surface-enhanced raman scattering of a single ...the mixture is allowed to sit for ∼3 h and then...

Surface-Enhanced Raman Scattering of a Single Nanodumbbell:Dibenzyldithio-Linked Silver NanospheresM. Banik, A. Nag, P. Z. El-Khoury, A. Rodriguez Perez, N. Guarrotxena, G. C. Bazan, and V. A. Apkarian*

Department of Chemistry and Center for Chemistry at the Space-Time Limit, University of California, Irvine, California 92697,United States

*S Supporting Information

ABSTRACT: We describe combined AFM/Raman measurements on singlenanodumbbells, consisting of silver nanospheres linked with dibenzyl-4,4′-dithiol (DBDT). The measured surface-enhanced Raman scattering (SERS)enhancement factor, EFexp = 3 × 107 at 532 nm, corresponds to the observedsignal strength of a single DBDT molecule, the Raman cross section of whichwas determined to be dσ/dΩ = 6 × 10−28 cm2/sr. We show that the product ofthe local field enhancement, EFP = (Ei/E0)

2(Es/E0)2 = 3 × 106, and the

chemical contribution due to reduced detuning, EFC = (Δ0/Δ)2 = 12, accountfor the observed effect. The chemical contribution is assessed by exploringmodel structures Agn−S−DB−S−Agm (n, m = 0, 3, 7, 20). The π−π*transition at 287 nm, which determines the polarizability of the bare molecule,acquires a DBDT-to-silver charge-transfer character upon binding to silver.The CT transition near 400 nm reduces the detuning but remains nonresonant at 532 nm. We observe a soft polarizationdependence, which suggests optical activity, which in part is ascribed to coupling between plasmons and conjugated electrons ofDBDT. Modest enhancement factors are sufficient to detect single molecules through nonresonant SERS.

■ INTRODUCTIONBy taking advantage of the large plasmonically enhanced localfields at junctions of metallic nanostructures, one can attainRaman scattering with single-molecule sensitivity. Since theearly demonstrations,1−3 there has been significant develop-ment in this field, as highlighted in a recent review.4 Suchdevelopments have been made possible through enhancementof the feeble Raman effect through mechanisms collectivelyidentified as surface-enhanced Raman scattering (SERS). Sinceits discovery,5,6 SERS has developed as a field of wide impactand applications.7,8 Nevertheless, understanding the underlyingcoupled dynamics between molecular excitations and collectiveplasmons remains a challenge. In addition to its inherentinterest, exploration of single molecules [i.e., single-moleculeSERS (SMSERS)] can be expected to lead to a deeperunderstanding of the governing principles in SERS. Multipleapproaches have been pursued to reach and confirm single-molecule sensitivity.1,9−11 The common approach in SMSERSis to first create plasmonic structures and then coax moleculesinto interparticle gaps“hot spots”where the fields arelargest.4,12−15 This strategy generates a distribution of nano-junctions and, associated with them, a heterogeneous fieldterrain over which molecules are sprinkled with uncertainorientation. Given the nonlinearity of the SERS response,spatial and orientational averaging of observables leads touncertainty. We take a different approach. To investigatemolecules at a single well-defined structure, we rely onthiolation chemistry to link two nanospheres with the targetmolecule.16−18 By design, the linker is positioned at the hot

spot with an intersphere gap defined by the length of themolecule. This approach yields the required sensitivity tointerrogate single molecules under ambient conditions, asrecently illustrated using distyrilbenzene-linked silver nano-spheres in aqueous solution.19 In that case, the concept was toequip molecules with antennae to address them individually.Here, through combined atomic force microscopy (AFM) andRaman microspectroscopy, we investigate single dibenzyldithio-linked silver dumbbells that are dry-mounted and isolated on amicroscope slide. The 1.2 nm sulfur-to-sulfur length of the π-conjugated dibenzyl-4,4′-dithiol (DBDT) defines the inter-sphere gap, a consistency check of which is provided throughtransmission electron microscopy (TEM) images. Theimmobilized dumbbells, with defined structural and spatialalignment, allow analysis of the operative photophysics. Themost mundane of the considerations is the magnitude andmechanism of the enhancement that enables observations atthe single-molecule level, to which we limit the first of thisseries of reports.Enhancement factors as large as EF = 1011−1014 have been

reported in SMSERS studies.1,20,21 Such large values can arisefrom multiplicative contributions of physical and chemicalfactors, expressed as EF = EFPEFC, the latter implyingsignificant modification of the electronic structure of the targetmolecule. If indeed this were necessary, then the utility of

