Theoretical modeling of voltage effects and the chemical ......Rebecca L. Gieseking, Mark A. Ratner...

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Theoretical modeling of voltage effectsand the chemical mechanism in surface-enhanced Raman scattering†

Rebecca L. Gieseking, Mark A. Ratner and George C. Schatz *

Received 7th April 2017, Accepted 28th April 2017

DOI: 10.1039/c7fd00122c

Theoretical approaches can provide insight into the mechanisms and magnitudes of

electromagnetic and chemical effects in surface-enhanced Raman scattering (SERS),

properties that are not readily available experimentally. Here, we model the SERS

spectra of two geometries of the prototypical Ag20–pyridine cluster using

a semiempirical INDO/SCI approach that allows a straightforward decomposition of the

enhancement factors at each wavelength into electromagnetic and chemical terms,

with proper treatment of resonant charge-transfer contributions to the enhancement.

The method also enables us to determine the dependence of the enhancement on the

electrochemical potential. We show that the electromagnetic enhancements for the

Ag20 cluster are <10 far from resonance but can increase to 102 to 103 on resonance

with plasmon excitation in the cluster. The decomposition also shows that for the

systems studied here, the chemical enhancements are primarily due to resonance with

excited states with significant charge-transfer character. This term is typically <10 but

can be >102 at electrochemical potentials where the charge-transfer excited states are

resonant with the incoming light, leading to total enhancements of >104.

1. Introduction

Raman spectroscopy is a useful approach to gaining structural informationabout molecules; however, the scattering intensities are usually quite small andonly detectable for large ensembles of molecules. However, for molecules nearplasmonic metal nanostructures, the signal can be enhanced by many orders ofmagnitude, which is referred to as surface-enhanced Raman scattering(SERS).1–3 The enhancement factors (EFs) can be as large as 1010, which issufficient to allow the detection of single molecules.4,5 These large enhance-ments have enabled the development of SERS into an analytical technique for

Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA.

E-mail: [email protected]; Tel: +1-847-491-5657

† Electronic supplementary information (ESI) available: INDO/SCI excited-state energies and Ramanspectra of the Ag20–pyridine complex with an applied potential. See DOI: 10.1039/c7fd00122c

This journal is © The Royal Society of Chemistry 2017 Faraday Discuss., 2017, 205, 149–171 | 149

http://orcid.org/0000-0001-5837-4740

http://dx.doi.org/10.1039/c7fd00122c

http://pubs.rsc.org/en/journals/journal/FD

http://pubs.rsc.org/en/journals/journal/FD?issueid=FD017205

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ultrasensitive detection in elds such as biosensing6–8 and nanoscaleelectrochemistry.9–13

Although the primary mechanism of the SERS enhancement is an electro-magnetic mechanism (EM) related to enhancement of the local electric eld of thelight by the plasmonic metal nanostructure,3–5,14 chemical interactions betweenthe metal nanostructure and the molecule can also contribute to the enhance-ment. This chemical mechanism (CM) includes two proposed contributions: (1)chemical changes to the adsorbate ground-state electronic structure induced byinteractions with the metal surface, which we refer to as the GS mechanism, and(2) the introduction of excited states involving charge transfer (CT) between themetal and the molecule, which we call the CT mechanism.15–17 In addition,resonance of the molecular excitations with the light can lead to stronglyenhanced Raman spectra,4,17 but this is normally thought of as a distinct effect,namely surface enhanced resonant Raman scattering (SERRS), rather than as partof the CM. The magnitude and exact mechanism of the CM enhancements arestill somewhat controversial.18 Although early Raman scattering measurementson smoothmetal surfaces estimated chemical enhancements on the order of 10 to102,19–21 enhancements of up to 107 have been proposed experimentally fornanostructures where electromagnetic enhancement appears insufficient toexplain the observed enhancement.22–24

It has long been known that the SERS enhancement factors are stronglydependent on the applied voltage at a silver electrode.1,2,25,26 Although theseenhancements may be due in part to complexities in the electrochemical envi-ronment (including voltage-dependent changes in surface coverage, molecularorientation or binding sites, and variations in the double-layer properties), thesefactors are not sufficient to explain factors such as why the potential at which theRaman intensities are maximized depends on the incident photon energy,25,26 orthe differences in the potential dependence of the intensities of different vibra-tional modes.1,27,28 Although the EM provides the largest contribution to the SERSenhancement factor in many cases,3,18 it does not explain large voltage-basedchanges (in part because the carrier concentrations and therefore plasmonenergies are not strongly dependent on voltage for a plasmonic metal). Thus,differences in the intensity as the voltage is varied are likely based on changes inthe CM. In particular, both the GS electronic structure and the energies of the CTexcited states may in principle be perturbed in the presence of an appliedpotential.

Quantum mechanical calculations have the potential to provide insight intothe mechanism and magnitude of the CM enhancements that is not readilyavailable via experimental approaches. Models using density functional theory(DFT) approaches have predicted CT enhancements as large as 103 for theprototypical Ag20–pyridine complex (i.e., pyridine adsorbed on a Ag20 tetrahedron,where the silver cluster is known to have plasmonic excited states near 3.3–3.4 eV(ref. 29) and which therefore is a reasonable model for studying SERS) due to thepresence of low-energy CT excited states.30,31 These calculations also suggest thatthe primary direction of charge transfer is dependent on the chemical nature ofthe metal–molecule interaction.32,33 Although these computations have showngood agreement with some experimental trends in the chemical enhancementsfor Ag–thiol and Au–thiol systems,33 these models are still limited, as typical DFTfunctionals are well-known to underestimate the energies of CT excited states,

150 | Faraday Discuss., 2017, 205, 149–171 This journal is © The Royal Society of Chemistry 2017


