Impact of Electron Delocalization on the Nature of the Charge-Transfer

Oct 30, 2014 - Electronic delocalization effects have been proposed to play a key role in photocurrent generation in organic photovoltaic devices. Her...
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Impact of Electron Delocalization on the Nature of the ChargeTransfer States in Model Pentacene/C60 Interfaces: A Density Functional Theory Study Bing Yang,†,‡ Yuanping Yi,†,§ Cai-Rong Zhang,†,∥ Saadullah G. Aziz,⊥ Veaceslav Coropceanu,*,† and Jean-Luc Brédas*,†,⊥,& †

School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States ‡ State Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun, 130012, People’s Republic of China § Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China ∥ Department of Applied Physics, Lanzhou University of Technology, Lanzhou, Gansu 730050, People’s Republic of China ⊥ Department of Chemistry, King Abdulaziz University, Jeddah, 21589, Saudi Arabia S Supporting Information *

ABSTRACT: Electronic delocalization effects have been proposed to play a key role in photocurrent generation in organic photovoltaic devices. Here, we study the role of charge delocalization on the nature of the charge-transfer (CT) states in the case of model complexes consisting of several pentacene molecules and one fullerene (C60) molecule, which are representative of donor/acceptor heterojunctions. The energies of the CT states are examined by means of time-dependent density functional theory (TD-DFT) using the long-range-corrected functional, ωB97X, with an optimized range-separation parameter, ω. We provide a general description of how the nature of the CT states is impacted by molecular packing (i.e., interfacial donor/acceptor orientations), system size, and intermolecular interactions, features of importance in the understanding of the charge-separation mechanism.

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quantum-chemical models12,13 have been recently employed to address this issue. On the computational side, density functional theory (DFT) has become a method of choice for most current quantummechanical applications. However, obtaining an accurate theoretical description of the interfacial CT states by means of conventional DFT methods is challenging. The difficulties can be traced back to the fact that standard semilocal and global hybrid exchange-correlation functionals do not provide the correct evaluation of the long-range Coulomb interaction and result in a spurious self-repulsion of charge densities.14−17 Recently, it was shown that long-range-corrected (LRC) functionals with a system-optimized range-separation parameter provide for a physically correct asymptotic description of the long-range Coulomb interactions and for accurate CT excitation energies.18−20 In particular, the CT excitation energies of a pentacene/C60 complex have been evaluated using several LRC functionals with tuned range-separation parameters.21−23 However, these earlier studies have limitations since complexes involving just one pentacene molecule and one

INTRODUCTION

The achievement of high power conversion efficiency in organic photovoltaic cells (OPVs) requires the maximization of exciton dissociation and the minimization of recombination losses at the donor/acceptor (D/A) heterojunction.1−5 It is well established that the interface geometry/morphology strongly influences photocurrent generation.6−9 For example, the deposition conditions and (thermal or solvent) annealing procedures have been found in many cases to significantly improve efficiencies, most likely as a result of increased crystallinity, modification of domain sizes, and reduction in defect concentration. Therefore, to reach a better understanding of the working principles of OPV devices, it is important to gain a full picture of the structure−property relationships between interface morphology and excitondissociation/charge-recombination processes. In organic photovoltaic cells, exciton-dissociation and chargerecombination rates depend on the nature of the chargetransfer (CT) states formed at the interface between the electron-donor material and the electron-acceptor material.1−4 It has been recently suggested that the delocalization of the CT and excitonic states near the D/A interface might be a factor of particular importance.4,5,10 Both first-principles11 and effective © 2014 American Chemical Society

Received: July 23, 2014 Revised: October 21, 2014 Published: October 30, 2014 27648

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basic understanding of the effects, we decided to use simple cofacial orientations among the pentacene molecules instead of the crystal herringbone arrangement, which allows us to easily modulate the electronic couplings among the donor molecules.

