Article pubs.acs.org/JPCA
Nonequilibrium Chemical Effects in Single-Molecule SERS Revealed by Ab Initio Molecular Dynamics Simulations Sean A. Fischer,† Edoardo Aprà,† Niranjan Govind,*,† Wayne P. Hess,‡ and Patrick Z. El-Khoury*,‡ †
Environmental and Molecular Sciences Laboratory and ‡Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99354, United States S Supporting Information *
ABSTRACT: Recent developments in nanophotonics have paved the way for achieving significant advances in the realm of single-molecule chemical detection, imaging, and dynamics. In particular, surface-enhanced Raman scattering (SERS) is a powerful analytical technique that is now routinely used to identify the chemical identity of single molecules. Understanding how nanoscale physical and chemical processes affect single-molecule SERS spectra and selection rules is a challenging task and is still actively debated. Herein, we explore underappreciated chemical phenomena in ultrasensitive SERS. We observe a fluctuating excited electronic state manifold, governed by the conformational dynamics of a molecule (4,4′-dimercaptostilbene, DMS) interacting with a metallic cluster (Ag20). This affects our simulated single-molecule SERS spectra; the time trajectories of a molecule interacting with its unique local environment dictates the relative intensities of the observable Raman-active vibrational states. Ab initio molecular dynamics of a model Ag20−DMS system are used to illustrate both concepts in light of recent experimental results.
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nanometers.14,15 The structure16 and nature17 of the local electric fields are highly sensitive to nanometric structural heterogeneities sustained on the plasmonic metal. Moreover, both static and dynamic chemical effects may alter the recoded optical spectra in ways that are not fully appreciated.14,15,18,19 In this regard, a recent investigation of the modified optical absorption of molecules on metallic nanoparticles at submonolayer coverage revealed that spectral shifts, in what is essentially a condensed-phase UV−Vis spectrum, are the norm rather than the exception.20 Prior work,20 albeit limited to colloidal solutions, in principle questions the resonance conditions in decades of ultrasensitive SERS works. Interestingly, to the best of our knowledge, the optical absorption of a SM on a plasmonic metal nanostructure has not been experimentally captured. Perhaps the most restrictive difficulty associated with SM absorption spectroscopy,21 particularly under ambient conditions,22−24 is the relative absorption/ scattering efficiency of molecules with respect to plasmonic metals. Our current investigation is motivated by the latter realization. Here, we employ density functional theory (DFT) and time-dependent density functional theory (TDDFT) to explore some subtle phenomena of chemical origin that may affect the optical spectra of SMs interacting with metallic nanostructures.
INTRODUCTION The modified linear/nonlinear optical properties of molecules in the immediate vicinity of plasmonic metal nanostructures continue to be the subject of intensive research. Early observations of surface-enhanced Raman scattering (SERS),1−3 followed by demonstrations of single-molecule (SM) sensitivity using the same technique,4,5 have paved the way for more recent investigations, in which the ultimate limits of space, time, and detection sensitivity are accessible by coupling molecules to plasmonic antennae. For example, we can cite demonstrations of chemical imaging with Ångström resolution6,7 via tip-enhanced Raman scattering8−11 as well as the observation of vibrational wavepacket motion in a SM with femtosecond time resolution through surface-enhanced coherent anti-Stokes Raman scattering.12 In the realm of plasmonenhanced Raman nanospectroscopy, it is well recognized that signal enhancement mostly arises from resonant interaction between the incident photons and surface plasmon modes supported by the metallic construct, such that both the incident and scattered radiation fields are enhanced.13 Nonetheless, static and dynamic chemical effects also play a role; after all, what one records is the (modified) linear/nonlinear optical response of molecules interacting with metallic nanostructures. Beyond a handful of demonstrations under ultrahigh vacuum and ultralow temperatures, the interpretation of the enhanced Raman spectra of molecules coupled to plasmonic antennae is not trivial. This is particularly the case in the few-molecule/SM limit, where the local electromagnetic field−molecular interactions of interest take place on a length scale of a few © XXXX American Chemical Society
Received: December 2, 2016 Revised: December 21, 2016 Published: January 24, 2017 A
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Figure 1. (A) Total and partial (molecule-only and metal-only contributions) density of states in the Ag20−DMS complex. Note that only orbitals 246−265 in the complex, namely, those involved in the four excited electronic states of interest, are considered in this analysis. Also shown are the energies of orbitals 246−265 (vertical dashed lines). Inspection of the curves shown in this panel readily reveals the composition of the frontier orbitals in the complex, for example, electron densities in the HOMO−1, HOMO, and LUMO orbitals are localized on the metallic, molecular, and metallic subunits, respectively. This is readily evident in (B), where the frontier molecular orbitals are also shown.
