

Σ0 )

SP ∝ 0.0069|Ryy + Rzz | 2 + 0.021[|Ryz | 2 + |Rzy | 2] + 2 2 0.0068(R* yzRzy + RyzR* zy) + 0.020[|Rxy | + |Rxz | ]

(6)

PS ∝ 0.014|Ryy + Rzz | 2 + 0.042[|Ryz | 2 + |Rzy | 2] + 2 2 0.014(R* yzRzy + RyzR* zy) + 0.20[|Ryx | + |Rzx | ]

and the depolarization ratio is

PP ∝ 0.32|Rxx | + 0.046[|Ryy | + |Rzz | ] + 0.015(R* yyRzz + RyyR* zz ) 0.038(R* xxRyy + R* xxRzz + RxxR* yy + RxxR* zz ) + 2

2

2

F)

0.044[|Rxy | 2 + |Rxz | 2] + 0.22[|Ryx | 2 + |Rzx | 2] + 0.015|Ryz + Rzy | - 0.098(R* xyRyx + R* zxRxz + RxyR* yx + RzxR* xz) 2

3Σ2 10Σ + 4Σ2 0

(7)

(5)

If the last terms in the expressions for the PS and SP intensities are neglected, that is, if Ryx ) Rzx ) Rxy ) Rxz ) 0, then we obtain a 2:1 intensity ratio for the PS and SP spectra, in excellent agreement with experiment. Considering the axial symmetry of the free nanotubes and that strongly enhanced totally symmetric modes in resonance Raman have diagonal polarizability tensors, it is reasonable to assume that Rxx ) Ryy * Rzz are the only nonzero tensor elements for resonance with the J-band. We concede however, that the flattened nanotubes on the gold surface could result in Rxx * Ryy. In ref 3, the J-band of TSPP aggregates was found by flow-induced linear dichroism to be strongly polarized along the long axis of the aggregate, and incomplete polarization was attributed to imperfect alignment of the nanotube with the flow direction. However, if the J-band transition moment is completely polarized along the nanotube z axis, Rzz would be the only nonzero component of the polarizability. In this case, eq 5 predicts the intensity ratios PP/SS/PS/SP to be 6.6:2.7:2.0:1.0, which is a larger relative intensity for the PP spectrum than is observed in experiment. The assumption that only one diagonal element of R is nonzero also leads to depolarization ratios of 1/3 for the solution phase aggregate in contradiction to our results for the low-frequency modes. We conclude that the J-band has components of the transition moment both parallel and perpendicular to the nanotube axis. Unfortunately, even if an axially symmetric and diagonal polarizability tensor is assumed, the presence of real and imaginary parts prevents the unique determination of Rxx and Rzz from the experimental relative intensities. To make a rough estimate, the relative magnitudes of the polarizabilities, Ryy and Rzz, were arbitrarily assumed to be real and the relative intensities of the SS and SP spectra were used to determine |Ryy/Rzz | ≈ 0.06. This ratio was then used along with the relative intensities of PP and SP spectra to deduce |Rxx/Rzz| ≈ 0.4. Given that each component of the polarizability tensor RFF is proportional to the square of the transition moment |µF|2 in that direction, these results are consistent with a J-band transition that is largely, but not completely, polarized along the long axis of the nanotube. The larger ratio |Rxx/Rzz | compared to |Ryy/Rzz| is reasonable in light of the fact that the nanotubes are mostly collapsed in the x-direction.