Received: February 29, 2012Revised: April 9, 2012Published: April 12, 2012

Article

pubs.acs.org/JPCC

© 2012 American Chemical Society 10415 dx.doi.org/10.1021/jp302013k | J. Phys. Chem. C 2012, 116, 10415−10423

pubs.acs.org/JPCC

SMSERS would be somewhat limited. We demonstrate that thisis not the case. Rather modest enhancement factors, accessiblethrough locally enhanced fields, are sufficient to reach single-molecule sensitivity. This can be shown with some generality.Consider the Raman scattering intensity of a moleculeembedded in a medium, given in terms of its gas-phase,angle-integrated cross section σnm (cm2)22

ω σ=I L I( ) nm0

where I is the scattering rate (s−1) integrated over the Ramanline profile of the transition between vibrational levels m and nof the ground electronic state; I0 is the incident light intensity(photons cm−2 s−1), and L(ω) is the local field correction.L(ω) = 1 in rarified media, whereas in an isotropic dielectricsuch as that of a liquid, the correction is well-approximated bythe Clausius−Mossotti relation

ω =

= + +

L E E E E

n n

( ) ( / ) ( / )

[( 2)/3] [( 2)/3]i 0

2s 0

2

i2 2

s2 2

(2)

where ni and ns are the indices of refraction at the incident andscattered frequencies, respectively. In the standard approx-imation, the SERS intensity is given by

σ σ= =I I I(EF) (EF EF )nm nmSERS 0 P C 0 (3)

where EFP L(ω) is the local field correction, the same as ineq 2 but now arising from the plasmonic nanostructure,23−26

whereas EFC σ′nm/σnm recognizes that the molecular crosssection might be modified upon binding to the SERSsubstrate.27 The incident intensity in eq 3 cannot be arbitrarilyincreased. We observe that, consistent with prior analyses,28

intensities that significantly exceed 1 mW/μm2 (I0 = 2.5 × 1023

photons cm−2 s−1) perturb the nanojunction through light-induced forces. Within this limitation, to observe a singlemolecule at a count rate of 103 s−1 and a detection efficiency of10−2, the requirement is for the product to be EFσnm = 4 ×10−19 cm2. For a nonresonant scatterer such as benzene [σ =4π(dσ/dΩ) = 9 × 10−29 cm2 at 514 nm],29 an enhancementfactor of EF = 4 × 109 is required. With an astute choice ofwavelengths, in principle, such enhancements can be attained athot spots of nanosphere dimers, which have been extensivelyanalyzed previously through numerical22,30−32 and analyti-cal28,33−35 classical electrodynamics and quantum36−38 treat-ments. The Raman cross section of DBDT is 2 orders ofmagnitude larger than that of benzene, and is thereforedetectable with a modest EF of ∼107, as in the closely relateddistyrilbenzene system.19 For a resonant Raman scatterer, suchas the extensively used rhodamine dyes, for which σ = 4 × 10−22

cm2,39 an EF of 103 is sufficient to detect a single molecules.Clearly, resonant Raman (RR) spectroscopy of single moleculesis detectable by modest enhancements and competes withfluorescence. Both processes are determined by spontaneousradiation: RR prior to dephasing and fluorescence afterdephasing. As such, the branching ratio between the RR andfluorescence channels, kr/γ,

40 is determined by the competitionbetween the dephasing rate of the initially prepared state, γ, andthe enhanced rate of spontaneous radiation kr = (Es/E0)

2/τrthe local field effect that can be cast alternatively in terms of themodified vacuum or reradiation.31 Reduction of the nano-second radiation time of a dye molecule by 103 puts it in therange of dephasing times (ps), where RR competes withfluorescence.2 It would therefore be difficult to reconcile muchlarger enhancement factors with RR scatterers. Giant enhance-

ments would be expected only if an otherwise nonresonantresponse were to shift into resonance as a result of molecule−substrate coupling.Our experimental findings are consistent with the above

analysis. We show that a single nonresonant DBDT moleculethat bridges a nanosphere dimer is observable. Because themolecule is chemically attached to silver, we explore thepotential role of chemical contributions through electronicstructure calculations on model systems: Agn−S−DB−S−Agm(n, m = 1, 3, 7, 20).27,41−43 We conclude that the contributionof chemical effects to the overall EF is minor (EFC ≈ 10). Thesurprising finding is a mild polarization dependence of theRaman response of the dumbbell, which we cannot explain byexplicit analysis of linearly polarized local fields of idealizednanospheres. Beyond the failure of such idealization, forexample, due to faceting on the silver nanospheres anddeformation of the spheres at the junction, which could leadto polarization scrambling, we will ascribe this failure to thelimitations of analyses that treat the nanostructure as aneffective medium, ignoring coupling between plasmon andmolecule.