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presumably overestimating the CM when this happens.34–36 Consistent with this,it has been shown that the computed CM enhancements are quite sensitive to thechoice of functional, and in particular to the energies of the CT states.37 Inaddition, it is challenging to determine the relative contributions of the variousenhancement mechanisms using a single theory and structural model.38–40

Previous DFT models have approximated the CM enhancements as the non-resonance EFs and the EM enhancements as the ratio of resonance and non-resonance EFs.30,31,41 However, this approximation neglects non-resonant EMenhancements and assumes that CM enhancements are constant with energy. Onat metal surfaces where plasmonic excitation is forbidden, EM enhancementsrelated to reection of the incident light are on the order of 3–4.42 Even therelatively small metal clusters used in quantum mechanical studies are signi-cantly more polarizable than typical molecules, suggesting that minor polariza-tion effects on the electronic structure may lead to non-negligible EMenhancements far from resonance. In addition, the CM enhancements are likelyto be energy-dependent, particularly at photon energies near resonance with CTstates.

New theoretical approaches are needed to gain a deeper understanding of theCM enhancements and, in particular, the role and magnitude of the CT term. Wehave shown that the semiempirical INDO/SCI approach predicts absorptionspectra and plasmonic properties of prototypical Ag clusters without ligands ingood agreement with those computed using TD-DFT approaches.43,44 In addition,since INDO is free from self-interaction error, it has been shown in several casesto predict accurate CT state energies.45,46 We have also recently developed anapproach to apply a potential to metal clusters within the INDO approach47 usingan orbital energy shi approximation (OESA)48–51 which allows us to study thepotential dependence of the Raman spectra. This suggests that the INDO/SCIapproach can be used to model systems where Ag clusters interact with ligandmolecules, enabling the calculation of SERS spectra with the proper inclusion ofCT effects.

Here, we model the Raman spectrum of the prototypical Ag20–pyridine clusterusing a semiempirical INDO/SCI approach that allows a straightforward decom-position of the EFs at each wavelength into EM and CM terms, and which alsoenables us to describe the effect of changing the electrochemical potential (i.e.,varying the Fermi energy) in the SERS substrate. We show that the EMenhancements for the Ag20 cluster are <10 far from resonance but can increase to102 to 103 on resonance with plasmon excitation in the cluster. The decomposi-tion also shows that for the systems studied here, the CT term is the dominantcontributor to the CM enhancement. This term is typically <10 but can be >102 atpotentials where the CT excited states are resonant with the incoming light,leading to total enhancements of >104 at potentials where the CT states are nearresonance with the plasmon.

2. Computational methodology

Although the important new content of this work is based on semiempiricalcalculations, we performed density functional theory (DFT) calculations todetermine the geometries and vibrational frequencies of all the species studied,and to provide reference results for the INDO studies. For the small prototypical




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Ag–ligand clusters, geometry optimizations were performed using a DFTapproach with the BP86 functional52,53 and the def2-TZVP basis set54 with aneffective core potential for Ag.55 For benchmarking studies, the excited states anddipole moments were then computed at the EOM-CCSD/def2-TZVP level.56 Thesecalculations were performed using QChem 4.4.57

The geometries and vibrational frequencies of the pyridine molecules and theAg20–pyridine complexes were computed using the BP86 functional with the TZPSlater-type basis set. We consider a tetrahedral Ag20 cluster with pyridine adsor-bed such that the nitrogen atom interacts either with the central atom of one ofthe triangular sides of the cluster (“Surface”) or with one of the tip atoms of thetetrahedron (“Vertex”). The 1s–4s core was frozen for Ag, and an all-electron basisset was used for all other atoms. Scalar relativistic effects were accounted forusing the zeroth-order regular approximation (ZORA).58 The excited states werealso computed at the TD-DFT level. Frequency-dependent Raman intensities werecomputed using the AOResponse module in ADF with a lifetime broadening ofG ¼ 0.004 a.u. (0.1088 eV). This value is comparable to the plasmon width basedon commonly used Drude functions for silver, and it has been used extensively inearlier theory work.30 We assume that this applies to all excited states in this studyincluding local pyridine excited states and charge-transfer states. We note that theresonance contributions to the Raman intensities scale approximately as 1/G4.59

(Here we note that charge transfer states are oen considered to be broader thanplasmons, in which case the present results will serve as an upper bound to theimportance of CT states in SERS.)60 The Raman intensities were computed at2.00 eV and on resonance with the main plasmonic peak (3.45 eV in the Surfacegeometry; 3.43 eV in the Vertex geometry). These calculations were performedusing the Amsterdam Density Functional (ADF) 2014 program.61

Semiempirical calculations using the Intermediate Neglect of DifferentialOverlap (INDO) Hamiltonian were performed as single-point calculations usingparameters adapted from our recently benchmarked parameter set for Ag43,62 andZerner’s INDO/S parameters63 (where the parameters were optimized for spec-troscopic properties) for all other atoms. Unless otherwise specied, the one-electron, two-center resonance integrals for Ag were set to bsp ¼ �2.5 eV andbd ¼ �30 eV. The excited states were computed using a conguration interaction(CI) approach using single excitations (SCI). All possible single excitations withinthe INDO basis were generated, and the lowest 7000 congurations were includedin the CI matrix; this matrix was diagonalized to obtain the lowest 2000 excitedstates. Since this method uses a minimal basis set and replaces the calculation oftwo electron integrals with empirical expressions, we are able to compute fairlyaccurate CT state energies45,46 at a computational cost roughly an order ofmagnitude smaller than that of previous DFT-based approaches.

