Importance of Correctly Describing Charge-Transfer Excitations for

Aug 19, 2012 - Rebecca L. GiesekingMark A. RatnerGeorge C. Schatz. 2016,1-22 ... John L. Payton , Seth M. Morton , Justin E. Moore , and Lasse Jensen...
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Letter pubs.acs.org/JPCL

Importance of Correctly Describing Charge-Transfer Excitations for Understanding the Chemical Effect in SERS Justin E. Moore, Seth M. Morton, and Lasse Jensen* Department of Chemistry, The Pennsylvania State University, 104 Chemistry Building, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: The enhancement mechanism due to the molecule−surface chemical coupling in surface-enhanced Raman scattering (SERS) is governed to a large extent by the energy difference between the highest occupied molecular orbital (HOMO) of the metal and the lowest unoccupied molecular orbital (LUMO) of the molecule. Here, we investigate the importance of correctly describing charge-transfer excitations, using timedependent density functional theory (TDDFT), when calculating the chemical coupling in SERS. It is well-known that TDDFT, using traditional functionals, underestimates the position of charge-transfer excitations. Here, we show that this leads to a significant overestimation of the chemical coupling mechanism in SERS. Significantly smaller enhancements are found using long-range corrected (LC) functionals as compared with a traditional generalized gradient approximation (GGA) and hybrid functionals. Enhancement factors are found to be smaller than 530 and typically less than 50. Our results show that it is essential to correctly describe charge-transfer excitations for predicting the chemical enhancement in SERS. SECTION: Plasmonics, Optical Materials, and Hard Matter

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be important when the incident light is not resonant with a molecular or charge-transfer excitation of the system. Using a two-state model, Morton and Jensen14 found that CHEM is related to orbital interactions between the metal and molecule complex and scales as (ωX/ωe)4, where ωX is the HOMO−LUMO excitation energy of the free molecule and ωe is lowest charge-transfer excitation energy of the metal− molecule complex. Similar expressions have recently been shown to describe the chemical enhancement in surfaceenhanced hyper-Raman scattering15 and coherent anti-Stokes Raman scattering.16 This model has also been extended to describe the enhancement of individual normal modes by considering the deformation potential.17 To correctly describe the chemical enhancement in SERS, it is important to correctly describe the CT excitations. Due to the relatively large size of the systems needed for describing the chemical mechanism in SERS, electronic structure studies have been predominately performed using time-dependent density functional theory (TDDFT).2,13 Although TDDFT has been demonstrated to be accurate for many molecular systems, it is well-known that conventional exchange−correlation (XC) functionals have certain categorical failures, such as describing CT excitations between weakly interacting systems and in condensed-phase systems.18−21 Recently, progress has been made with the introduction of

etal nanoparticles that can support plasmon excitations are known to generate large local fields at the surface of the particles. This strong local field can greatly affect the optical properties of molecules situated near the metal surface and has led to a whole range of surface-enhanced spectroscopic techniques, with surface-enhanced Raman scattering (SERS)1−4 being the best known. These techniques all rely on the strong local field to enhance the optical properties of molecules near the surface of the metal nanoparticle. Using SERS, it is possible to detect and identify a single molecule due to the large enhancements.5−9 The fundamental enhancement mechanisms for SERS have been extensively studied over the last 4 decades, and it is generally accepted that there are two mechanisms contributing to SERS,1−4,10−13 (1) the electromagnetic mechanism (EM) due to the strong local field and (2) the chemical mechanism (CM). The largest enhancements in SERS stem from EM, which is generally considered to be independent of the molecule. In contrast, the CM depends strongly on the specific molecule and the local environment of the metal surface because it results from the overlap between the wave functions of the molecule and the metal nanoparticle. This overlap results in a renormalization of the molecular orbitals as well as the introduction of new mixed charge-transfer states. Both of these effects will contribute to the CM enhancement of the Raman signal and can be classified as the nonresonant chemical mechanism (CHEM) and a resonant charge-transfer chemical mechanism (CT), respectively.2,13,14 In the following, we will only consider the nonresonant mechanism that is expected to © XXXX American Chemical Society

Received: April 21, 2012 Accepted: August 18, 2012

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Figure 1. Simulated Raman spectra for pyridine using (a) LC-PBE, (b) B3LYP, and (c) BP86 functionals and for pyridine-Ag20 using (d) LC-PBE, (e) B3LYP, and (f) BP86. The BP86 results were taken from ref 14.