■ EXPERIMENTAL AND COMPUTATIONALMETHODS

Sample Preparation. The synthetic strategy and methodhas been previously reported in some detail.18 Briefly, acolloidal suspension of 35 ± 5 nm citrate-capped silvernanospheres was prepared with a narrow size distribution.The citrate was then exchanged with bis(p-sulfonatophenyl)phenylphosphine (BSPP), which serves as a protective cappingagent. A 1 mM DBDT solution is added to the suspension, andthe mixture is allowed to sit for ∼3 h and then centrifuged. Theresulting solution consisted of ∼50% nanosphere dimers, asevidenced by TEM images (see Figure 1. Inspection of

suspensions stored over extended periods of time (severalmonths) revealed a gradual increase in the monomer fraction.We take the low yield of aggregates as indication that fewDBDT linkers are attached to a given nanosphere. Although avariety of intersphere gap morphologies are observed in TEMimages, ranging from sharp protrusions to elongated inter-sphere planar channels, the intersphere gap of inspected dimersis ∼1 nm, consistent with the length of the linker. Whereaselectron microscopy does not resolve the number or location oflinker molecules, it does establish the success of the synthetic

Figure 1. TEM image of a freshly prepared sample and close-up of adumbbell.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp302013k | J. Phys. Chem. C 2012, 116, 10415−1042310416

strategy to prepare DBDT-linked silver nanospheres (dumb-bells).Combined AFM/Raman Measurements. Joint AFM/

Raman measurements were carried out under ambientconditions, on dry mounted particles prepared by spin coatingor drop casting a ∼5 pM solution on a 150-μm-thickmicroscope slide. A dilute solution of poly(vinyl alcohol)(PVA) was added to the aqueous suspension prior to coating,and the slides were either preheated or heat cycled on a hotplate after preparation. The polymer film provides themechanical stability required for AFM imaging and serves asthe essential heat sink for thermal stability under tightly focusedlaser irradiation. A schematic of the combined scanning probe(NT-MDT, Wilsonville, OR)/micro-Raman instrument isshown in Figure 2. The scanning head was assembled on an

inverted optical microscope frame (IX71, Olympus, CenterValley, PA). The AFM tip was aligned with the laser bymonitoring backscattered light. The sample was scanned forimaging purposes. Either a tuning-fork AFM (TFAFM)instrument or a cantilever was used, with approximately thesame spatial resolution obtained in both cases. The TFAFMtips were prepared by electrochemical etching of a 100-μm-thick tungsten wire, followed by ion-beam milling to producetips with cone radii as small as 20 nm. The excitation sourcewas a continuous-wave, single-mode laser (CrystaLaser, Reno,NV) operating at λ = 532 nm. A 1.25-numerical-aperture (-NA)oil-immersion lens was used to focus the laser on the sampleand to collect the backscattered Raman light through a pair ofnotch filters (1:106 extinction, Semrock, Rochester, NY). Thespatially filtered scattered light was spectrally dispersed in a0.25-m monochromator and recorded on a charge-coupleddevice (CCD) array (V401-BV, Andor, Belfast, Ireland). Theeffective instrument resolution was 10 cm−1.Computational Methods. Calculations were performed

using the methodologies implemented in Gaussian 09.44 Wetruncated the multielectron problem by approximating silvernanoballs with six different models: (i) single silver atoms, (ii)three silver atoms, and (iii) seven silver atoms, each on eitherone or both sides of DBDT. Unconstrained geometryoptimization was performed using the B3LYP45 functional.All reported calculations employed the def2-TZVP basis set46

with matching pseudopotentials for silver (>1000 basisfunctions). The optimized structures were verified to not

have imaginary vibrational frequencies. Vertical transitionenergies calculated for all considered structures were at theB3LYP/def2-TZVP minima. Three additional functionals weretested: (i) the PBE0 functional,47 (ii) the CAM-B3LYPfunctional,48 and (iii) the M06-HF functional.49 The B3LYPfunctional employs three empirical parameters to combineexact exchange, gradient-corrected exchange, and local-spindensity exchange, whereas the PBE0 functional uses perturba-tion theory to define a ratio of 25% HF exchange and 75%exchange from the functional. The CAM-B3LYP functional is ahybrid exchange-correlation function featuring a long-rangecorrection to B3LYP using the Coulomb attenuating method.The M06-HF functional has full Hartree−Fock exchange,which eliminates self-exchange interactions at long range. Tobridge between the current and previous works, we alsocomputed the Raman spectrum of DBDT bound to tetrahedralAg20.

