determining molecular orientation with surface-enhanced raman scattering using inhomogenous electric...

Determining Molecular Orientation With Surface-Enhanced RamanScattering Using Inhomogenous Electric FieldsDhabih V. Chulhai and Lasse Jensen*

Department of Chemistry, The Pennsylvania State University, 104 Chemistry Building, University Park, Pennsylvania 16802, UnitedStates

*S Supporting Information

ABSTRACT: The inhomogenous electric field near the metal surface of plasmonicnanoparticles allows molecular orientation to be determined from surface-enhanced Ramanscattering (SERS). We illustrate this by simulating the effects of the field-gradient on theSERS spectrum of benzene and pyridine. To do this, we present an origin-independentformalism describing the effects of the local electric-field gradient in SERS. Using thisformalism, we found that the field-gradient led to observation of Raman-inactive modes inbenzene and allowed for extraction of orientation information from the SERS spectra ofboth benzene and pyridine. It was also observed that the SERS electromagneticenhancement factor, when considering field-gradient effects, depends on the field-gradientmagnitudes and is only approximately described by |E|4 for certain modes. The field-gradientmechanism may also lead to a weakening of intensities as compared to a homogeneous localfield. Thus, inclusion of field-gradient effects are crucial in understanding relative intensitychanges in SERS.

I t is well-known that the Raman scattering of moleculesadsorbed onto metal surfaces that support plasmon

resonances may be enhanced, a phenomenon that is referredto as surface-enhanced Raman scattering (SERS).1−4 In somecases, enhancement may be large enough (>108) for resolutionof single molecules, an effect referred to as single-moleculeSERS (SMSERS).5−10 While the basic theory of SERS has beenknown for a while,1,11,12 the intricate details of the enhance-ment mechanisms are still being debated due to thecomplicated nature of the metal−molecule interface.13−15

The SERS enhancement mechanisms may be broadly placedinto two categories: the chemical mechanism (CM) and theelectromagnetic (EM) mechanism. Enhancement under theCM may be further classified into a charge transfer (CT)mechanism where the incident light is in resonance with acharge transfer excitation between the metal−molecule system,a nonresonant chemical (CHEM) mechanism due to non-resonant interactions between the metal−molecule system, anda molecular resonance mechanism where the incident beam isin resonance with a molecular excitation.13,14 The EMmechanism arises from the strong local electric field at themetal surface due to excitation of the surface plas-mon.1,11−14,16,17 This mechanism is largely independent ofthe molecule and known to be the major contributor to theSERS enhancement with an approximate enhancement factorof |E|4, where E is the local field enhacement.13,18,19

Theoretical work20,21 has shown that the magnitude of thelocal electric field can vary greatly over the space of a fewnanometers. This feature of the local electric field, termed thelocal electric field-gradient (FG), is strongest for smallnanoparticles and surface features described by small radii ofcurvature (near sharp tips, for example). In these systems, one

should expect a significant contribution to the EM mechanismfrom the FG. This concept was first considered in the early1980s in order to account for the observation of vibrationalmodes in the SERS of benzene and related molecules that areforbidden in normal Raman scattering (NRS).22−25 Moskovitsand co-workers22−25 have argued that large FGs will contributeto the induced dipoles through the electric dipole−electricquadrupole polarizability (A) tensor (an effect that issometimes referred to as quadrupolar-SERS or SEQRS).Since then, FG effects have been largely ignored until recentlywhere descriptions of surface-enhanced Raman optical activity(SEROA), SERS through near-field optical microscopes(NSOM), and SMSERS necessitated such contributions.Janesko and Scuseria26 have considered the local field andgradient from dipolar and quadrupolar spheres in generatingdressed-polarizability tensors in order to describe SEROA.Jahncke and co-workers27,28 have considered local fields thatare functions of the normal coordinate of vibration in order todescribe NSOM-SERS. Apkarian and co-workers29 consideredthe FG and magnetic field around a nanodumbbell in order totrack the trajectory of a single molecule. Recently, Takase andco-workers demonstrated that FG effect can induce otherwiseforbidden transition in SERS of carbon nanotubes.30,31

In this paper, we derive an origin-independent formalismnecessary to describe SERS due to inhomogeneous localelectric fields. This formalism is similar to the dressedpolarizability formalism presented by Janesko and Scuseria to

Received: June 25, 2013Revised: August 21, 2013Published: August 22, 2013

Article

pubs.acs.org/JPCC

© 2013 American Chemical Society 19622 dx.doi.org/10.1021/jp4062626 | J. Phys. Chem. C 2013, 117, 19622−19631

pubs.acs.org/JPCC

describe SEROA, although their approach was origin-depend-ent.26 Origin-independence was achieved by recognizing thatthe fields and molecular properties need to be expanded arounda common origin. We then used the local field and FG from adipolar sphere in order to simulate the SERS spectra of benzeneand pyridine. Early SERS on benzene24,32 attributed theobservation of normally forbidden modes to a FG effect, andselection rules for such observations were derived.22,23 Here weverify these selection rules using the FG SERS formalism andshow how it may be used to predict relative orientation ofmolecules with respect to the substrate surface. For pyridine, inaddition to information about molecular orientation, we alsoshow that the local FG may give rise to effects that are generallyassociated with a CM mechanism. Finally, we show that theseFG effects are naturally included in simulations that account forthe atomistic structure of the metal nanoparticle such as therecently developed atomistic discrete interaction method/quantum mechanics (DIM/QM) method.21,33,34 Our resultsshow the importance of the FG mechanism in interpretingSERS spectra.

■ THEORYSERS in an Inhomogenous Electric Field. The oscillating

induced dipole, μ, responsible for Raman scattering of amolecule in the vicinity of a metal nanoparticle is given by

μ α= + + + ···α αβ β αβγ βγ αβ βE A E G B13 (1)

where α, A, and G are the electric dipole−dipole, electricdipole−quadrupole, and electric dipole−magnetic dipole polar-izabilities, respectively. In order to describe Raman scattering,these polarizabilities should be understood to represent thetransition polarizability tensors, i.e., derivatives of the polar-izability tensors with respect to the vibrational normal mode.The fields perturbing the molecule are due to an incident planewave field E(0) (described by frequency ω and propagationvector ni) and an inhomogeneous local field Eloc, and may bewritten as

κ= + | | + ··· +α α α αω−E r t E i r E E e( , ) ( ) i t(0) (0) loc

(2a)

κ= + ··· +αβ β α αβω−E r t i n E E e( , ) ( ) i ti (0) loc

(2b)

κω

εω

ε= + ··· −α αβγ β γ αβγ γβω−⎜ ⎟

⎛⎝

⎞⎠B r t n E

iE e( , ) i ti (0) loc

(2c)

where Eα, Eαβ, and Bα are the total electric field, electric FG, andmagnetic field perturbing the molecule respectively, and κ = ω/c. The Einstein summation convention is employed forrepeated indices.For particles significantly smaller than the wavelength of

light, we can ignore contributions on the order of κ and higher.Using these fields, we rewrite the induced dipole in terms of amodified polarizability tensor α′, defined as