C60 molecule were considered; thus, the impact of delocalization effects, which is the main topic of the present work, could not be evaluated. Delocalization effects can occur when a well-ordered (crystalline-like) domain is present in at least the donor or acceptor material near the interface. Therefore, here, to gain a conceptual understanding of the importance of electronicdelocalization effects on the characteristics of the interface CT excitations, we have investigated several model pentacene/C60 complexes in which a C60 molecule interacts with up to five pentacene molecules. To investigate the role of molecular packing on the CT excitation energies, we have examined four different model geometry configurations of the pentacene/C60 complexes (see Figure 1). We considered two parallel

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COMPUTATIONAL DETAILS The excited-state transition energies and oscillator strengths were obtained by means of time-dependent DFT (TD-DFT) calculations. We have shown recently23 that in the case of complexes made of a single pentacene and a single C60, the use of LRC functionals with the default values of the rangeseparation parameter, ω, leads to a strong dependence of the derived CT energies on the choice of the functional; however, upon tuning the range-separation parameter, all the LRC functionals we considered gave comparable results for both local and CT states. Therefore, here the TD-DFT calculations were performed by using only the ωB97X functional with an optimized range-separation parameter. The ω value for each pentacene−C60 complex was obtained according to the tuning procedure used previously by minimizing the expression J(ω):20 J(ω) = JIP (ω)2 + JEA (ω)2

(1)

ω JIP (ω) = |εHOMO (N ) + E Dω(N − 1) − E Dω(N )|

(2)

ω JEA (ω) = |εHOMO (M + 1) + EAω(M ) − EAω(M + 1)|

(3)

εωHOMO(N)

εωHOMO(M

where and + 1) are the highest occupied molecular orbital (HOMO) energies for the neutral pentacene cluster nPEN (made of n pentacene molecules) and the anion of C60, respectively; EωD(N) and EωA (M) are the corresponding total energies of nPEN and C60. For the sake of a better understanding, the natural transition orbitals (NTOs) for the lowest CT excitations were also evaluated.26 The 6-31g(d,p) basis set was employed in all instances. All calculations were performed using Gaussian 09 Rev B.01.27 The geometries of the isolated pentacene and C60 molecules were optimized at the DFT/B3LYP level. The optimized molecular geometries of pentacene and C60 were used to construct all model complexes. The distances between C60 and the closest pentacene (dT or dP) in pentacene−C60 complexes were initially set according to the results of our recent groundstate potential energy calculations:23 dP5 = 3.17 Å, dP6 = 3.30 Å, dT5 = 3.56 Å, and dT6 = 3.25 Å. The structures of larger nPEN− C60 (n = 2−5) complexes are built by successively adding a pentacene molecule in a cofacial fashion (see Figure 1) with a fixed intermolecular distance, d, between the pentacene molecules set to 3.5, 4.0, or 4.5 Å. The benefit of considering various intermolecular distances between cofacial pentacenes is that it allows us to easily evaluate, in an effective way, the impact of the degree of electronic coupling, and thus of electron delocalization, on the nature of the charge-transfer states.

Figure 1. Structures of the nPEN−C60 (n = 1−5) complexes: in P5 [P6], the closest pentacene is parallel to a pentagon [hexagon] of C60; in T5 [T6], the pentacene is perpendicular to a pentagon [hexagon] of C60.

(cofacial), that is, face-on, configurations with the central ring of pentacene centered over either a five-membered ring (configuration denoted as P5) or a six-membered ring of C60 (P6) as well as two T-shaped, that is, edge-on, configurations with the long axis of a pentacene molecule aligned along the axis connecting the center of the C60 molecule with either the center of a five-membered ring (T5) or a six-membered ring (T6). According to experimental investigations and the results of molecular dynamics simulations, both face-on and edge-on configurations can be found in actual pentacene/C60 bulk heterojunctions.24,25 Because we are essentially interested in a

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RESULTS AND DISCUSSION The tuned ω values of the nPEN−C60 complexes for various intermolecular distances between the pentacenes are listed in Table 1. The optimized values are smaller than the default ω value of 0.3 bohr−1 (we recall that 1 bohr = 0.529 Å) of the ωB97X functional. The optimized ω value for the 1PEN−C60 complex is 0.18 bohr−1. This value slightly decreases initially as 27649