with the PBE exchange−correlation functional33 in conjunction with the def2-SVP basis set34 and a fitting basis35 for the evaluation of the Coulomb potential. Our choice of starting structure, namely, the Ag20 vertex-bound DMS model, was made empirically; this model has been previously found to reproduce both the ensemble-averaged as well as the fewmolecule/SM SERS spectra of DMS19 and structurally related aromatic dithiols.14 All of the atoms were relaxed in the AIMD simulations,36 in which a time step of 10 atomic units (∼0.2419 fs) was used. Using this time step in our AIMD scheme conserved the total energy of the system to within 1 kcal/mol. For the trajectories used to sample configurations for UV−Vis spectral simulations, we ran the trajectories in the canonical ensemble via the stochastic velocity rescaling thermostat of Bussi et al.,37 with a relaxation parameter of 100 atomic units. Randomly selected structures from this trajectory were used for UV−Vis spectra simulations. Alternatively, we performed AIMD simulations in the microcanonical ensemble for the trajectories used to generate the vibrational density of states and Raman spectra.36 The starting structures used to simulate the vibrational properties were selected from the preliminary constant-temperature AIMD simulation. TDDFT absorption spectra from the ground-state minimum were broadened with Gaussians using a full width at half-maximum (fwhm) of 0.2 eV, while those averaged over snapshots from the trajectories were broadened by 0.1 eV; the conformational sampling recovers a portion of the line broadening. Vibrational spectra from the AIMD simulations were obtained by Fourier transforms of the relevant autocorrelation functions; velocity and polarizability autocorrelation functions were used to compute the vibrational density of states and Raman spectra, respectively.36 Further details of the calculations and results may be found in the Supporting Information.
The quest for understanding the chemical mechanisms that are operative in plasmon-enhanced optical spectroscopy using DFT and TDDFT has been pursued by several groups over the years in an effort to rationalize SERS observables. These simulations often involve small−medium sized organic molecules chemi- or physisorbed onto finite metal clusters or small metal slabs. The pioneering works of Schatz,25 Zhao,26 Jensen,27 Neaton,28 Aspuru-Guzik,29 as well as Lombardi and Birke30 come to mind in this context. Of particular relevance to this work is the early study of Aspuru-Guzik and co-workers,29 where the effects of chemical bonding on Raman scattering from a benzenethiol (BT) molecule chemisorbed on silver clusters was explored. Using different finite silver cluster models (Agn, n = 6−11), the previous work29 illustrated the need to consider various conformations of BT with respect to the finite cluster to correlate the metal-induced changes in the electronic structure of a molecule to its SERS enhancement. Of the different effects governing SERS enhancement, three were identified: (1) the relative orientation of the π framework with respect to the metal cluster, (2) the local symmetry of the benzene ring, and (3) the relative proximity of the various vibrational modes in BT to the binding site.29 In this work, rather than considering different clusters to sample different conformations of the molecule with respect to metal clusters, we perform ab initio molecular dynamics (AIMD) simulations to systematically explore how conformational evolution along the time trajectory of a single 4,4′-dimercaptostilbene (DMS) molecule chemisorbed onto the vertex of a tetrahedral Ag20 cluster affects its electronic and vibrational properties. The tetrahedral Ag20 cluster is widely used as a model system for SERS simulations, ever since the early works of Schatz,25 Jensen,26 and co-workers. Herein, particular emphasis is placed on understanding how molecular reorientation dynamics affects the first elementary process involved in SERS, that is, the absorption of a photon. Keeping the works of Lombardi and Birke in mind,30,31 particular attention is devoted to tracking excited electronic states involving charge transfer from DMS to Ag20 along the AIMD trajectories.
