Vivronic spectroscopy of single molecules: Exploring electronic-vibrational frequency correlations within an inhomogeneous distribution

JOURNAL OF

LUMINESCENCE ELSEVIER

Journal of Luminescence 58(1994)161 167

Invited paper

Vibronic spectroscopy of single molecules: exploring electronicvibrational frequency correlations within an inhomogeneous distribution Anne B. Myers*, Paul Tchénio’, W.E. Moerner IBM Alniaden Research Center, 650 Harry Road, San Jose, CA 95120-6099, USA

Abstract

Vibrationally resolved dispersed fluorescence spectra have been obtained from single molecules of terrylene in polyethylene at 1.5 K using excitation wavelengths from 577 to 566 nm, spanning both sides of the inhomogeneously broadened electronic origin. The spectra of different molecules exhibit significantly different frequency and intensity patterns. There is a weak overall correlation between ground state vibrational frequencies and wavelength of the electronic origin, with the redder-absorbing molecules tending to have higher vibrational frequencies. The red-shifted absorbers may reside in smaller cavities in the matrix, thus experiencing both stronger dispersive interactions and more severe atom atom repulsions.

1. Introduction Electronic and vibrational spectra of molecules in condensed phases are usually broadened considerably relative to the corresponding gas phase spectra. In most cases this broadening greatly exceeds the lifetime-limited width, and is therefore attributed to variations in the energies of the relevant molecular states caused by interactions with the environment. This source of broadening may be denoted “pure dephasing”, “spectral diffusion”, or “inhomogeneous broadening” depending on whether the fluctuations in a single molecule’s envi-

ronment, and thereby its state energies, are faster than, comparable to, or slower than the time scale of the measurement. In solids at low temperatures many of the relevant fluctuations can be quite slow, and frequency-selective techniques such as spectral hole burning and fluorescence line narrowing allow spectroscopy to be performed with a frequency resolution considerably better than the full inhomogeneous bandwidth. These methods work by selecting a subset of molecules “labeled” by their spectral position within the inhomogeneous distribution. The logical extension of such procedures is the selection of a single molecule out of the en-

Corresponding author. Permanent address Department of

semble, and this has been shown to be quite feasible for appropriately chosen physical systems under

Chemistry, University of Rochester, Rochester, NY 146270216, USA. Permanent address: Laboratoire A. Cotton, CNRS II Universite Paris XI, Bat. 405, 91405 Orsay, Cedex, France.

the right experimental conditions [1]. Several groups have now studied a variety of spectroscopic and dynamic processes at the single molecule level

*

0022-2313/94/$07.00 © 1994 Elsevier Science By. All rights reserved 55D10022-2313(93)E0177-Y

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Journal of Luminescence 58 (1994) 161 167

including saturation and power broadening, photophysical hole burning, spectral diffusion, Stark effects, fluorescence lifetimes, photon bunching and antibunching, and magnetic resonance. To date, nearly all single-molecule spectroscopy has utilized “total” (long-wavelength) fluorescence to detect optical absorption, and only the electronic origin features have been studied due to the greatly increased line widths of higher vibronic transitions. Recently, however, we presented the first vibrationally resolved dispersed fluorescence spectra of single molecules [2,3]. These vibrational (properly vibronic) spectra are much richer than the electronic zero-phonon excitation spectra and are potentially more sensitive to local features of the chromophore-matrix interactions. Moreover, since the frequency of the electronic origin transition is still utilized to achieve selection of a single molecule, correlations between vibronic spectra (ground state vibrational frequencies and fluorescence line intensities) and position within the electronic inhomogeneous distribution may be probed. The presence or absence of such correlations, and their physical significance, have long been subjects of experimental and theoretical investigation. All previous experimental studies, however, suffered from the limitation that even with single or multiple site selection techniques, ensembles of molecules were always observed. Many of the ambiguities inherent in ensemble averaging can now be eliminated by examining a large number of molecules, one at a time. Our first effort at obtaining single-molecule vibrational spectra was a very preliminary study of the “classic” mixed crystal system, pentacene in p-terphenyl [2]. After establishing the feasibility of similar experiments in the polycyclic aromatic hydrocarbon terrylene in a polyethylene host, we have concentrated on this system, which has already been shown through fluorescence excitation [4] and photon correlation techniques [5] to exhibit a rich array of dynamic behaviors. A previous publication focused on analysis of the vibrational spectra and assignment of the two distinct types of frequency and intensity patterns observed to terrylene molecules in two distinct polymer environments [3]. In this paper, we present additional single-molecule data and address the question of

correlations between the vibrationally resolved emission spectra and the position of the electronic origin within the inhomogeneously broadened absorption band. The weak correlations observed are then discussed in terms of the nature of the interactions that broaden the vibrational and electronic spectra in this system.

