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Resonance Raman Intensity Analysis of Cresyl Violet Bound to SiO2 Colloidal Nanoparticles Weinan Leng and Anne Myers Kelley* Department of Chemistry, Kansas State University, Manhattan, Kansas 66506-3701 Received April 15, 2003. In Final Form: May 29, 2003 Resonance Raman spectra and absolute cross sections have been measured for cresyl violet in aqueous solution and bound to the surface of SiO2 colloidal nanoparticles. The absorption spectra of cresyl violet on SiO2 have previously been interpreted to show formation of H-type dimers on the surface. The spectra of the monomers in solution are simulated to obtain the excited-state geometry change along each normal mode and the electronic spectral broadening parameters. The spectra of the dimers on SiO2 are then simulated with a model that assumes transition dipole coupling between the vibronic transitions on the two monomers. The simulations require increases in both the electronic homogeneous line width and the inhomogeneous line width upon binding to the colloid. The general features of the resonance Raman spectra are reproduced fairly well, but significant differences in the relative intensities of certain Raman lines upon binding to the surface suggest specific vibrational or vibronic effects not considered in this simple model.
Introduction The transfer of charge and/or excitation among molecules in condensed phase environments is of crucial importance to the function of organic electronic devices (e.g., second- and third-order nonlinear optical materials, light-emitting diodes (LEDs), organic photovoltaics), photobiological systems (e.g., the light-harvesting complexes in photosynthesis), and future optically or electrically driven nanomachines. Understanding how molecules communicate with one another through comparatively weak noncovalent interactions is a difficult problem and one that will become increasingly important for the promise of supramolecular chemistry to be realized. Spectroscopic approaches, broadly defined, constitute the most direct approach to addressing these questions. In a molecular aggregate, excitonic coupling among transition dipoles on neighboring chromophores splits the electronic transitions into a broad band of states with different frequencies and oscillator strengths. The vibrational frequencies and normal modes may also be altered by dipole-dipole coupling between vibrational transitions and structural modifications that occur upon aggregation. Resonance Raman spectroscopy is a powerful spectroscopic technique that reports on both ground-state structure (from the Raman frequencies) and excited-state structure and dynamics (from the resonance Raman intensities). We and others have developed experimental and computational methods for characterizing excited electronic states of large molecules in condensed phases by simultaneous modeling of the linear absorption spectra and absolute resonance Raman excitation profiles.1 We can determine the vibronic structure of the electronic spectrum (i.e., the reorganization energies of all the modes that are Franck-Condon active in the transition) even in the presence of severe solvent broadening, as well as the solvent reorganization energy and an estimate of the electronic inhomogeneous broadening. Almost all of these * Corresponding author. Address effective 1 July 2003: Division of Natural Sciences, University of California, Merced, P.O. Box 2039, Merced, CA 95344. (1) Myers, A. B. In Laser Techniques in Chemistry; Myers, A. B., Rizzo, T. R., Eds.; Wiley: New York, 1995; pp 325-384.
studies, however, have involved chromophores in dilute solution or in the gas phase. While some resonance Raman spectra of chromophore aggregates have been reported,2-6 we are aware of no quantitative analysis of the intensities and Raman excitation profiles of an aggregate. We have chosen to begin by studying the electronic absorption and resonance Raman spectra of dimers. A number of cationic dyes that are monomeric in polar solvents have been shown to form H-dimers when adsorbed to the surface of negatively charged colloidal nanoparticles.7-13 In an H-dimer, the interacting transition dipoles are oriented such that the dimer has a strongly allowed state at higher energy than the monomer absorption and a weakly allowed or forbidden state at lower energy. The electronic absorption spectrum therefore shifts to the blue in the dimer. Electronic excitation to the allowed state is followed by rapid internal conversion to the lower forbidden state, so most H-aggregates are only weakly fluorescent, making them promising candidates for resonance Raman studies. The specific system examined here is cresyl violet7,9,10,13 (Chart 1) adsorbed onto SiO2 colloids in aqueous solution. Cresyl violet exhibits a strong blueshift in its absorption spectrum upon addition of SiO2 or SnO2, and the concentration dependence of the spectra has been interpreted as indicating that the dominant spectral changes arise from formation of dimers on the surface.9,13 The resonance Raman spectra and excitation (2) Akins, D. L.; Zhuang, Y. H.; Zhu, H.-R.; Liu, J. Q. J. Phys. Chem. 1994, 98, 1068-1072. (3) Chen, D.-M.; He, T.; Cong, D.-F.; Zhang, Y.-H.; Liu, F.-C. J. Phys. Chem. A 2001, 105, 3981-3988. (4) Guo, C.; Aydin, M.; Zhu, H.-R.; Akins, D. L. J. Phys. Chem. B 2002, 106, 5447-5454. (5) Okamoto, H.; Hamaguchi, H.; Tasumi, M. J. Raman Spectrosc. 1989, 20, 751-756. (6) Diers, J. R.; Zhu, Y. W.; Blankenship, R. E.; Bocian, D. F. J. Phys. Chem. 1996, 100, 8573-8579. (7) Martini, I.; Hartland, G. V.; Kamat, P. V. J. Phys. Chem. B 1997, 101, 4826-4830. (8) Nasr, C.; Hotchandani, S. Chem. Mater. 2000, 12, 1529-1535. (9) Liu, D.; Kamat, P. V. Langmuir 1996, 12, 2190-2195. (10) Liu, D.; Kamat, P. V. J. Chem. Phys. 1996, 105, 965-970. (11) Barazzouk, S.; Lee, H.; Hotchandani, S.; Kamat, P. V. J. Phys. Chem. B 2000, 104, 3616-3623. (12) Liu, D.; Kamat, P. V. J. Electrochem. Soc. 1995, 142, 835-839. (13) Liu, D.; Hug, G. L.; Kamat, P. V. J. Phys. Chem. 1995, 99, 1676816775.