50 The B3LYP/def2-TZVP frequency-dependent polar-izability derivatives were computed using the ROA module inGaussian 09, in which these tensor elements are computed as asum over all electronic states, n51,52

∑α ωω ω

=⟨ |μ | ⟩⟨ |μ | ⟩

−≠

n n2

Re[ 0 0 ]jk

nn

j k

n00

02

i2

(4)

where j, k = x, y, z; ωn0 is the excitation energy from the groundstate to excited state n; and ωi is the frequency of the incidentlight. The polarizability derivatives with respect to normalmodes were computed at the optimized ground-state geometry(denoted by re)

51

ν α ν ν α νω

α α⟨ | | ⟩⟨ | | ⟩ =

∂∂

∂∂

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟Q Q

12jk p p jk

p

jk

pr

jk

pr

0 1 1 0

e e (5)

where v0 and v1p are the ground and first excited vibrationalstates, respectively, of the pth normal mode, Qp, and ωp is theharmonic frequency of this vibration. The differential Ramanscattering cross sections are defined in terms of scatteringintensities, Si

σ π ωπ ω

ωΩ

= − − −hc

hc k T Sdd

(2 )45 8

[1 exp( / )]p

p

4s

4

2 B1

i(6)

in which ωs is the scattering frequency in cm−1 and Si = (45α′p2

+ 7γ′p2), where α′p and γ′p are the spherical part and anisotropy,

respectively, of the polarizability derivative of the pth normalmode. This definition is appropriate for orientationallyaveraged scatterers, detected at 90° relative to excitation. Formolecules oriented in space, individual tensor elements (eq 5)are used, and the factor of 45 is dropped in eq 6.

■ RESULTS AND DISCUSSIONThe AFM image of a dumbbell and its Raman spectrum areshown in Figures 3 and 4, respectively. Although the verticalspatial resolution of the AFM measurements is reliable, thelateral resolution is determined by tip convolution. The clearlyresolved dumbbell (Figure 3a) is canted relative to the surfaceplane, in part because of the asymmetry of the nanospheres.The ellipsoid (Figure 3b) appears as a fused dumbbell, whichdoes not show any Raman activity. AFM was used to establishthat the nanostructure was a dumbbell of consistentdimensions, to define its spatial orientation, and to ensurethat it was isolated in the field of view of the micro-spectrometer. Under typical irradiation intensities of ∼1

Figure 2. Schematic of the AFM/Raman setup. The tip and sample areon independent scanning stages. The tip is aligned with the laser usingbackscattered light that is spatially filtered and monitored using aphotodiode. Imaging is accomplished by scanning the sample. Thespectra are recorded in the backscattered geometry, using a spatialfilter to establish confocality. Obj, objective; BS, beam splitter; PD:photodiode; NF, notch filters; DPSSL, diode-pumped solid-state laser.



mW/μm2, we did not detect Raman activity on isolated singlenanospheres. At intensities of ∼50 mW/μm2, which led to

melting and fusion of dumbbells, we observed faint spectra onsome single nanospheres. Consistent with our prior report,19 anupper limit of ∼10−3 was found on the relative intensity ofRaman scattering on a single sphere versus a dimer. In a fewcases, such as structure b in Figure 3, we located what appearedto be dumbbells that did not exhibit Raman activity. This canbe ascribed to either loss of the linker during preparation of theslide or light-induced fusion of dumbbells that were not well-anchored by the PVA film. Otherwise, the Raman intensities ofdifferent dumbbells were comparable (∼103 photons/s).Whereas the synthetic route afforded nanospheres coatedwith many DBDT molecules, the absence of a detectableRaman signal from single spheres establishes that the observedspectra arose from molecules located at the hot spots ofdumbbells. The spectra did not show spectroscopic signaturesof interacting linkers, such as splittings observed in clusters.19

The indications are thus that the observed spectra are those ofsingle molecules. The enhancement factors that we obtainedare consistent with this assumption.We give two independent determinations of the SERS

enhancement factor. The first relies on the observed signalstrength and the measured cross section of DBDT. The secondrelies on the relative measure of the number equivalent ofDBDT molecules that yields the same signal. We establishedthat the Raman cross section of the aromatic CC stretch ofDBDT, at 1580 cm−1, is 2 orders of magnitude larger than thesymmetric stretch of benzene. Experimentally, we foundσ(DBDT)/σ(benzene) = 200 by measuring spectra of liquidbenzene and DBDT/ethanol solutions contained in a thin cell(30 μm) under identical conditions. The measurement agreeswith our DFT calculations, which yield a ratio of 100 (dσ/dΩ =6 × 10−28 for bare DBDT). For a single molecule immobilizedin the field of view of the objective, to detect the observedcount rate of 1.2 × 103 photons s−1 in Figure 4, the required EFcan be determined from

