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End-Group-Induced Charge Transfer in Molecular Junctions: Effect on Electronic-Structure and Thermopower Janakiraman Balachandran,† Pramod Reddy,*,†,‡ Barry D. Dunietz,*,§ and Vikram Gavini*,† †

Department of Mechanical Engineering and ‡Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109 § Department of Chemistry & Biochemistry, Kent State University, Kent, Ohio 44242 S Supporting Information *

ABSTRACT: We analyze triphenyl molecules coupled to gold electrodes through five different end groups to understand the effect of end groups on the thermoelectric properties of molecular junctions. Our investigation suggests that end-group-mediated charge transfer between the molecule and electrodes plays an important role in the resulting thermoelectric properties. We find that the direction of charge transfer, which is governed by the electronegativity of the end-group functionalized molecule, is strongly correlated to the degree of reorganization of frontier molecular orbitals (HOMO− LUMO). In particular, isocyanide, nitrile, and amine end-group molecular junctions, with charge (electron) transfer out of the molecule, exhibit a strong overall downward shift in the energies of frontier molecular orbitals, whereas thiol and hydroxyl end-group molecular junctions, with charge transfer into the molecule, exhibit a smaller overall downward shift. Finally, our study shows that the sign of the thermopower of molecular junctions is closely related to the HOMO−LUMO energies and electronegativity of isolated molecules. SECTION: Molecular Structure, Quantum Chemistry, and General Theory

N

the resulting thermoelectric properties needs further elucidation. The present work bridges this gap by illustrating the role of end groups on the resultant electronic-structure. Furthermore, this work also provides a qualitative understanding of the relationship between the pertinent characteristics of isolated molecules (HOMO, LUMO energies, electronegativity) and the thermopower of MJs created from them. In this work, we begin by analyzing the electronic-structure of triphenyl dithiol (SS3) and triphenyl di-isocyanide ((NC)23) molecules (Figure 1a) using density functional theory (DFT) calculations performed with Q-CHEM software26 by employing B3LYP functional27,28 and LANL2DZ basis sets.29−31 The computed HOMO and LUMO energy levels of these molecules are presented in Table 1. These results indicate that the Fermi energy (EF) of Au, which is ∼ −5.2 eV,32 lies in the HOMO− LUMO gap of these molecules and is closer to the HOMO energy level. Interestingly, recent experimental and computational studies12 suggest that Au-(NC)23-Au junctions exhibit a LUMO-dominated transport, whereas Au-SS3-Au junctions exhibit HOMO-dominated transport. This observation raises an important question: How do end groups inf luence the reorganization of molecular orbitals upon contact with electrodes? To obtain insight into the end-group-mediated reorganization of energy levels, we compared the molecular density of

anometer-sized molecular junctions (MJs), where a single molecule bridges two metal electrodes, have great potential for advancing future electronic1−3 and energy conversion4−7 technologies. The end groups of the MJs play an important role in determining their transport properties such as electrical conductance and thermopower8−13 (also called the Seebeck coefficient). Reliable experimental measurements of electrical conductance of MJs with different end groups10,11,14,15 have provided important insight into the effect of end groups on their conductance. However, conductance measurements alone cannot delineate the nature of charge transport in the MJs.16 Thermoelectric measurements can provide this additional insight.9,16,17 In particular, a positive thermopower indicates a scenario where transport is dominated by states immediately below the Fermi energy (EF) (HOMOdominated or p-type transport), whereas a negative thermopower indicates a scenario where transport is dominated by states immediately above the EF (LUMO-dominated or n-type transport). Recent thermopower measurements12,13,18,19 demonstrate the ability to tune the nature of transport in aromatic MJs by changing the end group. Furthermore, thermoelectric properties have also been studied using the Green’s function approach in the Landauer formalism of transport.20−22 Such computational studies12,23−25 have provided important insight into the length and end-group dependence of the thermoelectric properties of MJs. However, the underlying mechanism that relates the effect of end groups on the electronic-structure and © XXXX American Chemical Society