Table 1. HOMO−LUMO Gap for Complex (ωX−Ag), HOMO−LUMO Gap for Free Molecule (ωX), and Integrated Enhancement Factor (EFint) for Each Substituted Pyridinea LC-PBE

a

B3LYP

BP86

LC-PBE

B3LYP

BP86

functional group

ωX−Ag

ωX

ωX−Ag

ωX

ωX−Ag

ωX

EFint

EFint

EFint

p-N(CH3)2 p-CH3 H p-CFClH p-CN (m-CN,p-CN) p-NO2

0.200 0.173 0.170 0.149 0.124 0.109 0.100

0.363 0.389 0.388 0.369 0.359 0.351 0.334

0.084 0.063 0.060 0.036 0.020 0.010 0.014

0.208 0.229 0.227 0.210 0.202 0.196 0.173

0.052 0.030 0.023 0.008 0.003

0.147 0.155 0.152 0.136 0.129

3.87 3.82 3.40 4.57 10.53 14.12 38.79

4.51 6.26 6.41 170.18 9718.89 156262.00 57.77

5.77 17.98 52.3 7491.35 1135.62

HOMO−LUMO gaps are in Hartrees. The BP86 results were taken from ref 14.

long-range corrected (LC) functionals.22−25 These functionals are based on the separation of the Coulomb operator into longand short-range parts and shows great promise for correctly describing the excited states of large molecules. Because these functionals offer a better description of CT excitations, it is likely that they will provide a more accurate description of the chemical enhancement in SERS as well. In this Letter, we will investigate the CHEM enhancement in a series of pyridine derivatives (pyr-X) and small molecules interacting with a small silver cluster (Ag20) using TDDFT in combination with a LC functional. We will also compare CHEM enhancements obtained using the B3LYP functional, which include a fraction of Hartree−Fock exchange. The substituted pyridine consisted of X = H, p-CH3, pN(CH3)2, p-CFClH, p-CN, (m-CN,p-CN), and p-NO2. We also consider the following small molecules, CO, PH3, NH3, N2, and CS. Except for the pyridines with X = (m-C N,p-CN), p-NO2, and CS, the molecules are the same as those in our previous work. These molecules were chosen to give a wide range of partial charge transfer from the molecule to

the cluster due to the binding interactions. This quantity is used to classify the functional groups as either donating or accepting relative to hydrogen. To understand the importance of correctly describing the CT excitations on CHEM, we calculate the Raman cross section of the free molecules and the molecules absorbed on the Ag20 clusters using the LC-PBE functional26 and compare the results to the B3LYP and BP86 functionals. The LC-PBE functional is chosen because it has been previously shown to provide a good description of the electronic and optical properties of small silver clusters.27 The simulated Raman spectra for pyridine-Ag20 and the free pyridine as calculated using LC-PBE, B3LYP, and BP86 are shown in Figure 1. The BP86 spectra is taken from our previous work and was calculated using a TZP basis set.14 Comparing the Raman spectrum of pyridine calculated using BP86/TZP, B3LYP/6-311G*, and LC-PBE/6-311G*, we see that there is generally good agreement between the three spectra, although the intensities calculated using LC-PBE/6311G* are smaller. The main differences between the three spectra are the relative intensities of the two ring breathing 2471

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Table 2. HOMO−LUMO Gap for Complex (ωX−Ag), HOMO−LUMO Gap for Free Molecule (ωX), and Integrated Enhancement Factor (EFint) for Each Small Moleculea LC-PBE

a

B3LYP

BP86

LC-PBE

B3LYP

BP86

molecule

ωX−Ag

ωX

ωX−Ag

ωX

ωX−Ag

ωX

EFint

EFint

EFint

PH3 N2 CO NH3 CS

0.209 0.189 0.134 0.133 0.116

0.467 0.580 0.528 0.471 0.398

0.044 0.047 0.039 0.042 0.025

0.300 0.402 0.349 0.295 0.226

0.117 0.030 0.033 0.105

0.240 0.304 0.258 0.222

0.57 69.74 153.87 1.601 532.44

0.52 385.08 515.55 1.34 46.67

4.31 1652.34 531.96 5.11

HOMO-LUMO gaps are in Hartrees. The BP86 results were taken from ref 14.

