Single Molecule SERS Spectral Blinking and Vibronic Coupling - The

Mar 1, 2011 - Department of Chemistry, The City College of New York, New York, New York ... We examine the time evolution of spectral blinking behavio...
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Single Molecule SERS Spectral Blinking and Vibronic Coupling John R. Lombardi* and Ronald L. Birke Department of Chemistry, The City College of New York, New York, New York 10031, United States

Gilad Haran Department of Chemical Physics, Weizmann Institute of Science, 76100, Rehovot, Isreal ABSTRACT: We examine the time evolution of spectral blinking behavior of single molecule surface-enhanced Raman spectra (SERS). For the molecules examined, it is found that the on-off behavior of the spectral lines is not always in tandem and that the spectral lines can be divided into subsets with separate tandem blinking behavior. One group, despite fluctuating somewhat, is relatively steady in intensity, until they either abruptly or sometimes more gradually disappear. A second group, blinks more sharply, on briefly or off for a longer period. They appear more erratically and often are more intense while on. The former set of lines are found to obtain most of their intensity through Franck-Condon terms in the polarizability expression, while lines for which the Raman intensity is correlated with vibronic coupling tend to blink with sharper on-off differences. We interpret these observations in terms of the theory of vibronic coupling as applied to SERS.

“So JJ puts in a word doing the toff about one story was good until you heard another and blinking facts and the Nelson policy putting your blind eye to the telescope and drawing up a bill of attainder to impeach a nation and Bloom trying to back him up in moderation and botheration and their colonies and their civilization.” James Joyce, Ulysses, The Modern Library, Random House, Inc., 1934, p 319

’ INTRODUCTION The observation of surface-enhanced Raman spectra (SERS) from single molecules1-3 has reinvigorated the field of surfaceenhanced Raman studies and led to considerable hope that SERS can in fact be useful for ultrasensitive molecular detection devices. These were observed with single molecules adsorbed on one or between two or more Ag nanoparticles.4-7 One of the intriguing features of such single molecule studies is the observation of blinking behavior of the Raman signal. This is characterized by sudden, sharp changes in the intensity of Raman bands, sometimes with total disappearance of the signal, only to return later at the same spot. In many of these spectra it is observed that not all of the spectral lines blink in tandem but have separate blinking patterns. We have investigated the nature of the blinking behavior by examining time series in detail and observed that by and large these separate sets of lines appear to divide into two distinct blinking patterns. One group of lines, although they fluctuate somewhat, is relatively steady in intensity, until they either abruptly or sometimes more gradually disappear. A second group, on the other hand, by comparison blinks more erratically, on more briefly, and off for a longer period, and often more intensely while on. Analysis of the spectral assignment of these lines indicates that the former set is usually totally symmetric, r 2011 American Chemical Society

while the latter tend to be nontotally symmetric. Where the molecule does not have sufficient symmetry to have nontotally symmetric lines (as in the case of rhodamine 6G, below), the second set may be characterized by strong vibronic coupling. It is well-known that the nontotally symmetric lines in Raman spectroscopy draw their intensity through a vibronic coupling mechanism8,9 in which intensity is borrowed from an allowed nearby transition. On the other hand, the totally symmetric lines obtain most of their intensity through a Franck-Condon term (sometimes called the A term) which is not vibronic in origin, although it is possible to have additional contributions to totally symmetric lines from vibronic coupling as well. These latter contributions are usually assumed to be considerably smaller, but to be complete they should be included. In the next section, we examine the blinking behavior of several individual molecules, chosen only because clear time-line spectra (or other data) were available for examination of the details of their blinking behavior (i.e., not because they fit our thesis). In the following section, we show how the well-known equations for SERS intensities bear on these observations, in that, as suggested, the vibronically active (usually nontotally symmetric) bands show sharper blinking behavior than those which are totally symmetric, and then suggest a mechanism which may explain these results.

’ EXAMINATION OF BLINKING BEHAVIOR OF INDIVIDUAL MOLECULES In this section we examine in detail the spectral blinking of several molecules. Since the spectra were taken under varying Received: November 29, 2010 Revised: January 24, 2011 Published: March 01, 2011 4540

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lines have considerably different blinking behavior than the other lines in the SM SERS spectra.