Received: May 24, 2012 Accepted: July 4, 2012

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These Green’s functions are calculated using an efficient recursive algorithm.35 In our calculations, the self-energy operators of the electrodes are computed only at EF, which is commonly referred to as the wide band scheme and has been shown to be a good approximation for MJs created from Au electrodes with density of states dominated by the s band.36 We now describe the procedure to compute the M-DOS for the three aforementioned scenarios. The retarded Green’s function, Gr(z), that is subsequently used to compute M-DOS, is given by Gr (z) = [zS − H − ΣL − ΣR ]−1 ,

z = E + iη

(1)

where E is the energy and η is a small parameter to regularize the Green’s function. In the above expression, H and S denote the Hamiltonian and overlap matrix of the system under consideration. ΣL/R denote the self-energy matrices corresponding to the left and right leads. In the case of IM and EM systems, the ΣL/R are set to zero. The density of states, D(E), is then obtained from Gr(z) by 1 D(E) = − Tr(Im[Gr (z)S]) π Figure 1. (a) Isolated triphenyl dithiol (SS3) and triphenyl diisocyanide ((NC)23) molecules. (b) M-DOS of SS3 molecule in different scenarios (IM, EM, and open quantum system). (c) M-DOS of (NC)23 molecule in different scenarios. The M-DOS of the IM, EM, and open quantum system are denoted by blue dotted line, red dashed line, and green continuous line, respectively. The purple arrows indicate the magnitude of the M-DOS shift.

To compute M-DOS, we performed the trace in eq 2 only over the orbitals that are centered on the molecule. Natural atomic orbital (NAO)37 basis, which is an orthonormal basis with localized functions, is used for computing the M-DOS. We begin with our electronic-structure analysis of the SS3 and (NC)23 molecular systems. The computed M-DOS for the IM, EM, and open quantum systems for SS3 and (NC)23 are shown in Figure 1b,c, respectively. A comparison between the M-DOS of IM and EM for both systems shows that the HOMO and LUMO states of EM shift to lower energies in comparison with IM. However, it is interesting to note that this downward shift in energies (Table 1) is significantly larger in the case of (NC)23. In particular, the shift of HOMO and LUMO states in the case of SS3 is 0.35 and 0.25 eV, respectively, whereas in the case of (NC)23, these shifts are significantly larger: 0.9 eV for HOMO and 1.05 eV for LUMO. To validate the independence of the obtained results on the choice of basis functions, we repeated our calculations using a second basis set comprising of the primitive atomic orbitals (Figure S5, SI), whose results are in good agreement with the results obtained using NAO basis. A comparison of the M-DOS of EM and open quantum systems in Figure 1b,c shows that the energies corresponding to the dominant peaks are almost identical. To verify that this observation is not an artifact of the wide band scheme adopted in our calculations, a full tight binding computation was also performed (Figure S6, SI), which did not affect the results. This suggests that for the purpose of understanding the reorganization of the molecular states, the shifts in the dominant peaks of the EM are representative of the respective shifts in the open quantum systems. Although these results demonstrate that end groups play an important role in realigning the molecular orbitals, the dominant mechanism that leads to the differences in the magnitude of these shifts is yet to be identified. As a first step towards answering this question, we compare the number of electrons present in the isolated and extended molecular systems. The insights obtained from such an analysis are also expected to be valid for the open quantum system because the shift of the M-DOS is completely captured by the extended molecule. To quantify the change in the number of electrons in

Table 1. Computed Values of HOMO and LUMO Energy Levels and Electronegativity (χ) of Isolated Molecules. The Computed Charge Transfer (ΔN) (see eq 3), Computed Shift of HOMO (ΔεH) and LUMO (ΔεL) Energy Levels after Contact with Au Electrodes. system

HOMO (eV)

LUMO (eV)

ΔN

χ (eV)

ΔεH (eV)

ΔεL (eV)

SS3 (NC)23 OO3 (CN)23 (NH2)23

−5.65 −6.28 −5.47 −6.53 −4.68

−1.14 −1.93 −0.82 −2.20 −0.41

−0.66 0.16 −0.25 0.12 0.27

5.13 4.15 5.12 4.40 2.57

0.35 0.9 0.24 0.8 0.96

0.25 1.05 0.23 0.86 0.92

(2)

