Computational Study of the Resonance Enhancement of Raman

Article pubs.acs.org/JPCC

Computational Study of the Resonance Enhancement of Raman Signals of Ligands Adsorbed to CdSe Clusters through Photoexcitation of the Cluster Nathaniel K. Swenson, Mark A. Ratner, and Emily A. Weiss* Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, United States ABSTRACT: This paper describes density-functional-theory-based computations of resonance Raman (RR) spectra of ligand molecules adsorbed to the surface of a Cd16Se13 cluster. Signals from asymmetric vibrational modes of ligand binding groups, such as the asymmetric O−C−O stretching modes of carboxylates, are enhanced relative to the symmetric vibrational modes when the excitation energy is on-resonance with the excitonic energy of the cluster. Certain ligand molecules have frontier orbitals with the correct energies and symmetries to mix with the orbitals of the CdSe cluster, and as a result, the wave functions of the electron and the hole delocalize from the cluster onto the ligand molecules; experimentally, this delocalization results in a bathochromic shift of the band edge excitonic absorption. Increased excitonic delocalization results in greater vibronic coupling between the exciton and the ligand vibrations and, on average, preferential enhancements in the RR signals of those vibrations. This work suggests that the use of exciton-delocalizing ligands to optimize electronic coupling between neighboring CdSe nanoparticles may, at the same time, enhance the rates of nonradiative exciton decay by coupling the exciton and ligand vibrational modes.

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INTRODUCTION This paper describes the computational simulation of resonance Raman (RR) spectra of a variety of organic ligands bound to Cd16Se13 clusters (diameter, 0.9 nm),1 to determine some defining characteristics of vibrational modes of the ligands that are vibronically coupled to the exciton of the cluster. In this study, we take advantage of the detailed information that can be obtained from quantum mechanical Hessian computations to map RR enhancements to vibrational modes of specific types and symmetries. The orbitals of certain ligand molecules2−9 have the correct energies and symmetries to mix with the orbitals of Cd16Se13; this mixing results in the delocalization of the exciton from the Cd16Se13 core onto the ligand molecule and is experimentally observable as a decrease in the bandgap of the cluster. In the present study, we correlate the degree of this mixing, measured through the bandgap of the cluster, with vibronic coupling of the exciton to the vibrational modes of the ligands. The clusters in this study serve as model systems for ligandcoated colloidal quantum dots (QDs). In general, the types of ligands that best stabilize and solubilize dispersions of QDs are long-chain aliphatic phosphonates, carboxylates, and amines, and are electrically insulating.10−13 So-called “exciton-delocalizing ligands,” such as those with thiolate and dithiocarbamate headgroups, offer a strategy for maximizing electronic coupling between a QD and its surroundings2−9 and therefore also the yield of charge carrier extraction from QD excitonic states or the electrical mobility of QD films. Replacement of the alkyl chain with a conjugated group such as an aromatic ring further decreases the energy barrier for charge extraction from a QD. © XXXX American Chemical Society

This study aims to determine whether the delocalization of the electron wave function of the QD core into interfacial states formed upon mixing of QD and ligand orbitals results in vibronic coupling of the lowest excitonic transition to vibrational modes in these ligands (manifest RR enhancement of these modes upon excitation of the cluster core) and thereby introduces new nonradiative pathways by which the exciton could decay. It also aims to identify which modes of the ligands are preferentially coupled to the exciton. This type of knowledge allows for chemical tailoring of ligands to perform the exciton delocalization function with minimal decrease in the quantum yield of photoluminescence or charge extraction. Raman signals from vibrational modes of the ligand molecules bound to semiconductor NPs can be enhanced by factors as high as ∼106 when the NP is resonantly excited,14−16 even when the excitation is not resonant with any electronic states of the isolated ligand molecules. This enhancement has been experimentally observed in several semiconductor nanoparticle−molecule systems, including those that contain NiO,17 TiO 2 , 18 PbTe, 19 PbS, 20 GaP, 21 InAs/GaAs, 22 CdSe/ CdZnSeMg,15 CdS,23,24 CdTe,25 ZnS,26 ZnO,27,28 ZnSe,16 and CuTe nanoparticles.14 The electromagnetic mechanism for surface-enhanced raman spectroscopy (SERS) is usually of little concern for semiconductors with bandgaps in the visible spectrum; these enhancements are dominated by the so-called Special Issue: Richard P. Van Duyne Festschrift Received: March 17, 2016

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DOI: 10.1021/acs.jpcc.6b02804 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

which are computed from the elements of the finite-difference derivative polarizability tensor matrix, α′, according to eqs 1 and 2.

