Article pubs.acs.org/JPCC
Intersubunit Electron Transfer (IET) in Quantum Dots/Graphene Complex: What Features Does IET Endow the Complex with? Cunku Dong,†,§ Xin Li,†,‡,* Pengfei Jin,† Wei Zhao,† Jia Chu,† and Jingyao Qi‡,* †
Department of Chemistry, Harbin Institute of Technology, Harbin 150090, China State Key Lab of Urban Water Resource and Environment, Harbin Institute of Technology, Harbin 150090, China § School of Chemistry, Monash University, VIC 3800, Australia ‡
S Supporting Information *
ABSTRACT: First principles calculations of quantum dots (QDs)/graphene (QDs/ GR) hybrid nanomaterials were performed to investigate the interfacial electron−hole separation process at the atomistic level for verifying the tentative mechanism and unveiling the functionalities endowed by the intersubunit electron transfer. Our calculated results unveil the intersubunit electron transfer mechanism of QDs/GR nanomaterials: upon visible light adsorption, the ground electron of CdS QD in nanomaterials is first promoted to the excitated state, which then injects into the conduction band of graphene and transports along graphene layer through π* orbitals to achieve interfacial electron−hole separation. Adiabatic and nonadiabatic methods are used to estimate the electron transfer time at the heterogeneous interface from CdS QD to graphene. Our findings suggest a new route to facilitate the design of QDs@GR based nanodevices.
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INTRODUCTION The quantum dots (QDs)/graphene (QDs@GR) complex has been attracting ever-increasing attention over the past few years due to versatile potential in many areas, such as fluorescence imaging, biomolecule sensors, photocatalysis, and photovoltaics.1−4 In essence, the QDs@GR complex combines the unique features of QDs and graphene with each other to become a novel class of nanomaterials.5 That is to say, this class of nanomaterials processes the outstanding nature of subunit graphene, including superior thermal conductivity and spindependent transport at room temperature,6−9 together with the excellent photoelectronic characteristics of subunit QDs.10 Of greater importance, the incorporation of these species endow the nanomaterials with new, amazing properties for wide-area applications. Guo et al.11 produced a novel layered QDs/ graphene based electron transfer system for photovoltaic devices, in which photoresponses, especially photocurrent, is significantly improved. Li et al.12 reported a high efficient graphene-CdS photocatalyst for photocatalytic H2 production under visible-light irradiation. Of particular interest, CdTe/ graphene-based nanodevice was proposed with chemotherapeutic drug delivery and photo imaging of cancer cells.4 However, QDs@GR nanomaterials seem like a “black box” device, in which the internal operation mechanism is unclear, especially for electron and energy transfer in photocatalysis and photovoltaics. As a result, the intersubunit electron transfer process that determines the nature of QDs@GR nanomaterials is generally explained by a tentative mechanism.12,13 The lack of accurate electron transfer mechanism inhibits the further development of QDs@GR based nanomaterials and new © 2012 American Chemical Society
applications of these nanomaterials, as efficient electron transfer across the QDs/graphene interface is the key for converting light energy into electricity or other fuels.14 Addressing this long-standing puzzle could shed light on the conversion mechanism of solar energy to electricity or chemical energy in these nanomaterials. Herein, we present results from firstprinciples simulations, based on the realistic model of graphene-supported CdS QDs, to explore interfacial electron−hole separation process at the atomistic level for verifying the tentative mechanism and unveiling the functionalities endowed by the intersubunit electron transfer. We expect our endeavor may provide theoretical foundation for further development of QDs@GR nanomaterials and open up a new pathway into QDs@GR based nanodevices.
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COMPUTATIONAL METHODS
Geometric optimization and electronic structure calculations were performed within density functional theory (DFT) framework implemented in the Gaussian03 program package.15 The DFT was treated by Becke’s three-parameter hybrid method with the Lee, Yang, and Parr gradient-corrected correlation functional (B3LYP).16−18 The clean graphene was optimized under B3LYP/6-31G* level while bare Cd4S4 cluster and Cd4S4@GR were optimized using the hybrid basis set 631G*/Lanl2DZ.19 The split-valence basis set 6-31G* was applied to C, S and H atoms while Lanl2DZ was used for Cd Received: May 12, 2012 Revised: June 24, 2012 Published: June 26, 2012 15833
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Figure 1. DFT-optimized structure of Cd4S4@GR at B3LYP/6-31G * and Lanl2DZ level: front view (left) and top view (right). The marked bond length for Cd4S4 cluster is calculated in Å units. Gray balls represent the carbon atoms on graphene sheet, and goldenrod and yellow balls are the Cd and S atoms of Cd4S4 cluster, respectively.
states and electronic structure of bare Cd4S4 cluster. Table 1 lists the singlet excited states of Cd4S4 cluster with oscillator
atoms. The lowest 10 singlet excited states of bare Cd4S4 cluster were calculated within the framework of time-dependent DFT.20 In the analysis of electronic structures, an effective density of states (DOS) was simulated from discrete molecular orbital levels through an arbitrary Gaussian broadening of the individual orbital contributions by full width at half-maximum (fwhm) of 0.5 eV.