μ α αω

ε= + + −α αβ β αβ β αβγ βγ αβ βγδ γδE E A Ei

G E13

ind (0) loc loc loc

(3a)

α δω

ε= + + −αγ βγ γβ

αγδ γδβ

αγ γδε δεβ

β⎡⎣⎢

⎤⎦⎥F A F

iG F E( )

13

loc, loc, loc, (0)

(3b)

α= ′αβ βE(0)(3c)

where Fβ(γ)loc,α describes the local field (gradient) enhancement in

the β (γ) direction resulting from polarization in the αdirection. This equation ignores terms on the order of κ andhigher. At the same order, Fαβ

loc is symmetric (Fαβloc,γ = Fβα

loc,γ) andthere is no contribution to the local magnetic field; we willtherefore ignore terms that are dependent on this field.Similarly, the quadrupole induced by an incident and localfields may be defined as

θ δ= + +αβ δ αβ γδ δγ

αβ δε δεγ

γ⎡⎣⎢

⎤⎦⎥F C F E( )

13

ind,

loc,,

loc, (0)

(4a)

= ′γ αβ γE,(0)

(4b)

where and C are the molecule’s electric quadrupole−dipoleand electric quadrupole−quadrupole polarizabilities, respec-tively.The fields from the radiating dipole and quadrupole may also

be enhanced by the plasmonic nanoparticle at the Raman-shifted frequency. This leads to an effective scatteringpolarizability tensor α″ expressed as

α δ ω α ω

δ ω α δ ω

ω

ω δ ω

ω

″ = + ′ + ′

= + +

+

+ +

+

αβ αγ γα

γβ γδα

β γδ

αγ γα

γδ βδ δβ

γδε δεβ

γδα

ε γδ βε εβ

γδ εζ εζβ

{}

{}

F F

F F

A F

F F

C F

[ ( )]13

( )

[ ( )] [ ( )]

13

( )

13

( ) [ ( )]

13

( )

S S

S L

L

S L

L

loc, loc,,

loc, loc,

loc,

loc,,

loc,

,loc,

(5)

where Floc(ωL) and Floc(ωS) are the local field enhancements atthe incident and Raman-shifted frequencies. The effectivepolarizability described here is similar to the dressed-polar-izability tensor formalism of Janesko and Scuseria,26 with theinclusion of the quadrupole induced by the local field gradient(which is of the same order in κ) through the C-tensor. Fromeq 5, it is easy to show that we recover the free moleculepolarizability tensor ααβ″ = ααβ within the limit of no local fields.In the formalism presented here, the polarization of the metalnanoparticle due to interactions with the molecule is neglectedsince these effects are generally small.21

The local fields from the nanoparticle (eqs 2b and 5) areapplied at some fixed point in the molecule. This point, chosenfor convenience, is the center-of-mass of the relevant moleculefor results shown in this paper. However, the resultingexpression is origin-dependent since there are no mutualcancellations of origin-dependent contributions from the A, ,and C-tensors for fields coupled into the polarizability tensors.This is because these tensors describe the multipoles induced atthe origin of the coordinate system of the molecule (QM) dueto a field or FG, whereas the local fields are calculated in aseparate substrate coordinate system (QS). In order to maintainorgin-independence, we need a common-origin description ofthe local fields. This is achieved through a Taylor expansion ofthe fields about the center-of-mass (or about the vector in QMthat describes the change in gauge origin). The derivation andproof of this common-origin solution is available in theSupporting Information. This expansion of the local fieldcoupled into the polarizability tensors leads to an origin-

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp4062626 | J. Phys. Chem. C 2013, 117, 19622−1963119623

invariant expression of the effective dipole required forcorrectly describing inhomogenous field effects in SERS.Electric-field gradient effects are expected to be important for

nanoparticles with a small radii of curvature such as atomicroughened surfaces, nanoparticles with sharp tips, and junctionsbetween different nanoparticles. To model this and obtainanalytical expressions for the fields, we assume for simplicity adipolar sphere model for the metal nanoparticle. Such a modelneglects nonlocal and quantum effects which are expected to beof importance for nanostructures with small dimensions.35−37

Such effects are likely to reduce the strength of the local fieldand thus will affect the ratio between the electric field and theFG. While the simple dipole model will not provide an accuratedescription of the absolute enhancements it can be used todetermine the relative importance of the electric fields and FG.Furthermore, while the fields and field gradients in this workare obtained using the dipole approximation, the formalismpresented remains valid for any fields obtained from complexgeometries using classical electrodynamics simulations. In thisdipolar model, the polarizability αS of the metal nanoparticledepends on the radius of the sphere a and a function g of thefrequency and dielectic constant and can be written as αS = a3g.Assuming a point−dipole approximation, the fields at thesurface of the sphere (for |R| = a) may be expressed as E ∼ α/|R|3 = g and are independent of the sphere’s radius. The FG atthe surface, using the same model, is ∇E ∼ α/|R|4 = g/α and istherefore dependent on the radius of the sphere. Larger sphereshave smaller FG magnitudes than those for smaller spheres. Weuse this relationship to examine the SERS FG effects where adecrease in the sphere’s radius results in an increase in its FGwhile the magnitude of the local field at the surface remainsunchanged. It should be noted that the radius is used in thispaper to vary the field gradient to field strength ratios and istherefore a representation of the curvature of the local surfaceroughness responsible for these FG ratios; it is not the actualsize of the metal nanoparticle. Also, for a dipolar model, it iseasy to show that Bα

loc = −i/ω εαβγFγβloc ∝ 1/c, which implies that

local magnetic fields are 2−3 orders of magnitude weaker thanthe local electric FG (and within the quasi-static approximation,Bloc = 0 for κ = 0). As such, we have ignored contributions fromthe local magnetic field in the derivation of eq 5 and insimulations in this paper.