modes at around 1000 cm−1. For BP86, the lower-frequency breathing mode is the strongest, whereas the reverse is true for both B3LYP and LC-PBE. Experimentally, the lower-frequency breathing mode is found to be the strongest,28 in agreement with the BP86 results. Previous work has also found this,29,30 although the relative intensities of these two modes have been found to be sensitive to basis set, functional, and solvent effects.29,30 In contrast, we find significant difference for the spectra of pyridine-Ag20, both in terms of the absolute and relative intensities. The intensities predicted using LC-PBE/6311G* are an order of magnitude lower than the BP86/TZP intensities, lowering the CHEM enhancement. Comparing the intensities obtained with LC-PBE with that obtained using B3LYP, we find that the intensities are about a factor of 2 smaller using LC-PBE. We also find that the intensities of the modes at 598, 1204, and 1573 cm−1 relative to the ring breathing modes at around 1000 cm−1 are predicted very differently using the BP86 functional. These modes have been shown experimentally to depend strongly on the electrode potential in SERS measurements on roughened Ag electrodes and are therefore associated with the CM mechanism.31 These results show that the CHEM enhancement is very sensitive to the functional chosen. To quantify the effect of using the LC-PBE functional, we collect the CHEM enhancement for the different substituted pyridines in Table 1. Following our previous work, we quantify the CHEM enhancement using the integrated Raman enhancement factor, which is defined as EFint =

between 10 and 1000, depending on the actual molecule and the vibrational mode.1,2,32 The smaller enhancements predicted from LC-PBE are thus in closer agreement with experimental estimates. We also calculate the enhancement factors for five small molecules (CO, PH3, NH3, N2, CS), and the results are listed in Table 2. For the small molecules, we also find that LC-PBE predicts significantly smaller enhancement factors than both BP86 and B3LYP. For N2, the enhancement calculated using LC-PBE is smaller by a factor of ∼20 compared with BP86 and a factor of ∼5 compared with B3LYP. For CO, the LC-PBE enhancement is smaller by a factor of ∼3 compared with the other two functionals. Experimental evidence for the CM effect in SERS shows that CO is enhanced by two orders of magnitude compared with N2, even though their gas-phase cross sections are identical.1,33 Using both LC-PBE and B3LYP, the enhancement factor for CO is predicted to be larger than N2, which is in agreement with the experimental observation, although we only find a difference of a factor of 2 in their CHEM enhancements. In contrast, the results obtained using BP86 find N2 to be more enhanced than CO. The significantly lower enhancement predicted in the simulations indicate that differences in the SERS enhancement for these two small molecules are not due to CHEM but rather a resonance effect with a CT excitation.1,32 Rather surprisingly, LC-PBE and B3LYP predict a de-enhancement for PH3. Previously, we showed that when using BP86, the CHEM enhancement scales as

∑k IXk − Ag ∑j IXj

model EFint

(1)

where IkX−Ag and IjX are the Raman cross sections of the kth and jth normal modes for the complex and isolated molecule, respectively. The improved description of the HOMO−LUMO gap when using LC-PBE and B3LYP enables us to calculate the enhancements for the (m-CN,p-CN) and p-NO2 substituted pyridines; using BP86, we were previously unable to converge the SCF due to the vanishing HOMO−LUMO gap. From Table 1, we clearly see that the enhancement factors calculated using LC-PBE are significantly smaller that the values predicted using BP86 and B3LYP. The largest enhancements found for the pyridines are around 39 using LC-PBE, which is about 2−3 orders of magnitude smaller than the largest enhancements predicted using BP86 and B3LYP. Although it is not possible to directly measure the CHEM enhancement experimentally because the EM contribution cannot be separated out, the chemical contribution to SERS has been estimated by comparing different vibrational modes of several organic adsorbates on cold-deposited silver films in ultrahigh vacuum.1,2,32 Experimental estimates of the CM effect range