η σ= ∂∂Ω

Ω ≈ −I IEF d 10 s03 1

(7)

based on the excitation intensity of I0 = 2.5 × 1023 photonscm−2 s−1 (1 mW/μm2), the detection efficiency of η = 0.1, andthe collection solid angle of dΩ = ∫ sin(v) dv dφ = π [oil-immersion lens with NA = n sin(v) = 1.25, n = 1.47]. Weobtained EF = 2(±1) × 107. The largest error in thisdetermination is the CCD conversion of photons to counts.Separately, we quantified the EF by recording the spectrum ofDBDT dissolved in ethanol using the same apparatus. A 5 mMDBDT solution, sandwiched between two coverslips, yielded asignal comparable to that observed from a single dumbbell. Toobtain the essential scattering volume of the liquid, we assumedthe Rayleigh waist of the objective (0.4 μm) and measured thedepth profile by recording the Raman signal of a silicon waferby translating it along the z axis of the objective. The obtainedvolume, 2.5 ± 0.5 pL, yields an experimental enhancementfactor of EF = V M NA = 7.5 × 106 relative to the molecule in asolution of molarity M. Taking the liquid local field correctionin eq 2 into account and using n = 1.5 for the index ofrefraction of ethanol, we obtain [(n2 + 2)/3]4 = 4 and thusEFexp = 3(±1) × 107. The two different determinations are thesame within the errors of the methods.As long as the excitation intensity was maintained near ∼1

mW/μm2, within our spectral resolution, the observed Ramanlines did not show spectral fluctuations. This is illustrated inFigure 4 with the set of consecutively recorded spectra at an

Figure 3. AFM image showing (a) an isolated dumbbell, on which thespectra in Figure 4 were recorded, and (b) a fused dumbbell, whichdoes not exhibit Raman activity. The associated line profiles arehighlighted in the insets. The heights correctly measure the diametersof the nanospheres, whereas the lateral profiles are determined by thetip convolution.

Figure 4. (a) Raman spectra recorded consecutively on a dumbbell(10-s exposure per spectrum). The spectra are vertically displaced forclarity. (b) Power-dependent intensities of the (■) 1579, (▲) 1492,and (●) 1271 cm−1 fundamentals. The ordinates are the calibratedcounts of photons/s.



exposure time of 10 s per spectrum. The subtraction of one ofthe spectra from the rest shows a slow fluctuation in overallintensity, but no spectral shift. That the excitation intensitycannot be increased arbitrarily is illustrated by the non-monotonic intensity dependence of the Raman lines shown inFigure 4b. The sudden drop in spectral intensity is indicative ofa change in the enhancement factor, which is controlled by thelocal field vectors and is therefore dictated by the orientation ofthe molecule relative to the dumbbell axis. Both spectral andintensity variations can be induced optically at high intensities,leading to both reversible and irreversible Raman trajectories.Here, we simply note that the observed intensity threshold forsuch light-induced manipulation is consistent with priorestimates of field strengths required to move polarizablemolecules and to collapse the dumbbell by the intersphereattractive force of light-induced dipoles on the metalspheres.26,28,30,34 We limit the present report to unperturbeddumbbells.The Raman spectrum of DBDT on a single dumbbell is

nearly indistinguishable from that of the solvated molecule andis reproduced by the computed spectrum shown in Figure 5.

The comparison is to the B3LYP/def2-TZVP spectrum ofAg7−S−DB−S−Ag7, scaled by a factor of 0.976 to align thearomatic CC stretch with its experimental counterpart at1580 cm−1, and with the lines broadened by 10 cm−1 (fwhm) tomatch the instrument resolution. The agreement between theexperimental and computed spectra gives confidence to theassignments collected in Table 1. There are small differences inthe calculated spectra of the considered silver structures (seeSupporting Information). We found the calculated spectral shiftof a given mode to vary by ∼2 cm−1 in the consideredstructures, well within our experimental resolution of 10 cm−1.These variations can be associated with the chemical effects invarious binding structures, as noted in a prior analysis.41 Theeffects are minor, undetectable in our system, and the bindingto the nanosphere seems to be captured by the Ag7−S−DB−S−Ag7 model. The similarity between the dumbbell and liquid-phase spectra in Figure 5a,b is also remarkable, because it is notobvious that the spectrum of a molecule fixed in spatialorientation should mimic the orientationally averaged liquid-phase spectrum. This occurs in the aromatic DBDT moleculebecause the polarizability determined by the π−π* transition at285 nm is strongly anisotropic: For all Raman-active modes,α′xx ≫ α′jk, where x defines the long axis of the molecule and j,k = x, y, z. The same holds for the molecule upon binding tosilver, even though the DBDT-to-silver charge-transfertransition (Figure 5 inset) determines the polarizability inthis case. The orientationally averaged spectra are dominated bythe x-polarized component. Assuming an enhanced local fieldalong the dumbbell axis, the appearance of the spectrum inFigure 5 is essentially unchanged for ±50° angles betweenmolecule and dumbbell. Whereas the relative intensities of theobserved modes are preserved, the overall intensity drops uponreorientation. This is the basis of the interpretation of theintensity drop seen in Figure 4.Given the fact that the polarizability along the long axis of the

molecule dominates and that the same holds for thepolarization of the dumbbell, a dramatic contrast betweenexcitation parallel and perpendicular to the intersphere axiswould be expected. This is not the case, however, as shown inFigure 6. We observed a soft polarization dependence with acontrast ratio between maximum and minimum intensity of 5−20 seen on different dumbbells. A survey of polarization-dependent studies of SERS on similar dumbbell structuresshows a similar range of results, for example, 5:1,53 10:1,54 andcontrasts larger than 10:1 being difficult to extract based on thesignal-to-noise ratio of reported spectra.55 Two experimentalconsiderations can be suspected to reduce the contrast ratio:tilting of the dumbbell relative to the slide plane and