states (M-DOS) of SS3 and (NC)23 before and after making contact with Au electrodes. Specifically, the M-DOS is calculated for three different scenarios: (a) isolated molecule (IM); (b) extended molecule (EM), where the molecule is coupled to Au clusters through the most stable adsorption site (system geometries discussed subsequently); and (c) open quantum system, where the extended molecule is connected to semi-infinite electrodes. Past work indicates that the hollow site (Figure S1 in Supporting Information (SI)) and the top site (Figure S2, SI) are the most stable adsorption sites for the SS323,33 and (NC)2334 molecules respectively. Furthermore, in the case of SS3, the hydrogen in the thiol group is assumed to have deprotonated upon contact with Au. A schematic of the extended molecule system geometry is shown in Figure S4 of the SI, where the Au clusters include four {111} planes of six Au atoms each, in addition to the contacting Au atoms. For the open quantum system, the effect of semi-infinite electrodes is modeled by projecting the Green’s functions of electrodes through the self-energy operators onto the extended molecule. 1963

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We note that the effect of charge transfer between a molecule and electrodes, upon contact, can also be described in terms of interface dipoles.41−44 In fact, past work has invoked this picture to understand quantitatively the barriers to electron/ hole injection at the interface of organic molecular layers and metal electrodes in the context of organic light emitting diodes and photovoltaic devices.45,46 In the present work, the computed M-DOS accounts for both the effect of charge transfer and the stabilization of energy levels resulting from the bond formation at the electrodes. Furthermore, we subsequently also relate the resulting electronic-structure to the thermoelectric properties of single-molecule junctions. To further test the above hypothesis, we extend our study to triphenyl molecules terminated with other end groups: dihydroxyl (OO3) and dinitrile ((CN)23) (Figure 3a). Similar

the IM and EM systems, we define the electrode-coupling induced charge transfer (ΔN) as ΔN = NIM − NEM

(3)

where NIM denotes the number of electrons in the IM and NEM denotes the number of electrons in the spatial location of the molecule in the EM system. NEM is computed by expressing the single particle density matrix ρ̂ in the NAO basis and performing the trace only over the orbitals which are centered on the molecule

NEM =

∑ i ∈ Mol

ρiî

(4)

This approach is commonly referred to as natural population analysis.38 In the case of (NC)23, NIM is simply obtained from the total number of electrons in the IM. However, in the case of SS3, because the hydrogen atoms are assumed to have deprotonated, the electrons contributed by them are excluded from NIM. The ΔN values for SS3 and (NC)23 (see Table 1) indicate that SS3 molecule gains a 0.66 electron partial charge upon contact with Au atoms. Such a gain in electronic charge is in agreement with recent studies.32,39,40 In contrast, (NC)23 molecule loses 0.16 electron partial charge to Au atoms. It is interesting to note that the magnitude of the shift in M-DOS between IM and EM systems is greater for (NC)23, which loses electrons, whereas the shift is smaller for SS3, which gains electrons. On the basis of this observation, we hypothesize that the magnitude of the shift in M-DOS is correlated to the endgroup-mediated charge transfer between Au atoms and the molecule. In particular, the shift in M-DOS is governed by two important factors: (i) the stabilization of energy levels induced by contact to the Au cluster and (ii) the change in electron− electron interactions (Coulomb repulsion and exchangecorrelation effects) arising from the charge transfer. The effect of stabilization is to shift the energy levels to lower energies, whereas the effect of electron−electron interactions is to increase their energies. In the case of SS3, the partial electron gain enhances the electron−electron repulsion, in turn reducing the overall downward shift of the energy levels. In the case of (NC)23, the charge transfer is out of the molecule, which reduces the electron−electron repulsion, resulting in a large overall downward shift of the energy levels. A schematic presentation of the proposed mechanism is shown in Figure 2.

Figure 3. (a) Isolated triphenyl dihydroxyl (OO3) and triphenyl dinitrile ((CN)23) molecules. (b) M-DOS of OO3 molecule in different scenarios (IM, EM, and open quantum system). (c) M-DOS of (CN)23 molecule in different scenarios. The M-DOS of the IM, EM, and open quantum system are denoted by blue dotted line, red dashed line, and green continuous line, respectively. The purple arrows indicate the magnitude of the M-DOS shift.