■ COMPUTATIONAL DETAILSAll calculations presented in this work were performed using alocal version of the Amsterdam density functional (ADF)program package.38,39 The Becke-Perdew (BP86) XC-poten-tial40,41 and an even-tempered quadruple-ζ slater type basis setwith three polarization functions (ET-QZ3P) from the ADFbasis set library were used unless stated otherwise. Thevibrational frequencies and normal modes were calculatedanalytically within the harmonic approximation, where theBP86 functional results in harmonic frequencies of pyridineclose to experimental results without the use of scalingfactors.42 Frequency dependent α, A, and C-tensors werecalculated using the AOResponse module implemented inADF, with a excited state lifetime of Γ = 0.1 eV.42−46 Tensorderivatives were calculated by numerical three-point differ-entiation with respect to Cartesian displacements.Polarizability of the isotropic spheres were calculated using

experimental frequency-dependent complex dielectric functionsof silver at 354 nm, and is ε = −1.9858 + 0.2854i.47 We’ve alsosimulated fields from substrates using the discrete interaction

model (DIM)48,49 which uses atomistic electrodynamics. Thismodel has been combined with time-dependent densityfunctional theory (TDDFT) which also allows us to simulatelinear-response properties of molecule/substrate complexes inwhat is termed the DIM/quantum mechanics (DIM/QM)method.21,33,34 All simulated spectra have been broadened by afull width at half-maximum (fwhm) of 20 cm−1.The averaged Raman intensity may be calculated from the

effective polarizability tensor similar to that of traditionalRaman scattering. For linearly polarized incident light and ascattering angle of 90°, this is given as

α γ δ⟨ ⟩ = ″ + ″ + ″IK

45(45 7 5 )p

pp p p

2 2 2

(6)

where αp″2, γp″2, and δp″2 are invariants of the effectivepolarizability derivatives with respect to vibrational mode p,(α″)p. The effective polarizability derivatives need not besymmetric and therefore the tensor invariants are given by50−52

α α α″ = ″ ″αα ββ*1

9( ) ( )p p p

2

(7)

γ α α α α α α″ = ″ ″ + ″ ″ − ″ ″αβ αβ αβ βα αα ββ* * *3

4[( ) ( ) ( ) ( ) ]

12

( ) ( )p p p p p p p2

(8)

δ α α α α″ = ″ ″ − ″ ″αβ αβ αβ βα* *3

4[( ) ( ) ( ) ( ) ]p p p p p

2

(9)

For Stokes scattering with an experimental setup as describedabove, the parameter Kp is given by53

πε

ν νπ ν ν

= − − −

Kh

c hc k T( )

81

1 exp[ / ]p pp p B

2

02 0

42

(10)

where ν0 and νp are the frequencies of the incident light and ofthe pth vibrational mode, respectively.In order to describe the fields originating from a model

substrate we will consider a sphere of isotropic, frequency-dependent polarizability αS(ω) located in some coordinatesystem QS. This polarizability is given as

α ω ε ωε ω

= −+

a( )( ) 1( ) 2

S 3

(11)

where ε(ω) is the material’s complex, frequency-dependentrelative dielectic function and a is the radius of the sphere. Thelocal field enhancement factors from this dipolar sphere aregiven as

ωδ

α ω=| |

−| |α

β α γ αγγβ

⎛⎝⎜

⎞⎠⎟F

R R

R RR( ; )

3( )S

5 3(12a)

ω

δ δ δα ω

= −| |

++ +

| |

αβδ α β γ

αβ γ αγ β βγ αγδ

⎛⎝⎜

⎞⎠⎟

FR R R

R

R R R

R

R( ; )15

3( )( )S

7

5

(12b)

where R describes the vector separating the molecule anddipolar sphere. The common-origin expression of the localfields needed to maintain origin-invariance is included in theSupporting Information.



■ RESULTS AND DISCUSSIONEnhancement Factors in an Inhomogenous Electric

Field. The EM enhancement in SERS is usually approximatedas |E′|2|E|2, where |E|2 is the local field enhancement of theincident field and |E′|2 is the radiated field enhancement.13,18,19

For simplicity, E and E′ represent the appropriate componentsof the local fields which depend on the relative orientation ofthe molecule with respect to these fields. For small Ramanshifts, we may assume that E′ ∼ E, from which we obtain anapproximate enhancement factor of EF ∼ |E|4. This factor,however, ignores the effects of an inhomogeneous local field orthe presence of local magnetic fields. In traditional Ramanscattering, we consider a plane-wave of frequency ω withelectric FG and magnetic field contributions on the order of iκand κ/ω, respectively. As such, the A and G-tensors contributenegligibly to the induced dipoles and can safely be ignored(except in cases of Raman optical activity). However, nearmetal surfaces, the local electric FG is expected to be on thesame order as the local electric field (see eq 2a) and therewould be a significant contribution to the induced dipoles fromthe A-tensor as well.23

We have shown in eq 5 that, by considering aninhomogeneous local field on the surface of a metalnanoparticle, we obtain an effective polarizability tensor ofthe form α α″ ∼ + + +A C. The SERS intensities areproportional to the square of this effective polariability, or

α α∝ | ″| ∼ | + + + |I A CSERS 2 2. This results in terms thatresemble |α|2, |A|2, | |2, |C|2, as well as a number of couplingterms (see Table 1). The |α|2 and |A|2 terms can be thought of

as being the Raman intensities resulting from dipoles inducedby electric fields and FGs, whereas the | |2 and |C|2 terms arefrom the quadrupoles induced by the fields and FGs,respectively. The remaining terms describe the interferencebetween these types of induced multipoles. Scattering frominduced magnetic dipole moments due to the local field andgradient are ignored in this formalism since they scatter on theorder of κ, but will become important in descriptions ofSEROA.26 The appropriate enhancement factors for thesevarious contributors to the SERS intensity are given in Table 1,where E and ∇E are the field and FG enhancement factors,respectively. This suggests that modes that are α-tensor(Raman) active are enhanced as |E|4. |E|2|∇E|2 is the appropriate

enhancement factor for modes that are A-tensor active,23 while|∇E|4 is the relevant enhancement factor the |C|2 terms. Theinterference terms may also contribute by either enhancing orweakening of the SERS intensities through the enhancementfactors shown in Table 1.

SERS of Benzene. SERS of benzene often serves as a modelsystem for understanding adsorption of aromatic molecules onmetal surfaces. This is also the prototypical system forinvestigating FG effects in SERS since vibrational modesnormally forbidden in Raman scattering are observed forbenzene on rough metal surface.22−25 A typical SERS spectrumis shown in Figure 1.22,24,25,32,54−56 In addition to the Raman-

active a1g (ν1 and ν2), e1g (ν10), and e2g (ν6, ν7, ν8, and ν9)vibrational modes, Raman-inactive a2u (ν11), e1u (ν18, ν19, andν20), and e2u (ν16 and ν17) modes are sometimes observed. Theappearance of these modes have generally been attributed to aFG effect rather than a lowering of molecular symmetry orimage charge effects.22−25 The selection rules for these FGmodes have also been considered.22,23 Briefly, it states thatmodes that belong to representations that include a cubictransformation will be FG-active since the A-tensor transformsas the product of three translations. Benzene’s high symmetry(D6h) means that the modes that are enhanced by a local field(a1g, e1g, and e2g) are distinct from those that are enhanced bythe local FG (a2u, b1u, b2u, e1u, and e2u).