10.1021/la034638a CCC: $25.00 © 2003 American Chemical Society Published on Web 07/11/2003
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profiles of the closely related dye nile blue in dilute ethylene glycol solution have been analyzed quantitatively,14 but we know of no prior resonance Raman studies of the surface-adsorbed and/or aggregated forms of either of these molecules. The physical and spectroscopic properties of cresyl violet present some complications for the experiments and analysis we wish to perform. First, cresyl violet and related dyes aggregate rather readily not only on surfaces but also in solution, the aggregation equilibria depending on pH and ionic strength.15-18 Therefore, we must work at very low concentrations in order to measure the monomer spectra needed for comparison. Second, the tendency of these dyes to adsorb not only to colloidal SiO2 particles but also to the surfaces of glassware makes it difficult to carry out experiments at well-defined concentrations. Third, the strong and minimally Stokes-shifted fluorescence of monomeric cresyl violet presents a severe interference to the resonance Raman spectra of the monomer. As a result, Raman spectra of the monomer can be obtained only with excitation far to the blue side of the absorption maximum. Finally, we know of no prior vibrational analyses that would aid in the molecular-level interpretation of the resonance Raman spectra. In fact, we have found no prior Raman studies of any sort on cresyl violet. This paper presents absorption and resonance Raman spectra of cresyl violet as the monomer in aqueous solution and as bound to the surface of aqueous colloidal SiO2. The absolute resonance Raman cross sections for the vibrations of monomeric and surface-bound forms are measured at two (for the monomer) or three (for the dimer) excitation wavelengths. The absorption spectra and resonance Raman intensities of the monomer are simulated computationally to determine the change in equilibrium geometry upon electronic excitation along each vibrational mode. We then employ a simple model of excitonically coupled molecular H-dimers to predict the absorption spectrum and resonance Raman intensities of the dimer and compare these with experimental results for the SiO2bound species. Experimental Methods Cresyl violet perchlorate (Aldrich) and aqueous colloidal SiO2 (15%, 4 nm particles, Alfa Aesar) were used as received. Solutions of cresyl violet were prepared in appropriate buffers (phosphate for pH 4, borate for pH 9, carbonate for pH 11) or in distilled water containing 28 mM Na2SO4 (pH ≈ 6). Samples on SiO2 were obtained by diluting the stock colloid solutions in buffer or sulfate solution and adding concentrated dye solution. Determination of the actual concentrations in aqueous solution was complicated by gradual adsorption of the dyes to the surfaces of the glassware used to prepare the samples, causing the concentrations to change slowly over time. This was not a serious problem in alcoholic solvents. Therefore, the molar absorptivity of cresyl violet monomer in aqueous solution was determined by (14) Lawless, M. K.; Mathies, R. A. J. Chem. Phys. 1992, 96, 80378045. (15) Steinhurst, D. A.; Owrutsky, J. C. J. Phys. Chem. B 2001, 105, 3062-3072. (16) Spencer, W.; Sutter, J. R. J. Phys. Chem. 1979, 83, 1573-1576. (17) Braswell, E. J. Phys. Chem. 1968, 72, 2477-2483. (18) Mukerjee, P.; Ghosh, A. K. J. Am. Chem. Soc. 1970, 92, 64086412.