Figure 1. Entire time-dependent spectral trajectory of a single R6G molecule, illuminated with a laser power of 10 W/cm2. Each row contains one color-coded spectrum, and the time advances from top to bottom. The strong fluctuations of the bands at 614 and 774 cm-1 relative to the other lines at higher wavenumber are particularly conspicuous in this figure. See Weiss and Haran, ref 10. (Reproduced with permission from ref 10.)

conditions and with different instrumentation, the results are of variable quality and not always strictly comparable from one molecule to another. However, we believe they all contribute to a pattern discussed in the previous section.

’ RHODAMINE 6G (R6G) Weiss and Haran10 have studied the blinking behavior of R6G. In Figure 1 (their Figure 3), they show the time-scanned spectrum of a single molecule of R6G in 1 s steps. The total intensity has been normalized in such a way that only relative fluctuations are displayed in the figure. There are clear differences between the on-off times of the 614 and 774 cm-1 lines when compared with the lines of the rest of the spectrum. The two lines, which blink in tandem, have only rare but intense bright spots, while the other lines are generally weaker but steadier in intensity with time. Weiss and Haran quantify this effect in Figure 4 of their paper by showing the ratio of intensities of 614 to 774 cm-1, and in comparison the ratio of intensities of 614 to 1650 cm-1 with time. The former is almost constant over time, while the latter fluctuates considerably. The 614 and 774 cm-1 bands are exactly those shown by Hildebrand and Stockburger11 to be associated with vibronic coupling. Using TD-DFT calculations, Jensen and Schatz12 have also suggested that the bands at 614 and 775 cm-1 are due to vibronic coupling. Guthmuller and Champagne13 confirmed that these two lines are more strongly enhanced when the excitation wavelength is near 530 nm which is the maximum of the absorption spectrum of R6G. In a 2D correlation study of single molecule R6G, Moore et al.14 have shown that the 623 cm-1 (presumably the same as the 614 line) is much less correlated with the intensities of the lines at higher wavenumbers. Despite the fact that R6G has no symmetry, we may ascertain from these studies that the vibronically coupled

’ 4-MERCAPTOPYRIDINE (4-MPY) Wang and Rothberg15 have reported the time-resolved spectra of two separate single molecules of 4-mercaptopyridine (4-MPy) on Ag. In the first molecule (their Figure 2A), the initial spectrum is that of deprotonated 4-MPy adsorbed perpendicular to the surface through the -S, forming a strong Ag-S bond. After 58 s, there appears an abrupt shift, indicating a protonated form, and then after 108 s, there is an abrupt reversion to the deprotonated form. This is evidenced by the shift of the υ8b (b2) line from the position characteristic of the deprotonated form (1580 cm-1) to the position characteristic of the protonated form (1604 cm-1). Additionally the b2 line at 1395 cm-1 and lines of b1 symmetry (760 and 920 cm-1) appear during the “protonated” interval, as well as an a1 line at 1206 cm-1 (υ9a). Note that the a1 line at 1099 cm-1 (υ12) remains throughout the observation time. A possible alternative explanation uses the assignment of Hu et al.16 who suggest that the line at 1604 cm-1 is a1. Here all lines are assumed to be of a deprotonated molecule. With this assignment, the nontotally symmetric b1 and b2 lines blink while the a1 modes do so only to a small extent. In either case, nontotally symmetric vibronically coupled bands are seen to blink more sharply and erratically than the more steady intensity of totally symmetric lines. The charge-transfer (and therefore vibronically coupled) nature of these lines has been clearly demonstrated by Shegai et al.17 Charge transfer contributes over 3 orders of magnitude to the overall enhancement factor. The second molecule observed by Wang and Rothberg (Figure 2B) appears to be one of the rare molecules lying flat on the surface. This does not contribute much to the overall spectrum, and the spectrum does not appear to vary much over the time observed, so little information can be gained for the present analysis. ’ P-AMINOTHIOPHENOL (PATP)/P,P0 -DIMERCAPTOAZOBENZENE (DMAB) Fromm et al.18 have observed single molecule spectra (see their Figure 2) for the molecule p-aminothiophenol (PATP). The SERS spectrum of PATP has seven prominent bands. Two at 1077 and 1590 cm-1 show relatively steady intensity, while five others at 1160, 1195, 1325, 1380, and 1450 cm-1 fluctuate in tandem with sharp and frequent intensity changes. At the time the first two lines were assigned to a1 normal modes, while five others were assigned to normal modes of b2 symmetry. However, there have recently been a series of studies which indicate that PATP undergoes a photoinduced dimerization to p,p0 -dimercaptoazobenzene (DMAB) in the presence of Ag19-22 and that the lines previously assigned as b2 in PATP are totally symmetric (ag) in DMAB. While this evidence is compelling, it is still the subject of a lively debate. It is not our intention to wade into this controversy at this point, except to note that regardless of their source, the sharply fluctuating lines show quite different behavior than the other two. This was also observed by Canpean, Iosin, and Astilean22 on Au in experiments which show that the autocorrelation functions of the two sets of lines are quite different. They interpreted this as having both PATP and DMAP present, although we present here a different interpretation of these results. 4541