23 Included in the FG-active modes are the IR-active a2u and e1u modes, but we willnot differentiate between FG-active/IR-active and FG-active/IR-inactive modes since the selection rules for IR are not, ingeneral, related to those for FG SERS.We aim to show the FG surface selection rules by

considering the contributions to the SERS of benzene,enhanced by the local electric field and gradient, in twodifferent orientations. The local electric field contribution tothe SERS spectrum of benzene parallel to the surface of thesphere (flat orientation) is described by the |α|2 term (shown inFigure 2 top) and resembles that of benzene’s NRS spectrum.The relative intensity of the observed modes may be explainedusing surface selection rules with a greater enhancement of thea1g(αzz) mode at 990 cm−1 (ν1). (The surface normal runs

Table 1. Terms Contributing to the SERS Intensity andTheir Relevant Enhancement Factorsa

term enhancement

|α|2 |E′|2 · |E|2

|A|2 |E′|2 · |∇E|2

| |2 |∇E′|2 · |E|2

|C|2 |∇E′|2 · |∇E|2

Re(αA†) |E′|2 · E · ∇E

α †Re( ) E′ · ∇E′ · |E|2

Re(αC†) E′ · ∇E′ · E · ∇E†ARe( ) E′ · ∇E′ · E · ∇E

Re(AC†) E′ · ∇E′ · |∇E|2†CRe( ) |∇E′|2 · E · ∇E

aE and E′ are the field enhancement at the incident and Raman-shiftedfrequencies whereas ∇E and ∇E′ are the field gradient enhancement atthe incident and Raman-shifted frequencies respectively.

Figure 1. SERS spectrum of benzene on silver colloids excited at 488nm.24 Indicated are the symmetry subgroup (assuming D6h symmetry)as well as the Raman selection rule, either Raman-active (R) orinactive (IA).



along the z-axis for benzene parallel to the surface.) The FGcontribution to the SERS spectrum described by the| | + | |A 2 2 terms leads to predicted FG-active modes. Forbenzene in the flat orientation, the Raman-inactive ν11 and ν18are observable (Figure 2 middle). The relative intensities ofthese modes are as expected when considering FG surfaceselection rules with ν11 [a2u(Azzz)] being more intense than ν18[e1u(Azzx,Azzy)]. These surface selection rules are also seenwhen the plane of the benzene ring is perpendicular to thesubstrate surface (vertical orientation, Figure 3 middle) wherethe Raman-inactive ν14, ν15, and ν19 are observable. Each ofthese modes contain large Ayyy and/or Axxx components and aretherefore expected to be enhanced for large FGs along theplane of the benzene ring. The |C|2 contributions to the SERSintensity are plotted in the bottom spectra of Figures 2 and 3.While this term describes a field-gradient effect (the enhance-

ment of the near field of an oscillating quadrupole induced by afield gradient), it selects modes that are typically Raman-active(ν1 and ν10 in a flat orientation and ν1, ν6, and ν9 in the verticalorientation). The local electric field-enhanced SERS of benzenein the vertical orientation (Figure 3 top) is very similar to theNRS and the field-enhanced SERS of flat benzene with smallchanges in relative intensities. Therefore, inclusion of the FGmechanism is essential for assignment of molecular orientationbased on relative intensities. The |α|2, |A|2, and |C|2

contributions in Figures 2 and 3 were normalized, and theirrelative contributions to the observed SERS spectrum dependon the ratio of ∇E/E. The interference terms are not shown.These terms are only significant when the appropriatepolarizability tensor gradients describe the same mode. TheRaman-active and FG-active modes in benzene are distinct,leading to little interference between the dipoles induced by theα and A or α and tensors. In general, the Re(αA†)contribution for benzene is 6 orders of magnitude weaker thanits |α|2 and |A|2 contributions.As we have shown, FG surface selection rules can give

information about the relative orientation of the molecule withrespect to the substrate surface (similar to the SERS sufaceselection rules). Alternatively, relative intensities of these FGmodes can give information about the nature of the localelectric field in the vicinity of the molecule. Based on thesearguments one can deduce, for the experimental spectrum inFigure 1,24 an averaged ensemble orientation where benzene istilted at some small angle. Indeed, we are able to reproduce therelative intensities of the FG modes in Figure 1 by assuming atilt of ∼10° of the plane with respect to the surface, shown inFigure 4. We are able to correctly reproduce the experimental

spectrum seen in Figure 1 with the modes in the region of1100−1600 cm−1 being weaker than those in the experimentalspectrum. These modes may be weaker by comparison due toan overestimation of the enhancement of ν1. The ν10 out-of-plane CH bending mode is particularly interesting since this is aRaman-active mode. However, in the model presented here,this mode is enhanced by a field-gradient effect through the |C|2

term and is not observed for a homogeneous local field. The

Figure 2. Contributions to the SERS of benzene flat on a surface fromthe local electric field (|α|2, top), the dipole−quadrupole terms(| | + | |A 2 2, middle), and the quadrupole−quadrupole term (|C|2,bottom).

Figure 3. Contributions to the SERS of benzene perpendicular to asurface from the local electric field (|α|2, top), the dipole−quadrupoleterms (| | + | |A 2 2, middle), and the quadrupole−quadrupole term (|C|2, bottom).

Figure 4. Simulated SERS of benzene titled at 10° with respect to thesurface (orientation shown in inset). The radius of the substrate wastaken to be 10 bohrs to reproduce the relative intensities seen inFigure 1.



evidence presented here confirms that lowering of molecularsymmetry is not required in order to observe Raman-inactivemodes. Indeed, the intensity of modes that become Raman-active as a result of symmetry relaxation is generally very weak,and therefore a symmetry relaxation argument is usuallyinsufficient to describe the intensities seen for Raman-inactivemodes in experimental SERS.SERS of Pyridine. Another model system typically explored

using SERS is pyridine adsorbed onto metal surfaces, wherethere is competition between the tendency to adsorb flat due tointeractions with the π-system or upright (vertical) throughinteractions with the lone pair on the nitrogen. Pyridine possessC2v symmetry which means that, unlike benzene, there are nodistinct FG modes; all modes are both Raman and FG-active.The observation of FG modes, however, can give informationabout the relative orientation of the pyridine molecule withrespect to the surface through FG surface selection rules. Theexact orientation of pyridine on a metal surface is dependent onfactors such as coverage, temperature, substrate, and electro-chemical potential.22,57−62 While there is evidence that pyridinebinds through its nitrogen lone pair,63−66 scanning tunnelingmicroscopy (STM) experiments60−62 suggest that pyridine isprimarily flat (or tilted) at low temperatures and coverages. Forpyridine oriented vertically and considering only the local fieldenhancement, one would expect the a1(αzz) modes to be themost intense, followed by the b2 modes with the b1, a2, anda1(αxx,αyy) modes predicted to be very weak or unobservable. Inthe SERS spectrum of pyridine in this orientation (Figure 5a)enhanced by the local field only (black spectrum), we observethat the most intense peaks are the a1 ring breathing modes ν1and ν12, with contributions from ν6a, ν8a, ν9a (a1), and ν6b andν9b (b2). These are also the most intense modes in the NRS andthe SERS spectra of pyridine flat on the surface (Figure 5b).We then looked at the SERS spectra of pyridine with FG