To distinguish CM and EM contributions to the enhancement, the excitedstates were also computed using a modied INDO parameter set, indicated byINDO-EM, where the overlap of Ag atomic orbitals with atomic orbitals on anyother element was neglected. To determine the excited states with an appliedpotential, we invoked an orbital energy shi approximation (OESA) in which theINDO parameters corresponding to the Ag s, p, and d atomic orbital energies wereshied by a value corresponding to the applied potential, and the excited stateswere computed as described above. As has been previously done in semiempiricalmodels,47–49,51 we assume that a 1 eV shi in the orbital energies corresponds to




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a�1 V change in potential, and all potentials are referenced to the standard INDOparameters. These calculations were performed using a code incorporatingportions of MOPAC 7.1 (ref. 64) and the INDO/CI code from Jeffrey Reimers.65

Since the INDO/S parameters are designed to reproduce spectroscopic prop-erties and perform poorly for geometries and vibrational modes, the Raman andSERS intensities at the INDO/SCI level were computed using the BP86/TZPgeometries, normal coordinates, and vibrational frequencies. The frequency-dependent polarizabilities aij(u) were computed using a sum-over-states (SOS)approach using the INDO/SCI excited states as

aijðuÞ ¼Xe

hgjmijei�e��mj

��g�Ege � ħu� iGge

þ hgjmijei�e��mj

��g�Ege þ ħuþ iGge

(1)

where g is the electronic ground state and e is an electronic excited state, mirepresents the dipole moment operator for Cartesian axis i, Ege is the excitationenergy from state g to state e, u is the frequency of the incident light, and Gge is thelifetime broadening of excited state e, set to 0.004 a.u. for consistency with theresponse function results. The differential polarizabilities were computed bynumerical differentiation with respect to displacement of the system by �0.01 Aalong each normal coordinate.

Using these polarizabilities, the scattering factor S was computed as

S ¼ 45a0p2 þ 7g0

p2 (2)

where the prime indicates a derivative with respect to normal coordinate p. Theisotropic derivative a0

p is dened by

a0p2 ¼

Xi

��13ða0iiÞp

��2

(3)

and the anisotropic derivative g0p is given by

g0p2 ¼ 1

2

��a0xx � a0

yy

��2 þ ��a0yy � a0

zz

��2 þ ja0zz � a0

xxj2�þ 3

��a0xy

��2 þ ��a0yz

��2þ ja0

zxj2�

(4)

The differential cross-section for Stokes scattering with a 90� scattering angleand perpendicular plane-polarized light is66

vs

vU¼ p2

302

�u� up

�4 h

8p2cup

S

45

1

1� exp��hcup

�kBT

� (5)

where up is the vibrational frequency of mode p.To compare the overall enhancement factors between systems, the integrated

Raman enhancement factors EFint were computed as32

EFint ¼I totAg20�pyrI totpyr

¼Pk

IkAg20�pyrP

j

Ijpyr

(6)

where IkAg20�pyr is the differential Raman cross-section for the kth vibrational modeof the Ag20–pyridine complex, and correspondingly Ijpyr is the differential Raman




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cross-section for the jth vibrational mode of the isolated pyridine molecule. Thesummations over j and k include all modes with vibrational frequencies between500 and 2000 cm�1. This choice ensures that only modes corresponding to pyri-dine motions are included for the Ag20–pyridine complex, and it also neglects thehigh-frequency modes that are not usually measured experimentally and couldhave smaller EM enhancements due to their large Stokes shis.

Raman intensities at the INDO/SCI level were computed at 2.00 eV and onresonance with the plasmonic excitation in the Ag20–pyridine cluster (3.30 eV forthe Surface geometry; 3.44 eV for the Vertex geometry). For frequencies away fromthe plasmon resonance, the SOS polarizabilities converge slowly with the numberof excited states, so the differential polarizabilities for the Ag20–pyridine complexwere averaged for numbers of states from 1000 to 2000 in 100-state steps. We notethat in some cases the selected numbers of states led to anomalously large Ramanintensities due to reordering of the states such that states with signicantcontributions to the polarizability derivative were included only in certain dis-placed geometries; in these cases, the number of states included in the SOSpolarizabilities was shied by 5–10 states.

3. Results and discussion3.1. Benchmarking of INDO parameters for Ag–ligand interactions

Evaluating the SERS chemical enhancements requires accurate modeling of theinteraction of the molecule of interest with a metal cluster. Since our recentbenchmarking of the Ag INDO parameters focused solely on Ag clusters andneglected interactions of Ag with other atoms,43 here we benchmark the Ag one-electron, two-center resonance integrals bsp (for s and p orbitals) and bd (ford orbitals) for a series of 13 prototypical Ag–ligand clusters, including the Ag atomwith OH, SH, NH2, PH2, and CH3 ligands, and the Ag2 and Ag4

2+ clusters with SH2,NH3, PH3, and pyridine ligands. The bsp and bd parameters are used within thecalculation of the off-diagonal elements of the Hamiltonian to scale the overlapintegrals of atomic orbital pairs centered on different atoms. We use the EOM-CCSD/def2-TZVP values for the rst excited-state energies and dipole momentsas a reference.