Leng and Kelley preparing a solution of the dye in water, transferring a measured volume to a spectrophotometer cell and rapidly measuring the absorption spectrum, and then evaporating the water under N2, redissolving in a measured volume of ethanol, and remeasuring the absorption spectrum. The maximum molar absorptivity of 83 000 M-1 cm-1 at 603 nm in ethanol19 was used to determine the concentration of cresyl violet, and hence its molar absorptivity in water. These molar absorptivities were then used for determining the actual concentrations in each resonance Raman experiment (8-14 µM for the monomers in water, 4.7 µM for the dimers on SiO2). Where SiO2 concentrations are quoted, these are in terms of SiO2 formula units, not colloidal particles. Absorption spectra were measured on a Hitachi U-3010 UV/ vis spectrophotometer. Raman spectra were obtained on a Spex 1877 triple spectrograph equipped with a Spex Spectrum One liquid nitrogen cooled CCD. Raman spectra were excited with 10-20 mW at 476.5, 488.0, or 496.5 nm from a Lexel argon-ion laser. Samples of about 2 mL volume were contained in a rotating cylindrical cell, and the Raman scattering was collected in a 90° geometry unless otherwise noted. Care was taken to ensure that scattering was collected only from the solution and not from the cell windows because of the propensity of cresyl violet to adsorb to surfaces. The scattered light was passed through a polarization scrambler and collected and focused onto the spectrograph entrance slit with an ellipsoidal mirror. Spectra were corrected for the wavelength dependence of the spectrograph throughput and detector sensitivity as described elsewhere.1 No reabsorption corrections were necessary because the samples had maximum optical densities at the scattered wavelengths of less than 0.05 over the estimated 1 mm scattering path length. Integrated peak areas were determined by fitting regions of the spectrum to sums of mixed Gaussian-Lorentzian peaks (Grams32) after subtraction of a low-order polynomial to remove underlying fluorescence. In addition, a suitably scaled aqueous sulfate Raman spectrum was subtracted prior to integration of the bands in order to remove interference from the water bending vibration that underlies the 1644 cm-1 line of cresyl violet. The absolute differential resonance Raman cross sections (dσ/dΩ) of the monomer were determined by measuring the integrated areas of the Raman bands of the dye relative to that of the 981 cm-1 line of sulfate via eq 1,1
dσ (dΩ )
)
CV
ICV Csulfate dσ Isulfate CCV dΩ
( )
sulfate
(1)
where Ix is the measured integrated intensity of a Raman band of species x and Cx is its molar concentration. Reference 20 reports total cross sections for sulfate ion (integrated over all scattered directions and polarizations) of 137 × 10-14 Å2 at 476.5 nm, 124 × 10-14 Å2 at 488.0 nm, and 99.3 × 10-14 Å2 at 514.5 nm. The differential cross section is related to the total cross section via eq 2,
dσ (dΩ ) ) 8π3 (11++2FF )σ
Tot
(2)
with the depolarization ratio F ) 0.04 for sulfate.20 The differential cross sections at these three wavelengths are reproduced to within much better than 1% by a pure υ4 dependence (i.e., negligible preresonance enhancement):
(dσ/dΩ)sulfate ) Kυ0(υ0 - υv)3
(3)
where υv ) 981 cm-1, υ0 is the laser excitation frequency in cm-1, and K ) 9.37 × 10-31 Å2 sr-1 cm4.
Computational Methods The absorption and resonance Raman spectra of monomeric cresyl violet in aqueous solution were simulated via the time-domain wave packet method as de(19) Birge, R. R. Kodak Laser Dyes; Eastman Kodak: Rochester, NY, 1987. (20) Loppnow, G. R.; Mathies, R. A. Biophys. J. 1988, 54, 35-43.
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scribed elsewhere.1,21,22 The ground and electronically excited potential energy surfaces were treated as a collection of simple displaced harmonic oscillators having equal frequencies in both states. No mixing of the normal modes (Duschinsky rotation) or coordinate dependence of the electronic transition moment was considered. The broadening of the electronic absorption spectra was divided into a static Gaussian distribution of electronic zerozero energies (inhomogeneous broadening) and an exponential decay in the time domain (homogeneous broadening). The latter carries an implicit assumption that the homogeneous line width represents pure lifetime decay. In reality, the dominant source of homogeneous broadening for most molecules in solution is solvent reorganization which is better modeled as a Brownian oscillator, giving nonexponential decay and a non-Lorentzian line shape;23,24 however, use of the Brownian oscillator line shape was not practical for the dimer calculations described below, which had to be performed in the frequency domain. The electronic transition is therefore defined by the following parameters: a frequency ωi (obtained directly from the Raman spectrum) and a displacement ∆i (the difference between ground and excited-state equilibrium geometries along that normal mode in dimensionless normal coordinates) for each vibrational mode i, the transition length µ (chosen to reproduce the integrated absorption strength), the electronic zero-zero frequency ω0, the electronic inhomogeneous broadening standard deviation, and the homogeneous Lorentzian line width Γ. The ∆i, ω0, and broadening parameters were adjusted to obtain the best simultaneous fit to the absorption spectrum and the absolute resonance Raman cross sections. The visible absorption spectrum of cresyl violet in solution was assumed to originate from a single electronic transition. Our calculations included the 30 vibrational modes between 400 and 1700 cm-1 observed in the resonance Raman spectrum of aqueous cresyl violet. Cresyl violet on SiO2 was modeled as an H-dimer of monomers coupled through the interaction of their electronic transition dipoles. The dipole-dipole interaction operator is given by25