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RESULTS AND DISCUSSION The ground-state electronic structure of the Ag20−DMS model can be gauged by inspecting Figure 1. Figure 1A shows the total and partial (DMS-only and Ag20-only contributions) electronic density of states; the molecular orbital energies are marked by dashed vertical lines for reference. Examining both Figure 1A and the molecular orbitals plotted in Figure 1B reveals that (1) both the lowest unoccupied molecular orbital (LUMO) and
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COMPUTATIONAL METHODS All calculations discussed in the following sections were performed using a local development version of NWChem,32 B
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Figure 2. (A) Computed vertical transition energies (200 singlet states) of the Ag20−DMS complex using three different density functionals (see the Supporting Information for more details). Four low-lying excited electronic states of mixed molecule−metal character are identified and marked with numbers 1−4 for the td pbe/def2-SVP curve and with color-coded asterisks for their td pbe0/def2-SVP and td lc-pbe/def2-SVP analogues. (B) Charge density difference association with promoting the complex into states 1−4. States 1 and 2 are best described as molecule-to-metal charge transfer states.
Figure 3. (A) Total energy as a function of propagation time from a constant-temperature AIMD simulation of the Ag20−DMS complex (pbe/def2SVP). Ten randomly selected structures from the trajectory shown in (A) were used as starting structures for UV−vis simulations (200 singlet states); the results are shown in (B), where the static spectrum is compared to the AIMD spectrum. Both the static and AIMD UV−vis spectra are represented as sums of Lorentzians centered at the predicted transition energies and broadened by 0.2 eV. (C,D) Selected UV−vis spectral “snapshots” taken at different time points along the trajectory shown in (A) are shown and compared to the static spectrum computed at the minimum. Note that the AIMD UV−vis snapshots were broadened by 0.1 eV. Both the energy and oscillator strength of states 1−4 (defined in Figure 2) exhibit substantial variations along the AIMD trajectory, which samples different conformations.
LUMO+1 orbitals are localized at the Ag20 moiety, (2) the highest occupied molecular orbital (HOMO, orbital 254) is delocalized along the π framework of DMS, and (3) the HOMO−1 orbital (orbital 253) is localized to the linker sulfur and tetrahedral Ag20 vertex region that is closest to the linker. The computed UV−Vis spectra of Ag20−DMS using three different exchange−correlation functionals are shown in Figure 2A. Four excited electronic states involving charge transfer from
DMS to Ag20 are identified and enumerated (states 1−4 in Figure 2A). As the bright states of interest involve charge transfer (see the Supporting Information), their energies are expected to be underestimated using the pure DFT functional (PBE). Although quantitative estimates of the vertical transition energies are not the focus of this paper, we ensure that the choice of exchange−correlation functional used throughout this paper does not affect the physical picture painted by our C
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Figure 4. (A) Experimental SM SERS spectrum (line + open symbols, taken from ref 43) compared to SERS spectra obtained through the Fourier transforms of the polarizability autocorrelation functions along five different constant-energy AIMD trajectories of Ag20−DMS (solid lines). For each trajectory, the molecular system was propagated for a time period of ∼3.5 ps. (B) Experimental ensemble-averaged SERS spectrum (line + open symbols, recorded from a substrate described in ref 19) compared to the orientationally averaged SERS spectra (solid lines) computed at the optimized Ag20−DMS geometry.
dye isolated in a PMMA matrix. Nonetheless, prior observations44 suggest that even relatively weak interactions between a SM and immediate local environment (PMMA) have dramatic effects on the ground- to excited-state transition energies and strengths. On the basis of our current observations and previous works,20,44 we propose that a similar effect governs the optical absorption spectra of SMs interacting with plasmonic metal nanostructures. In a series of recent reports from our group,40−43 we examined various manifestations of the tensorial nature of SM Raman scattering in SERS and TERS measurements. Namely, observations of time-dependent relative intensity fluctuations in nonresonant SERS and TERS spectral sequences recorded under ambient conditions were associated with molecular reorientation dynamics following