Fig. 1 shows that the mean absolute error (MAE) in the excited-state energies isminimized at 0.25 eV when bsp ¼ �2.5 eV and bd ¼ �30 eV, signicantly smallerthan the MAE of 0.47 eV using our previous parameters43 bsp ¼ �3.0 eV and bd ¼�40 eV. In contrast, the MAE in the dipole moments is much more weaklydependent on the INDO parameters for Ag, primarily due to overestimation of thedipole moments at the INDO level. This may be due to the limitations of theminimal valence-only basis set used in the INDO approach, as similarly largeerrors in the dipole moments have previously been seen for Au complexes at theINDO level.65

The new parameters improve the accuracy of interactions between Ag andother atoms without signicantly changing the plasmonic properties of larger Agclusters. As shown in Fig. 1 (bottom), the absorption spectrum of the tetrahedralAg20 cluster retains one primary absorption peak; as expected for a plasmonicexcited state,29,43,67 the triply degenerate main absorbing state involves a linearcombination of many single-particle excitations with additive contributions to thetransition dipole moment. The absorption spectrum is also consistent with the



Fig. 1 Mean absolute errors in the INDO/SCI (top) excited-state energies and (middle)dipole moments of 13 small Ag–ligand clusters relative to the EOM-CCSD/def2-TZVPvalues as a function of the INDO parameters for Ag. (Bottom) Absorption spectrum of Ag20at the INDO/SCI and BP86/TZP levels.

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TD-DFT spectrum at the BP86/TZP level, although with nearly twice the oscillatorstrength. This consistency demonstrates that our newly benchmarked parameterscan be used for the interactions of Raman-active molecules with plasmonic Agclusters.

3.2. Absorption and Raman spectra of pyridine

We now turn to the optical and spectroscopic properties of the pyridine molecule.At both the INDO/SCI and BP86/TZP levels, the rst several excited states ofpyridine are weakly absorbing, and a pair of strongly absorbing p–p* transitionsare higher in energy, as shown in Fig. 2a. The computed energies are largelyconsistent with the experimental absorption spectrum,68 which has weakabsorption peaks at 4.96 and 6.36 eV and a strong absorption peak at 7.04 eV; thetotal oscillator strength of the main absorption peak is quite comparable betweenINDO/SCI and experiment (1.42 and 1.36, respectively). Although INDO/SCIunderestimates the energy of the main absorption peak by 0.5 eV relative toexperiment, these states are far enough from resonance at the energies of interestfor Raman spectroscopy (<4 eV) that the effect of this error on the polarizability isrelatively small. The orientationally averaged polarizability is underestimated atthe INDO/SCI level relative to DFT, primarily due to signicant underestimationof the polarizability perpendicular to the p plane resulting from the limitations ofthe minimal basis set in INDO.

The Raman spectrum of pyridine at the INDO/SCI level (Fig. 2c) is largelyconsistent with the BP86/TZP spectrum (Fig. 2d), with the intensities of most ofthe major peaks approximately doubled. We note that since the INDO parametersare designed to reproduce spectroscopic and not geometric properties, we use thegeometries and vibrational modes from the BP86/TZP computations, and thus the

Fig. 2 (a) Absorption spectrum of pyridine. (b) Convergence of the Raman intensities at2.00 eV with number of INDO/SCI excited states in the SOS expression. Normal Ramanspectra of pyridine at 2.00 eV at the (c) INDO/SCI and (d) BP86/TZP levels.




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only difference between the two spectra is the Raman intensities. The INDOpolarizability derivatives are computed by nite differencing the SOS polariz-abilities using geometries displaced along each normal coordinate; these polar-izabilities and Raman intensities are well converged by 150 excited states (27 eV),as shown in Fig. 2b. Even though the sum does not fully converge until 150 excitedstates for pyridine, the dominant contributions come from the pair of stronglyabsorbing states around 6.5 eV. The main Raman-active modes are two in-planering deformation modes at 595.3 and 649.9 cm�1, two ring breathing modes at976.8 and 1023.4 cm�1, a symmetric C–H wag at 1205.0 cm�1, and a pair of ringstretching modes at 1566.7 and 1570.9 cm�1. The largest difference between thetwo spectra is that several of the out-of-plane bending modes at 850 cm�1 and 900cm�1 have unphysically large Raman cross-sections at the INDO/SCI level, likelyrelated to limitations of the minimal basis set used in the INDO model. As will beshown in the next section, these modes are in general weakly enhanced incomplexes with Ag20 compared to the in-plane modes; thus, we focus on the othermodes and neglect this limitation.

3.3. Absorption and Raman spectra of Ag20–pyridine clusters

We now compare the bare pyridine absorption and Raman spectra to results fortwo geometries of the Ag20–pyridine complex, with the pyridine adsorbed eitheron one of the triangular faces (“Surface”) or on a tip (“Vertex”) of the tetrahedralAg20 cluster; these two prototypical cluster geometries have been used previouslyfor DFT studies of Raman enhancements,30,31 and the Surface complex especiallyleads to results that compare favorably with SERS experiments. Since experi-mental SERS studies of pyridine have been performed on much larger nano-structures than our Ag20 clusters,1,2,69 we focus primarily on comparisons amongdifferent levels of theory, rather than on comparisons with experiment. Theabsorption spectra of the Ag20–pyridine complexes (Fig. 3a and b) are dominatedby the absorption of the bare Ag20 cluster, with minimal changes due to theintroduction of localized pyridine excited states and charge-transfer excitedstates. We note that in the Vertex complex, the INDO/SCI plasmonic absorptionpeak is slightly broadened, with six excited states between 3.23 and 3.44 eV havingoscillator strengths greater than 1. This noticeable effect of a single molecule onthe plasmon is possible because of the small cluster size and is expected tobecome less signicant with increasing size; however, experimental studies haveshown that the Raman intensity is nonlinearly dependent on surface coverage dueto the inuence of induced dipoles in the adsorbed molecules on the plasmonlocal eld.70,71 One signicant difference between the DFT and INDO/SCI excitedstates is in the energies of the rst excited states with signicant CT character. Atthe BP86/TZP level, the rst states with substantial CT character occur at 2.23 and1.59 eV in the Surface and Vertex complexes, respectively; at the INDO/SCI level,the rst CT states occur at 3.47 and 3.89 eV in the same complexes. This differenceis unsurprising given the tendency of GGA functionals to signicantly underes-timate CT state energies.34–36

We focus rst on the normal Raman scattering (NRS) spectrum at 2.00 eV(¼477 nm). Although previous computational studies of this complex havecomputed the NRS at 2.41 eV (¼514.5 nm)30,31 corresponding to the energy used inearly experimental studies of pyridine on Ag,1 this energy is nearly resonant with



Fig. 3 (Top) Absorption spectra at the INDO/SCI and BP86/TZP levels and (bottom)convergence of the normal Raman intensities at 2.00 eV with the number of INDO/SCIexcited states in the SOS expression for the (a and c) Surface and (b and d) Vertexgeometries of the Ag20–pyridine complex.