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Table 1. Optimized ω Values (in bohr−1) for the nPEN−C60 Complexes nPEN−C60

d = 3.5 Å

d = 4.0 Å

d = 4.5 Å

1PEN−C60 2PEN−C60 3PEN−C60 4PEN−C60 5PEN−C60

0.18 0.16 0.15 0.15 0.15

0.18 0.16 0.16 0.16 0.16

0.18 0.17 0.16 0.16 0.16

the size of the pentacene complex increases but converges already for systems containing three pentacene molecules: to 0.15 bohr−1 for intermolecular distances between pentacene molecules of 3.5 Å and to 0.16 bohr−1 for larger intermolecular distances. These results are similar to those found recently with regard to the dependence of the range-separated parameter on chain length and the extent of conjugation in π-conjugated systems.28 The ωB97X calculations on the basis of the tuned-ω values for the 1PEN−C60 complex give a good agreement between the computed IP values for both pentacene (6.03 eV) and C60 (7.54 eV) and the respective experimental values of 6.59 eV29 and 7.69 eV.30 The calculated EA values of pentacene and C60 are 0.89 and 1.79 eV, respectively; these estimates are somewhat smaller than the experimental values of 1.39 eV31 and 2.68 eV.30 For all model complexes, the HOMO and the lowest unoccupied molecular orbital (LUMO) levels are localized on the pentacene stacks and C60, respectively (see Supporting Information (SI) for more detail). The intermolecular interactions among pentacenes, as was underlined previously for benzene dimers,32 lead to a decrease in the IP value (destabilization of the HOMO) of the pentacene clusters as the number of molecules increases. The experimental IP of the pentacene crystal is about 5.1 eV.33 The difference between the gas-phase and the solid-state IP values, here about 1.5−1.6 eV, is usually defined as the (hole) polarization energy, with this difference often attributed exclusively to the electronic and nuclear polarization effects. However, as shown in Figure 2a, in the presence of significant electronic couplings between adjacent molecules in a crystal, a component to the polarization energy also comes from the delocalization (resonance) energy, that is, from the formation of electronic bands (when using one-dimensional stacks of cofacial pentacenes with an intermolecular distance of 3.5 Å, a model configuration that leads to very large couplings, the difference between the IP values of the individual molecules and the 1D stack reaches 1.5 eV). Thus, the effects of both electronic (and nuclear) polarization and electronic delocalization have to be considered when evaluating the evolution of the ionization potentials (or electron affinities) between gas phase and solid state. As expected, the LUMO energies of the nPEN−C 60 complexes, being localized on C60, are insensitive to the size of the pentacene cluster. However, there is a 0.35 eV difference between the LUMO energies of the edge-on and face-on configurations; as a result, there is a similar energy difference between the fundamental gaps34 in these two types of configuration. Inspection of the LUMO energies indicates that the energy levels of both edge-on configurations are stabilized by about 0.1 eV with respect to the LUMO level of the isolated C60 while those of the face-on configurations are destabilized by about 0.25 eV. This effect is due to the difference in electrostatic interactions arising from the

Figure 2. (a) Evolution of the ionization potential (IP) of a pentacene cluster as a function of the inverse number of pentacene molecules (1/ n) with different intermolecular distances between pentacenes (d = 3.5, 4.0, 4.5 Å); the dashed lines represent the results from an exponential fit: E(n) = E∞ + (E1 − E∞)exp[−a(n − 1)]. (b) HOMO/ LUMO levels of the nPEN−C60 complexes with d = 4.0 Å.

interaction of C60 with the multipole moments of face-on and edge-on pentacene molecular clusters (which is related to the molecular-packing dependence of the electronic polarization energy35); in the face-on configurations, C60 interacts mainly with the negative poles of the pentacene quadrupole moments (leading to a destabilization of the C60 electronic levels), while in the edge-on configurations, it interacts mainly with the positive poles (leading to a stabilization of the C60 levels). Because in the present calculations the electrostatic interactions are mostly related to the permanent multipole moments of the molecules, calculations that would account for contribution due to the induced multipole moments could provide a more complete picture. The energies of the lowest singlet CT and local states of the nPEN−C60 complexes with d = 4.0 Å are collected in Figure 3. As can be seen from this figure, the energy of the lowest C60 local state (LE(C60)) is only slightly affected by the size of the complex. As expected, a significant decrease is obtained for the energy of the lowest local pentacene (LE(nPEN)) state with increasing size of the pentacene stack (Figure 3b). While the energy of the LE(nPEN) complex, in general, strongly depends on the complex geometry, this difference rapidly decreases for 27650

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Figure 3. Lowest singlet excitation energies of the nPEN−C60 complexes with d = 4.0 Å: (a) charge-transfer state; (b) pentacene local state, LE(nPEN); (c) C60 local state, LE(C60); (d) lowest pentacene local state with a large oscillator strength with respect to the ground state.