V ˆ AB ) -
µˆ Aµˆ B
(2 cos θA cos θB 4π0RAB3 sin θA sin θB cos φ)
where µˆ i is the scalar dipole moment operator for molecule i and RAB is the distance between molecular centers. The z axis is defined to lie along the line connecting the molecular centers. θi and φi define the orientation of the dipole of molecule i in the usual spherical polar coordinate system, and φ ) φB - φA. For this problem we set θA ) θB ) 90° and φ ) 180°, which means that the two monomers are stacked in exact register, coplanar with their transition dipoles antiparallel. The distance between their centers was left as an adjustable parameter. The matrix of the dipole-dipole interaction was set up in a basis which includes all states that are electronically excited in one of the two chromophores and have up to three quanta of vibration in any combination of modes in each chromophore. The vibronic eigenstates of the coupled mono(21) Myers, A. B. Acc. Chem. Res. 1997, 30, 519-527. (22) Myers, A. B.; Mathies, R. A. In Biological Applications of Raman Spectroscopy; Spiro, T. G., Ed.; Wiley: New York, 1987; Vol. 2, pp 1-58. (23) Li, B.; Johnson, A. E.; Mukamel, S.; Myers, A. B. J. Am. Chem. Soc 1994, 116, 11039-11047. (24) Kelley, A. M. J. Phys. Chem. A 1999, 103, 6891-6903. (25) Stone, A. J. The Theory of Intermolecular Forces; Oxford University Press: New York, 1996.
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Figure 1. Absorption spectrum of cresyl violet in water (pH ≈ 6) as a function of concentration.
Figure 2. Absorption spectra of 2 µM cresyl violet in aqueous buffers as a function of pH. All spectra are scaled to the same maximum. The pH 11 spectrum is noisier and has a scattering background because of the tendency of cresyl violet to precipitate out of solution at high pH.
mers were then calculated by direct numerical diagonalization of this matrix, and the absorption spectrum and resonance Raman excitation profiles calculated from the usual sum-over-states expressions.1,22 Our approach is essentially equivalent to that described by Siebrand and co-workers,26 but generalized from a single vibrational mode to the multimode case. The details of the computational methods for absorption spectra, resonance Raman excitation profiles, and first hyperpolarizabilities of molecular dimers are described in detail elsewhere.27 Results Figure 1 shows the absorption spectra of cresyl violet in aqueous solution as a function of chromophore concentration. At concentrations below about 30 µM, cresyl violet appears to exist almost exclusively in its monomeric form with an absorption maximum at about 580 nm. Increasing the concentration causes the development of a second, blue-shifted absorption band at about 550 nm, indicating the formation of H-type dimers and/or higher aggregates. Figure 2 shows the effect of pH on the absorption spectrum of cresyl violet in aqueous solution at low concentration. As the pH is increased to ≈11, a new blueshifted band appears at 474 nm. This is presumably the (26) Gregory, A. R.; Henneker, W. H.; Siebrand, W.; Zgierski, M. Z. J. Chem. Phys. 1975, 63, 5475-5489. (27) Kelley, A. M. J. Chem. Phys., in press.
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Figure 3. Resonance Raman spectra of cresyl violet (476.5 nm excitation, 10-20 µM) as a function of pH. Asterisks mark prominent Raman lines of the buffers. Spectra were obtained in a backscattering geometry.
Figure 4. Absorption spectra of cresyl violet (9.5 µM) in aqueous sodium sulfate solution (28 mM SO42-) as a function of colloidal SiO2 concentration.
absorption maximum of the deprotonated form. Deprotonation may be accompanied by aggregation, as solutions at pH > 10 in water or buffer are not stable and gradually precipitate from solution. The precipitates, redissolved in acetone or dimethyl sulfoxide (DMSO), give a single blueshifted absorption band characteristic of the deprotonated form. Figure 3 shows the corresponding resonance Raman spectra as a function of pH. The strong shift of intensity from ∼1640 to ∼1495 cm-1 at high pH is consistent with formation of a new species, probably deprotonated. Upon addition of colloidal SiO2 to solutions of cresyl violet at low concentration in water, the absorption spectra develop a narrowed, blue-shifted absorption that increases in intensity with increasing SiO2 concentration. Figure 4 shows the dependence of the absorption spectrum on added SiO2. The dramatic change upon adding SiO2 has been interpreted to indicate formation of H-dimers on the surface of the SiO2 colloid.7-10,13 The absorption maximum shifts to 501 nm, somewhat to the blue of the aggregated form in solution, and the integrated absorbance is reduced to about 2/3 that of the monomer. The spectra in Figure 4 were measured in 28 mM Na2SO4, the same conditions under which the resonance Raman spectra of the dimer were obtained. In the absence of this added electrolyte, the blue-shifted spectrum develops at much lower SiO2 concentrations. Salt effects on the aggregation equilibria of cresyl violet have been discussed by other workers.15,28 (28) Isak, S. J.; Eyring, E. M. J. Phys. Chem. 1992, 96, 1738-1742.