“chemical mechanism,” which has three primary contributions: (i) resonance with charge-transfer (CT) states of mixed ligand−nanoparticle character (the kind we model here), (ii) resonance with molecular excitations, and (iii) nonresonant changes in the molecular polarizability upon binding to a surface.29−31 Lombardi and Birke32 applied Herzberg−Teller corrections to a Born−Oppenheimer model to describe the SERS intensity of molecules attached to semiconductor NPs. Akin to the Albrecht A-, B-, and C-terms,33 they decompose SERS enhancement into resonances with the plasmon, charge-transfer states, and molecular excitations. Prediction of RR intensities of vibrational modes of molecules attached to a semiconductor NP, however, remains nontrivial because the various resonance mechanisms are coupled, and the system cannot be cleanly partitioned into molecule and semiconductor portions.32 This coupling is especially relevant for the cluster−thiolate and cluster−dithiocarbamate systems we study here, which are interesting, in part, because of the large degree of interfacial orbital mixing and resulting bathochromic shift of the absorption spectrum of the complex.2−9 Our methodology of numerically evaluating frequencydependent polarizability derivatives simultaneously takes into consideration all the coupled resonances and nonresonance effects that contribute to the chemical enhancement mechanism. We learn that (i) asymmetric vibrational modes of ligand binding groups are strongly enhanced in RR spectra when the excitation is resonant with the excitonic state, and we thus identify these asymmetric modes as likely channels for the nonradiative dissipation of electronic energy; and (ii) there is a correlation between the decrease in bandgap of the cluster that occurs upon mixing of cluster and ligand orbitals and the RR enhancement of the vibrational modes of these excitondelocalizing ligands. Computational Methods. To compute a Raman spectrum, we first performed a geometry optimization to obtain the ground-state structure of each cluster−ligand complex within density functional theory (DFT), using the gradient-corrected Becke−Perdew BP86 functional and a polarized triple-ζ (TZP) basis set. The BP86 density functional and TZP basis set have been used successfully for predicting resonance Raman intensities in both molecular systems (Rhodamine 6G dye34) and in ligated metal clusters (Au19−thiophenolate31 and Ag20− pyridine35). We then performed a Hessian computation to obtain vibrational modes and also to confirm the geometrical stationary point, as evidenced by the absence of imaginary frequencies. For each vibrational mode, we obtained the polarizability derivative by computing the polarizabilities at the (+)- and (−)- displaced vibrational mode geometries and then subtracted the resulting polarizability tensors, α. We computed these polarizabilities using the AO Response module within the Amsterdam Density Functional (ADF) software package, with the same level of theory as for the geometry optimizations. The AOResponse module uses a time-dependent DFT (TDDFT) linear response model to obtain the frequency-dependent polarizabilities; to achieve convergence near electronic resonances, the model includes a damping parameter (Γ) that describes a finite lifetime of the electronic states. For our calculations, we use Γ = 0.004 au, which was previously reported to be reasonable in most cases.36,37 From these derivative polarizability tensors, α′, for each mode, we obtained the isotropic (αp̅ ′) and anisotropic (γ′p) polarizability derivatives

αp̅ ′ =

γp′ 2 =

1 3

∑ (ααα′ )p

1 2

∑ [3(ααβ′ )p (ααβ′ )p − (ααα′ )p (ααα′ )p ]

(1)

α

(2)

αβ

We then used these polarizability derivatives to compute the scattering factor, S, of each mode (eq 3). S = 45αp̅ ′ 2 + 7γp′ 2

(3)

From the scattering factor S, frequency of incident light ν̃in and frequency of vibrational mode p, ν̃p , we obtained the differential cross section for Stokes scattering

dσ dΩ

(eq 4).

2

dσ h 1 π = 2 (νiñ − νp̃ )4 2 (S /45) dΩ 1 − exp[−hcνp̃ /kBT ] 8π cνp̃ ε0 (4)

We performed all geometry optimization, Hessian, and polarizability computations with the Amsterdam Density Functional (ADF) electronic structure program, version 2014.06a. The calculations described above provide a Raman intensity for each vibrational mode, creating a “stick”-spectrum. We then applied a Lorentzian broadening function to each peak with a uniform width of 10 cm−1 for visualization purposes. We note that the excited-state energies we compute using the BP86 functional are underestimated relative to experiment; this is a well-known problem with generalized gradient functionals that is caused by spurious self-interaction error and is exacerbated by excited states with Rydberg character.38 For the purposes of this work, this offset between excitation energies computed with BP86 and experimental values is not problematic; by computing the resonance Raman spectrum at incident frequencies that correspond to TDDFT excitation energies, we simulate the physical situation of electronically resonant Raman excitation for our systems.