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The Journal of Physical Chemistry C The same distinction among spectral lines was observed in excitation energy dependence of the electrochemical experiments by Osawa et al.23 Those same lines which fluctuate strongly in the single molecule experiments have a strong and almost linear excitation wavelength dependence of the electrochemical potential maximum. This behavior can only be attributed to charge-transfer transitions,24 even if the normal modes involved are totally symmetric (see eq 2a below). It has been shown that charge-transfer transitions in SERS derive their intensity through Herzberg-Teller vibronic coupling9 (see eq A1 of the Appendix). However, the same two lines which do not fluctuate as much in the single-molecule experiments, do not have a strong potential dependence in Osawa’s experiments, indicating a lack of charge-transfer contributions and are therefore not likely to be vibronically coupled.

’ PERYLENE Luo et al.25 have studied the blinking behavior of single molecules of perylene. They have found that the most enhanced line of the spectrum is at 1400 cm-1, which is assigned to the b1u nontotally symmetric mode in the gas phase. In Figure 2, they show clearly that the intensity of this line relative to the totally symmetric line at 1371 cm-1 fluctuates considerably as a function of time, indicating quite distinct blinking behavior between the two lines. Since it appears that the spectra were normalized to the intensity of the 1400 cm-1, it is impossible to determine which line blinks more erratically. However, the clear difference in behavior in the totally symmetric and the nontotally symmetric line is evident. ’ FULLERENE Recently Luo et al.26 have observed the single molecule spectrum of fullerene (C60) at 785 nm at concentrations as low as 10-15 M. Additional enhancement is provided by proximity to an absorption of the fullerene molecule at 1.74 eV.27 This highly symmetric molecule shows only small shifts in the vibrational frequencies, but considerable differences in relative intensities in comparison to the spectrum at 1064 nm. In the latter SERS spectrum, the dominant mode is the Ag pentagonal pinching mode at 1467 cm-1, while the 785 nm spectrum shows the Hg mode at 269 cm-1 to dominate the spectrum. This behavior is characteristic of the involvement of nearby charge transfer or molecular resonances in the SERS spectrum and therefore strong vibronic coupling.9 The authors then examine the time-dependent spectra of three hot spots obtained at intervals of 1.5 min, shown in their Figure 4 (a-c). In 4a, the line at 492 cm-1 is assigned to an Ag mode and is relatively steady at all times, while the line at 561 cm-1, assigned to a T1u mode, appears intermittently, most prominently in the last two spectra. ’ CRYSTAL VIOLET (CV) Perhaps the most studied molecule in the single molecule SERS field is crystal violet (CV). It is especially attractive due to the presence of a large π-π* absorption spectrum in the visible region of the spectrum and high symmetry (D3). Numerous experiments have been carried out over the years. Kneipp et al.28 showed that using concentrations of 10-14 M and exciting at 830 nm, detection could be made at the single molecule level. In their Figure 1, a time series of spectra at one second shows clear blinking behavior. The lines at 1584, 1174, and 915 cm-1 show

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considerable time-dependent fluctuations. We have shown that these lines (and numerous other prominent lines) are of e symmetry.29 These assignments are in agreement with earlier depolarization studies.30,31 Haran and co-workers32 observed blinking behavior in the spectrum of CV at 633 nm. They showed that the spectrum lies on top of a continuum, that the region of the spectrum below 1100 cm-1 had much larger fluctuations than that above, and that both the spectral lines and the continuum blinked in tandem. They explained this by suggesting that since the molecule lies flat on the surface, the lower lying lines are more likely to be out-of-plane modes, which are more prone to blinking due to charge-transfer dynamics. They also showed that these fluctuations were dependent neither on laser power nor on solvent viscosity. Relevant to understanding these studies is a resonance Raman study by Jiang, Burstein, and Kobayashi33 in which the excitation profile of the 203 cm-1 line was studied as a function of polarization. They found that two resonances could be identified. One at around 600 nm, polarized parallel to the plane of the molecule (XX, YY), was identified as a π-π* (1E r 1A1) transition, while another polarized perpendicular to the plane was identified as a charge-transfer transition (1A2 r 1A1) to higher wavelength. Thus vibronic coupling to activate the e modes in SERS is achieved through the Herzberg-Teller selection rules as Γ(μmol)  Γ(μCT) = E  A2 = e. Even though the line at 203 cm-1 is identified as a totally symmetric a1 vibration, it is clear that there are both molecular and charge-transfer resonance contributions depending on excitation wavelength. (Haran was not able to see the 203 cm-1 line due to instrumental limitations.) The significance of these studies by Jiang et al. is that for CV even the totally symmetric a1 modes can have chargetransfer character and are therefore strongly vibronically coupled. Therefore our distinction between totally and nontotally symmetric modes is not so sharp for this molecule. Apparently all modes, including totally symmetric ones, can have at least some vibronic coupling. This explains why Kneipp also sees strong blinking behavior in the a1 line at 1620 cm-1.