effects included. In order to visualize the changes caused by theFG terms in the spectra, we increase the ∇E/E ratio bydecreasing the radius of the model substrate (from 40 to 15bohrs for the spectra shown in Figure 5). This gives us a clear

picture of the modes that are enhanced (or weakened) by theFG mechanism. For pyridine perpendicular to the surface(Figure 5a), we observe the largest enhancement due to the FGmechanism in ν19a with contributions from ν1, ν3, ν6a, ν12, ν14,and ν18b. The most intense of these FG-enhanced modes (ν14and ν19a) are also the modes enhanced by the FG mechanismfor benzene in the same orientation (Figure 3 middle). Theirrelative intensities are therefore similarly described using FGsurface selection rules, with the a1(Azzz) mode (ν19a) beingmore intense followed by the b2(Ayzz) modes (ν3 and ν14). Inthis orientation, we also observe weakening of ν2 and ν15 due tothe FG mechanism. This is due to the interference between themultipoles induced by local fields and FGs described by theinterference terms. The contribution from the Re(αA†) and

α †Re( ) terms (labeled as Re(αA†) in Figure 6), for pyridine

Figure 5. SERS of pyridine with the plane of the ring (a) perpendicular and (b) parallel to the surface showing how the absolute intensities of eachmode changes as we decrease the radius of the sphere from 40 bohrs (purple spectra) to 15 bohrs (red spectra), with the spectra enhanced by thelocal field only (black spectra) also shown.

Figure 6. Major contributors (in addition to the |α|2 term) to the FGSERS spectrum of pyridine perpendicular to the surface of a 10 bohrradius sphere. The interference terms may result in either enhance-ment or weakening of modes.



in this (vertical) orientation, is only an order of magnitudeweaker than the |α|2 term and is the same order of magnitude asthe |A|2 terms and therefore contributes significantly to theobserved spectrum (see Figure 6). This term weakens theintensity of ν3, ν6a, ν12, and ν15, while enhancing ν6b, ν14, andν19a. The |A|2 term, on the other hand, enhances ν3, ν14, ν15,ν18b, and ν19a. The Re(αC†) contribution, which describes theinterference between the dipoles induced by an electric fieldand the quadrupoles induced by an electric field gradient,shows an enhancement of ν1, ν6a, ν12, and ν15 and a weakeningof ν9a. This suggests that ν6a, ν9a, ν12, and ν15 are eitherenhanced or weakened depending on the ratio of ∇E/E. Theresults also indicate that the relative intensities of ν6a and ν6band of ν1 and ν12 may change due to FG contributions.Understanding the relative behavior of ν1 and ν12 is particularlyimportant since they are the characteristic modes of pyridineand their relative intensities change with change from NRS toSERS and also with change in electrode potential.FG surface selection rules lead to a very different picture for

pyridine lying flat on the surface (Figure 5b). In thisorientation, the most intense FG modes are ν4 and ν11 (b1),with ν10a and ν10b also observable. Surface selection rulespredict that b1(Axxx) modes would be most intense for large FGperpendicular to the plane of the pyridine ring (x-axis). We alsoobserve negligible contribution from the interference terms inthis orientation, with intensities that are 2 orders of magnitudeweaker than the |α|2 and |A|2 terms. As such, we observe noweakening of modes in the presence of strong FGs.The effects of the FG mechanism on the SERS of pyridine

simulated in this paper have been observed on electrodes athigh negative potentials67−69 and on low temperatureroughened surfaces under vacuum.22 Moskovits et al.22

observed contributions from ν4, ν11, ν14, ν15, ν19a, and ν19b inthe SERS spectra of pyridine on cold-evaporated silver surfaces,which were absent in the SERS spectra of pyridine on silvercolloids. The appearance of these modes have been attributedto the FG effect due to surface roughness. We have shown thata FG contribution to the EM mechanism is required to observethese modes (Figure 7) and that the relative intensity of ν4 and

ν11 observed22 suggests that pyridine is (nearly) flat on thesurface for the majority of molecules in the ensemble. Figure 7(top) shows the experimental data for pyridine on cold-deposited silver under vacuum22 which we are able toreproduce (Figure 7 bottom) using the FG mechanism, byassuming a tilt angle of 25° and a high ∇E/E ratio (a 10 bohrdipolar sphere). We are able to reproduce most of the relativeintensities observed with the exception of ν1 and ν12 (which isincorrectly described using the BP86 functional70,71) as well asthe intensity of ν15. This argument of an (almost) flatorientation of pyridine on roughened silver electrode was alsomade by Creighton considering surface selection of the α-tensor,67 and by STM experiments at low temperatures andcoverages.60−62 These modes disappear at higher temper-atures22 even though STM results show that pyridine remainsin a flat or tilted orientation60 indicating that observation ofthese modes may be due to roughness on an atomic level. Theobservation of these effects in the SERS spectra for pyridine onsilver electrodes at high negative potentials may also be partiallyexplained using FG arguments. Experiments have shown thatincreasing negative electrode potentials result in increase in theintensitiy of ν4, ν9a, and ν11 (among others) and decrease inν12.

68,69 These are all behaviors that are also observed (with theexception of ν9a) under a FG mechanism (see Figure 5). Theintensity of ν4 and ν11 in particular suggests a (nearly) flatorientation in these experiments. Predicting orientation changewith electrode potential using the FG mechanism is difficult,but one can show the relative behavior of all modes (with theexception of ν9a) if a small (fixed) tilt angle is assumed and the∇E/E ratio is increased with increasing potential. Therefore,the behavior of these modes as seen in experiments are likelynot entirely due to the CM mechanism and may be partiallyexplained by an EM FG mechanism.

Field-Gradient Effects in Atomistic Models. The SERSspectra of benzene and pyridine simulated in this work (Figures2, 3, 4, 5, and 7) suggest that radii of curvature on the order of10−40 bohrs is needed to produce observable FG effects.These small radii of curvature indicate surface roughness on theorder of a few atoms (previously suggested after observation ofthese forbidden modes in pyridine only at low temperatures22).This implies that an atomistic model may be required for abetter description of the FG resulting from surface roughness.Quantum mechanical simulations of SERS based on thedipole−dipole polarizability for a supermolecule system(molecule plus small part the metal nanoparticle) alreadyaccount implicitly for the FG effects.13,72 However, this has notbeen demonstrated explicitly since such simulations alsoinclude contributions from the CM mechanism.We will show that FG contributions are included in a

supermolecule dipole−dipole polarizability using the DIM/QMmodel, which retains a detailed atomistic structure of thenanoparticle and provides a natural bridge between theelectronic structure methods and the macroscopic electro-dynamics description. Furthermore, since CM effects are notincluded in the DIM/QM model the spectral changes are onlydue to interactions between the molecule and an inhomoge-nous electric field. We will examine the extreme case ofbenzene sitting flat on the vertex of an Ag2057 icosahedron(inset in Figure 8). The small radius of curvature at the tip ofthe icosahedron ensures that the FG perpendicular to the planeof the ring in the vicinity of the molecule is very pronounced,and one would expect large enhancement of ν11. Figure 8ashows the SERS spectrum simulated using the DIM/QM