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RESULTS AND DISCUSSION Selection of the Model System. We chose to use the Cd16Se13 cluster (Figure 1) as a model system because (i) it is computationally convenient to compute the full Raman spectrum of a system this size, because the polarizability derivatives of a single mode can be obtained within 6 h on 12 processor cores; (ii) the particle’s core contains a wurtzite lattice similar to larger quantum dot analogues; and (iii) despite the small size of Cd16Se13, it possesses a well-defined CdSelocalized band-edge transition at 3.4 eV according to TDDFT when computed with the hybrid B3LYP functional. The CdSe cluster-portion of the cluster−ligand complex therefore can be resonantly excited without directly exciting ligand-localized electronic transitions. Signals from Asymmetric Vibrational Modes of Ligand Binding Groups are Particularly Resonantly Enhanced. We attach anionic ligand molecules (X) to a CdSe cluster (Cd16Se13(NH3)12(X)6) and use time-dependent DFT to determine the energy of the CdSe cluster’s lowest excitation. We computed the RR spectrum of each cluster− ligand complex by calculating polarizability derivatives with the Raman excitation equal to the energy of the lowest TDDFT B


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Figure 1. (A) Structure of the Cd16Se13 cluster, coordinated by six anionic phenyl dithiocarbamate (PTC) ligands and 12 neutral NH3 molecules, which are needed to satisfy the unsaturated Cd valences. (B−F) Structures of five anionic ligands used in this study: (B) ethyl thiolate, (C) acetate, (D) thiophenolate, (E) benzoate, and (F) phenyl dithiocarbamate.

Figure 2. (A) Portion of the simulated (BP86/TZP) RR spectrum of the acetate-ligated cluster, Cd16Se13(NH3)12(Ac)6. (B) The same RR spectrum (blue), over a wider range in energies, overlaid with the offresonant “normal” Raman spectrum (NRS) (red) of the same cluster. The NRS spectrum is multiplied by 1000 so that the cross sections of the phonon peaks are the same (not shown). Both spectra are magnified to show the peaks of the ligand vibrations. Some vibrational modes are enhanced to a greater degree than others when the excitation wavelength is resonant with the CdSe cluster’s lowest singlet excited state. In particular, the asymmetric O−C−O stretching modes of the acetate ligands (1512−1528 cm−1) are enhanced, on average, by a factor of 3.3 × 104. The abbreviation “sr” indicates steradians or square radians, the SI unit for solid angle.

excitation, as described in detail in Computational Methods. We then computed the “normal” (off-resonant) Raman spectrum using the same procedure as the resonant case, except with the energy of the incident radiation set to half of the resonant case, so that the incident radiation would not be resonant with any part of the complex. We plot the computed RR spectrum of the Cd16Se13 cluster with acetate ligands in Figure 2A. The difference in mass between the heavy atoms of the cluster (Cd and Se) and the lighter second- and third-row elements in the ligands results in a convenient division of the vibrational spectrum: Cd−Se cluster phonon modes generally have energies less than 250 cm−1, and ligand-specific vibrations have energies greater than 250 cm−1. Our simulations show that the Cd−Se phonon modes generally have Raman cross sections that are a factor of 100 greater than the most intense ligand vibrational modes. The Cd−Se phonon modes are furthermore easily categorized into acoustic and optical phonon modes, with a clean division between them around 109 cm−1, as can be seen in Figure 2A. To determine how the RR cross sections of the ligand vibrational modes are affected by excitation on resonance with the exciton of the CdSe core, we overlay the resonant (RRS) spectrum with the off-resonant normal Raman spectrum (NRS) spectrum (Figure 2B) of each ligand-coated CdSe cluster. The first main result of our computations is that asymmetric vibrational modes of the binding groups of ligand molecules are preferentially resonantly enhanced upon excitation of the cluster. To demonstrate this point most clearly, we first examine the acetate-coated cluster. The Raman spectrum of acetate is dominated by three main features, all associated with the carboxylate functional group: the O−C−O bending mode (950 cm−1), the symmetric O−C−O stretching mode (1350 cm−1), and the asymmetric O−C−O stretching mode (1512−