Figure 2. (a,b) Molecular orbital of an isolated molecule is initially at EIM indicated by blue dotted ellipse. The stabilization (brown dashed arrow) resulting from contact with Au cluster lowers the energy of the molecular orbital. (a) Partial charge gain (SS3) increases the electron− electron repulsion (orange dotted arrow), resulting in a small overall downward shift (purple double-headed arrow) to EEM (red ellipse). (b) Charge loss ((NC)23) decreases the electron−electron repulsion, in turn resulting in a larger overall downward shift to EEM (red ellipse).

to the thiol end group, the hydroxyl end group is assumed to have deprotonated upon contact with Au.8 The stable adsorption sites for OO3 and (CN)23 are, respectively, the hollow and top47 sites. The HOMO−LUMO energy values for the corresponding isolated molecules are presented in Table 1. Similar to the previous systems, the EF lies in the HOMO− LUMO gap with the HOMO level being closer to the EF. The ΔN values calculated for these systems are shown in Table 1. These values suggest that the OO3 molecule gains partial electron from the Au atoms, whereas the (CN)23 loses partial electron to Au atoms. Following our hypothesis, we expect a smaller overall downward shift in the M-DOS of OO3, resulting in the HOMO level remaining closer to EF. In contrast, for (CN)23, a larger overall downward shift in the M-DOS is predicted, resulting in the LUMO level being closer to EF. The computed M-DOS for OO3 and (CN)23 molecular systems are 1964

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(NC)23, (CN)23, and (NH2)23 is below that of the Au cluster, which implies that there is a tendency for these molecules to lose electrons to the Au cluster. Finally, we investigate the effect of end-group-mediated electron transfer on the transport properties of the MJs. We begin with the transmission function, τ(E), which is computed in the Landauer formalism by employing the Green’s function approach

shown in Figure 3b,c and are in good agreement with these qualitative predictions. We next consider the amine end group that has garnered significant experimental and computational interest for its ability to form reproducible contacts.10,18,48−50 In this study, we choose triphenyl diamine molecule ((NH2)23) (Figure 4a),

τ(E) = Tr[ΓR Gr (z)ΓLGa(z)]

(5)

a

where G (z) is the advanced Green’s function and is the complex conjugate of Gr(z). The broadening functions ΓL/R are related to ΣL/R through ΓL/R = i[ΣL/R−Σ†L/R]. Our approach to computing the transmission function is described in refs 12, 20−22, and 52. The computed transmission functions for all MJs considered in the present study are shown in Figure 5a,b

Figure 4. (a) Isolated triphenyl diamine ((NH2)23) molecule. (b) MDOS of (NH2)23 molecule in different scenarios (IM, EM, open quantum system). The M-DOS of the IM, EM, and open quantum system are denoted by blue dotted line, red dashed line, and green continuous line, respectively. The purple arrows indicate the magnitude of the M-DOS shift.

whose stable adsorption site corresponds to the atop site of Au trimer25 (Figure S3, SI). The computed HOMO−LUMO energies of the isolated molecule are provided in Table 1. Interestingly, unlike the other end groups, the HOMO level of the isolated molecule is above the EF of Au electrode. The computed ΔN for this molecular system (Table 1) indicates that the (NH2)23 molecule loses partial charge to Au atoms. On the basis of our hypothesis, we expect a significant overall downward shift of the M-DOS to lower energies. This relaxation would move the HOMO level below the EF resulting in HOMO-dominated transport. The computed M-DOS of the (NH2)23 molecular systems (see Figure 4b) is indeed consistent with the proposed hypothesis. We note that our results are in agreement with recent experimental and computational studies,18,19,25 which have indicated that triphenyl and other aromatic molecules with amine end groups exhibit HOMO-dominated transport. In all of the molecular systems studied in the present work, the predictions obtained from the proposed hypothesis are in good agreement with detailed electronic-structure calculations. We next extend our analysis to the relationship between endgroup chemistry and charge transfer. The direction of charge transfer between the molecule and the Au atoms is governed by the electronegativity (χ) of molecule and that of the Au cluster. We use the Mulliken definition of electronegativity in the present work, defined as the average of ionization energy (IE) and electron affinity (EA), χ = ((IE + EA)/2).51 The computed χ values for the molecules considered in the present study are provided in Table 1. The χ of Au cluster with {111} layers representing the hollow site configuration (Figure S1 and S4, SI) is computed to be 4.9 eV, whereas that of the top site configuration (Figure S2 and S4, SI) is 4.81 eV. Our data indicate that SS3 and OO3 are more electronegative than the Au clusters. Hence, there is a tendency for these molecules to gain partial charge from the Au cluster. However, the χ of