calculations and ensuing analysis. This is accomplished by testing the performance of the global hybrid PBE038 functional and its long-range corrected39 variant, namely, the LC-PBE0 functional. We find that the inclusion of Hartree−Fock (HF) exchange and long-range correction systematically blue shifts the predicted vertical transition energies as expected; see Figure 2A. Nonetheless, the nature of all four excited electronic states of interest is affected by neither the choice of density functional nor the choice of basis set (see the Supporting Information). Charge density difference plots upon promotion of Ag20−DMS to states 1−4 are visualized in Figure 2B, which reveals that all four electronic transitions involve charge transfer from the molecular to the metallic moiety with varying extent of charge transfer for the different states of interest. The change in total energy as a function of propagating Ag20−DMS along a constant-temperature AIMD trajectory is plotted in Figure 3A. The starting structure consists of a fully optimized Ag20−DMS structure, which results in relatively fast equilibration time. Several randomly selected structures along this trajectory, after equilibration, were used to compute vertical transition energies. In Figure 3B, the static TDDFT spectrum computed from the minimum-energy geometry is compared to the total AIMD spectrum, which is obtained by averaging 10 TDDFT snapshots along the trajectory. The difference between the static and AIMD spectrum is evident in Figure 3B, and its origin may also be discerned by inspecting Figure 3C ,D, where five selected TDDFT snapshots are compared to the static spectrum. We observe that both the energies and relative intensities of the predicted DMS to Ag20 charge transfer transitions are time-, and hence, conformation-dependent. It appears that the relative orientation of the molecule with respect to the metal cluster not only affects its enhanced Raman spectra, as recently demonstrated in SERS and TERS experiments,40−43 but also modifies the electronic absorption profiles of a SM interacting with a metallic nanostructure. Although experimental verification of the latter is not amenable at present, a recent broad-band Fourier approach that allowed recording the excitation spectra of individual molecules under ambient conditions is informative.44 Namely, the excitation spectra of single quaterrylene diimide molecules embedded in a poly(methyl methacrylate) (PMMA) matrix were found to exhibit dramatic variations. Evidently, a DMS molecule chemisorbed onto a metallic cluster is very different from a
Sn 2 ∝
∑ |εslαn′(Ω)εil|2 n
in which εli,s are the enhanced incident and scattered local electric fields, α′n are the molecular polarizability derivative tensors of the nth vibrational eigenstate, and Ω = α,β,γ are the Euler angles that dictate molecular orientation relative to the local fields. Accordingly, the optical response of a single scatterer recovers the full tensorial nature of Raman scattering, and the orientation of a molecule with respect to the local fields dictates the intensity of the nth vibrational state in the Raman spectrum.40−43 The above treatment assumes separable molecular and metallic polarizabilities, that is, the molecular polarizabilities that govern Raman scattering activities are invariant to molecular (re)orientation with respect to a metal substrate. As noted in a prior analysis,45 this treatment does not accurately describe resonant SERS and TERS schemes, in which molecular orientation dependence stems from the orientation of the transition dipole vector, which is vibrational state-independent (at least in the Condon approximation). Our present observation of “blinking” excited electronic resonances adds another degree of complexity to the theoretical analysis of SM SERS and TERS experiments. The implications of our findings may be rationalized within Lombardi and Birke’s unified view of SERS.30,31 Briefly, following Albrecht’s original analysis,46 the unified SERS theory expands molecular polarizability (α) into the sum of three terms, α = A + B + C. The first term (A) only involves Franck−Condon terms and D
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polarizability associated with π-conjugated electrons in typically employed SERS molecules (such as DMS43) results in α′xx components that largely predominate over αyy ′ , αzz ′ , and αij′ (i ≠ j) polarizability tensor elements. As such, the conformational subspace that should be spanned by the AIMD trajectory that fits the experimental observables is large, that is, the solution reached herein is not unique and multiple solutions are amenable without running thousands of AIMD trajectories or, alternatively, a very long AIMD trajectory. A stringent test for our premise comprises the use of model SERS reporters with anisotropic molecular polarizability elements in combined AIMD and experimental SM Raman studies. Though exhaustive, the latter might be key to understanding beyondequilibrium chemical effects in SERS in the few-molecule/SM regime.