1528 cm−1). In the NRS (Figure 2B, red), the symmetric modes of the carboxylate group (O−C−O bending at 950 cm−1 and symmetric O−C−O stretching at 1350 cm−1) have a much higher Raman cross section than the asymmetric O−C−O stretching mode (1512−1528 cm −1 ). In contrast, the asymmetric O−C−O stretching mode dominates the RR spectrum (Figure 2B, blue). The asymmetric O−C−O stretching mode is enhanced by a factor of 3.3 × 104 when the excitation is resonant with the excitonic state of the cluster, whereas the O−C−O bending mode and the symmetric O− C−O stretching mode are both enhanced by only a factor of 190 under the same conditions. We find a similar result with benzoate ligands as we do with acetate ligands: the asymmetric O−C−O stretching mode is enhanced by a factor of 5.3 × 103, while the symmetric O−C− O modes are enhanced by a factor of only 39. The S−C−S binding group of phenyl dithiocarbamate (PTC) is analogous to the carboxylate binding group, and in PTC, we also see the asymmetric S−C−S stretching mode enhanced by a factor of 426, while the symmetric S−C−S stretching mode is enhanced by a factor of 65. Resonance of the excitation wavelength with the exciton produces a change in selection rules; when the excitation is off-resonant with the exciton, symmetric modes generally have higher intensities than asymmetric modes, and when the excitation is on-resonant with the exciton, the Raman intensities of the asymmetric modes are preferentially enhanced C


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alignment with the valence and conduction band-edges of CdSe. As a result, we observe differing degrees of wave function delocalization onto these ligands. This delocalization leads to stabilization of the excited state (exciton) and a lower calculated bandgap. We performed a TDDFT computation with the BP86 functional and TZP basis set on our Cd16Se13 cluster and find that the bandgap is 2.40 eV with benzoate ligands (in a bridging geometry), 2.33 eV with thiophenolate ligands (in a bridging geometry), 2.16 eV with PTC ligands (in a chelating geometry), and 1.81 eV with PTC ligands (in a bridging geometry). The trend in bandgap is consistent with the trend in the degree of CT between the cluster and ligand that we calculated through the NBO analysis, as described above. We note that the BP86 functional typically underestimates these excited-state energies relative to experiment, but the trend in energies, which is the result of interest here, should be predicted correctly by this method. We then identify 17 of the vibrational modes of the phenyl functional group that benzoate, thiophenolate, and PTC all have in common, Figure 3. These vibrational modes include

over the symmetric modes. This change in selection rules occurs despite the fact that the excitation is off-resonant with any electronic states of the carboxylate or dithiocarbamate molecules themselves. Previous theoretical work has demonstrated that resonant enhancement of nontotally symmetric modes (here, asymmetric O−C−O stretching modes) of molecules bound to nanoparticles (NPs) is strong evidence for either molecule-toNP or NP-to-molecule charge transfer.32 Enhancement of asymmetric vibrational modes due to CT interactions has also been reported experimentally; for example, asymmetric modes of 4-mercaptopyridine (4-Mpy) ligands are enhanced on the surface of ZnSe nanoparticles under excitation that is resonant with the ZnSe exciton. Upon adsorption to the ZnSe surface, the b1 and b2 (asymmetric) vibrational modes were found to dominate the Raman spectrum.32 We hypothesize that, in the case of our Cd16Se13 system, enhancement of the asymmetric modes of the carboxylate ligands is due to charge transfer between the ligands and the Cd16Se13 cluster, probably as a result of mixing between the frontier orbitals of the ligand and the valence and conduction bands of the cluster. To quantify the CT that occurs between the ligand and the cluster, we performed a population analysis of our cluster− ligand system using the Natural Bond Orbital (NBO) 6.0 software.39 In an isolated state, the anionic ligands we studied have a charge of −1.0; however, upon adsorption, they donate some electron density to the CdSe cluster. In the bound state, benzoate has a charge of −0.83, thiophenolate a charge of −0.79, and PTC a charge of −0.77. Our simulations of the RR spectrum of clusters coated with benzoate and PTC show that the ratio of RR cross sections of asymmetric and symmetric stretching modes of the binding groups of these ligands (O− C−O in benzoate or S−C−S in PTC) increases with the degree of ligand-to-cluster charge transfer. Specifically, with resonant excitation of the cluster, the ratio of cross sections, asymmetric:symmetric, for the S−C−S stretching modes in PTC is 2.13:1, and the ratio of cross sections, asymmetric:symmetric, for the O−C−O stretching modes in benzoate is 0.55:1. For both benzoate and PTC, however, the Raman cross section of the asymmetric stretching mode is resonantly enhanced more than the symmetric stretching mode. Specifically, with offresonant excitation of the cluster, the ratio of the cross sections, asymmetric:symmetric, for the S−C−S stretching modes in PTC is 0.29:1, and the ratio of the cross sections, asymmetric:symmetric, for the O−C−O stretching modes in benzoate is 0.0057:1. Resonance Raman Enhancement of the Ring Modes of Aromatic Ligands Depends on the Strength of the Electronic Coupling between the Cluster and the Ligand. To systematically investigate the relationship between wave function delocalization onto adsorbed ligands (enabled by CT between the cluster and ligand orbitals) and vibronic coupling between the exciton and the vibrational modes of those ligands, we simulate the RR spectra of various aromatic ligands, with different binding headgroups, bound to Cd16Se13. We minimize the geometry of the Cd16Se13 cluster with each of three similar aromatic ligand molecules: thiophenolate, benzoate, and phenyl dithiocarbamate (Figure 1D−F). When the molecular orbitals of the ligand mix with the frontier orbitals of the CdSe cluster, the wave functions of the electron and/or hole spatially delocalize from the CdSe core into the interfacial region.2,5 Thiophenolate, benzoate, and PTC all offer different molecular orbital energies, symmetries, and energetic