2. Experimental The experimental setup is described in detail elsewhere [3]. Samples of 10 6 or 10 mass fraction terrylene in polyethylene were attached to the tip of a single-mode polarization-preserving optical fiber and maintained in a helium cryostat at a ternperature of 1.5 K. The output of a single-frequency tunable dye laser (bandwidth < 3 MHz) was coupled into the fiber to excite the fluorescence. The emission was collimated with a paraboloidal reflector and bearnsplit outside the cryostat, with half going through a long-pass filter to a photomultiplier as a “total fluorescence” detector, and the other half focused into a 0.75 rn single spectrograph and detected with a Princeton Instruments thinned, back-illuminated, liquid-nitrogen-cooled silicon CCD for the dispersed emission measurements. Single molecules were first selected by scanning the excitation laser until an isolated feature was identifled in the total fluorescence excitation spectrum. The laser frequency was then set to the peak of the excitation spectrum while the dispersed fluorescence was collected on the CCD. In many cases, spectral diffusion caused the molecule to jump out of resonance with the laser for part of the accumulation time [3], but it was still possible to record useful spectra. Our typical spectrograph slit width of 200 ~m provided a spectral resolution of approximately 6 cm 1, and the estimated accuracy 01 our reported vibrational frequencies is + 2 cm ‘~

3. Results

As we describe elsewhere [3], the frequency and intensity patterns in the single-molecule emission spectra of terrylene in polyethylene fall into two discrete classes. “Type 1” spectra are characterized

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Journal of Luminescence 58 (1994) 161 167

by a strong low-frequency line near 243 cm and a doublet near 1272: 1283 cm 1, while “type 2” spectra have their strong low-frequency line near 215 cm and show almost no intensity near 1283 cm j. The two types of spectra have been tentatively attributed to terrylene molecules located in the crystalline and amorphous regions, respectively, of the polyethylene matrix. We have obtained emission spectra in the low-frequency region (150—550 cm ‘)of 25 type 1 and six type 2 single molecules having electronic origins ranging from 577.19 to 566.46 nm. Spectra in the fingerprint region (1200—1600 cm i) have been measured for I S type 1 and three type 2 molecules at excitation wavelengths from 577.19 to 567.12 nm. Figs. I and 2 summarize the spectra of the type 1 molecules in both frequency regions as a function of excitation wavelength. Fig. 3 presents a rough excitation profile of the 243 cm ‘ mode (the strongest line in the emission spectrum) in the bulk sample. It shows the depend-

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Fig. 3. Excitation profile ofthe 243 cm ‘mode of a bulk sample of terrylene (structure shown) in polyethylene. The maximum number of counts above baseline in the peak channel of the 243cm emission line, divided by the incident laser power in nW, is plotted as a function of laser excitation wavelength. The

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Fig. 1. Low-frequency region of the dispersed fluorescence spectra of type 1[3] single molecules of terrylene in polyethylene, displaced along the vertical axis as a function of laser excitation (electronic origin) wavelength The x-axis is the shift ofthe emission frequency from that ofthe laser. Different spectra represent data accumulation times ranging from 120 to 600 s, and have been scaled to the same baseline-to-peak amplitude. Where needed, a nonresonant background spectrum has been subtracted as described in Ref. [3].

energy level diagrams denote the physical processes giving rise to the detected signals in the indicated spectral regions, as described in the text. The vertical lines along the x-axis indicate the laser wavelengths used to obtain single-molecule spectra.

ence on excitation frequency of the emission that is shifted to longer wavelength by one quantum of the 243 cm mode. By selecting a feature in the resolved emission spectrum known to arise