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the rst shoulder peak in the INDO/SCI absorption spectrum of the Ag20–pyridinecomplexes. Our selection of a slightly lower energy removes the possibility ofresonance enhancement from this shoulder peak. Unlike for the isolated pyridinemolecule, the Raman intensities for both Ag20–pyridine complexes (Fig. 3c and d)at 2.00 eV show noticeable uctuations between 1000 and 2000 excited states (8.1–9.6 eV). Since excited states beyond the rst 2000 cannot be computed due tomemory limitations in the current code, we compute the Raman intensities as theaverage of the values from 1000 to 2000 excited states in 100-state steps. Althoughthe uctuations in the Raman intensities may appear large in some cases, theseuctuations are proportionally much smaller in systems with larger Ramanintensities, particularly where resonance enhancements from one or a few stateshave the dominant contributions to the differential polarizabilities, so theuncertainties in Fig. 3c and d refer to small enhancement factors that are lessrelevant to SERS experiments.

At 2.00 eV, the EFs are somewhat smaller overall at the INDO/SCI level than atthe BP86/TZP level as shown in Fig. 4, although the major trends are consistentbetween the two levels of theory (Table 1). The weaker enhancements at the INDO/SCI level can be attributed at least in part to the higher energies of the CT states: atthe BP86/TZP level, both complexes (in particular the Vertex complex showingstronger enhancement) have CT states relatively close to resonance with theincoming light, whereas at the INDO/SCI level the rst CT states are well over 1 eVhigher in energy than the incoming light. The modes that are most stronglyRaman active in the isolated pyridine molecule are in general the most stronglyenhanced, and the out-of-plane modes that had anomalously large enhancementsat the INDO/SCI level for the isolated pyridine are much less prominent in the



Fig. 4 Normal Raman scattering spectra at 2.00 eV for the (a and c) Surface and (b and d)Vertex geometries of the Ag20–pyridine complex at the (top) INDO/SCI and (bottom)BP86/TZP levels. Error bars in the INDO/SCI spectra indicate the standard deviations of theRaman intensities computed using 1000 to 2000 excited states in the SOS expression in100-state steps.

Table 1 Enhancement factors and frequency shifts of selected Raman modes for theAg20–pyridine complex at photon energies of 2.00 eV (NRS) and on resonance with theplasmon (SERS)

Mode (cm�1) Shi (cm�1)

EFNRS EFSERS

BP86/TZP INDO/SCI BP86/TZP INDO/SCI

Surface595.3 14.6 7.9 12.8 � 2.5 42 274.0 5298 � 55649.9 �0.6 0.6 1.4 � 0.1 57.6 987.7 � 1.5976.8 13.1 8.8 3.6 � 0.6 6159.2 978.6 � 3.81023.4 0.5 2.8 1.6 � 0.5 3904.5 448.9 � 2.61205.0 �1.0 3.5 8.4 � 2.8 3461.0 1955 � 221570.9 11.3 11.2 7.6 � 2.9 2509.1 2288 � 21EFint — 8.0 3.9 � 0.3 6528.4 932.0 � 2.5

Vertex595.3 21.5 24.9 2.2 � 0.7 11 887.0 1162 � 18649.9 �0.9 0.5 1.6 � 0.1 327.1 24.1 � 0.2976.8 18.2 5.9 3.4 � 0.6 3002.0 62.9 � 1.11023.4 3.7 22.1 1.9 � 0.5 1629.3 39.0 � 1.01205.0 0.4 14.3 14.0 � 3.5 12 094.2 1594 � 271570.9 17.0 66.2 4.3 � 1.8 3309.5 106.2 � 1.9EFint — 18.3 2.7 � 0.2 3843.2 124.3 � 0.9

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Ag20–pyridine complex. The shis in the vibrational frequencies are consistentwith those that have been described in detail in previous theoretical work.30

As expected, the “SERS” enhancement factors on resonance with the plas-monic absorption peak are roughly two orders of magnitude larger than the NRSenhancements (Fig. 5). We note that due to splitting of the plasmon peak in theVertex complex, we select an energy of 3.44 eV to compute the SERS enhance-ments, on resonance with the higher energy of the two plasmonic excitations withtransition dipole moments along the axis of the Ag20–pyridine interaction.Although many excited states contribute to the differential polarizability, thedominant contribution is from the sensitivity of the plasmonic excited stateproperties to geometric displacement, producing quite large imaginary compo-nents of the differential polarizability. The enhancements are larger in the Surfacecomplex than in the Vertex complex, by a factor of 2 at the BP86/TZP level anda factor of 7 at the INDO/SCI level (Table 1). The relative intensities of thevibrational modes are also strongly geometry-dependent. In particular, at bothlevels of theory, the mode around 1205 cm�1 is much more strongly enhanced inthe Vertex complex than in the Surface complex. This is consistent with previoustheoretical work that suggests that the intensity of this mode is particularlysensitive to chemical interactions.27

3.4. Decomposition of Raman enhancement factors

The use of the INDO model has advantages over previous computationalapproaches to modeling Raman enhancements not only because it predicts more

Fig. 5 Surface-enhanced Raman spectra for the (a and c) Surface and (b and d) Vertexgeometries of the Ag20–pyridine complex at the (top) INDO/SCI and (bottom) BP86/TZPlevels. Error bars in the INDO/SCI spectra (shown by the sizes of the black dots) indicatethe standard deviations of the Raman intensities computed using 1000 to 2000 excitedstates in the SOS expression in 100-state steps.