Figure 7. SERS of pyridine on cold-deposited rough silver undervacuum22 (top), and the simulated NRS and SERS spectra assuming atilt angle of 25° with respect to the surface of a 15 bohr diametersphere with contributions from only the local electric field, and boththe local electric field and gradient.



method, whereas Figure 8b,c shows the same system with thelocal field and gradient coupled in separately using eq 6. Thelocal fields in Figure 8b and c are calculated using the DIMmethod and should be identical to those used in Figure 8a, withthe only difference being the way in which they are coupled.Figure 8a shows contributions from ν11 and ν19, which areRaman-inactive but FG-active. The intensities of Raman-activeν6, ν8, ν9, and ν10 are very weak. We are therefore only able tosimulate these Raman-inactive modes after including the FGfrom the icosahedron (Figure 8c). It should also be noted thatDIM/QM interaction21 results in shifting of vibrationalfrequencies, as seen in Figure 8, which is not captured usingeq 6. While benzene sitting flat on a surface tip may beunphysical, it clearly shows that the supermolecule polarizabilitycalculated using the DIM/QM method includes contributionsfrom local electric FG. In addition to this, DIM/QM allows usto account for the shift in vibrational frequencies due tosubstrate/molecule interactions.Theoretically, the CM mechanism is elucidated from full QM

calculations where the substrate is also treated using QM.However, since these results also contain effects of the FG, itbecomes difficult to separate the two mechanisms based onthese types of calculations. As we have shown in this paper, alot of the effects typically attributed to the CM mechanism forpyridine may also be explained by a FG mechanism.

■ CONCLUSIONIn this work we derived an origin-independent SERS expressionwhich includes the effects of the FG. We used this expression tosimulate the SERS spectra of benzene and pyridine on modelsubstrates and examined the effects of the FG. We found thatwe are able to correctly describe observed Raman-inactivemodes in the SERS spectrum of benzene without lowering ofmolecular symmetry and that our results verified surfaceselection rules previously outlined for FG effects in SERS. Wewere also able to reproduce experimental results assuming a 10°tilt of the benzene plane with respect to the surface. For

pyridine, we found that FG effects may lead to bothenhancement and weakening of modes (the exact behavior isdependent on the FG to field strength ratio) and that we areable to describe modes observed in a low temperature, lowcoverage experiment by assuming a tilt angle of 25°. Also, forpyridine, we observed that the FG mechanism correctlydescribes effects that are generally associated with the CMmechanism. Enhancement under the FG mechanism requiredsurface roughness of atomic dimensions and we showed thatthe DIM/QM (atomistic) method accounted for these effectsin the calculation of the polarizability of the molecule−substratecomplex. Electromagnetic hotspots in the junction betweennanoparticles are typically only a few nanometers in dimensionsand thus should have small radii of curvature. Since hotspotsare responsible for the largest enhancements in SERS we expectthat FG effects should be considered. The results presentedhere demonstrate the importance of FG effects in under-standing relative SERS intensities.

■ ASSOCIATED CONTENT*S Supporting InformationSpecific details regarding the solution to the origin-dependenceof the effective polarizability. This material is available free ofcharge via the Internet at http://pubs.acs.org/.

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

■ ACKNOWLEDGMENTSThis work was supported by the NSF Center for ChemicalInnovation dedicated to Chemistry at the Space-Time Limit(CHE-082913) and the NSF CAREER program (Grant No.CHE-0955689) . We acknowledge helpful discussions with V.A. Apkarian, and support received from Research Computingand Cyberinfrastructure, a unit of Information TechnologyServices at Penn State.

■ REFERENCES(1) Moskovits, M. Surface-enhanced spectroscopy. Rev. Mod. Phys.1985, 57, 783−826.(2) Campion, A.; Kambhampati, P. Surface-enhanced Ramanscattering. Chem. Soc. Rev. 1998, 27, 241−250.(3) Kneipp, K.; Kneipp, H.; Itzkan, I.; Dasari, R. R.; Feld, M. S.Ultrasensitive Chemical Analysis by Raman Spectroscopy. Chem. Rev.1999, 99, 2957−2976.(4) Link, S.; El-Sayed, M. A. Optical Properties and UltrafastDynamics of Metallic Nanocrystals. Annu. Rev. Phys. Chem. 2003, 54,331−366.(5) Kneipp, K.; Wang, Y.; Kneipp, H.; Perelman, L. T.; Itzkan, I.;Dasari, R. R.; Feld, M. S. Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS). Phys. Rev. Lett. 1997, 78, 1667−1670.(6) Nie, S. M.; Emory, S. R. Probing single molecules and singleNanoparticles by Surface-Enhanced Raman Scattering. Science 1997,275, 1102−1106.(7) Michaels, A. M.; Nirmal, M.; Brus, L. E. Surface Enhanced RamanSpectroscopy of Individual Rhodamine 6G Molecules on Large AgNanocrystals. J. Am. Chem. Soc. 1999, 121, 9932−9939.(8) Xu, H.; Bjerneld, E. J.; Kall, M.; Borjesson, L. Spectroscopy ofSingle Hemoglobin Molecules by Surface Enhanced Raman Scattering.Phys. Rev. Lett. 1999, 83, 4357−4360.

Figure 8. SERS spectrum of benzene sitting flat on the vertex of anAg2057 icosahedron (inset) simulated with (a) the DIM/QM method,(b) local field from the DIM system, and (c) local field and gradientfrom the DIM system. The systems were excited at 488 nm which isfar from the plasmon resonance of the Ag2057 cluster and results inenhancement of the NRS spectrum by a factor of ∼10.



http://pubs.acs.org/

mailto:[email protected]