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Figure 5. Resonance Raman spectra of cresyl violet dimerized on SiO2 (CD ) 4.7 µM) and cresyl violet monomer (CM ) 13.2 µM). The excitation wavelength for both spectra is 488 nm. The asterisk marks the Raman line of the sulfate internal standard.
Figure 5 compares the resonance Raman spectra of cresyl violet in its aqueous and SiO2-bound forms. Cresyl violet at 13 µM in solution should be almost exclusively monomeric (refer to Figure 1). While some unbound dye must be present in the SiO2 solutions, free monomeric cresyl violet is expected to make a negligible contribution to the resonance Raman spectra at these excitation wavelengths because its resonance enhancement should be much weaker than that of the blue-shifted surfacebound dimers. The spectra show small but significant and reproducible changes upon dimerization on the surface. The relative intensities of all of the lower-frequency lines are increased in the SiO2-bound form at these excitation wavelengths on the blue side of the monomer absorption band. The lines at 1341 and 1556 cm-1 in the monomeric form shift up and down in frequency, respectively, by about 3 cm-1 on binding to SiO2, and their intensities relative to nearby lines increase. A weak line at 1368 cm-1 in the monomer almost disappears in the dimeric form while a shoulder at 1388 cm-1 grows in. Interpretation of these changes would require solid vibrational assignments for the modes which are currently lacking. However, the very close similarity between most of the frequencies of the two forms suggests that the ground-state structure is not strongly perturbed by binding to SiO2. The frequencies of the resonance Raman lines are determined by the ground-state structure of the chromophore, while their intensities reflect the geometry change upon electronic excitation along each normal mode. These geometry changes are also reflected in the FranckCondon factors that determine the absorption band shape, but the information is largely hidden by the low resolution of the absorption spectrum. We extract the geometry changes along each normal mode by simulating, with a common set of parameters, the absorption spectrum as well as the resonance Raman intensities at several excitation wavelengths. The strong interfering fluorescence of the monomer allows resonance Raman measurements to be made only on the blue side of the absorption band, at 476.5 and 488.0 nm. Table 1 summarizes the best-fit parameters for the monomer, while Figure 6 compares the experimental and calculated absorption spectra. The relative intensities of the different Raman lines in the simulated profiles are determined mainly by their relative displacements. The total width of the absorption spectrum is determined mainly by the overall scaling of the displacements, which dictates the strength of the vibronic progressions in each mode, and to a lesser extent
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Table 1. Resonance Raman Intensities and Spectral Simulation Parameters for Monomeric Cresyl Violeta
Raman shift/cm-1
∆
404 469 492 527 575 594 675 752 834 857 952 1008 1119 1137 1155 1192 1219 1254 1306 1339 1371 1403 1427 1441 1497 1510 1529 1556 1592 1644
0.36 0.82 0.39 0.38 0.28 0.98 0.39 0.27 0.3 0.1 0.27 0.1 0.1 0.1 0.255 0.365 0.08 0.164 0.23 0.24 0.17 0.17 0.17 0.16 0.3 0.16 0.17 0.19 0.12 0.35
Raman cross section/ 10-11 Å2 sr-1 (476.5 nm) expt calcd 3 28 5 9 9 65 14 9 14 2 15 2 4 4 24 50 3 11 18 27 14 15 17 16 52 16 13 23 11 83
4 27 7 7 5 65 14 8 13 2 15 2 3 3 21 46 2 11 23 27 14 15 16 14 55 16 13 24 10 95
Raman cross section/ 10-11 Å2 sr-1 (488.0 nm) expt calcd 6 40 11 11 6 101 20 13 18 2 22 4 5 5 31 71 3 17 36 39 19 24 21 21 79 20 15 34 13 138
6 42 11 12 8 101 21 13 20 2 22 3 4 5 31 69 4 16 35 40 21 23 24 21 83 24 19 37 16 144
a Other parameters: electronic zero-zero frequency ω ) 16 530 0 cm-1, transition length µ ) 1.97 Å, homogeneous (Lorentzian) line width Γ ) 120 cm-1, inhomogeneous broadening (Gaussian) standard deviation ) 300 cm-1.