⎛ ⎞4 ⎛ ω X ⎞4 ω X ⎟ = ⎜ Xe−Ag ⎟ ≈ A⎜ ⎜ω −bω X2−Ag ⎟ ⎝ ωe ⎠ + e ⎝ X−Ag ⎠

(2)

where ωXe and ωX−Ag are the lowest excitation in the free e molecule and the lowest charge-transfer excitation in the complex, respectively.14 We have found that the better description of the HOMO−LUMO gap and charge-transfer excitations given by LC-PBE eliminates the need for scaling factors from this two-state model, simplifying it to model EFint

4 ⎛ ω X ⎞4 ⎛ ω ⎞ e X ⎟⎟ = ⎜ X−Ag ⎟ ≈ ⎜⎜ ⎝ ωe ⎠ ⎝ ωX−Ag ⎠

(3)

This assumes that the excitation energies can be approximated by the HOMO−LUMO gap. Although this cannot be expected to be a very good approximation, test calculations showed that the ratio of the two excitations could be approximated by the ratio of the HOMO−LUMO gaps (see the Supporting Information). We report the HOMO−LUMO gap for both the complex (ωX−Ag) and the isolated molecule (ωX) in Tables 1 and 2. For each of these systems, we determine the HOMO− 2472

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Figure 2. The integrated enhancement, EFint, for each molecule versus the model integrated enhancement, EFmodel int , calculated using the two-state model. The blue dots (●) represent the substituted pyridines, the red triangles (▼) represent CO, N2, and CS, and the green squares (■) represent NH3 and PH3. The line shown is y = x. The yellow box indicates a range of experimental estimates for the chemical mechanism.1,2,32 The r value is the Pearson correlation coefficient.

Looking at the enhancements factors calculated using LCPBE plotted in Figure 2a, we see that there are three distinct groups of molecules. The group of molecules that shows the largest enhancement contains CS, CO, and N2 and are all known to readily accept π-back-bonding. The substituted pyridines that bind to the metal cluster through a combination of σ-bonding and π-back-bonding fall in the middle range, with enhancements between 3 and 40. The final group, which shows the least enhancement, consists of NH3 and PH3, which are known to bind weakly though σ-bonding. For this last group, the two-state approximation fails to correctly predict the enhancements and is likely due to the importance of many states contributing to the bonding character.34 This supports our previous results, in which molecules that show significant stabilization of the HOMO−LUMO gaps (such as those that readily accept π-back-bonding) would be likely to have strong CHEM enhancement. In summary, we have investigated the importance of correctly describing CT excitations for modeling the CHEM effect in SERS. To do this, we studied a series of pyridine derivatives (pyr-X) and small molecules interacting with a small silver cluster (Ag20) using TDDFT in combination with a LC functional. Our results show that the LC functional predicts significantly smaller enhancement factors due to the improved description of the HOMO−LUMO gap and charge-transfer excitations as compared with traditional functionals. We confirm that the magnitude of the CHEM enhancement is, to a large extent, governed by the energy difference between the highest occupied energy level of the metal and the lowest unoccupied energy level of the molecule. Thus, molecules that show significant stabilization of the HOMO−LUMO gaps (strong π-back-bonding) are likely to have strong CHEM enhancement. Enhancement factors are found to be less than 530 and typically less than 50, in agreement with experimental estimates. Surprisingly, we found that the LC-PBE (and B3LYP) predicts a de-enhancement for PH3 likely due to the weak σ-bond with the metal cluster.