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Journal of Luminescence 58 (1994) 161 167

from terrylene, we exclude contributions to the excitation spectrum from stray laser light, Raman scattering from the matrix, or emission from any impurities that might be present. For this experiment the laser frequency was not locked, but was allowed to scan freely over a range of 15 GHz, about 100 times the low-intensity line width of a single molecule’s origin transition [4]. The intent here was not to select a single molecule, but rather to obtain the fluorescence intensity averaged over an ensemble of molecules absorbing in a frequency range small compared with the total inhomogeneous width. However, due to the small total number of molecules in the illuminated volume and the narrowness of the laser scanning range, the purely statistical fluctuations in the number of molecules on resonance in different frequency regions are not insignificant and are responsible for much of the “noise” in the excitation profile. The maximum in the excitation profile near 569 nm corresponds to the inhomogeneously broadened electronic origin with its associated phonon side bands, and its shape should be essentially equivalent to the absorption spectrum in the origin region. The maximum near 561 nm corresponds to the origin plus the excited state analog of the 243 cm 1 ground-state vibration, consistent with its separation of 235 250 cm ‘ from the longwavelength maximum. However, the near-equality of the intensities of the two maxima does not imply that the absorption spectrum has this same profile. When exciting into the electronic origin, emission to the vibrationally excited electronic ground state is detected, and the intensity of this process is proportional to <0e10g>12 where 0 and 1 label the quantum level of the 243 cm vibration and g and e label ground and excited electronic states. When exciting into the vibronic side band, the corresponding red-shifted emission arises from vibrational relaxation to the electronic zero-point level followed by emission to the ground state zeropoint level, the intensity of which depends on ~ As long as the ground- and excited-state vibrational frequencies are similar, these two products of vibrational overlaps will be nearly equal, resulting in the two peaks of nearly equal amplitude in the excitation profile. The am-

plitudes of these two features in absorption, on the other hand, are proportional to I <0~ 2 and <1 ~l°g>12 respectively, which are not expected to be equal. The ensemble-averaged ground and excited state frequencies for the strong low-wave number mode are in fact virtually identical, as evidenced by the observation that even at the bluest excitation wavelength used (558.98 mm), the shift from the laser frequency of the strong emission line (which now gives the excited state vibrational frequency) is within 1 cm 1 of the average ground-state frequency. Fig. 3 also indicates the excitation wavelengths at which single-molecule emission spectra were obtamed. Although our samples were not sufficiently dilute to allow single-molecule features to be isolated near the very peak of the electronic origin transition, molecules absorbing both to the red and to the blue of the maximum were observed. Fig. 4 gives a compressed summary of the vibrational frequencies as a function of excitation wavelength for all of the single molecules examined, both type 1 and type 2. The type 2 molecules, shown as filled symbols, exhibit a dramatically lower frequency for the strong low-wave number line (this is the principal criterion that identifies them as type 2) and a somewhat lower frequency for the strong fingerprint mode near 1562 cm The type 2 molecules are few and span a limited range of excitation frequencies, and it does not appear fruitful to seek electronic-vibrational frequency correlations within such a small subset. The type 1 molecules are more numerous and span a wider range of electronic origin frequencies, and they seem to exhibit a weak correlation between vibrational frequencies and position within the electronic inhomogeneous line width. The overall spread in vibrational frequencies among different type 1 molecules is 7 10 cm 1 for all four vibrations examined in detail, and the redder-absorbing molecules tend to have higher frequencies for all four vibrations. The seven type 1 molecules absorbing above 575 nm exhibit average fingerprint frequencies of 1273.0 + 1.6, 1359.7 + 2.7, and 1563.0 + 1.7 cm ‘, respectively, while the eight molecules below 575 nm have corresponding frequencies of 1269.6 + 1.6, 1356.1 ±1.0, and 1559.3 + 1.2 cm In the low-frequency region, the six molecules with electronic origins above ~.

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frequency of 1551 cm ‘for its highest main fingerprint line has its other fingerprint lines at the fairly normal frequencies of 1272 and 1356 cm More dramatic than the modest vibrational frequency differences among molecules are the inten-

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have not been able to identify any clear correlations between the vibronic intensities and the wavelength of the electronic origin. Given the 1.1% natural abundance of ‘3C, more than one-third of the molecules in our sample should be isotopically substituted, and such substitutions are expected to cause modest frequency

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frequencies (1273, 1362, and 1564cm 1, and 1273, 1357, and 1562 cm ~, respectively), and the type 2 molecule at 575.51 nm that has an unusually low

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Journal of Luminescence 58 (1994) 161 167

shifts (up to 10 cm 1 or so) and intensity redistributions in the fingerprint region [2,3]. However, the calculated mono-’3C shifts in the strong low-

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568 570 572 574 576 Excitation wavelength (nm) Fig. 4. Correlation between laser excitation wavelength and frequency of four vibrational modes for all of the single molecules studied. Open and filled symbols denote type 1 and type 2 molecules, respectively (see the text and Ref. [3]).