From the experimental value of F ) 0.5, we conclude |Rxx Rzz|2 ≈ 2.5|2Rxx + Rzz|2. If Rxx and Rzz are taken to be real, we get |Rxx/Rzz| ≈ 0.14, in reasonable agreement with the average of |Ryy/Rzz| and |Rxx/Rzz| of 0.23 obtained above for the surface Raman spectra. Resonance Raman Spectra with H-Band Excitation. Figure 6 shows the resonance Raman spectrum of the solution phase aggregate excited at a wavelength of 413 nm, which is close to the ∼420 nm shoulder assigned to the H-band. Two features of this data are very different from what is seen with J-band excitation: weak intensity of the low frequency modes and the presence of a fluorescence background. The modes at 240 and 314 cm-1, which dominate the Raman spectrum with J-band excitation, are quite weak in the H-band excited spectrum. In contrast, the strongest modes observed with 413 nm excitation are at 1236, 1371, and 1536 cm-1. The first and last of these are also observed in the RR spectrum of the aggregate excited at 488 nm, as reported in ref 17, but with lower relative intensity compared to the low-frequency modes. The mode at ∼1540 cm-1 is also seen in the Raman spectrum of the monomer diacid, where the value of F ) 3/4 indicates that it is nontotally symmetric. The relative intensities of the Raman bands shown in Figure 6 are rather different from those of the monomer diacid reported in ref 7, despite the probable overlap of the H- and B-bands. The appearance of Soret band emission, while uncommon, has been reported for both monomeric34 and aggregated27 tetraphenylporphyrins. This background introduces uncertainty in the determination of the depolarization ratios, especially for the weak low-frequency modes, but it appears that F is close to 1/3 for the three strongest modes. Figure 7 shows the surface resonance Raman spectrum of the TSPP aggregate on Au(111) excited at 413 nm. The background fluorescence is suppressed in the surface Raman spectra and there is probably less contribution from residual monomer. The low-frequency modes are more easily discerned than in solution and as shown in the inset have very different relative intensities as compared to the same sample excited at 488 nm. The relative intensities of the 240 and 314 cm-1 modes are quite similar, with PP ≈ SS > PS > SP. The higher frequency modes in the 1400-1600 cm-1 range also have similar intensities for various polarizations, with the PP intensity the largest and SP generally the smallest.

Returning to the solution phase values of F ) 0.5, random orientation or the nanotubes permits this depolarization ratio to be related to invariants of the polarizability tensor as described in ref 33. In the present case, assuming now that the polarizability is axially symmetric, the isotropic part of the polarizability Σ0 and the symmetric anisotropy Σ2 are given by

The relative intensities PP/SS/PS/SP of the 314 cm-1 mode are 2.4:2.4:1.6:1.0. As in the previous section, we attempted to account for these relative intensities using the Fresnel coefficients at the incident and scattered wavelengths to derive equations similar to eq 5 but with different numerical factors resulting from the dispersion in the Fresnel coefficients:



Figure 6. Polarized and depolarized resonance Raman spectra of the solution phase TSPP aggregate excited at 413 nm. The raw data in (a) reveal the background Soret band fluorescence, while in (b) the background has been subtracted and the depolarized spectrum scaled by a factor of 3.

Figure 7. Raman spectrum of TSPP aggregates adsorbed on Au(111) and excited at 413 nm. The inset shows the low-frequency modes at 240, 320, and 420 cm-1 on an enlarged scale. SS ∝ 0.012[|Ryy | 2 + |Rzz | 2] + 0.0039|Ryz + Rzy | 2+ 0.0039[R* yyRzz + RyyR* zz ] SP ∝ 0.0042|Ryy + Rzz | 2 + 0.013[|Ryz | 2 + |Rzy | 2] + 2 2 0.0042(R* yzRzy + RyzR* zy) + 0.017[|Rxy | + |Rxz | ]

PS ∝ 0.0091|Ryy + Rzz | 2 + 0.027[|Ryz | 2 + |Rzy | 2] + 2 2 0.0091(R* yzRzy + RyzR* zy) + 0.17[|Ryx | + |Rzx | ]

PP ∝ 0.37|Rxx | 2 + 0.030[|Ryy | 2 + |Rzz | 2] + 0.010(R* yyRzz + RyyR* zz ) 2 2 0.018(R* xxRyy + R* xxRzz + RxxR* yy + RxxR* zz ) + 0.039[|Rxy | + |Rxz | ] +

0.19[|Ryx | 2 + |Rzx | 2] + 0.010|Ryz + Rzy | 2 0.086(R* xyRyx + R* zxRxz + RxyR* yx + RzxR* xz)

(8) In this case, however, the assumption of a diagonal polarizability tensor does not neatly account for the relative intensities. For example, again neglecting the last term in the expression for the SP and PS intensities, the PS intensity is predicted to be 2.2 times the SP intensity, somewhat higher than the observed ratio of 1.6. Making an assumption consistent with the theory for an excitonically coupled helical aggregate, we consider the relative intensities that would result in the case that Rzz is zero but Rxx and Ryy are not. In this case, the SS/SP intensity ratio would be about 2.9 compared to the observed value of about 2.4, a reasonable level of agreement, but the assumption does not readily account for the observed similar intensities of the SS and PP spectra. Attempts to find a ratio |Rxx/Ryy| that could account for the experimental intensity ratios within the assumption that Rzz and all off-diagonal components are zero were unsuccessful. It is possible that off-diagonal components of the