Figure 3. Seventeen different vibrational normal modes of the phenyl functional group. Here, benzoate ion is pictured, but we match these modes with analogous vibrational modes of thiophenolate and PTC ligands to determine relative intensities. Included are (A, B) C−H stretching modes, (C, D, E, F, I, J, K, L) C−C stretching modes, (G, H) in-plane C−H bending modes, (M, N) out-of-plane C−H bending modes, (O, P) in-plane C−C bending modes, and (Q) ring twisting. In M, N, and Q, the red and blue dots denote movement perpendicular to the plane of the ring. The mode frequencies listed here are the frequencies of these vibrations in the Cd16Se13−benzoate cluster.

C−H and C−C stretching modes, in-plane and out-of-plane C−H and C−C bending modes, and a ring twisting mode. Because the Cd16Se13 cluster is always coordinated by six of each specified ligand, each mode shown in Figure 3 is approximately 6-fold degenerate in the cluster−ligand complex. The 6-fold degeneracy arises from the various combinations of D


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each of the 17 phenyl vibrational modes that we identified in each aromatic ligand against the bandgap of the Cd16Se13 cluster when that ligand is bound to the surface. The points are the average RR cross section of all phenyl vibrational modes for each ligand, and the error bars show the total range (not standard deviation) of values across the 17 modes. We find that, on average, the RR cross sections of vibrational modes of the phenyl group decrease monotonically as the bandgap of the Cd16Se13 cluster increases. When we plot the RR cross section versus bandgap energy for each mode separately (Figure 4, bottom, A−Q), we find that the RR cross sections of almost half of the vibrational modes (modes A, E, G, H, I, L, M, and P; underlined in Figures 3 and 4) show monotonic dependence on the band gap energy, while some of the others, but not all, are nearly monotonic. These results suggest that delocalization of the excitonic state onto ligand molecules (resulting in a smaller bandgap for the cluster−ligand complex) is correlated with a larger RR cross section and therefore with the availability of nonradiative decay pathways by which the exciton can directly exchange energy with ligand vibrations. We do not yet know why the RR cross sections of some modes are more precisely correlated with a decrease in the cluster’s bandgap than other modes. It is difficult to discern any defining characteristics of a “correlated” versus “uncorrelated” mode. For example, the set of modes with the most monotonic dependence of RR cross section on bandgap represent a mixture of a and b symmetries, different frequencies of vibration, and different types of vibrations (C−H and C−C stretches and bends). One complicating factor is that the phenyl ring modes are coupled to different degrees with the binding group modes in the different ligands, and depending on the symmetry and frequency of the binding group mode to which they couple, the RR cross section of the phenyl ring mode is perturbed (upward or downward). Nonetheless, the correlation between the degree of exciton delocalization into the ligand shell (as measured by the cluster’s bandgap) and the average RR enhancement of ligand modes that are spatially removed from the QD surface illustrates that delocalization results in an increase in vibronic coupling between the exciton of a particle and modes belonging to ligands to which its core states are coupled electronically.