LUMO gap of the silver−molecule complex to be the difference in energy between the HOMO on the metal and the lowest unoccupied orbital that matched the LUMO on the free molecule. In Figure 2a, we plot the enhancement factors calculated using LC-PBE versus the two-state approximation given by eq 3, and in Figure 2c and b, we plot the enhancement factors calculated using BP86 and B3LYP, respectively, versus the twostate approximation given in ref 14. From these figures, we see that there is a moderate to strong correlation between the calculated enhancement factor and that predicted using the two-state approximation for all three functionals. The Pearson correlation coefficients are r = 0.45, 0.99, and 1.00 for LC-PBE, B3LYP, and BP86, respectively. Thus, the correlation is significantly stronger for the B3LYP and BP86 data. This is not that surprising because for both functionals, the range of enhancement factors is larger, and the model enhancements in eq 2 include fitting parameters, which improves the correlation. While B3LYP offers a better description of the CHEM enhancement than BP86, it still predicts very large enhancements for molecules with small gaps. This is further illustrated by the yellow box highlighting the experimental estimations of the chemical mechanism, in which both B3LYP and BP86 predict enhancements above this range (up to 103).1,2,32 LC-PBE predicts lower enhancement factors due to an improved description of the HOMO−LUMO gap of the complex and thus the lowest charge-transfer excitation. This illustrates the importance of correctly describing charge-transfer excitations for predicting SERS enhancements. Another possible explanation for the difference in the enhancement factors predicted by the three different functions is that they provide a different description of the binding energy of the molecules interacting with the Ag20 cluster. Therefore, we plotted the enhancement factors calculated using the different functionals versus the binding energy (see the Supporting Information). This shows that all three functionals qualitatively provide a similar range of the binding energies, although there is significant variation in the predicted binding energies. More importantly, we find that the binding energy is not correlated strongly (r < 0.2 for all three functionals) with the observed enhancements, in good agreement with our previous result.

■

COMPUTATIONAL DETAILS The geometries for most of the molecules were taken from our previous works.14 The Ag20 cluster previously adapted corresponds to the global minimum structure using the 2473

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national scientific user facility sponsored by the U.S. Department of Energy’s Office of Biological and Environmental Research and located at the Pacific Northwest National Laboratory, operated for the Department of Energy by Battelle.

Sutton−Chen potential and represents an adatom site on a metal nanoparticle. The pyridine is assumed to bind to the silver cluster through the nitrogen. For the new molecules studied in this work, we optimized the geometry using Amsterdam density functional (ADF)35 following the method described in our previous work.14 All coordinates for the new molecules are given in the Supporting Information. Test calculations showed that reoptimizing the geometries using LCPBE or B3LYP only led to minor changes, and thus, the BP86 geometries were used for all simulations. Vibrational frequencies and polarizabilites were calculated using the NWChem program package36 for both the isolated molecule and the molecule adsorbed to a Ag20 cluster. LC Perdew, Burke, and Ernzerhof (LC-PBE) and B3LYP XC functionals were used with a LANL2DZ ECP basis set for all Ag atoms, and a 6-311G* basis set was used for all other atoms, all from NWChem’s standard library. The Raman spectrum for each system was calculated using a three-point numerical differentiation method. Absolute Raman intensities are presented here as the differential Raman scattering cross section. For Stokes scattering with an experimental setup of a 90° scattering angle and perpendicular-plane-polarized light, the cross section is given by37 dσ dΩ π2 h = 2 (νiñ − νk̃ )4 2 [45αk̅ ′2 + 7γk′2] ε0 8π cνk̃ 1 45(1 − exp(−hcνk̃ /kBT ))

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Ik =

(4)

where ν̃in and ν̃k are the frequencies of the incident light and the kth vibrational mode, respectively. α̅k′ and γk′ are the isotropic and anisotropic polarizability derivatives with respect to the vibrational mode k. We used a wavelength of 512.15 nm (sodium D line) in eq 4 to calculate the Raman cross sections.

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ASSOCIATED CONTENT

S Supporting Information *

Plots of enhancement versus binding energies for the different functionals, comparison between CT excitation energies and HOMO−LUMO gaps, and tables containing optimized geometries. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.J. acknowledges the CAREER program of the National Science Foundation (Grant No. CHE-0955689) for financial support, start-up funds from the Pennsylvania State University, and support received from Research Computing and Cyberinfrastructure, a unit of Information Technology Services at Penn State. S.M.M. acknowledges the Academic Computing Fellowship from the Pennsylvania State University Graduate School. This research was performed in part using the Molecular Science Computing Facility (MSCF) in the William R. Wiley Environmental Molecular Sciences Laboratory, a 2474

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