Table 1. Selected Calculated Singlet Excitation Energies (E), Wavelength (λ), Electronic Transition Configurations and Oscillator Strengths ( f) for the Optical Transitions with f > 0 of the Adsorption Bands in Visible Region for Cd4S4@GRa
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RESULTS AND DISCUSSION Considering that the chemical functionalization of graphene oxide (GO) disrupts its sp2 bonding networks,21 reduced graphene oxide (RGO) tends to be applied in QDs@GR nanomaterials because of the graphene-like electrical conductivity.22 The graphene sheet terminated with hydrogen atoms (D6 h) was adopted as the substrate for anchoring semiconductor CdS QDs. CdS QDs with Td point group was carefully chosen in this study, denoted as Cd4S4. We think that the model can be representative of CdS-graphene coupling that is present in RGO-based CdS hybrid nanomaterials.23,24 The optimized configuration of Cd4S4@GR is shown in Figure 1. In the initial configuration of Cd4S4@GR, we place Cd4S4 cluster above the graphene with one Cd atom over C atom of graphene. After full optimization, the Cd atom of Cd4S4 cluster moves over the C−C bond near the central benzene ring of graphene with the vertical distance of 2.90 Å off graphene surface. This calculated result also indicates that C−C bond site is the preferable position for Cd4S4 cluster adsorption on graphene. The configuration of adsorbed Cd4S4 changes slightly in comparison with bare cluster. Of note, the Cd−S bond length ranges between 2.61 and 2.67 Å in Cd4S4@GR, whereas Cd−S bond distance is identical (2.63 Å) for bare Cd4S4 cluster due to the Td symmetry itself (Figure S1, Supporting Information). By contrast, the graphene structure is influenced very slightly by Cd4S4 cluster adsorption, partially due to its chemical inertia resulting from large-range π−π conjugation. The geometrical change of Cd4S4 cluster reveals the electronic interaction between adsorbate and substrate, also confirmed by the adsorption energy (Eads = 1.86 eV), which is the precondition for efficient electron transfer or energy transfer in the photocatalyst and photovoltaics.25 As the photoexcitation of QDs is the driving force of QDs@ GR nanomaterials’ functionality, we first focus on the excitated
state no.
E (eV)
f
main contributionsb
S4 S5 S5
2.43 2.43 2.43
0.0345 0.0345 0.0345
H-1 → L (+77%), H → L (+15%) H → L (+77%), H-1 → L (15%) H-2 → L (+93%)
a
Complete data presented in the Supporting Information. bThe capital H and L represent HOMO and LUMO, respectively.
strength f > 0. Interestingly, we note that three excited states have the same excitation energy and oscillator strength, resulting from the high spatial symmetry of Cd4S4 cluster. Furthermore, the electronic transition is of triple-degenerate occupied MOs (HOMO-2, HOMO-1, HOMO) to LUMO character (Figure 2).26 The same photoexcitation character can also be seen for Cd4S4@GR as discussed below. The density of states (DOS) of hybrid nanomaterials is investigated to understand the electronic structure. A small band gap is noticed for the coupled system (Egap(Cd4S4@GR) = 2.04 eV), which is completely attributed to subunit graphene (Figure 3a). In fact, it is well-known that intrinsic graphene is considered to be a semimetal or zero-gap semiconductor.27 The resultant band gap originates from the nonperiodic graphene substrate model adopted here. But, it will not violate the conclusion we made in this paper. In the following part, the electron transfer and electronic coupling of Cd4S4/periodic graphene are discussed in detail. In Figure 3, we can also notice that all the discrete occupied and unoccupied molecular orbital (MO) levels of the adsorbate Cd4S4 are well merged into the graphene valence band (VB) and conduction band (CB), revealing the direct electronic coupling between Cd4S4 cluster and graphene. How is interfacial electron−hole separation achieved in Cd4S4@GR? Answers can be retrieved from exploring the electron density distribution in Cd4S4@GR before and after photoexcitation of QDs. For adsorbed Cd4S4 cluster, before 15834