phases of the vibration when distributed across the six ligand molecules. For each ligand adsorbed to the Cd16Se13 cluster (benzoate, thiolate, PTC bridging, and PTC chelating), we locate each of the vibrational modes shown in Figure 3 (and its degenerate images) in the normal mode spectrum of our cluster−ligand complex, and then compute its RR cross section (eq 4) as the average of the RR cross sections of all the vibrational mode’s degenerate images. We then scale the cross sectional spectra of each ligand by the integrated area under its acoustic phonon peak (Figure 2A, between 0 and 109 cm−1). This normalization procedure is necessary because (i) we are using an excitation frequency that corresponds to the resonance with the lowest singlet excited state of the cluster, but, as stated earlier, the frequency of that electronic resonance varies with the type of ligand on the surface of the cluster, and (ii) the Raman cross section inherently depends on excitation frequency, both in the fourth-power dependence on ν̃in in (eq 4) and in the TDDFT computation of the frequencydependent (dynamic) polarizability tensors needed to compute α′ used in eqs 1 and 2. To remove the inherent dependence of the Raman cross section on excitation frequency, we scale the intensities in the RR spectra using the integrated cross section of the acoustic phonon peak, which should not depend on surface treatment.40 We present the results of our analysis in Figure 4. In the top panel, we plot the average of the scaled RR cross sections of

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CONCLUSIONS

We used DFT-based methods to compute resonance Raman spectra of Cd16Se13-cluster ligand complexes, with an excitation frequency that corresponds to resonance with the lowest singlet excited state. Enhancements of RR spectral intensities rely on changes of electron and hole distributions on the ligand molecules on going from the ground to excited states; therefore, the RR enhancements we report here on small clusters are probably larger than one would observe in a CdSe QD with hundreds to thousands of atoms and hundreds of ligands. Our results show that asymmetric stretching modes of the binding groups of carboxylate and dithiocarbamate ligands are resonantly enhanced to a greater degree than the corresponding symmetric modes and serve as likely pathways for nonradiative decay of the exciton through the vibronic coupling to ligand vibrations. We hypothesize that the RR enhancement of asymmetric modes occurs because of ground-state charge transfer that we observe between the Cd16Se13 cluster and adsorbed ligand molecules; natural bond orbital analysis reveals

Figure 4. (Top) Average (symbols) and range (error bars) of the normalized RR cross sections of all 17 vibrational modes of the phenyl functional group of ligand molecules attached to Cd16Se13, as a function of the bandgap of the Cd16Se13 cluster coated with that ligand. “Normalized” means scaled to the integrated intensity of the acoustic phonon peak in the same spectrum. (Bottom) Individual plots (A−Q) of the normalized resonance Raman intensity for all 17 phenyl vibrational modes versus bandgap energy, extracted from the top panel. The labels A−Q here correspond to the labels in Figure 3, and the labels that are underlined indicate the modes where the RR cross section has a monotonic dependence on the bandgap of the cluster. E


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that as much as 0.23 electrons (in the case of PTC) are transferred from the ligand to the cluster upon binding. We compute the RR intensities of the vibrational modes of the phenyl rings of three different ligand molecules: benzoate, thiophenolate, and phenyl dithiocarbamate. TDDFT computations show us that the bandgap of Cd16Se13 coated with PTC ligands is 0.6 eV smaller than that of Cd16Se13 coated with benzoate ligands. Such shifts occur when a ligand molecule has the correct orbital energies and symmetries to mix with the orbitals of Cd16Se13 and delocalize the wave functions of the electron or hole (or both) from the CdSe cluster onto the ligand molecules. We find that, on average, greater wave function delocalization is correlated with both greater groundstate charge transfer between the cluster and adsorbed ligands and with greater RR cross sections for the phenyl ring modes on the delocalizing ligands. While ligands that cause this delocalization of carriers in the core of a cluster or QD into the ligand shell are potentially useful for increasing the electronic coupling for carrier extraction,2,5 our study suggests that this delocalization can also enhance coupling between the excitonic state and vibrational modes of the ligand molecules that leads to nonradiative dissipation of electronic energy.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 847-491-3095. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Army Research Office via the Presidential Early Career Award for Scientists and Engineers (PECASE) to E.A.W. (W911NF1110075), as part of the Center for Bio-Inspired Energy Science, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award # DE-SC0000989, and by the Northwestern University Materials Research Science and Engineering Center (NUMRSEC), funded by the National Science Foundation (DMR1121262).

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Computational Study of the Resonance Enhancement of Raman

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