vanishes off-resonance,30,31 much like in conventional resonance Raman scattering.46 Terms B and C stem from electronic transitions involving charge transfer from/to the molecular and metallic moieties and derive their intensity through Herzberg− Teller coupling to nearby allowed molecular transitions.30,31,46 With the results shown in Figures 1−3 and recent works in mind,20,44 it is not entirely clear whether or not typical driving lasers are resonant with molecule-to-metal (or vice versa) charge transfer transitions for DMS specifically and other SERS reporters more generally. Regardless of the molecular and plasmonic system-dependent resonance conditions, it is obvious that all three terms would be affected to various degrees by conformational dynamics that are accompanied by blinking charge transfer resonances. At one end, the resonance conditions are time- and molecular conformation-dependent; the selection rules in sequentially recorded SERS trajectories are governed by different rules at different times. On the other hand, in far from resonance conditions, where the B and C terms dominate,30,31 the above-described effect would be less dramatic but should still be discernible with the typical signalto-noise ratios in ultrasensitive SERS measurements. Beyond removal of orientational averaging 40−43 and fluctuating excited-state manifolds, the properties of a SM interacting with its distinct local environment along its time trajectory are not equivalent to the properties of a SM in an ensemble.47 The latter is one of the major drivers behind the rise of SM spectroscopy, whereby the molecule itself becomes a nanoscopic probe of its immediate local environment.48 This concept has been recently explored in SERS; the magnitudes and vector components of the local electric fields can be inferred from the Raman spectrum of a SM.14,19 In the present work, a similar concept was encountered while considering AIMD Raman spectra36 obtained from the Fourier transforms of the polarizability autocorrelation functions along constant energy simulations; see Figure 4A. Five different trajectories (∼3.5 ps/trajectory) initiated from the different starting structures used to compute the TDDFT spectra shown in Figure 3 were used to compute AIMD Raman spectra. Comparing the computed spectra to a previously reported SM SERS spectrum of DMS43 reveals that only one trajectory (Traj 1 in Figure 4A) recovers the relative intensities of the three major Raman bands observed in the laboratory in the 1000−1800 cm−1 spectral region. We stress that the SM Raman spectrum is distinct from its ensemble-averaged analogue.43 A comparison between the spectra plotted in Figure 4A,B readily reveals the latter. Namely, (i) the distinct relative intensities of the observable vibrational states at 1575, 1186, and 1085 cm−1 in the experimental ensemble-averaged vs SM SERS spectra and (ii) the largely suppressed vinyl CC stretching mode at 1625 cm−1 in the SM SERS spectrum are noted. With this in mind, the observations highlighted in Figure 4A underscore how a fluctuating excited-state manifold affects the Raman spectrum of a SM; sampling the relevant conformations along one particular trajectory (Traj 1 in Figure 4A) recovers the experimentally measured polarizabilities that are measurable in SERS. More specifically, the unique molecular trajectories sampled in our AIMD simulations are starting structure- and initial condition-dependent. This translates into unique AIMD Raman spectra from the finite trajectories computed herein, governed by a fluctuating excited-state manifold. Only one of our five AIMD Raman spectra recovers the experimental observables; the unique in silico molecular trajectory seems to resemble its experimental analogue. Note that the large
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CONCLUSIONS It is important to point out that the choice of level of theory used herein,49 the minimal Ag20−DMS model system, and the otherwise limited experimental evidence inevitably hinder us from a more quantitative analysis of the optical absorption of a single DMS molecule interacting with a plasmonic metal nanostructure. That said, the underlying mechanisms revealed by our simulations, namely, (1) conformational-dependent absorption spectra and (2) distinct AIMD Raman spectra from different finite trajectories, are consistent with recent experimental observations by our group and others and may be viewed as general. Admittedly, a direct experimental verification of these two mechanisms, particularly, the first, remains a challenge. Nonetheless, our results motivate a more detailed examination of nonequilibrium chemical effects in SM SERS, which will lead to a better understanding of the modified selection rules in SM Raman measurements and, ultimately, to further development of this powerful technique.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b12156. A more detailed description of the computational methods and additional calculations and analyses (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (N.G.). *E-mail:
[email protected] (P.Z.E.). ORCID
Edoardo Aprà: 0000-0001-5955-0734 Wayne P. Hess: 0000-0002-3970-9282 Patrick Z. El-Khoury: 0000-0002-6032-9006 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS P.Z.E. acknowledges support from the Laboratory Directed Research and Development Program at Pacific Northwest National Laboratory (PNNL). W.P.H. acknowledges support from the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences. S.A.F. and N.G. acknowledge E
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support from the U.S. DOE, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery, through the Advanced Computing (SciDAC) program (Award Number KC030106062653). This research benefited from resources provided by PNNL Institutional Computing (PIC). A portion of the research was also performed using EMSL, a DOE Office of Science User Facility sponsored by the Office of Biological and Environmental Research and located at PNNL. PNNL is operated by Battelle Memorial Institute for the United States Department of Energy under DOE Contract Number DE-AC05-76RL1830.
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DOI: 10.1021/acs.jpca.6b12156 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jpca.6b12156 J. Phys. Chem. A XXXX, XXX, XXX−XXX