polarizability tensor contribute to this discrepancy. Vibronic coupling of two dipole-allowed excited electronic states results in a nondiagonal polarizability tensor and could be operating in the H-band RR spectrum. Such coupling is consistent with the appearance of strongly enhanced nontotally symmetric modes. The higher frequency modes are less dependent on polarization than the low-frequency ones. The strong bands at 1234 and 1540 cm-1, for example, both show relative intensities PP/ PS/SS/SP of about 1.6:1.3:1.1:1. We speculate that this could result from a more random distribution of direction cosines than was assumed in arriving at eqs 5 and 8, consistent with contribution from residual monomer. Note, however, that eq 5 is valid for a frequency shift of about 300 cm-1. Given the limitations of the model in accounting for the relative intensities for the 314 cm-1 vibration, it was not considered fruitful to extend the calculation of the Fresnel coefficients to larger wavenumber shifts. Because the low-frequency modes are very weak in the solution phase resonance Raman spectrum, the depolarization ratios are rather uncertain, but they appear to deviate from 1/3. They are clearly not equal to 1/8, as would be expected for a helical exciton with a doubly degenerate transition polarized perpendicular to the tube axis. Unlike the RR data resonant with the J-band, experimental limitations prevented us from obtaining more favorable resonance with the H-band maximum. Symmetry Considerations for the H- and J-Band Transitions. The RLS data and the H- and J-band excited RR spectra are quite consistent with one another. A strong RLS signal in the vicinity of the J-band and the absence of one at wavelengths near the H-band indicates that the degree of coherence is much larger for the J-band. Thus, the model depicted in Figure 5 gives good agreement with the relative intensities of the polarized RR spectra for J-band excitation because the symmetry of the Raman tensor is well-defined in the nanotube coordinate system. The H-band excited state, on the other hand, is not coherent, as evidenced by the absence of resonance light scattering and lack of resonance enhancement of low-frequency Raman modes. The failure of the model of Figure 5 to account for the relative intensities of the polarized surface Raman data for H-band excitation appears to be consistent with the results of flowinduced linear dichroism experiments in ref 3, which found the H-band to be equally intense for light polarized along and perpendicular to the aggregation direction. This suggests that the H-band transition moments on different chromophores are not well-aligned relative to one another. We consider here how this could result from a model that is based on structural data from our STM experiments. In the free porphyrin diacid with 4-fold symmetry, the degenerate Soret (B) band would have two equal and orthogonal transition dipole moments polarized in the plane of the molecule, µge(x) ) µge(y) ) 11.6 D. Nonplanar distortion induced by protonation of the pyrrole nitrogens could result in unequal transition dipole components, however, such that the component along the aggregation direction might be increased at the expense of the component in the perpendicular direction, and could conceivably contribute to the diminished intensity of the H-band relative to J and Q. Upon assembly into the putative cyclic 16mer, the transition dipole moments perpendicular to the plane of the ring couple to bring about the blue-shifted H-band, while the components parallel to the plane of the ring result in the red-shifted J-band. The direction of the shift is decided by the sign of the near-neighbor coupling strength V

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V)

µ2ge

[uˆ1 · uˆ2 - 3(uˆ1 · rˆ)(uˆ2 · rˆ)] hcr3

Friesen et al.

(9)