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accurate CT state energies but also because it enables us to modify the parametersin ways that allow practical decomposition of the Raman enhancements. Asdetailed in the Introduction, previous DFT studies have been limited in theirability to distinguish between CM and EM enhancements as a function of photonenergy.30,31,41 The INDO model provides a new approach to decomposing the totalenhancement into EM and CM components by comparing the Raman intensitiescomputed using two parameter sets: the standard INDO parameter set thatincludes both EM and CM contributions, and our INDO-EM parameter set wherethe overlap of the Ag atomic orbitals with the pyridine N, C, and H atomic orbitalsis set to zero. This INDO-EM model allows the two moieties to interact via theirelectron densities, approximating the effect of the EM interaction, but turns offthe CM interactions by forbidding both ground-state CT between the twomoietiesand enhancement via CT excited states. Notably, this decomposition approachallows us to compute the dependence of both the EM and CM enhancements onwavelength. Since the wavelengths under consideration at <4 eV are far fromresonance with any molecular transition, molecular resonance is not a signicantcontributor to the Raman intensities.

In the NRS spectra at 2.00 eV (Fig. 6a and b), there are notable differences inthe enhancementmechanisms between the two cluster geometries. The INDO-EMresults show that the EM enhancement of the Raman spectrum is relatively smallin both geometries: approximately 2 in the Surface complex and 3 in the Vertexcomplex as listed in Table 2, comparable in magnitude to the expectedenhancement for at surfaces.42 Even though the two structures have quite

Fig. 6 (a and b) Normal and (c and d) resonance Raman spectra for the (a and c) Surfaceand (b and d) Vertex geometries of the Ag20–pyridine complex at the INDO/SCI level. Redlines indicate spectra computed using the standard INDO parameters, and green linesindicate spectra computed using the INDO-EM parameters which neglect all overlapbetween orbitals localized on the Ag20 and pyridine moieties.



Table 2 Decomposition of the integrated enhancement factors for the Ag20–pyridinecomplex

Complex

EFNRS EFSERS

EM CM Total EM CM Total

Surface 2.2 � 0.3 1.7 � 0.4 3.9 � 0.3 208.9 � 2.1 4.5 � 0.1 932.0 � 2.5Vertex 3.1 � 0.4 0.9 � 0.2 2.7 � 0.2 24.7 � 0.5 5.0 � 0.1 124.3 � 0.9


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similar degrees of ground-state CT from Ag20 to pyridine (0.376 e in the Surfacecomplex and 0.370 e in the Vertex complex), there are signicant differences inthe CM enhancements. In the Surface geometry, the intensities of nearly all of themodes in the Raman spectrum are enhanced by the consideration of CM inter-actions, on average by nearly a factor of 2, and the CM enhancements are rela-tively uniform across the spectrum. In contrast, in the Vertex geometry, only a fewmodes, such as that at 1205 cm�1, show any CM enhancement, and many modesare slightly weakened by the chemical interactions. Although the total EFs aresmall, the combination of these two terms leads to larger total enhancement inthe Surface complex even though the EM enhancement is larger in the Vertexcomplex, which demonstrates the value of this approach in examining the EMand CM contributions independently. Signicantly, contrary to previousassumptions,30,31 our results show that the EM enhancement is larger than the CMenhancement even far from resonance.

On resonance with the plasmon, the trends in the enhancement factors aredifferent. Unsurprisingly, the EM enhancements are much larger than in the NRScase, by a factor of nearly 100 in the Surface complex and 8 in the Vertex complex.The substantially larger EM enhancement in the Surface complex is related todifferences in the excited-state structure between the two complexes. In theSurface structure, the plasmonic absorption peak is composed of a group of threenearly degenerate excited states with transition dipole moments along each of thethree principal axes. Any change with normal coordinate displacement in thesethree states is nearly resonant with the incoming light and will thereforecontribute strongly to the resonance enhancement. In contrast, the EMenhancement in the Vertex structure results from a broader distribution of statesdue to splitting of the plasmon by the adsorbed molecule. Thus, the resonanceenhancement is smaller since only a portion of the plasmon contributes signi-cantly to the resonance enhancement at any one photon energy. This effect isa consequence of the use of a small cluster model for studying SERS and wouldnot occur with larger clusters.

The CM enhancements are also somewhat stronger on resonance than in theNRS spectrum. Since the plasmon resonance is only a few tenths of an eV belowthe rst CT resonances as described previously, the CT enhancements are largerat the plasmon resonance. Although the integrated CM enhancements arecomparable in magnitude for the two complexes, there are signicant differencesin which modes are enhanced. The ring deformation modes between 600 and 650cm�1 are strongly enhanced in both complexes; however, the ring breathingmodes around 1000 cm�1 are strongly enhanced only in the Surface complex(Fig. 6c). Also, the C–H wag at 1205 cm�1 is enhanced only in the Vertex complex




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(Fig. 6d), providing further conrmation that the sensitivity of this mode togeometry is related to chemical effects.27

Since the SOS approach allows us to easily compute the polarizabilities at anyphoton energy, we also consider the integrated EFs as a function of energy from 1to 4 eV (Fig. 7). At 1 eV, well below any excited-state energy, the EM enhancementsare close to 2 and the CM enhancements are approximately 1 in both geometries.The EM enhancements have peaks near the absorption maxima of bothcomplexes, with a peak value of <10 near the small absorption shoulder around2.3–2.4 eV and a much larger peak value of �100 near the plasmon around 3.2–3.4 eV. As mentioned previously, the EM enhancement on resonance with theplasmon is larger in the Surface complex than in the Vertex complex in part due tosplitting of the plasmon in the Vertex complex; this splitting and mixing of theplasmon with lower-energy states leads to larger EF enhancements in the Vertexcomplex around 2.4 eV. Although we focus here on one cluster size, the EMenhancements have previously been shown to depend on the cluster size and onthe distance of the molecule from the cluster center31 and are in general expectedto increase for larger clusters.