’ THIACYANINE Kitahama, Tanaka, Itoh, Ishikawa, and Ozaki34 have examined single J-aggregate spectra of thiacyanine molecules on Ag nanoparticles. A time series at intervals of 6 s is shown in their Figure 4a. The lower wavenumber line at about 584 cm-1, which is attributed to an out-of-plane vibration35 blinks on and off much more erratically than the lines at higher wavenumbers (>1100 cm-1) such as the ones at 1570 and 1623 cm-1, which are attributed mostly to in-plane vibrations. Similar results are also obtained in single thiacyanine molecules36 on Ag, where the low lying lines at 623 and 653 cm-1 as well as 898 cm-1 tend to dominate the time-series spectra (see their Figure 1). These low lying bands have been shown37 to arise from the Albrecht B-term8 and therefore are vibronically coupled. ’ ANALYSIS From the above observations it appears that there is a strong correlation between blinking in single molecule SERS and vibronic coupling. Those lines which are strongly coupled vibronically appear to have the brightest most intermittent signals, while those which are governed by Franck-Condon factors have lesser blinking and often fade in and out in a more gradual way. We now turn to a theoretical derivation of SERS intensity 4542

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recently published,9 in which the lowest order nonzero contribution to SERS was derived, using Herzberg-Teller coupling, and including the metal states explicitly. This formula is an extension of the Albrecht8 expression previously derived for normal Raman spectroscopy. The polarizability may be written as a sum of three terms: R ¼ AþBþC

ð1Þ

The A term involves totally symmetric Franck-Condon factors Æi|jæÆj|f æ , where j are exicted state vibrational quantum numbers and i, f are vibrational quantum numbers of the ground electronic state. Due to the sum rule (∑j |jæÆj| = 1) and orthogonaliity (Æi|fæ = δif), far from any resonance, this term is identically zero and all the intensity comes from the B or C terms. However, almost all SERS experiments involve one or more of three resonances, a surface plasmon, a charge transfer, or a molecular resonance, and therefore we expect the A term to account for much of the intensity of totally symmetric lines. B and C involve sums over all the excited molecular and charge-transfer states. B contains molecule-to-metal charge transfer and C contains metal-tomolecule charge-transfer resonances as the lowest lying contributions for most metals (see the Appendix for a brief detailed description of one of the terms in C). We wish to emphasize that there are terms in this sum which do not depend on chargetransfer transitions but instead include references only to molecular transitions. In general, however, we expect the chargetransfer transitions to lie lower than the corresponding molecular transitions. Vibronic coupling can involve both charge transfer as well as molecular contributions. In the following, we will use only C, recognizing that it can easily be replaced by B if needed in the following discussion. The terms in B or C involve products of three possible resonance denominators, the surface plasmon resonance, the charge-transfer resonance, and the molecular resonance. The numerator contains terms which link these resonances, and involve products of two transition moments (usually one for the charge transfer the other for the molecular resonance) and a Herzberg-Teller coupling constant (h). This constant stems from the vibronic coupling terms, which couple the zero-order Born-Oppenheimer states. The requirement that the numerator be nonzero leads to the Herzberg-Teller selection rules,9 which have successfully been used to predict the relative SERS intensities. These considerations lead us to distinguish the intensities of the totally symmetric bands (ITS) from the nontotally symmetric bands (INTS) as follows ITS ¼ ðA þ CTS Þ2 2