575 nm have an average frequency of 245.2 + 3.3 cm 1, while the nineteen molecules below 575 nm have an average frequency of 242.6 ±1.3 cm The correlations among the frequencies of different modes within the same molecule are considerably stronger. For example, the four molecules that show the highest frequencies for the mode near 1562 cm 1(1564 1565 cm 1) all have fairly high frequencies for the other two fingerprint modes examined (1273 1275 and 1359 1364cm 1), while the four molecules having the lowest frequency for this line (1558 1559 cm 1) have their other fingerprint modes at 1267 1270 and 1355 1356 cm On the other hand, the two reddest-absorbing molecules, which have their strong low-wave number line at anomalously high frequencies of 249 and 250 cm 1, do not exhibit extremely high fingerprint ~.

wave number line do not exceed 1 cm 1, ~ the differences among molecules in this frequency region must be due to other factors. Also, the expected shifts of < 2 cm 1 in the electronic origin frequency due to mono-’3C substitution [2] are a small fraction of the full inhomogeneous line width so while isotopic substitutions may account for some of the frequency and intensity variations in the fingerprint region, they are unlikely to contribute to the correlations between vibrational frequencies and electronic origin wavelength. .

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4. Discussion Theories of environmental perturbations of electronic and vibrational frequencies typically partition the solvent solute interaction into a repulsive part arising from the hard-sphere contacts between neighboring atoms and an attractive part due to longer-range electrostatic interactions [6,7]. For nonpolar solutes in nonpolar or weakly polar environments, the attractive part is usually dominated by the dispersion (induced dipole-induced dipole) interactions. The observed shift of a spectroscopic transition depends on the difference between the solvent solute interactions experienced by the solute

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Journalof Luminescence 58 (1994) 161 167

in its initial and final states. Strong, delocalized electronic transitions of conjugated hydrocarbons such as terrylene typically exhibit red shifts with increasing medium refractive index, indicating a dominance of the attractive dispersion interactions which stabilize the more polarizable excited state more than the ground electronic state. Shifts of purely vibrational transitions are determined by the same balance between attractive and repulsive forces, but the shifts are typically far smaller and somewhat more difficult to predict. Vibrational excitation usually increases the molecular polarizability and contributes to a vibrational red-shift, but the increased amplitude of vibrational motion in the excited state also increases the repulsive interactions and contributes to a shift of the vibration to higher energy. Increasing the pressure on a liquid, for example, increases the magnitude of both the repulsive interactions (by raising the density) and the attractive ones (by increasing the refractive index), and the delicacy of the balance between the two forces is demonstrated by the observation that many vibrational frequencies first decrease and then increase with increasing pressure, as first the attractive and later the repulsive interactions dommate [6]. A similar effect, interpreted somewhat differently, has been observed for electronic transitions in glassy media [7]. The electronic origin transition of terrylene in polyethylene at 1.5 K appears, from the excitation profiles of Fig. 3, to be inhomogeneously broadened with a full width at half maximum of about 125 cm j. This presumably arises from a distribution in the magnitude of (primarily) the dispersive solute solvent interaction for terrylene molecules in different sites in the polymer matrix. For example, molecules located in sites of higher local density or smaller free volume should feel a stronger dispersive interaction with the medium and undergo a larger red-shift of their electronic transitions. This is the mechanism postulated by Altmann et al. to explain their hole burning/Stark effect data on centrosymmetric dye molecules in polymeric matrices [8]. They found that the matrix-induced dipole moment increased on tuning the hole-burning wavelength from blue to red, and suggested that the redder-absorbing molecules reside in smaller solvent cages and thus feel stronger