Figure 5. Raman spectra: (a) 5 mM DBDT/ethanol solution, (b)SERS on a single dumbbell, (c) orientationally averaged spectrum ofAg7-DBDT-Ag7 computed at the B3LYP/def2-TZVP level, (d)computed spectrum for excitation and detecton polarization alignedalong the long axis of the molecule. Shown next to the individualspectra are schematic representations of (a) solvated DBDT, (b) adumbbell, (c,d) electron/hole density of the DBDT-to-silver charge-transfer (CT) transition.

Table 1. Experimental and B3LYP/def2-TZVP Vibrational Frequencies, Relative Intensities, and Spectral Assignmentsa

calculated experimental

relative intensities relative intensities

modefrequency (cm−1)(Ag(7)−Ag(7)) DBDT Ag(7)−Ag(7)

frequency (cm−1)(SERS) solution SERS assignment

1 1579 1 1 1580 1 1 aromatic CC stretch coupled to CC stretch2 1492 0.03 0.01 1493 − 0.05 HCCH rock3 1271 0.30 0.15 1267 0.44 0.28 CC ctretch4 1183 0.05 0.08 1185 0.06 0.13 HCCH dihedral bend5 1071 0.11 0.35 1065 0.30 0.24 CS stretch6 1010 0.01 0.02 994 0.04 0.07 in-plane aromatic ring deformation

aSee text for more details.



longitudinal polarization generated by high-NA objectives. Inthe focal plane, high-NA objectives partially convert transverseelectromagnetic fields (ET) to polarization parallel to thedirection of propagation (longitudinal field, EL). Accordingly,even if the excitation is polarized parallel to the dumbbell axis inthe far field, because the local field has components E0 = ET

0 +EL0, it will have components both parallel and perpendicular to

the dumbbell axis, E∥0 + E⊥

0 . The same consideration holds forthe polarization of the collected Raman radiation from themolecle. Accordingly, the observed polarization dependence ofSERS will generally be controlled by the sum of enhancementfactors (β∥E∥

0)4 + (β⊥E⊥0 )4, to which we fit the data. Both the tilt

angle of the dumbbell relative to the focal plane and thefocusing geometry affect the angular dependence of thescattered radiation. Explict analysis shows that these consid-erations do not change the main conclusion that the observedsoft polarization dependence is possible only if the enhance-ments E∥/E∥

0 and E⊥/E⊥0 , are comparable: β∥/β⊥ ranges

between 1.5 and 2. This finding cannot be explained whenonly linear polarization is assumed, as we show below.We computed the local fields of an ideal dumbbell using

finite-difference time-domain (FDTD) methods,56 with theexperimentally determined dielectric response of silver as theinput.57 Dumbbells have been extensively considered pre-viously,24,28,31−37,58 and we cross-checked the general agree-ment of our calculations against several prior studies.33,59 Theenhanced local fields of a dumbbell consisting of two perfect Agspheres of 30-nm diameter separated by a 1-nm gap and placedon a glass substrate is shown in Figure 7. The assumed incidentfield is meant to represent the polarization delivered by large-NA objectives, which, in combination with the slide, canproduce as much as 35% of the field polarized along thedirection of propagation, z.60 We note that, in addition to thehot spot proper, local fields at the contact between Ag and glassare also enhanced, as previously pointed out.25,26,61 At thecontacts, we find |E|/E0 = 2.9, Ex/E0 = 1.9, and Ez/E0 = 2.4,which are negligible in comparison to the hot spot between thespheres, for which Ex/Ex,0 = 32.2. Larger enhancements areattained on fused spheres. In the crevice of such structures, thefields reach enhancements as high as |E|/E0 = 120. The

computed spectral dependence of the enhancement |E/E0|4 for

intact and fused dumbbells are shown in Figure 8. The response

Figure 6. Polarization dependence of SERS on the single dumbbell,represented by the intensity of the aromatic CC mode at 1580cm−1. The fit is to the form (β∥E∥

0)4 + (β⊥E⊥0)4, assuming logitudinal

and transverse polarization components of the incident field deliveredby microscope objectives of 0.56 and 0.83. Assuming no opticalactivity, the observed soft contrast between the extrema (and, inparticular, the nonzero value reached when the field is orthogonal tothe dumbbell axis) would suggest that β∥/β⊥ ≈ 2.