Figure 4. Natural transition orbitals (isovalue surface corresponding to 0.02 atomic unit) of the lowest-lying charge-transfer state in the nPEN−C60/ P5 complexes with the interpentacene distance d = 4.0 Å and the distance between C60 and the closest pentacene dP5 = 3.17 Å.

work8 underline that the lowest CT state should be found about 1 eV below the local states of pentacene and C60. Two further computational aspects would need to be taken into account to achieve a better description of the CT-state energies: (1) The use of a larger basis set (preliminary calculations indicate that a basis set such as 6-311G(d, p) could improve the evaluation of the electron affinity of C60 and, accordingly, result in a decrease of the CT-state energies by about 0.4 eV) and (2) the explicit consideration of the medium polarization, which will act to stabilize CT states versus local states. In the case of edge-on configurations (T5 and T6) of the 1PEN−C60 complex, the calculations place the CT states about 0.5 eV above the first excited state of pentacene. In the face-on models (P5 and P6), because of substantial intermolecular π−π

large systems. The oscillator strength of the lowest excited state in a pentacene cofacial complex vanishes (dark state), as expected from Kasha et al.’s molecular exciton theory;36 also, the energy of the first local pentacene state with a significant transition dipole moment is very close to the energy of the first excited state of the isolated pentacene molecule (estimated at 2.3 eV) and depends only slightly on both complex size and complex geometry (except in the 1PEN−C60 complex), see Figure 3d. At this stage, it is useful to note that, while this feature will not alter the conclusions of our work regarding the nature and characteristics of the CT states, the present calculations locate in most instances the CT-state energies above the pentacene local state energy. However, experimental data3 for similar systems and simple considerations expressed in our earlier 27651

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Figure 5. Natural transition orbitals (isovalue surface corresponding to 0.02 atomic unit) of the lowest-lying charge-transfer state in the nPEN−C60/ T5 complexes with the interpentacene distance d = 4.0 Å and the distance between C60 and the closest pentacene dT5 = 3.56 Å.

the size of the pentacene cluster. Thus, we can assume that the second term on the right-hand side of eq 4 is constant for a given nPEN−C60 configuration and that the position of the CT state is mainly defined by the interplay between the IPnPEN and Eint contributions. We first discuss the face-on P5 configurations, see Figure 4. In the case of 1PEN−C60, the hole-NTO is delocalized on both the C60 and the pentacene molecules. This pattern is significantly changed when going from 1PEN−C60 to 2PEN− C60, where the hole-NTO is now localized on the pentacene molecule adjacent to C60. The shape of the hole-NTO found in 2PEN−C60 remains basically unchanged for the larger systems. A simple Mulliken charge population analysis indicates that the amount of charge transferred (QCT) from pentacene to C60 in the first CT state increases from 0.78 e (where e is the electron charge) to 0.90 e in going from 1PEN−C60 to 2PEN−C60; QCT remains nearly the same in the larger systems. The modest decrease in CT energy of 2PEN−C60 in comparison to 1PEN− C60 can be thus attributed to the stabilization energy of the electrostatic interactions (more negative Eint term) that has been partially compensated by the hole localization effect (larger IP term). The fact that both the IP values and electrostatic interactions are only slightly affected by the increase in pentacene cluster size beyond 2PEN−C60 explains why the CT energy in face-on configurations shows only a modest dependence on the pentacene cluster size. In contrast, in the case of edge-on configurations, see Figure 5, the holeNTO becomes more delocalized as the number of pentacene molecules in the cluster increases. The QCT is about 0.95 e and is complex-size independent. Although some change in Eint of the complex can be expected with the increase in cluster size, the lowering of the CT energy can be essentially attributed to the decrease in IPnPEN as a result of the increased hole delocalization. Indeed, the comparison of Figure 5 and Figure 3 indicates that the change in CT energy parallels that of the IPnPEN.