where uˆ1 is a unit vector in the direction of the transition moment of molecule 1 and similarly for molecule 2, r is the distance between neighboring molecules, and rˆ is a unit vector in the direction connecting their centers. In the cyclic aggregate, each component of the degenerate Soret band is split into 16 excitons with k ) 0, (1, (2,..., (7, 8. Hereafter, we refer to the cyclic 16-mers as “rings” and associate them with the 6 nm disks, which constitute the flattened nanotubes, as reported in ref 17. Eq 9 predicts that coupling of the component of the Soret band transition moments which are perpendicular to the plane of the ring of the cyclic N-mer results in a positive value of V, that is, an H-band. Conversely, coupling of the in-plane components of the transition moments leads to V < 0 and a red-shifted J-band. The k ) 0 state, polarized perpendicular to the plane of the ring, is the only state within the H-band manifold that carries oscillator strength, while the degenerate k ) (1 transition, polarized in the plane of the ring, is the only allowed component of the J-band. Thus, in the absence of further exciton coupling within the helical nanotubes, RR spectra excited within the Hand J-bands would lead to F ) 1/3 and 1/8, respectively. Excitation within the H-band of the solution phase aggregate does lead to F values close to 1/3. However, this could result just as easily from an incoherent, nondegenerate resonant electronic state as from a coherently coupled one polarized perpendicular to the plane of the rings. Given the RLS results and the failure of a Raman tensor defined in the nanotube frame to account for the H-band excited surface Raman data, the former is more likely. Because J-band excitation clearly does not result in F ) 1/8, further coupling of the J-band transition moments of the rings on assembly into the nanotube is suggested. Transition dipole coupling preserves the total intensity such that the H-band transition moment in the 16-mer is µH,Z ) Nµge, while the J-band has equal orthogonal components µJ,X ) µJ,Y ) N/2µge. Here, the subscripts Z and X,Y denote the directions perpendicular and parallel to the ring, respectively. The increased transition dipole would increase in the strength of the inter-ring exciton coupling compared to the intraring coupling of the molecular transition dipoles. However, this increase is more than offset by the much larger separation of neighboring rings (on the order of 6 nm) compared to the intermolecular distances (about 1 nm) within the ring, such that the inter-ring excitonic coupling is less than a tenth as strong as that operating within the ring. This means that assembly of the rings into the nanotube will lead to only small perturbations to the frequencies of the H- and J-bands, but significant changes to the symmetries of these transitions results. The k ) (1 transition dipoles of the individual 6 nm rings can be resolved into components parallel and perpendicular to the long axis of the nanotube. These lead, respectively, to transitions which are slightly red-shifted and blue-shifted compared to the J-band of the 16-mer. The red-shifted (parallel) component is nondegenerate and the blue-shifted (perpendicular) component is doubly degenerate, in accord with the assumed structure of the polarizability tensor Rxx ) Ryy * Rzz for the free nanotubes. In a separate paper, we consider a structural model for the assembly of the nanotube that can account for the Raman and optical absorption data.35 We note that a range of coherence numbers Nc for the J-band of the TSPP aggregate have been determined from different

experiments. The ratio of the line width of the monomer diacid absorption band to that of the aggregate J-band results in Nc ≈ 11.27 Taking thermal broadening of the absorption band into account, Koti et al.36 obtained Nc ≈ 16. Maiti et al.37 used fluorescence anisotropy to deduce a value of 22 for Nc, while the determination of excited state polarizability from Stark spectroscopy resulted in a value as large as 60-80.38 It is possible that this range of values represents differing degrees of hierarchal assembly, though it is also possible that the timescale of the experiment or assumptions in analyzing the data account for these disparities. Since the optical spectrum is largely decided by the formation of the rings, further assembly into nanotubes is not easily determined from ordinary absorption data. For example, the presence of both parallel and perpendicular J-band transitions with slightly different frequencies would result in an underestimated value of Nc from the comparison of the absorption widths of the monomer and J-band. The consistent optical absorption data from various laboratories and the observation of an isosbestic point are evidence that the 16-mer forms in one step, but the extent of further assembly into nanotubes may depend on sample preparation. The relative intensity of the H-band when separated from the B-band of residual monomer is estimated here to be about half that of the J-band. The absence of strong excitonic coupling in the vicinity of 420 nm is consistent with the weakness of this band. Apparent weak H-band intensity and concomitant increase in the Q-band have been observed in other porphyrin aggregates27,39 such that it is reasonable to ask if there is a link. If the local environment of the molecule in the aggregate resulted in the loss in intensity for the component of the Soret band which is polarized perpendicular to the direction of aggregation, this would explain the lack of coherence of the H-band. We find the integrated intensity of the Soret band of the monomer diacid to be about 10 times the intensity of the Q-band. The Q-band intensity associated with the aggregate is estimated to be about 3-fold larger than that of the monomer. We also note that, as shown in ref 17, the Q-band is further red-shifted and enhanced in the aggregate. In his four-orbital model for the optical spectra of porphyrins, Gouterman13 showed that perturbations of A1g, A2g, B1g, and B2g symmetry are capable of configurational mixing and an increase in the Q-band intensity at the expense of the B band. Saddling (B1g) or ruffling (A2g) distortions of the porphyrin core are nonplanar distortions that could lead to the formation of closed rings. The increase in the Q-band intensity of the porphyrin monomer on protonation of the porphyrin core is consistent with the known nonplanarity of tetraphenylporphyrin diacids and our previously reported single molecule images of the diacid monomer.20 The saddling distortion, however, corresponds to a change from the D4h to the D2d point group, a distortion that preserves the double degeneracy of the Soret band. The question is whether the further increase in the Q-band on aggregation is the result of (a) increased nonplanarity, (b) excitonic coupling of the B- and Q-bands in the aggregate, or (c) vibronic coupling of the Band Q-bands. If (a) is operative, we assume the H- and J-bands would be equally diminished in intensity. It is difficult to rule out this mechanism owing to the uncertainty in establishing the J-band transition strength. Mechanisms (b) and (c) would have to lead to greater B-Q coupling for the H-band than the J-band. Given the low-intensity of the H-band and the experimental evidence presented herein, we consider that excitonic coupling of the H-band with the Q-band is probably not significant. We therefore consider whether the local symmetry of the porphyrin molecule in the aggregate can result in vibronic coupling