INTS ¼ ðCNTS Þ

ð2aÞ ð2bÞ

Normally, totally symmetric lines near resonance are said to stem from the A terms, which are generally assumed to be much more intense that the totally symmetric contributions from C (i.e., CTS), but we include these latter for completeness, and to account for intensities far from resonance. Note here CTS represents all the terms in the sum which follow selection rules for totally symmetric bands, while CNTS includes the appropriate nontotally symmetric terms in the sum. We can now see that since C includes vibronic coupling and A depends only on Franck-Condon factors, then if we associate blinking with vibronic coupling, we have a clear theoretical explanation of the above observation as to the difference in blinking between totally symmetric and nontotally symmetric bands. The A term provides a relatively steady base of intensity, while the C terms

blink. Since the numerators of CNTS and CTS are not the same, there should be no necessary correlation between the TS and NTS blinking. Thus the CTS and the CNTS would be expected to blink at different times. The blinking of NTS lines should be more drastic than that of the TS lines, since there are no FranckCondon contributions to the intensities of these lines. This is as observed. It should also be pointed out that if the signs of the two terms (A and CTS) in (2a) are different, destructive interference may result in net lowering of the intensity of totally symmetric lines. In order to understand this effect in more detail, we must examine the vibronic coupling term, hIF  + * DV   eN  ð3Þ hIF ¼ I  F  DQk  This is the matrix element of the operator which represents the deformation of the electron-nuclear potential energy (VeN) with changes in the kth normal mode Qk. The states F and I are the charge transfer and/or molecular ground states in the zeroorder Born-Oppenheimer limit. Following Niu et al.38 it can be shown that DVeN D Z0 e2 ¼ DQ R, σ DQ jrR - Rσ j

∑

¼

1 Dqσj Z0 e ðrRj - Rσj Þ pffiffiffiffiffiffiffi ∑ ∑ M DQ jr - R j3 R, σ j 2

σ

R

σ

ð4Þ

In this expression, rR and Rσ are the coordinates of the Rth electron and σth nucleus, qj = x,y,z represent the Cartesian coordinates, Mσ is the mass, and Z0 is the charge of nucleus σ. This is the term which must change suddenly and sharply in order to explain its connection to blinking of SM-SERS. Sudden changes in |rR - Rσ|, can result in sudden changes in the spectral intensity of the mode Qk. This is unlikely to be the result of diffusion of the molecule in and out of the hot spot, since this would cause blinking of the entire spectrum simultaneously, which is contrary to observation. It would also be viscosity dependent, which is also not observed32 at least in CV, whereas in R6G it is. Ozaki and co-workers34,36 have examined the statistics of blinking in thiacyanine dyes and found an important component of power law in the probability distribution (t-m). This type of dependence is usually attributed to diffusion effects. However there are several kinds of diffusion which should be considered.39,40 One is due to Brownian diffusion of the molecule away from the nanoparticle. This has been ruled out as shown above. It should, however, be noted that there is sometimes observed a gradual diminishing of the overall signal, and this is likely due to diffusion away from the hot spot. However, this is not responsible for the sharp, recurring blinking of interest here. The second possibility is fluctuations of the surface charges on the nanoparticle resulting in changes in the electronic energy. This is especially important on semiconductor nanoparticles.39 The blinking could, for example, occur from a sudden change in charge, such as a molecular protonation or deprotonation (as implicated in the 4-MPy results above) or the pickup or loss of an electron or adsorbed anion by the Ag nanoparticle from the solution. This could cause the vibronic coupling constant to change due to a sudden change in ∂VeN/∂Q. We might expect such an occurrence to be accompanied by a change in the location or orientation of the molecule with respect to the 4543

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expression, the μ represents transition dipoles between various states of the molecule-metal system. I is the ground state of the system, F is an excited molecule-metal charge-transfer state, and K is an excited molecular state. The term hIF is the HerzbergTeller vibronic coupling constant, and Æi|Qk|fæ is the vibrational matrix element for the normal mode represented by Qk. For a harmonic oscillator in the ground state, i = 0 and f = 1. The terms ε1 and ε2 are the real and imaginary parts of the dielectric constants of the metal, while ε0 is the dielectric constant of the surrounding medium. The laser frequency is given by ω, while ωFK and ωIK are optical transition frequencies. Corresponding damping factors are given by γ. The result is a typical sum over states, which is valid when ω is far from any of the resonances. Near a resonance, however, only a single (or at most a few) term in the expression dominates. The combined expression when the exciting laser is near one or more of the resonances is given by RIFK ðωÞ Figure 2. Schematic representation of two-state model for blinking in single molecule SERS. The molecule hops between two asymmetric minima either thermally or by tunneling. In the bright state there is a large derivative of VeN while for the dark state, this derivative is small.