Figure 6. Absorption spectra of monomeric cresyl violet. Thick line, experimental; thin line, calculated from the parameters of Table 1; dashed line, calculated from the four-mode approximation to the parameters of Table 1 (590 cm-1, ∆ ) 1.08; 900 cm-1, ∆ ) 0.68; 1250 cm-1, ∆ ) 0.64; and 1600 cm-1, ∆ ) 0.56; zero-zero energy ) 16 830 cm-1; transition dipole moment ) 2.01 Å, homogeneous line width ) 250 cm-1; inhomogeneous line width ) 300 cm-1). The arrows indicate the two Raman excitation wavelengths employed.
by the total homogeneous plus inhomogeneous electronic line width. The magnitudes of the absolute Raman cross sections, with the electronic transition length fixed by the integrated absorption cross section, then dictate how the broadening should be partitioned between homogeneous and inhomogeneous. Figure 6 and Table 1 show that the agreement between experiment and simulation for both
the resonance Raman cross sections and the absorption spectrum is quite good. We then turned to simulation of the spectra of the surface-bound dimer. Brute-force implementation of the method described in ref 27 is intractable for cresyl violet because the number of basis states that must be considered in a sum-over-states calculation becomes astronomical when there are a large number of Franck-Condon active modes. If states having a maximum of three vibrational quanta in any combination of only five vibrational modes are considered, there are 56 such states for the monomer and 562 ) 3136 states of the dimer. Inclusion of 30 modes is clearly not feasible. We therefore handled the cresyl violet problem in the following way. First, the 30 modes of Table 1 were collected into five groups: below 470 cm-1, 470-630, 630-1170, 1170-1460, and above 1460 cm-1. The effect of the lowest-frequency group of modes was lumped into an increased homogeneous line width (250 cm-1), and the other four groups of modes were each represented by a single frequency (590, 900, 1250, and 1600 cm-1, respectively) with each ∆ chosen such that its vibrational reorganization energy (λ ) ω∆2/2) was equal to the sum of the reorganization energies of all the modes in that group in the 30-mode set of Table 1. Figure 6 shows that this procedure reproduces the monomer absorption spectrum almost as well as the full 30-mode calculation. To calculate the intensity of each Raman line, a fifth mode was added to the calculation having the same frequency and displacement as in the best-fit monomer parameters of Table 1, and the ∆ for the mode representing the Raman mode’s frequency group was reduced such that the total reorganization energy for the modes in each group remained constant. This approach is suggested by the lessons of transform theory methods,22,29-32 which show that in a separable harmonic system, the resonance Raman profile of any given mode depends on all of the other modes only as their collective contribution to the absorption band shape. This “four-mode plus one” model reproduces the calculated resonance Raman intensities for all of the monomer lines to within 10% of the values obtained from the full 30-mode calculation of Table 1. Initially all of the parameters of the monomer were held constant and the interdimer spacing, which is the main determinant of the overall strength of the interaction, was adjusted to 5.4 Å to give the correct absorption maximum. The zero-zero energy of the monomer was held fixed at the value that properly reproduces its absorption maximum. The excitonic interaction between the monomers not only blue-shifts the absorption but also perturbs the underlying vibronic structure.27 The resulting calculated spectrum was considerably too narrow and its total oscillator strength too large, and the resonance Raman intensities were also mostly too large. We therefore reduced the transition dipole from 2.01 to 1.65 Å, consistent with the reduced absorbance of the dimer, increased the homogeneous line width to 360 cm-1 to reduce the Raman cross sections, and increased the inhomogeneous broadening to a Lorentzian of 500 cm-1 half-width at halfmaximum (HWHM) to better match the shape of the experimental spectrum. Figure 7 shows that these parameters generate a reasonable, although not excellent, fit to the experimental absorption spectrum. (29) Champion, P. M.; Albrecht, A. C. Annu. Rev. Phys. Chem. 1982, 33, 353-376. (30) Stallard, B. R.; Champion, P. M.; Callis, P. R.; Albrecht, A. C. J. Chem. Phys. 1983, 78, 712-722. (31) Tonks, D. L.; Page, J. B. Chem. Phys. Lett. 1979, 66, 449-453. (32) Patapoff, T. W.; Turpin, P.-Y.; Peticolas, W. L. J. Phys. Chem. 1986, 90, 2347-2351.
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dimer, and the 1192 cm-1 mode which is consistently more intense in the monomer than in the dimer. To obtain better fits to the experimental Raman intensities, it would be necessary to adjust the excited-state displacements in some or all of the modes. This was not attempted because of the length of time required to complete the calculation for a single set of parameters due to the lengthy matrix diagonalization step. Discussion
Figure 7. Thick curve: experimental absorption spectrum of cresyl violet dimers on SiO2. Thin curve: spectrum calculated for an excitonically coupled homodimer assuming four vibrational modes for each monomer (parameters of Figure 6 plus interdimer separation ) 5.4 Å, transition dipole moment ) 1.65 Å, homogeneous line width ) 360 cm-1, and Lorentzian inhomogeneous line width ) 500 cm-1). The absorption cross sections are expressed on a per dimer basis.