(9) Dieringer, J. A.; Lettan, R. B.; Scheidt, K. A.; Van Duyne, R. P. AFrequency Domain Existence Proof of Single-Molecule Surface-Enhanced Raman Spectroscopy. J. Am. Chem. Soc. 2007, 129,16249−16256.(10) Le Ru, E. C.; Etchegoin, P. G. Single-Molecule Surface-Enhanced Raman Spectroscopy. Annu. Rev. Phys. Chem. 2012, 63, 65−87 PMID: 22224704..(11) Metiu, H.; Das, P. The Electromagnetic Theory of SurfaceEnhanced Spectroscopy. Annu. Rev. Phys. Chem. 1984, 35, 507−536.(12) Schatz, G. C. Theoretical studies of surface enhanced Ramanscattering. Acc. Chem. Res. 1984, 17, 370−376.(13) Jensen, L.; Aikens, C. M.; Schatz, G. C. Electronic structuremethods for studying surface-enhanced Raman scattering. Chem. Soc.Rev. 2008, 37, 1061−1073.(14) Morton, S. M.; Silverstein, D. W.; Jensen, L. Theoretical Studiesof Plasmonics using Electronic Structure Methods. Chem. Rev. 2011,111, 3962−3994.(15) Moskovits, M. Persistent misconceptions regarding SERS. Phys.Chem. Chem. Phys. 2013, 15, 5301−5311.(16) Schatz, G. C.; Young, M. A.; Van Duyne, R. P. In Surface-Enhanced Raman Scattering - Physics and Applications, Kneipp, K.,Moskovits, M., Kneipp, H., Eds.; Topics in Applied Physics; Springer-Verlag: Berlin, 2006; Vol. 103, Chapter 2, pp 19−45.(17) Moskovits, M. Surface-enhanced Raman spectroscopy: a briefretrospective. J. Raman Spectrosc. 2005, 36, 485−496.(18) Gersten, J.; Nitzan, A. Electromagnetic theory of enhancedRaman scattering by molecules adsorbed on rough surfaces. J. Chem.Phys. 1980, 73, 3023−3037.(19) Le Ru, E. C.; Etchegoin, P. G. Rigorous justifaction of the |E|4

enhancement factor in surface enhanced Raman spectroscopy. Chem.Phys. Lett. 2006, 423, 63−66.(20) Feibelman, P. J. Microscopic calculation of electromagneticfields in refraction at a jellium-vacuum interface. Phys. Rev. B 1975, 12,1319−1336.(21) Payton, J. L.; Morton, S. M.; Moore, J. E.; Jensen, L. A discreteinteraction model/quantum mechanical method for simulating surface-enhanced Raman spectroscopy. J. Chem. Phys. 2012, 136, 214103.(22) Moskovits, M.; DiLella, D. P.; Maynard, K. J. Surface Ramanspectroscopy of a number of cyclic aromatic molecules adsorbed onsilver: Selection rules and molecular reorientation. Langmuir 1988, 4,67−76.(23) Sass, J. K.; Neff, H.; Moskovits, M.; Holloway, S. Electric fieldgradient effects on the spectroscopy of adsorbed molecules. J. Phys.Chem. 1981, 85, 621−623.(24) Moskovits, M.; DiLella, D. P. Surface-enhanced Ramanspectroscopy of benzene and benzene-d[sub 6] adsorbed on silver. J.Chem. Phys. 1980, 73, 6068−6075.(25) Wolkow, R. A.; Moskovits, M. Benzene adsorbed on silver: Anelectron energy loss and surface-enhanced Raman study. J. Chem. Phys.1986, 84, 5196−5199.(26) Janesko, B. G.; Scuseria, G. E. Surface enhanced Raman opticalactivity of molecules on orientationally averaged substrates: Theory ofelectromagnetic effects. J. Chem. Phys. 2006, 125, 124704.(27) Ayars, E. J.; Hallen, H. D.; Jahncke, C. L. Electric Field GradientEffects in Raman Spectroscopy. Phys. Rev. Lett. 2000, 85, 4180−4183.(28) Hallen, H. D.; Jahncke, C. L. The electric field at the apex of anear-field probe: implications for nano-Raman spectroscopy. J. RamanSpectrosc. 2003, 34, 655−662.(29) Banik, M.; El-Khoury, P. Z.; Nag, A.; Rodriguez-Perez, A.;Guarrottxena, N.; Bazan, G. C.; Apkarian, V. A. Surface-EnhancedRaman Trajectories on a Nano-Dumbbell: Transition from Field toCharge Transfer Plasmons as the Spheres Fuse. ACS Nano 2012, 6,10343−10354.(30) Aikens, C. M.; Madison, L. R.; Schatz, G. C. Ramanspectroscopy: The effect of field gradient on SERS. Nat. Photonics2013, 7, 508−510.(31) Takase, M.; Ajiki, H.; Mizumoto, Y.; Komeda, K.; Nara, M.;Nabika, H.; Yasuda, S.; Ishihara, H.; Murakoshi, K. Selection-rule

breakdown in plasmon-induced electronic excitation of an isolatedsingle-walled carbon nanotube. Nat. Photonics 2013, 7, 550−554.(32) Gao, X.; Davies, J. P.; Weaver, M. J. Test of surface selectionrules for surface-enhanced Raman scattering: the orientation ofadsorbed benzene and monosubstituted benzenes on gold. J. Phys.Chem. 1990, 94, 6858−6864.(33) Morton, S. M.; Jensen, L. A Discrete Interaction Model/Quantum Mechanical Method for Describing Response Properties ofMolecules Adsorbed on Metal Nanoparticles. J. Chem. Phys. 2010, 133,074103.(34) Morton, S. M.; Jensen, L. A discrete interaction model/quantummechanical method to describe the interaction of metal nanoparticlesand molecular absorption. J. Chem. Phys. 2011, 135, 134103.(35) García de Abajo, F. J. Nonlocal Effects in the Plasmons ofStrongly Interacting Nanoparticles, Dimers, and Waveguides. J. Phys.Chem. C 2008, 112, 17983.(36) Halas, N. J.; Lal, S.; Chang, W.-S.; Link, S.; Nordlander, P.Plasmons in Strongly Coupled Metallic Nanostructures. Chem. Rev.2011, 111, 3913−3961.(37) Toscano, G.; Raza, S.; Xiao, S.; Wubs, M.; Jauho, A.-P.;Bozhevolnyi, S. I.; Mortensen, N. A. Surface-enhanced Ramanspectroscopy: nonlocal limitations. Opt. Lett. 2012, 37, 2538−2540.(38) Baerends, E.; Autschbach, J.; Berces, A.; Bickelhaupt, F.; Bo, C.;Boerrigter, P.; Cavallo, L.; Chong, D.; Deng, L.; Dickson, R. et al.Amsterdam Density Functional, 2012; http://www.scm.com.(39) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; FonsecaGuerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T.Chemistry with ADF. J. Comput. Chem. 2001, 22, 931−967.(40) Becke, A. D. Density-Functional Exchange-Energy Approx-imation with Correct Asymtotic-Behavior. Phys. Rev. A 1988, 38,3098−3100.(41) Perdew, J. P. Density-functional approximation for thecorrelation energy of the inhomogeneous electron gas. Phys. Rev. B1986, 33, 8822−8824.(42) Zhao, L.; Jensen, L.; Schatz, G. C. Pyridine-Ag20 Cluster: AModel System for Studying Surface-Enhanced Raman Scattering. J.Am. Chem. Soc. 2006, 128, 2911−2919.(43) Jensen, L.; Autschbach, J.; Schatz, G. C. Finite lifetime effects onthe polarizability within time-dependent density-functional theory. J.Chem. Phys. 2005, 122, 224115.(44) Jensen, L.; Zhao, L. L.; Autschbach, J.; Schatz, G. C. Theory andmethod for calculating resonance Raman scattering from resonancepolarizability derivatives. J. Chem. Phys. 2005, 123, 174110.(45) Zhao, L. L.; Jensen, L.; Schatz, G. C. Surface-Enhanced RamanScattering of Pyrazine at the Junction between Two Ag20 Nano-clusters. Nano Lett. 2006, 6, 1229−1234.(46) Jensen, L.; Schatz, G. C. Resonance Raman Scattering ofRhodamine 6G as Calculated Using Time-Dependant DensityFunctional Theory. J. Phys. Chem. A 2006, 110, 5973−5977.(47) Johnson, P. B.; Christy, R. W. Optical Constants of the NobleMetals. Phys. Rev. B 1972, 6, 4370−4379.(48) Jensen, L. L.; Jensen, L. Electrostatic Interaction Model for theCalculation of the Polarizability of Large Noble Metal Nanoclusters. J.Phys. Chem. C 2008, 112, 15697−15703.(49) Jensen, L. L.; Jensen, L. Atomistic Electrodynamics Model forOptical Properties of Silver Nanoclusters. J. Phys. Chem. C 2009, 113,15182−15190.(50) Long, D. A. The Raman Effect: A Unified Treatment of the Theoryof Raman Scattering by Molecules; John Wiley & Sons, Ltd.: WestSussex, England, 2002; pp 85−152, 221−270.(51) Corni, S.; Tomasi, J. Theoretical evaluation of Raman spectraand enhancement factors for a molecule adsorbed on a complex-shaped metal particle. Chem. Phys. Lett. 2001, 342, 135−140.(52) Corni, S.; Tomasi, J. Erratum to: Theoretical evaluation ofRaman spectra and enhancement factors for a molecule adsorbed on acomplex-shaped metal particle [Chem. Phys. Lett. 2001, 342, 135−140]. Chem. Phys. Lett. 2002, 365, 552−553.(53) Neugebauer, J.; Reiher, M.; Kind, C.; Hess, B. A. Quantumchemical calculation of vibrational spectra of large molecules - Raman