At energies above 1.5 eV, the CM enhancements are in general signicantlylarger in the Surface complex than in the Vertex complex. Because of the smallereffective distance for charge separation and the larger spatial overlap of thepyridine and Ag20 moieties, the Surface geometry has lower CT state energies andallows for more mixing of CT character into lower-lying excited states, leading tolarger CT enhancements. Resonance with excited states having signicant CTcharacter, such as those around 3.8 eV in the Surface complex, leads to CTenhancements of >100. The CM enhancement also exhibits smaller peaks atenergies lower than the rst states with signicant CT character, around 2.4 eV inboth complexes and 3.1 eV in the Surface complex, related to shis in the excitedstate energies within the GS mechanism and non-resonant CT contributions. Thedifferences in the evolution of the EM and CM terms highlight the importance ofconsidering the energy dependence of both terms to understanding the totalRaman intensities. However, we should also note that the peak in the CMenhancement at 3.1 eV is at least somewhat of an artifact of using a small clustermodel for this study. In larger clusters, the plasmon excited-state energy will not

Fig. 7 Integrated enhancement factors as a function of photon energy. Solid linescorrespond to the total enhancement factors, dotted lines to the EM component, anddashed lines to the CM component.




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signicantly shi as a result of interaction of the metal cluster with an adsorbedmolecule, and thus the CM enhancement at energies below resonance with theplasmon or with CT excited states is expected to remain relatively small.

3.5. Effect of an applied potential on Raman enhancement factors

As described in the Introduction, voltage-based changes in the SERS enhance-ment factor for pyridine have been experimentally observed;1,2,25,26 however,theoretical modeling of this effect has been quite limited. It has been proposedthat the enhancement is related primarily to the CT mechanism, particularlysince the modes most strongly enhanced are those related to the geometricdisplacement between the neutral and anionic states of pyridine.27 To ourknowledge, modeling of the potential-dependent Raman intensities has beenlimited to studies where the potential was approximated by discrete changes inthe charge of the metal–molecule system72 or by a uniform electric eld.73

Our recently developed OESA approach for applying a voltage to an Ag clusterwithin the INDO model47 allows us to directly study the effect of varying theelectrode potential on SERS enhancements, focusing on the effect of the CT stateenergies on the EFs. Since the full electrochemical environment is quite complex,major simplications must be made to dene a computationally feasible model.We focus on the Ag20–pyridine cluster in the gas phase as a model system to gainchemical insight. Although we neglect the solvent, we have shown that theprimary effect of the solvent in this system is to lower the CT state energies,47

which should primarily change what potential is needed to achieve resonance ofthe CT states with the photon energies considered. The potentials here arereferenced to the standard INDO parameters, and work is in progress to bench-mark these potentials to standard electrodes. Although the range of potentialsaccessible experimentally is limited due to oxidation of both Ag and H2O, as wellas H2O reduction, these effects are beyond the scope of this work. Since thevibrational modes within our model are computed at the BP86/TZP level, weneglect any effects of the applied potential within the INDO/SCI model on thevibrational modes.

Potentials ranging from 0.0 to �2.0 V have relatively small effects on theground-state electronic structure, changing the charge on the pyridine moietyfrom 0.376 to 0.294 in the Surface geometry and from 0.370 to 0.304 in the Vertexgeometry. Since the GS enhancements are small at 0.0 V and a photon energy of2.00 eV, the changes in this term should be quite small across this series. Incontrast, the energies of the CT excited states are signicantly lowered uponincreasing the potential, as shown in Fig. 8. Because of the large density of localexcitations on the Ag20 moiety, the CT excitations are able to mix signicantly withthe local excitations, and there are many excited states with partial CT character.For each �0.2 V step in the potential, the energy of the rst CT state decreases byroughly 0.2 eV, with variation due to differences in the mixing of the local and CTexcitations. The range of voltages considered here tunes the energy of the rst CTstate from several tenths of an eV above the plasmon resonance to energies nearthe 2.00 eV “NRS” energy. Thus, we focus here on understanding the magnitudeand mechanism of the CT enhancements as the CT energy is tuned through theplasmon energy. As we will show, the CT enhancements are largest at potentialswhere the CT states are tuned to resonance with the photon energy. Within our



Fig. 8 Excited-state energies for the Ag20–pyridine complex at the INDO/SCI level withapplied potentials from 0.0 to �2.0 V. Solid red lines correspond to states with >50% Ag20/ pyridine CT character, dotted red lines to states with 20–50% CT character, and graylines to local Ag20 excited states.


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model, the EM enhancements are constant across the range of potentialsconsidered.

The CT enhancement is strongly voltage dependent, as shown in Fig. 9. Atpotentials of >�1.0 V, the NRS spectrum at 2.00 eV exhibits integrated EFs of <10

Fig. 9 Integrated enhancement factors in the (a) NRS spectra at 2.00 eV and (b) SERSspectra as a function of applied potential for two geometries of the Ag20–pyridinecomplex. Solid lines correspond to the total enhancement factors and dashed lines to theCM component.