Figure 5. (a) Transmission function τ(E) of SS3, OO3, and (NH2)23 molecular junctions (open quantum systems) plotted as a function of energy. (b) τ(E) of (NC)23 and (NC)23 molecular junctions plotted as a function of energy.

and are in agreement with previous studies.8,23,47,49,53 The transmission curves show that in SS3, OO3, and (NH2)23 molecules, the HOMO peak is closer to the EF, resulting in a HOMO-dominated transport, whereas in (NC)23 and (CN)23 the LUMO peak is closer to the EF, resulting in a LUMOdominated transport. These results are consistent with the computed M-DOS for all MJs, suggesting a strong correlation between τ(E) and M-DOS. The HOMO or LUMO character of the transport is also validated by performing the transmission eigenchannel analysis,54 which is presented in the SI (Figures S7−S9). The thermopower, S, of an MJ at low-temperature differentials is related to the slope of the transmission function (τ(E))16 as S=−

π 2kB2T ⎛ 1 ∂τ(E) ⎞ ΔV =− ⎜ ⎟ 3|e| ⎝ τ(E) ∂E ⎠ ΔT

E = EF

(6)

where e is the charge of an electron and T is the average absolute temperature of the junction (chosen to be 300 K). The thermopower of the MJs obtained using eq 6 is presented in Table 2. The predicted thermopower is in good agreement with previous experimental and computational values.9,12,13,17,19,23,25,53,55 The deviations of the computational results from experiments may arise due to the microscopic variations in the contact details, molecular vibrations,56 and interactions beyond the mean field approximation (especially for amines25) that are not accounted for in our current models. 1965

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(4) Malen, J. A.; Yee, S. K.; Majumdar, A.; Segalman, R. A. Fundamentals of Energy Transport, Energy Conversion, and Thermal Properties in Organic-Inorganic Heterojunctions. Chem. Phys. Lett. 2010, 491, 109−122. (5) Bergfield, J. P.; Stafford, C. A. Thermoelectric Signatures of Coherent Transport in Single-Molecule Heterojunctions. Nano Lett. 2009, 9, 3072−3076. (6) Macia, E. DNA-Based Thermoelectric Devices: A Theoretical Prospective. Phys. Rev. B 2007, 75, 035130. (7) Finch, C. M.; Garcia-Suarez, V. M.; Lambert, C. J. Giant Thermopower and Figure of Merit in Single-Molecule Devices. Phys. Rev. B 2009, 79, 033405. (8) Xue, Y.; Ratner, M. A. End Group Effect on Electrical Transport through Individual Molecules: A Microscopic Study. Phys. Rev. B 2004, 69, 085403. (9) Reddy, P.; Jang, S.-Y.; Segalman, R. A.; Majumdar, A. Thermoelectricity in Molecular Junctions. Science 2007, 315, 1568− 1571. (10) Venkataraman, L.; Klare, J.; Nuckolls, C.; Hybertsen, M.; Steigerwald, M. Dependence of Single-Molecule Junction Conductance on Molecular Conformation. Nature 2006, 442, 24. (11) Nitzan, A.; Ratner, M. A. Electron Transport in Molecular Wire Junctions. Science 2003, 300, 1384−1389. (12) Tan, A.; Balachandran, J.; Sadat, S.; Gavini, V.; Dunietz, B. D.; Jang, S.-Y.; Reddy, P. Effect of Length and Contact Chemistry on the Electronic Structure and Thermoelectric Properties of Molecular Junctions. J. Am. Chem. Soc. 2011, 133, 8838−8841. (13) Baheti, K.; Malen, J. A.; Doak, P.; Reddy, P.; Jang, S.-Y.; Tilley, T. D.; Majumdar, A.; Segalman, R. A. Probing the Chemistry of Molecular Heterojunctions using Thermoelectricity. Nano Lett. 2008, 8, 715−719. (14) Xu, B.; Tao, N. J. Measurement of Single-Molecule Resistance by Repeated Formation of Molecular Junctions. Science 2003, 301, 1221−1223. (15) Engelkes, V. B.; Beebe, J. M.; Frisbie, C. D. Length-Dependent Transport in Molecular Junctions Based on SAMs of Alkanethiols and Alkanedithiols: Effect of Metal Work Function and Applied Bias on Tunneling Efficiency and Contact Resistance. J. Am. Chem. Soc. 2004, 126, 14287−14296. (16) Paulsson, M.; Datta, S. Thermoelectric Effect in Molecular Electronics. Phys. Rev. B 2003, 67, 241403. (17) Tan, A.; Sadat, S.; Reddy, P. Measurement of Thermopower and Current-Voltage Characteristics of Molecular Junctions to Identify Orbital Alignment. Appl. Phys. Lett. 2010, 96, 013110. (18) Widawsky, J. R.; Darancet, P.; Neaton, J. B.; Venkataraman, L. Simultaneous Determination of Conductance and Thermopower of Single Molecule Junctions. Nano Lett. 2012, 12, 354−358. (19) Malen, J. A.; Doak, P.; Baheti, K.; Tilley, T. D.; Segalman, R. A.; Majumdar, A. Identifying the Length Dependence of Orbital Alignment and Contact Coupling in Molecular Heterojunctions. Nano Lett. 2009, 9, 1164−1169. (20) Taylor, J.; Guo, H.; Wang, J. Ab Initio Modeling of Quantum Transport Properties of Molecular Electronic Devices. Phys. Rev. B 2001, 63, 245407. (21) Datta, S. Nanoscale Device Modeling: The Green’s Function Method. Superlattices Microstruct. 2000, 28, 253−278. (22) Xue, Y.; Datta, S.; Ratner, M. A. First-Principles Based Matrix Green’s Function Approach to Molecular Electronic Devices: General Formalism. Chem. Phys. 2002, 281, 151−170. (23) Ke, S.-H.; Yang, W.; Curtarolo, S.; Baranger, H. U. Thermopower of Molecular Junctions: an Ab Initio Study. Nano Lett. 2009, 9, 1011−1014. (24) Pauly, F.; Viljas, J. K.; Cuevas, J. C. Length-Dependent Conductance and Thermopower in Single-Molecule Junctions of Dithiolated Oligophenylene Derivatives: A Density Functional Study. Phys. Rev. B 2008, 78, 035315. (25) Quek, S. Y.; Choi, H. J.; Louie, S. G.; Neaton, J. B. Thermopower of Amine-Gold-Linked Aromatic Molecular Junctions from First Principles. ACS Nano 2011, 5, 551−557.