matrix fields. If this is indeed the dominant mechanism giving rise to the inhomogeneous width in terrylene/polyethylene, the higher ground-state vibrational frequencies for the redder absorbing molecu les imply that the repulsive interactions are dominating the vibrational frequency shifts even though the dispersive interactions dominate the electronic shifts (i.e., the electronic and vibrational inhomogeneous distributions are partially anticorrelated). Normal mode calculations on terrylene predict that the 243 cm 1 mode (an overall long-axis ring expansion) and the 1562 cm mode (mostly C = C stretching with large contributions from the periphery of the ring) should be associated with relatively large volume changes and might be expected to feel strong repulsive interactions in a small solvent cage [3]. The 1272 and 1358 cm ‘ vibrations, on the other hand, are more localized CH rocking modes, and it is less clear that they should be sensitive to the local density of the environment. A more definitive interpretation of the single-molecule vibrational frequency and vibronic intensity variations among molecules must await further experimental and/or theoretical studies of terrylene’s vibrations as well as data addressing the sensitivity of the spectra to other, better defined experimental perturbations. While it is generally believed that nearly all spectroscopic transitions of molecules in low-temperature solids are inhomogeneously broadened, the correlations between the distributions affecting different transitions remain poorly understood. Inhomogeneous broadening has been treated theoretically by a variety of models that range from total correlation to zero correlation (see Ref. [9] and references therein). Experiments generally suggest that for most pairs of transitions the degree of correlation is greater than zero but significantly less than total. However, experiments that address correlations between electronic and ground-state vibrational inhomogeneous distributions, even for bulk samples, are few. It should be noted that probing such correlations through the most direct technique of line-narrowed dispersed fluorescence would be difficult in mixed crystal systems such as pentacene in p-terphenyl because the narrowness of the inhomogeneous distributions would necessitate using extremely narrow spectrograph slit widths to obtain sufficient spectral resolution.

A.B. Myers ci a!. / Journal of Luminescence 58 (1994) 161 167

Throughout this work we have assumed that the shifts between the excitation and emission frequencies yield the ground-state vibrational frequencies; that is, no energy relaxation occurs in the S~excited state prior to emission. Since the transitions we excite are extremely strong and have very narrow line widths of about 0.01 cm 1, they are almost certainly true electronic origin (zero-phonon) transitions. The question of whether the spectra shown in Figs. 1 and 2 are properly described as true fluorescence or resonance Raman spectra depends on the time scale on which the laser-driven coherence between the ground state and the zerophonon electronic state persists. This is an interesting and nontrivial question for future study, but it does not influence the analyses presented in this paper. To within the frequency resolution of this experiment, it should not matter whether we consider the spectra to arise from resonance Raman or fluorescence processes. The incompleteness of the correlations between electronic and vibrational inhomogeneous distributions implied by these experiments serves to emphasize the utility of single-molecule techniques for probing intermolecular interactions in solids. Total correlation would imply that molecules selected by their specific position within the electronic inhomogeneous distribution are in identical sites, and no further selection is required to remove the inhomogeneity. However, both this and most prior studies indicate that such is not the case, and that selection by electronic transition frequency leaves behind much “accidental” degeneracy which -

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must be lifted by further selection techniques. That is, “transition energy selection” is not equivalent to “site selection” [10]. The best way to assure selection of a unique site is to probe a single molecule. Interpretation of the resulting single-molecule spectra is the remaining challenge.

Acknowlegements We thank Dr. John Fetzer for the generous gift of a sample of terrylene, IBM for a Flory Sabbatical Award to A.B.M., and CNRS for support for P.T.

References [1] WE. Moerner and T. Basché, Angew. Chem. 32 (1993) 457.

mt. Ed. Eng.

[2] P. Tchénio, A.B. Myers and W.E. Moerner, J. Phys. Chem. [3] P. Tchénio, A.B. Myers and W.E. Moerner, Chem. Phys. Lett. 213 (1993) 325. [4] P. Tchénio, A.B. Myers and W.E. Moerner, J. Lumin., in press. [5] A. Zumbusch, L. Fleury, R. Brown, J. Bernard and M. Orrit, Phys. Rev. Lett. 70 (1993) 3584. [6] D. Ben-Amotz and D R. Herschbach, J. Phys. Chem 97 (1993) 2295. [7] J. Zollfrank and J. Friedrich, J. Phys. Chem. 96 (1992) 7889. [8] RB. Altmann, I. Renge, L. Kador and D. Haarer, J. Chem. [9] MM. Sevian and J.L. Skinner, Theor Chim. Acta 82(1992) 29. [10] H.J. Griesser and UP. Wild, J. Chem. Phys. 73(1980)4715.