interactions, there occurs a strong hybridization between the pentacene and the C60 molecular frontier orbitals. As a consequence, the lowest CT state is significantly lowered in energy in comparison to the edge-on models and mixes with local states. In fact, for the P6 configuration, the lowest excited state of the complex represents ca. 50:50 mixture23 of the local S1 of pentacene and of a CT component because of electron transfer from the pentacene HOMO to the C60 LUMO. With an increase in the number of pentacene molecules, the mixing of the local and CT states strongly decreases, as a result of the marked stabilization of the local pentacene state (see Figure 4); already in the case of the 2PEN−C60 complex, the CT for the P6 configuration is shifted above the first local pentacene excitation. As seen from Figure 3a, the energy of the lowest CT state decreases with the increase of the system size for all interface geometries. However, the decrease in energy for edgeon configurations is more significant than for face-on configurations. As a result, while for the 1PEN−C60 complex the CT state energies are higher in the case of edge-on configurations, the situation is reversed for larger complexes. We now turn to a discussion of the CT-state characteristics. Because the results for the P6 and T6 configurations are similar to those for the P5 and T5 configurations, we only discuss hereafter the results for the latter configurations (see SI for the P6 and T6 results). To provide insight into the meaning of the results, it is useful to consider that to a first good approximation the CT energy can be approximated as ECT = IPnPEN − EA C60 + E int

(4)

where IPnPEN denotes the ionization potential (IP) of a nPEN cluster, EAC60 denotes the electron affinity (EA) of C60, and Eint denotes the electrostatic energy between a hole on nPEN and an electron on C60 (Eint is thus a negative term). Figures 4 and 5 illustrate that the electron-NTO is entirely localized on the C60 molecule; as shown in Figure 2b, EAC60 is independent of 27652

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Figure 6. Energies of the lowest LE(nPEN) and CT states in (a) nPEN−C60/P5 and (b) nPEN−C60/T5 for different pentacene−C60 distances (with the interpentacene distance d = 4.0 Å).

Figure 7. Natural transition orbitals (isovalue surface corresponding to 0.02 atomic unit) of the lowest-lying CT state in the 5PEN−C60/P5 and 5PEN−C60/T5 complexes for the interpentacene distance d = 4.0 Å and different pentacene−C60 distances.

binding energy. This is consistent with the results of recent experimental work where it was shown that by modifying the D/A separation at the interface, it was possible to raise the energy of the CT states and to decrease the electrostatic barrier for charge separation.37 We now turn to the effect of the extent of the electronic interactions among the pentacene molecules, that is, to the impact of hole electronic delocalization within the electrondonor cluster. For this purpose, we performed TD-DFT calculations on complexes where we varied the intermolecular distances between adjacent pentacenes in the range 3.5−4.5 Å; the intermolecular electronic couplings generated in this way should be representative of the couplings in actual pentacene crystalline domains. The TD-DFT results obtained for three intermolecular pentacene distances are shown in Figures 8 and 9. To understand the results, it is important to bear in mind

Next, we consider the role of the extent of pentacene−C60 electronic interactions on the CT energies. We vary these interactions by pulling the C60 molecule away from the closest pentacene by 1 or 2 Å with respect to the optimal distance. The results are shown in Figures 6 and 7. The increase in pentacene−C60 distance is expected, in general, to decrease the electrostatic interactions and to reduce the impact of C60 on the hole delocalization. Indeed, a modest increase in hole delocalization is observed for both face-on and edge-on systems as the pentacene−C60 separation goes up (Figure 7). However, the energy stabilization due to delocalization (smaller IP term in eq 4) is exceeded by the decrease in electrostatic attraction (smaller negative Eint term); as a result, the CT state energies for both face-on and edge-on configurations increase with the pentacene−C60 distance (Figure 6). Thus, the increase in CT energy is accompanied here by a decrease in electron−hole 27653

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Figure 8. Evolution of the energies of the lowest LE(nPEN) and CT states in (a) nPEN−C60/P5 and (b) nPEN−C60/T5, with variation in the distance between adjacent pentacenes d = 3.5, 4.0, and 4.5 Å.