Figure 8. Effect of local symmetry on the degenerate B- and Q-bands of a saddled porphryin (a). In the aggregate, the x,y degeneracy of the B- and Q-band excited states is lifted (b), permitting vibronic interaction of Bx with Qy and By with Qx (c).

between the H-band and the Q-band, which is significantly different from that between the J-band and the Q-band. Consider the local symmetry of the porphyrin in the aggregate as shown in Figure 8 and its affect on the porphyrin transitions prior to excitonic coupling. The site symmetry is reduced to Cs and the transition moments for the precursors to the J- and H-band excited states are polarized parallel (A′) and perpendicular (A′′), respectively, to the plane of symmetry. Similarly, the x- and y-components of the Q-band excited states belong to different irreducible representations in the lowered site symmetry. A nontotally symmetric mode of A′′ symmetry is capable of mixing the B and Q excited states of different symmetry. Defining x and y to be directions perpendicular and parallel to the aggregation direction, respectively, two coupling strengths are defined:

( ) ( )

ˆ ∂H |Q0〉q ∂q 0 y ˆ ∂H V2 ) 〈B0y | |Q0〉q ∂q 0 x

V1 ) 〈B0x |

(10)

where q is the normal coordinate for the perturbing (nontotally) symmetric mode. Because the local symmetry lifts the x,y degeneracy of the free porphyrin, these two vibronic coupling matrix elements are not necessarily equal. Vibronic coupling results in the Bx state being increased in energy by 2(V1)2/∆E, while the Qy state is lowered by the same amount, where ∆E ) EB0 - EQ0 is the zero-order energy difference of the B and Q levels. Similarly, the By state is lifted by 2(V2)2 /∆E and the Qx state is lowered by the same amount. The transition moments connecting the perturbed states to the ground state are

V1 0 µ ∆E Q V2 0 ) µB0 + µ ∆E Q V2 0 ) µQ0 µ ∆E B V1 0 ) µQ0 µ ∆E B

µBx ) µB0 + µBy µQx µQy

(11)