Figure 8. Comparison of experimental and calculated resonance Raman spectra of cresyl violet on SiO2. Bar heights show the integrated absolute scattering cross sections, per dimer unit, of each transition. The calculations use the dimer parameters given in Figure 7 along with the individual mode displacement parameters of Table 1 as described in the text.
The resonance Raman spectra calculated from this same set of parameters are compared with the experimental values in Figure 8. Both the excitation wavelength dependence of the Raman cross sections (nearly flat from 476.5 to 496.5 nm for the higher-frequency modes, varying by nearly a factor of 3 for the 594 cm-1 mode) and the absolute magnitudes of the cross sections are reproduced fairly well for most of the modes. There are a few clear exceptions, for example, the modes near 1510 and 1497 cm-1, whose intensities reverse between monomer and
We are not aware of any previously published resonance Raman studies on cresyl violet, but an intensity analysis of the closely related dye nile blue (in which the amino group on the less-substituted phenyl ring is replaced by diethylamino) in ethylene glycol was reported by Lawless and Mathies.14 The parameters they obtained are generally similar to ours. For the two most intense lines in the Raman spectrum, their best-fit parameters with Lorentzian homogeneous broadening gave ∆ ) 0.70 for a mode at 590 cm-1 and ∆ ) 0.31 for a mode at 1640 cm-1, with transition dipole moment ) 2.2 Å, homogeneous width ) 85 cm-1, and inhomogeneous standard deviation ) 360 cm-1. Our corresponding values are ∆ ) 0.98 at 594 cm-1 and ∆ ) 0.35 at 1644 cm-1, µge ) 1.97 Å, Γ ) 120 cm-1, and inhomogeneous standard deviation ) 300 cm-1. There are significant differences in the intensities of some of the Raman lines; in particular, the fairly strong cresyl violet line at 1192 cm-1 has only a weak counterpart at 1195 cm-1 in nile blue. The 594 cm-1 overtone may contribute an unresolved shoulder to the 1192 cm-1 line, but as the calculated overtone intensity at our excitation wavelengths is more than an order of magnitude weaker than the measured 1192 cm-1 intensity, we have neglected any contribution from the overtone. The absorption spectra of excitonically coupled molecular homodimers have been categorized into several qualitatively different regimes according to the strength of the electronic coupling.26,33 If the ∼2700 cm-1 blue-shift of cresyl violet’s absorption maximum arises entirely from the coupling between the monomer transitions, that is, binding to the surface by itself does not shift the monomer absorption, cresyl violet on SiO2 is approaching the “strong coupling” limit33 where the interaction energy is larger than the vibronic bandwidth of the monomer spectrum. In this limit, the monomer absorption splits into two clearly separated transitions (one having zero oscillator strength for a pure H-dimer), each of which exhibits a fairly normal harmonic Franck-Condon progression, but with reduced vibronic intensities relative to the electronic origin. The apparent displacement parameters ∆ are all reduced by the square root of 2 owing to the delocalization of the electronic excitation over two monomers. This reduced vibronic intensity results in the well-known narrowing of the absorption bands of both J- and H-aggregates, which is particularly pronounced in larger aggregates. Narrowing near the absorption maximum upon binding to the surface is quite apparent in the cresyl violet absorption spectra of Figure 4. The intermolecular separation that best reproduces the blue-shift of the absorption spectrum is 5.4 Å. This value should not be interpreted too seriously for several reasons. First, the dipole-dipole interaction is a very crude approximation to the true interaction energy when the molecules are large compared with their separation and is not expected to give quantitative results. Second, any shift in the absorption maximum of the monomer upon (33) Fulton, R. L.; Gouterman, M. J. Chem. Phys. 1964, 41, 22802286.