Figure 9. Natural transition orbitals (isovalue surface corresponding to 0.02 atomic unit) for the lowest CT states of 5PEN−C60/P5 and 5PEN− C60/T5 with variation in the distance between adjacent pentacenes d = 3.5, 4.0, and 4.5 Å.

C60. In the case of edge-on configurations, although (as seen from Figure 9) the hole becomes more localized as a result of increased interpentacene distances, the related increase in IPnPEN is compensated by a comparable change in Eint that results in just a slight change in the CT energy. In contrast, when the intermolecular distance decreases from 4.0 to 3.5 Å, both the CT and the LE(nPEN) energies are lowered significantly for all complexes. As seen from Figure 9, the hole delocalization is considerably enhanced in this case. The effect is larger for the larger complexes; a cluster of at least four pentacene molecules is needed even in the case of face-on configurations to allow a full manifestation of the delocalization. Thus, the decrease in CT energy in the present case can be attributed to a larger change in IPnPEN in comparison to Eint. Most interestingly, in contrast to the previous case where we analyzed the impact of the variation in pentacene−C60 distance, here, the decrease in CT energy because of delocalization is expected to be accompanied by a decrease in electron−hole electrostatic interactions. This result belies the common

that the change in electronic coupling has a dual effect on the CT states. On the one hand, an increased electronic coupling (via the decrease in pentacene intermolecular distance) leads to an enhancement of hole delocalization (see Figure 9) and thus to a decrease in IPnPEN ; as a result, the CT energy would be lowered. On the other hand, a more extended hole delocalization leads to an increase in the effective distance between hole and electron, especially in the case of cofacial configurations; as a result, the hole−electron electrostatic attraction diminishes and the energy of the CT state goes up. As already emphasized, the actual CT energy depends on the competition between these two factors. As seen from Figure 8, when the intermolecular distance between pentacene molecules is increased from 4.0 to 4.5 Å, the energy of the CT state moderately rises for edge-on configurations and remains basically unchanged in the case of face-on configurations. In the latter case, this trend can be explained by the fact that, irrespective of the pentacene cluster size, the hole is localized on the pentacene molecule adjacent to 27654

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grateful to Dr. Stephen Bradforth, Dr. John Sears, and Dr. Thomas Koerzdoerfer for stimulating discussions.

assumption that the barrier for charge separation decreases only with an increase in CT state energy.

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CONCLUSIONS In this work, the energetics of pentacene/C60 complexes containing up to five pentacene molecules with four different geometrical configurations were investigated by means of a tuned ωB97X functional. Our results indicate that (a) The delocalization effects as a function of system size are more pronounced in the edge-on than in the face-on configurations. (b) The decrease in donor−acceptor interactions via an increase in the distance between donor and acceptor can lead to enhancement of charge delocalization. However, the main impact on the energy of CT states is due to the change in electrostatic interactions. The increase in the energy of CT states parallels in this case the decrease in electron−hole binding energy. (c) The enhancement in hole delocalization because of an increase in the size of the pentacene cluster or because of an increase of interpentacene molecular interactions results in a lowering of the energy of the lowest CT state (related to a lowering in the IP of the pentacene cluster), accompanied by a decrease in electron−hole binding energy. Extensions of the present work would be to consider complexes containing more C60 molecules in order to compare the donor- and acceptor-related delocalization effects. A challenge is that, to better describe the electron affinity of the fullerene clusters, a larger basis set should be used, which will be computationally demanding. Also, the consideration of the effect of the surrounding medium will help provide improved estimates of the CT-state energies. We are currently working along those lines.

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ASSOCIATED CONTENT

* Supporting Information S

Plots of the frontier molecular orbitals relevant for the description of the lowest CT state. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Present Address &

Solar and Photovoltaic Engineering Research Center, Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work at Georgia Tech was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia, under International Collaboration Grant No. D001-433, and by the Office of Naval Research under Grant No. N000141410171. B. Y. and C. R. Z. thank the Chinese Visiting Scholar Program sponsored by the China Scholarship Council for support of their stay at Georgia Tech. The authors are 27655

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The Journal of Physical Chemistry C

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