Equation 11 shows that the local symmetry in the aggregate can result in different levels of B-Q intensity borrowing for the H- and J-band precursors. The expressions in eq 11 and Figure 8 were obtained with a weak coupling model for simplicity, V1,2 , ∆E, but the qualitative predictions will be the same if we do not make this assumption. The model can account for the experimental trends if, as assumed in Figure 8, the magnitude of the coupling strength V1 is larger than that of V2. This would result in the component of the Soret band polarized perpendicular to the aggregation direction (i.e., perpendicular to the plane of the ring in the cyclic N-mer) lending intensity to the component of the Q-band, which is polarized parallel to the aggregation direction. Thus, the redshifted component of the Q-band is enhanced and the blueshifted component of the B-band diminished in agreement with experiment. We note that this also accounts for the observation reported in refs 3 and 19 that the red-shifted Q-band is polarized along the direction of aggregation. If the site symmetry is sufficient to result in significant lending of the Bx intensity to the Qy state, the former suffers a loss and the latter experiences an increase in excitonic coupling. Thus, the excitonic coupling of the Q-band transition moments with one another in the nanotube, albeit weaker than the coupling between the By-band transition moments leading to the J-band, would also lead to a J-type Q-band that is red-shifted and enhanced in intensity compared to the blue-shifted H-type Q-band. The red-shifted aggregate Q-band, however, is not motionally narrowed and does not give a strong RLS signal, so it is not clear how much of the red-shift of the Q-band can be attributed to excitonic coupling. The model may also explain the difference in the H- and J-band RR spectra of the aggregate. The strong activity of nontotally symmetric modes in the H-band excited spectrum is reasonably a consequence of vibronic coupling, which results in off-diagonal components of the polarizability tensor. These off-diagonal components make the analysis of the relative intensities of the PP, SS, SP, and PS spectra difficult to interpret, in contrast to the J-band excited data where a diagonal Raman tensor fits the data quite well. While it is not readily apparent why B-Q vibronic coupling should be stronger for the H-band than the J-band, the assumption appears to account for many aspects of the optical spectrum as well as the resonance Raman data. Conclusions Polarized resonance Raman spectroscopy of the TSPP aggregate in solution and on Au(111) has been used to address questions concerning the mesoscale structure of the aggregate and its relation to observed optical properties. In contrast to a frequently made assumption in the literature of chromophore aggregates, the presence of both red- and blue-shifted aggregate transitions need not imply the existence of different aggregate structures, owing to the lifting of Soret band degeneracy. However, H- and J-band transitions of the aggregate differ greatly in their intensity and degree of coherence, both of which are larger for the J-band. Coherent coupling within the J-band excited state results in strong activity of low-frequency Raman modes and intense resonance light scattering, while the weaker H-band exhibits much less RLS activity and less enhancement of low-frequency vibrations. In accord with a model in which cyclic N-mers are further assembled into a helical nanotube, low-frequency modes in the resonance Raman spectra excited within the J-band evidence an excited state which is not completely polarized along the long axis. Higher frequency

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modes, on the other hand, are less-strongly enhanced and have F values of 1/3 consistent with a nondegenerate resonant state. These modes apparently are not as strongly coupled to the delocalized transition and appear to behave as if enhanced by an incoherent resonant excited state or by one component of the delocalized J-band excited level rather than all three. The observed H-band is a shoulder to the overlapping B-band of residual monomer. Reasonable attempts to separate out its integrated intensity reveal that it is weaker than the J-band and less than half the intensity of the monomer B-band. At the same time, enhancement of the Q-band on aggregation appears to come at the expense of the H-band intensity, which we speculate could be the result of H-Q vibronic coupling permitted in the reduced symmetry of the aggregate. The lack of coherent coupling within the H-band excited state as indicated by the RLS spectrum correlates to weak activity of low-frequency modes in resonance Raman and the failure of a simple model for the polarizability tensor fixed in the nanotube coordinate system to account for the polarized surface Raman data. However, it is difficult to rule out other explanations of the origin of H-Q intensity sharing, such as increased nonplanarity of the diacid molecules on assembly into rings. Several models have been proposed for the TSPP aggregate structure and it is useful to consider whether they can account for the observed spectroscopic properties. For example, Gandini et al.6 suggested a tubular aggregate in which the porphyrin planes are arranged in stacked rings with their molecular planes perpendicular to the nanotube surface. Such a model could not result in a significant transition dipole in the direction of the long axis of the nanotube. Vlaming et al.19 proposed a helical aggregate built up from overlapping molecular planes in which the tilt angles were optimized to reproduce the optical spectra. However, the observed shell thickness of 2 nm suggests that the molecular planes are oriented perpendicular to the nanotube surface. In our proposed model, the arrangement of cyclic N-mers along the nanotube surface accounts for 2 nm shell thickness as well as the observation of a J-band which has components both along and perpendicular to the long axis. As discussed further in a separate paper,35 the doubly degenerate J-band of the cyclic N-mer undergoes further excitonic coupling on assembly into the nanotube resulting in slight splitting into a red-shifted transition polarized along the nanotube axis and a doubly degenerate blue-shifted component polarized in the orthogonal direction. Our proposed model is therefore in good agreement with both structural and spectroscopic data. Acknowledgment. The support of the National Science Foundation through Grant CHE-0848511 is gratefully acknowledged. J.L.M. and U.M. acknowledge helpful conversations with Prof. K. W. Hipps. J.L.M. wishes to acknowledge helpful discussions with Prof. Martin Moskovits. Supporting Information Available: Concentration-dependent absorption spectrum (Figure S1) and integrated absorbance, transition moments, and oscillator strength for the monomer and aggregate (Tables S1-S4). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Kano, H.; Kobayashi, T. J. Chem. Phys. 2002, 116, 184–195.

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JP106514G

Resonance Raman Spectroscopy of Helical Porphyrin Nanotubes

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