Table 2. Thermopower of Molecular Junctions Obtained From Equation 6, Experiments, and Other Computations thermopower (S) (μV/K)

a b

system

this work

experiments

past computations

SS3 OO3 (NC)23 (CN)23 (NH2)23

21.9 26.5 −1.6 −6.8 22.5

15.4 ± 1.012

14.06,23 ∼ 21.153

−1.0 ± 0.4a12 6.4 ± 0.419

24.3b25

Experimental value corresponds to triphenyl mono-isocyanide. Computed value neglects the interactions beyond the mean field.

To summarize, our calculations demonstrate a relationship between the chemistry of the end groups, the resultant electronic-structure, and the nature of electronic transport. In particular, the electronegativity of the molecule relative to that of the electrode can be used to determine the direction of charge transfer between the molecule and the electrode. Furthermore, our studies have demonstrated a simple qualitative relationship between the direction of charge transfer and the degree of reorganization of the molecular electronic states, which in turn determines the thermoelectric properties of MJs. We expect that the proposed approach has the potential to guide the design of MJs with desirable thermoelectric properties.

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ASSOCIATED CONTENT

S Supporting Information *

Contact models, M-DOS, and Eigenchannel analysis. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]; vikramg@ umich.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS V.G. and J.B. gratefully acknowledge the support from College of Engineering at University of Michigan. B.D.D. gratefully acknowledges support by a DOE-BES award through the Chemical Sciences Geosciences and Biosciences Division (DESC0004924), DE-FG02-10ER16174. P. R. acknowledges the support by DOE-BES as part of an EFRC at the University of Michigan (DE-SC0000957).

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REFERENCES

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The Journal of Physical Chemistry Letters

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dx.doi.org/10.1021/jz300668c | J. Phys. Chem. Lett. 2012, 3, 1962−1967