Figure 7. Local fields for an incident electric field of E0 = (0.65x e−ikzz),with norm |E0| = 1, of a silver nanosphere dimer mounted on a glassslide. (a) Norm of the electric field on the surface of the structure. Themaximum enhancement on the surface is |E| = 20.65, whereas themaximum field is attained between the nanoballs in (b) Ex and (c) Ez,where the maximum values reach 32.2 and 19.6, respectively. Thefields on the surface of the slide in (d) Ex and (e) Ez; the Eycomponent is negligible. (f) Field component Ex along the y axis,which is perpendicular to the connecting line between spheres.

Figure 8. Spectral dependence of the local field enhancement, |E|4, forinput field |E0| =1, at two incident polarizations: (blue) E0 = x e−ikzz,(red) E0 = ye−ikzz. The long axis of the dumbbell is along x . The hotspots where the spectra were computed are indicated in green: (a) 1-nm gap, spectrum at {0, 0, 0}; (b) fused nanospheres, spectrum at {0,0, 3.9} nm, 2 Å above the crevice. Note: For an x-polarized field at 532nm, the enhancement in panel a is 34 = 81 times larger than that inpanel b.



is broad, with a gentle decay over the relevant Raman windowof 532−580 nm. For the largest Raman shift, for long axis of thedumbbell aligned along the polarization of the incident laserfield, such that EP = (E532/E0)

2(E580/E0)2, values of 3 × 106 and

7 × 108 are attained for the intact and fused dimers,respectively. This range admits the detection of single DBDTmolecules. The enhancement accessible in the intact structureremains an order of magnitude smaller than the experimentallydetermined value, and this ocurs only if the long axis of themolecule lies along the line separating the nanospheres: theobservations are only consistent with molecules that bridge thetwo nanospheres. Although the Raman spectrum does notcontain any signature of interacting linkers, it is useful toestimate the number of scatterers that can be geometricallypacked in the hot spot. The profile of EFP in the planeseparating the spheres is shown in Figure 7f. The enhancementdrops to 50% of its maximum value at r = 1.5 nm. Based on thesurface coverage of benzenethiol self-assembled monolayers onsilver, 3.3 × 1014 cm−2,62 a radius of r′ = 3 Å can be associatedwith the footprint of DBDT, to estimate (r/r′)2 = 25 as themaximum number of scatteres that can be packed into the hotspot. Unlikely as this might be, it defines an upper limit. Finally,we note that, for polarization along the short axis, the fields inthe Raman window are actually reduced: |E/E0|

4 ≈ 10−3 (seeFigure 8). A polarization contrast ratio of ∼1010 would beexpected, in stark contrast with experiments. The experimentcannot be reconciled within a model limited to linearpolarization and dipolar transitions; optical activity is suggested.We also explored the chemical contribution to enhancement

upon binding of DBDT to silver atoms. The initial hypothesiswas that a systematic increase in the number of silver atomsmight show a clear trend. This was not found to be the case.Static scattering intensities calculated at the B3LYP/def2-TZVPlevel of theory were smallest for Ag(1), followed by Ag(7), andlargest for Ag(3). Vertical transition energies calculated withTD- DFT (TD B3LYP) showed that the effect is entirelycontrolled by the energy of the DBDT-to-Ag charge-transfer(CT) transition. The CT state, which carries the oscillatorstrength (0.1−0.5) in both singly and doubly substitutedstructures, dominates the sum over states in eq 4. This isrecognized by noting that the computed scattering intensities ofFigure 9a scale as S ∝ ECT

−2 of the vertical energies shown inFigure 9b, as dictated by the energy denominator in eq 4 whenone state dominates the sum over all states. It is recognized thatTD-DFT gives quantitatively and qualitatively incorrectdescriptions of CT transitions between spatially separatedregions.52 The problem is likely to become more severe withincreasingly larger clusters. Although no systematic trend wasobserved when the size of the cluster was increased within thesame method, a systematic blue shift was observed for a givenstructure in going from B3LYP to M06-HF functional (Figure9). The calculated energies of the CT transition converged atthe TD M06-HF/def2-TZVP level to ∼3.1 eV (∼400 nm), asalso illustrated in Figure 9.63 Consistent with this finding, weobserved fluorescence upon 405-nm excitation of dumbbellsand DBDT-coated silver wires. Although not in directresonance at 532 nm, the CT state is nearly resonant withthe dumbbell plasmon; see Figure 9. Moreover, the CT wavefunction has significant amplitude on the terminal Ag atoms(see inset in Figure 5). As such, it provides a bridge betweenthe oscillating electron densities on individual spheres. Either ascurrent oscillating through the molecule or as a charge transferin which the electron/hole wave function extends beyond the

confines of the molecule, a significant enhancement in thetransition dipole can be expected. Given the large fieldgradients (see Figure 7f), multipolar and magnetic transitionscan compete with dipolar transitions, and because the benzenerings of DBDT are staggered, dichroism and thus rotationalactivity can be expected. These considerations might hold thekey to understanding the polarization dependence. It wouldappear that the separation of the dumbbell into molecule andeffective medium is a poor assumption. Nevertheless, ignoringsuch coupling, it is possible to account for the overall EF.Because, in both bare and silver-bound molecules, a single statedominates the sum over states of the polarizability