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in both geometries of the Ag20–pyridine complex. The Surface complex showsa steep increase in EF at more negative potentials, with a CM enhancement of>100 at a potential of �2.0 V. In contrast, this increase in EF is largely absent inthe Vertex complex. This difference is related to the CT state energies in these twocomplexes and, in particular, to the potentials required to see resonance or near-resonance enhancement related to the CT states. The Surface complex has lowerCT state energies than the Vertex complex at each potential and, at a �2.0 Vpotential, has several states with signicant CT character at low enough energiesto contribute strongly to resonance or near-resonance enhancement. Even thoughthe CT states have much smaller contributions to the total absorption andpolarizability than the plasmonic excited states, their high sensitivity to normalcoordinate displacements leads to large changes in the differential polarizabilityand thus the Raman intensities near resonance. In contrast, the higher CT stateenergies in the Vertex complex do not allow for signicant CT resonanceenhancement at a photon energy of 2.00 eV within this range of potentials.

The SERS enhancements are also potential dependent, with the largestenhancements occurring at potentials where CT states are nearly resonant withthe plasmon or signicantly mixed with the plasmonic excited states. The largestintegrated EFs occur at �0.6 V and �1.6 V for the Surface complex and at �1.0 Vfor the Vertex complex, as shown in Fig. 9b. Mixing of CT states with the plasmonis particularly prominent in the Vertex complex at �1.0 V, with two states at 3.25and 3.37 eV having >10% charge-transfer character and transition dipolemoments of >10 debye. In both geometries, resonance with CT states leads to CTenhancements on the order of 100, leading to total enhancements of >104 at somepotentials. This suggests that, as has been previously assumed, the EM and CM

Fig. 10 (a and b) Normal and (c and d) resonance Raman spectra for the (a and c) Surfaceand (b and d) Vertex geometries of the Ag20–pyridine complex at the INDO/SCI level,showing the effects of applied potentials from 0.0 to �2.0 V within the OESA model.




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enhancements can be thought of as multiplicative effects that each contribute tothe total enhancement.

Although the overall trends in the integrated enhancement factors can beunderstood in terms of energies of charge-transfer states, the potential depen-dence of the enhancement factors varies between the different vibrational modes,as shown in Fig. 10 (see also Fig. S3–S6 in the ESI†). In both the NRS and SERSspectra of the Surface complex and in the SERS spectrum of the Vertex complex,the vibrational modes near 1205 and 1585 cm�1 are particularly stronglyenhanced by resonance with CT states. Similarly, although a pair of modesaround 990 and 1025 cm�1 have comparably large intensities at 0.0 V, the mode at990 cm�1 shows stronger CT enhancements. Interestingly, the relative intensitiesof the main Raman peaks are much more similar for the Raman spectra onresonance with a CT state than at 0.0 V.

4. Conclusions

Although large SERS enhancements are generally understood to be due primarilyto enhancements of the local electric eld of light on resonance with the plasmon,the contributions of chemical mechanisms are still strongly debated. Here, wehave benchmarked a semiempirical INDO/SCI approach and shown that itprovides reasonable Raman intensities relative to the DFT approaches previouslyused, but is free of the self-interaction errors that plagued the DFT results andmade it impossible to correctly determine the contribution of the chemical effectthat arises from the resonant excitation of CT states. The semiempirical approachalso enables us to gain chemical insight into the enhancements by decomposingthe enhancement factors in a way that allows us to consider effects on the EM, GS,and CT contributions.

By neglecting the coupling between the metal cluster and molecule, we havemodeled a system where only EM enhancement of the Raman intensities ispossible, allowing straightforward decomposition of the Raman enhancementsinto EM and CM terms. These results show that the EM enhancements for theAg20 cluster are on the order of 2–3 far from resonance and 30–200 on resonancewith the plasmon, which is smaller than previously computed using DFTapproaches but reasonable for a cluster of this size. The CM enhancements are<10 at both NRS and SERS wavelengths when the CT states are higher in energythan the plasmon and generally increase with increasing energy due to anincrease in the CT enhancements when approaching resonance with the CTstates.

This computational model also allows us to investigate the inuence of anapplied potential on the Raman enhancement factors. Within the range ofpotentials considered, there is little change in the ground-state electronic struc-ture, so the changes in the enhancement factors are predominantly due tochanges in the CT term. Resonance with a CT state can cause enhancements of10–100 overall, and of upwards of 103 for specic modes, leading to total SERSenhancement factors of >104 at potentials where the CT states are resonant withthe plasmon.

The chemical insight gained using this computational approach suggestsa number of further extensions and applications. For example, it has long beensuggested that the CT excited states have much broader absorptions than the




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local plasmonic excitations.60,74,75 Although we have assumed here that the life-time broadening in the SOS polarizabilities is the same for all states, our meth-odology provides a pathway to studying the effect of state-specic broadening onthe CT enhancements that is not possible via the response approaches typicallyused in DFT computations. Although we have focused here on a simple modelsystem, these approaches can also be used to gain chemical insight into the morecomplex systems commonly studied experimentally. In future work it will beimportant to study larger clusters, since some of the results we found for Ag20 areapparently artifacts of the small cluster used, as the adsorbed molecule is able toshi the plasmon energy by enough that it produces a noticeable resonant CMenhancement at energies that are well below the CT state energies. Theseapproaches can also be extended to other plasmonic metals such as Au. Also, itwill be important in future work to include solvation effects in modeling theelectrochemical experiments.

Acknowledgements

This research was supported by the Department of Energy, Office of Basic EnergySciences, under grant DOE DE-FG02-10ER16153. We thank Richard Van Duynefor valuable conversations.

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Theoretical modeling of voltage effects and the chemical ......Rebecca L. Gieseking, Mark A. Ratner...

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