nanoparticle. Canpean et al.22 (see their Figure 5) examined the spatial distribution of the 1081 and 1584 cm-1 lines (not vibronically coupled) of PATP/DMAB compared with the vibroncally coupled 1147 and 1440 cm-1 lines in a hot spot between Au nanoparticles and found the distributions of each pair to be quite different, with a rather asymmetric geometry. This rather asymmetric spectral geometry suggests the possibility of two (or more) spatially distinct types of hot spots within the domain of the nanoparticles. For a particular vibronically coupled normal mode Q, one of these types will be bright (i.e., with a large value of ∂VeN/∂Q) and the other dark (with a small value of ∂VeN/∂Q). The modes which are not vibronically coupled, will not be sensitive to ∂VeN/∂Q and presumably remain relatively bright in both spots. This is consistent with a suggestion by Haran of a two state geometry for the blinking in crystal violet32 or Ozaki34,36 for thiacyanine. We then might infer that a molecule trapped in a hot spot between two or more nanoparticles has access to two or more states, represented by corresponding spatial potential minima. This could come about by several possible mechanisms: the molecule-metal system suddenly picks up or loses an electron or proton from the surroundings or a change in orientation with respect to the nanoparticle. The particle hops between these states, assisted perhaps thermally or by tunneling, or even momentum transfer from an incoming photon,41 and in each state feels a very different electronnuclear potential field. This results in a sudden change of the vibronic coupling constant (due to changes in ∂VeN/∂Q), leading to the observed sharp blinking of the NTS modes. This is illustrated by the diagram in Figure 2. One possible experimental test of this is whether there is a correlation between the observed spectra and the location of the blinking within the hot spot, similar to the experiments of Canpean et al.22 mentioned above.

’ APPENDIX By deriving an expression for the polarizability (R) of a molecule-metal system which accounts for Herzberg-Teller coupling, we have shown9 that in SERS there are three possible sources of resonantly enhanced surface Raman spectra. In the

¼

μKI μFK hIF ÆijQk jf æ ððε1 ðωÞ þ 2ε0 Þ2 þ ε2 2 ÞðωFK 2 - ω2 þ γFK 2 ÞðωIK 2 - ω2 þ γIK 2 Þ

ðA1Þ The SERS enhancement factor is proportional to |RIFK(ω)|2. The denominator involves the product of three terms, each of which presents a resonance contribution to SERS. The first (ε1(ω) þ 2ε0)2 þ ε22 is due to the plasmon resonance at ε1(ω) = -2ε0. The second resonance, which may be potential (Fermi energy) dependent and represents charge transfer resonance (ωFK2 - ω2) þ γFK2 occurs at ω = ωFK, and the third (ωIK2 - ω2) þ γIK2 represents the molecular resonance at ω = ωIK. Note the above expression is one of the terms in the sum for either B or C in the Albrecht expression R = A þ B þ C and is vibronically coupled through hIF. The Herzberg-Teller selection rules come from the requirement that the numerator be nonzero. Qk may be either totally or nontotally symmetric. The A term involves only Franck-Condon factors of the form Æi|jæÆj|fæ and does not have hIF in the numerator. Thus A contributes only to totally symmetric vibrations, while as noted, the term (A1) can contribute to both totally and nontotally symmetric vibrations depending on the Herzberg-Teller selection rules.

’ ACKNOWLEDGMENT This project was supported by Award No. 2006-DN-BX-K034 awarded by the National Institute of Justice, Office of Justice Programs, United States Department of Justice. The opinions, findings, and conclusions or recommendations expressed in this publication/program/exhibition are those of the authors and do not necessarily reflect those of the Department of Justice. This material is based upon work supported by the National Science Foundation under CHE-1041832. We are also indebted to the Israel Science Foundation Grant No. 450/10 for support. Support was also received from PSC-CUNY awards of the City University of New York ’ REFERENCES (1) Nie, S.; Emory, S. R. Science 1997, 275, 1102. (2) Kneipp, K.; Wang, Y.; Kneipp, H.; Perelman, L.; Itzkan, I.; Dasari, R. R.; Feld, M. S. Phys. Rev. Lett. 1997, 78, 1667. (3) Xu, H.; Bjerneld, E.; K€all, M.; B€ orjesson, L. Phys. Rev. Lett. 1999, 83, 4357. 4544

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