αμ μ

γω⟨ ⟩ = −

⟨ | | ⟩⟨ | | ⟩

Δ + ℏΔ = ℏ − E

0 CT CT 0

i, wherejk

j ki CT

(8)

the principal chemical effect can be associated with thereduction in the detuning, Δ, which contributes quadraticallyto the scattering intensities, Si ∝ |α|4. Taking Δ0 for thedetuning of the bare molecule, determined by the π* state at285 nm, a factor of EFC = (Δ0/Δ)2 = 12 is obtained for thechemical contribution. The orders of magnitude of theexperimentally determined EF = 107 can be parsed as EFP =106 and EFC = 10.

Figure 9. (a) Static Raman intensities for the bright 1580 cm−1

vibrational normal mode calculated using four density functionals.Shown are the normalized computed intensities for DBDT (solid bluecircles), Ag−S−DB−SH (solid black squares), and Ag3−S−DB−SH(solid red circles). (b) Vertical transition energies, using four differentdensity functionals, for the seven different considered structures: Ag−S−DB−SH (solid black squares), Ag−S−DB−S−Ag (open blacksquares), Ag3−S−DB−SH (solid red circles), Ag3−S−DB−S−Ag3(open red circles), Ag7−S−DB−SH (solid green triangles), Ag7−S−DB−S−Ag7 (open green triangles), Ag20−S−DB−SH (solid bluediamonds). The intensities in panel a scale as E−2 of the verticaltransition energies shown in panel b.



■ CONCLUSIONSWe report SERS spectra obtained from single dumbbells ofseemingly single molecules. The primary evidence of SMSERSin the present study is the agreement of the experimentallydetermined enhancement factor with the absolute signalstrength expected from a single molecule. With the determinedcross section of the bare molecule, 6 × 10−28 cm2/sr, theobserved signal strength corresponds to that of a singlemolecule subject to the measured enhancement of 2 × 107.Clearly, such a determination carries uncertainty. Our analysisputs an upper limit of 25 for the number of molecules that canbe packed into the hot spot of the dumbbell, and this does notchange the essential conclusions that we make here. We showthat physical enhancement factors are, in effect, sufficient to seea single nonresonant scatterer, although an additional factor ofEFC = (Δ0/Δ)2 = 10 is effective in the measurements at 532nm. That the chemical effect is relatively small is manifested bythe unaltered spectrum of DBDT on the dumbbell. In both themolecular π−π* transition and the DBDT-to-silver CTtransition, the polarizability ellipsoid has the same anisotropy,dominated by the long axis of the molecule. This explains theobserved similarity in relative intensities of the Raman lines andthe independence of the spectrum on orientational averaging.Notwithstanding the successful accounting for the enhance-ment factors, the analysis assumes separation of the dumbbellinto molecule and plasmonic medium, with an admixture ofquantum and classical treatments of the constitutent parts. Thefailure in describing the observed soft polarization dependenceis noted. The classical treatment of the local fields and theassumption of idealized nanospheres that ignore faceting of thesilver and deformations of structure in the nanogap are suspect.More importantly, the electron/hole density (Figure 5)associated with the CT state suggests that at least electronicdegrees of freedom of the molecule should be intimatelycoupled with the collective charge-density oscillations of thenanostructure. This might be key to resolving the observed softpolarization dependence, the resolution of which requires acomplete treatment of fields and tensor elements of thepolarizability, which we take up in a followup report.

■ ASSOCIATED CONTENT*S Supporting InformationAdditional information as mentioned in text. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis research was performed under support from the NSFCenter for Chemistry at the Space-Time Limit, Grant CHE-0802913. The computational work was supported by theNational Science Foundation through TeraGrid (TG-PHY110040) and used the Extreme Science and EngineeringDiscovery Environment (XSEDE) (OCI-1053575). Weacknowledge helpful discussions with G. Schatz, R. VanDuyne, and W. van der Veer. A.R.P. gratefully acknowledgessupport through a National Science Foundation GraduateResearch Fellowship (DGE-0808392).

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surface-enhanced raman scattering of a single ...the mixture is allowed to sit for ∼3 h and then...

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