Cresyl Violet Bound to SiO2 Nanoparticles
binding to the surface is ignored. Third, if the ground and excited electronic states have different charge distributions, dimerization will cause the electronic transitions to shift even without any excitonic interaction, for the same reasons that the electronic transitions of most polar chromophores blue-shift or red-shift as the solvent polarity is varied. The concentration-dependent spectra in Figure 1 suggest that the H-dimerization in aqueous solution shifts the absorption maximum by only about 30 nm rather than the 80 nm observed on SiO2. Steinhurst and Owrutsky similarly report 580 and 550 nm as the λmax positions for cresyl violet monomers and dimers, respectively, in aqueous solution.15 Evidently dimers on SiO2 are spectroscopically different from dimers in solution, but how much of this is attributable to chromophoresurface interactions or solvation effects on the constituent monomers and how much to differences in the dimer geometry is not clear. The calculated results in Figures 7 and 8 assume that the interaction between monomers is purely the coupling between the two electronic transitions. Binding to the surface and dimerization are assumed not to affect the vibrational modes or the change in monomer geometry upon electronic excitation. These calculations do a reasonable job of reproducing the shape of the dimer absorption spectrum and the general pattern of the resonance Raman intensities (e.g., the relative enhancement of the lower-frequency lines in the dimer, particularly as the excitation wavelength is tuned toward the red), but there are some significant discrepancies in the relative intensities of different modes. This suggests that either binding to SiO2 and/or dimerization have some specific effects on the molecular vibrations as well. The obvious control experiment would be to obtain spectra of cresyl violet monomers on SiO2, but extracting this spectrum from those of the overlapping unbound and dimerized species does not appear feasible. Similarly, while H-dimers and/or higher aggregates do form in aqueous solution as shown in Figure 1, separation of the dimer spectrum from that of monomers and/or higher aggregates would be quite difficult. We have assumed that the monomers making up the dimer have exactly antiparallel transition dipoles such that only the higher energy of the two coupled electronic transitions has any oscillator strength. If the angle between the transition dipoles is less than 180°, the lowerenergy transition also carries some oscillator strength which appears as additional weak absorbance to the red of the main band. As the two transitions are perpendicularly polarized, polarization measurements are the most straightforward way to distinguish between the weak residual vibronic structure on the main transition and absorption to the weakly allowed second state. In particular, the resonance Raman excitation profiles are expected to show strong dispersion in the region where both states absorb.26,27 Unfortunately we were not able to obtain resonance Raman spectra when exciting to the red of 500 nm because of interfering fluorescence. Fluorescence from the dimer would imply some allowedness to the lowerenergy transition, but the small residual fraction of highly fluorescent monomer may account for the observed emission. The depolarization ratios measured for the dimer at both 476.5 and 496.5 nm excitation are 0.33 ( 0.02 for all of the major lines, but the presence of a weak perpendicularly polarized transition at longer wavelength would not affect these values significantly. Therefore we cannot draw any strong conclusions about the dimer
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geometry within the range of possibilities that place most of the oscillator strength into the blue-shifted transition. A considerable increase in both homogeneous and inhomogeneous electronic spectral breadths between monomer and dimer is required to fit the spectra. To reproduce the absolute cross sections for the dimer, the homogeneous line width has to be almost 50% larger in the dimer. The “homogeneous line width” for a system such as this can incorporate a multitude of sins. Usually it is dominated by solvent reorganization, which should be less important for the surface-bound species; however, the surface-bound H-dimer could undergo much faster electronic population relaxation or pure dephasing than the monomer in water, most obviously by radiationless decay from the allowed state to the lower-energy forbidden state of the dimer.34,35 We have used the simplest possible model for the inhomogeneous breadth, which assumes that there exists a distribution of electronic zero-zero energies within the ensemble of dimers but that both components of any given dimer have the same transition frequency. This is probably unrealistic in a number of ways. There is no reason the two monomers making up each dimer should have exactly degenerate transition frequencies, and also no reason the distributed quantity should be solely the electronic origin frequency; the intermolecular distance and angle are undoubtedly also inhomogeneously distributed in the real system. Consideration of these effects would result in a large increase in computational effort, and in the absence of any model for the nature of these distributions it seems unproductive to try to include them. Finally, while the dominant spectral changes in cresyl violet on SiO2 appear to result from dimerization, some of the spectral broadening may result from formation of higher aggregates on the surface. In our simple model, a Lorentzian form for the distribution of zero-zero frequencies gives a much better fit to the absorption spectrum than does the standard Gaussian, but this result should not be interpreted too literally in view of the number of possible physical effects the inhomogeneous broadening function may have to represent. Conclusions The absorption spectra and resonance Raman intensities of cresyl violet bound to colloidal SiO2 are consistent with formation of H-dimers. Binding to the surface and dimerization have some vibrational or vibronic effects beyond those expected for purely electronic transitiondipole coupling. A more detailed interpretation of these effects would require solid vibrational assignments for the observed modes. It will be interesting to compare these results with data on molecules that dimerize in homogeneous solution,36 where the assumptions underlying simple exciton coupling theory are more likely to be valid. Acknowledgment. This work was supported by National Science Foundation Grant No. CHE-0109920 and by Grant No. N00014-02-1-0584 from the Office of Naval Research. LA034638A (34) Anfinrud, P.; Crackel, R. L.; Struve, W. S. J. Phys. Chem. 1984, 88, 5873-5882. (35) Steinhurst, D. A.; Baronavski, A. P.; Owrutsky, J. C. J. Phys. Chem. B 2002, 106, 3160-3165. (36) Wu¨rthner, F.; Yao, S.; Debaerdemaeker, T.; Wortmann, R. J. Am. Chem. Soc. 2002, 124, 9431-9447.