http://www.scm.com

and IR spectra for Buckminsterfullerene. J. Comput. Chem. 2002, 23,895−910.(54) Lund, P.; Smardzewski, R.; Tevault, D. Surface-enhanced Ramanspectra of benzene and benzene-d6 on vapor-deposited sodium. Chem.Phys. Lett. 1982, 89, 508 −510.(55) Krasser, W.; Ervens, H.; Fadini, A.; Renouprez, A. J. Ramanscattering of benzene and deuterated benzene chemisorbed on silica-supported nickel. J. Raman Spectrosc. 1980, 9, 80−84.(56) Lund, P. A.; Tevault, D. E.; Smardzewski, R. R. Surface-enhanced Raman spectroscopy of benzene adsorbed on vapor-deposited sodium. Chemical contribution to the enhancementmechanism. J. Phys. Chem. 1984, 88, 1731−1735.(57) Demuth, J. E.; Christmann, K.; Sanda, P. N. The vibrations andstructure of pyridine chemisorbed on Ag(111): the occurrence of acompressional phase transformations. Chem. Phys. Lett. 1980, 76, 201−206.(58) Bader, M.; Haase, J.; Frank, K.-H.; Puschmann, A.; Otto, A.Orientational phase transition in the system pyridine/Ag(111): Anear-edge x-ray-absorption fine-structure study. Phys. Rev. Lett. 1986,56, 1921−1924.(59) Lee, J.-G.; Ahner, J.; Yates, J. T., Jr The adsorption conformationof chemisorbed pyridine on the Cu(110) surface. J. Chem. Phys. 2001,114, 1414−1419.(60) Dougherty, D. B.; Lee, J.; Yates, J. T. Role of Conformation inthe Electronic Properties of Chemisorbed Pyridine on Cu(110): AnSTM/STS Study. J. Phys. Chem. B 2006, 110, 11991−11996 PMID:16800507..(61) Hahn, J. R.; Ho, W. Imaging and vibrational spectroscopy ofsingle pyridine molecules on Ag(110) using low-temperature scanningtunneling microscope. J. Chem. Phys. 2006, 124, 204708−1−4.(62) Hou, J. Q.; Kang, H. S.; Kim, K. W.; Hahn, J. R. Bindingcharacteristics of pyridine on Ag(110). J. Chem. Phys. 2008, 128,134707.(63) Jeanmaire, D. L.; Van Duyne, R. P. Surface RamanSpectroelectrochemistry 0.1. Heterocyclic, Aromatic, and Aliphatic-Amines Adsorbed on Anodized Silver Electrode. J. Electroanal. Chem.1977, 84, 1−20.(64) Creighton, J. A.; Albrecht, M. G.; Hester, R. E.; Matthew, J. A.D. The dependence of the intensity of Raman bands of pyridine at asilver electrode on the wavelength of excitation. Chem. Phys. Lett. 1978,55, 55−58.(65) Krasser, W.; Kettler, U.; Bechthold, P. S. Luminescence andenhanced Raman spectra of pure and pyridine-bonded small silverclusters. Chem. Phys. Lett. 1982, 86, 223−227.(66) Clark, R. J. H.; Williams, C. S. The Far-Infrared Spectra ofMetal-Halide Complexes of Pyridine and Related Ligands. Inorg.Chem. 1965, 4, 350−357.(67) Creighton, J. Surface raman electromagnetic enhancementfactors for molecules at the surface of small isolated metal spheres:The determination of adsorbate orientation from sers relativeintensities. Surf. Sci. 1983, 124, 209−219.(68) Arenas, J. F.; Lopez Tocon, I.; Otero, J. C.; Marcos, J. I. Charge-Transfer Processes in Surface-Enhanced Raman Scattering. Franck-Condon Active Vibrations of Pyridine. J. Phys. Chem. 1996, 100,9254−9261.(69) Creighton, J. The resonance Raman contribution to sers:Pyridine on copper or silver in aqueous media. Surf. Sci. 1986, 173,665−672.(70) Moore, J. E.; Morton, S. M.; Jensen, L. Importance of CorrectlyDescribing Charge-Transfer Excitations for Understanding theChemical Effect in SERS. J. Phys. Chem. Lett. 2012, 3, 2470−2475.(71) Mullin, J. M.; Autschbach, J.; Schatz, G. C. Time-dependentdensity functional methods for surface enhanced Raman scattering(SERS) studies. Comput. Theor. Chem. 2012, 987, 32−41.(72) Kedziora, G. S.; Schatz, G. C. Calculating dipole and quadrupolepolarizabilities relevant to surface enhanced Raman spectroscopy.Spectrochim. Acta, Part A 1999, 55, 625−638.



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