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the degenerate energy of −5.82 eV (Figure 3b). Interestingly, in these occupied MOs, the electron is dominantly localized around Cd4S4 cluster, and thus we denote these MOs as HOMOs(CdS). Notably, we find that the electron density distribution around Cd4S4 cluster in HOMOs(CdS) has the typical feature of triple-degenerate HOMOs of bare Cd4S4 cluster by comparing their electron density distribution, despite the slight change of orbital shape owing to the electronic coupling between subunits Cd4S4 and graphene. Indeed, in these degenerate orbitals, electron is dominantly localized around Cd4S4 cluster with dominant S 2p-orbital and little Cd 4dz2-orbital character, thus indicating the ground-state electron of hybrid nanomaterials is localized around adsorbed cluster for further photoexcitation and following interfacial electron−hole separation. After excitation, PDOS peak at the CB edge, centered at ∼2.7 eV, partially originates from the LUMOs of adsorbed Cd4S4 cluster, i.e., LUMOs (CdS) (Figure 3a). A possible interpretation is that upon Cd4S4 cluster adsorption, the lowest unoccupied MOs energy levels of chemically anchored Cd4S4 cluster are split to a number of mixed CdS/graphene levels, similar to the dye/TiO2 system.28 We note that the mixed levels are dominated by LUMO of Cd4S4@GR in the CB edge. Of note, for LUMO of Cd4S4@GR, the adsorbed Cd4S4 has the distinct LUMO character of bare cluster with dominant Cd 5s orbitals character (Figure 2). Furthermore, the LUMO of Cd4S4@GR is also partially delocalized on graphene surface with the typical LUMO charater of clean graphene (Figure 4),
Figure 2. Molecular orbital energy diagram for bare Cd4S4 cluster and corresponding molecular orbitals plots with isovalue = 0.015. The red arrows describe the singlet excited transition of bare Cd4S4 cluster in the visible range.
excitation, PDOS peak at around −6.0 eV partially results from CdS unoccupied states. Considering the superposition of electronic states in the hybrid system, these states are mainly contributed by three highest occupied MOs of Cd4S4@GR (i.e., triple-degenerate, HOMO-5, HOMO-6, and HOMO-7) with
Figure 3. (a) Total DOS and PDOS of Cd4S4@GR. (b) Triple-degenerate unoccupied MOs of Cd4S4@GR. (c) Lowest unoccupied MOs of Cd4S4@ GR. In part a, the red vertical lines indicate the discrete MOs energy level of adsorbed Cd4S4 cluster and the comparative contribution to the PDOS. The electron density distribution plot of MOs is obtained with isovalue = 0.015. The electronic density around adsorbed Cd4S4 scaled with different suitable isovalues is located on the top of corresponding MO. 15835
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Figure 4. Electron density distribution plot of two degenerate lowest unoccupied MOs (LUMO and LUMO+1) for clean graphene with isovalue = 0.015.
dominated by Cd4S4 states and these adsorbate states are almost from S-2p orbital. Upon excitation, the excited Cd4S4 states emerge around 1.5 eV in CB top, which is mainly contributed by Cd-5s orbital. In order to gain a clear picture of electronic behaviors before and after photoexcitation, we investigate the electron density distribution of hybrid system at Γ point. We can find that in the occupied states of Cd4S4@periodic GR around −0.5 eV (HOMO-3, HOMO-2, and HOMO-1), electron is mostly localized around Cd4S4 cluster with triple-degenerate LUMO character of free Cd4S4 cluster. Upon light adsorption, Cd4S4 cluster in the hybrid system is promoted to excited states (around 1.5 eV) with distinct LUMO character of free Cd4S4 cluster, as shown in Figure S2b, Supporting Information. If the unoccupied MOs isosurface of Cd4S4@periodic GR is scaled up, we can obviously see the LUMO character of clean graphene sheet. The calculated results suggest that the excited electron of Cd4S4 cluster injects into the CB of graphene sheet, in line with the above conclusion drawn from Cd4S4@GR. The electron transfer at heterogeneous interface is key factor to determine the photoelectronic and photochemical performance of QD/GR hybrid nanomaterials system. At present, various approaches have been used to estimate the interfacial electron transfer time, involving nonadiabatic and adiabatic approaches. Nonadiabatic and adiabatic time-domain ab initio method has been used in the dynamics simulation of the interfacial electron transfer for elucidating the transfer mechanism.33−37 In particular, Prezhdo et al. reported a detailed analysis of the electron transfer mechanism, including adiabatic and nonadiabatic electron transfer, electron−phonon coupling and relaxation mechanisms.38 The electron transfer rate between a QD and a bulk semicondcutor can also estimated by both nonadiabatic and adiabatic methods. The adiabatic electron transfer method which handles the QD interaction with bulk graphene surface directly. By using developed Newns−Anderson approach, the adiabatic electron transfer from from Cd4S4 to graphene can be treated by the formula as follows:39
leaving hole around the cluster. As a result, the intersubunit electron transfer brings different functionalities to QDs@GR nanomaterials: (1) energy transfer through graphene networks for photovoltaics;11,29 (2) electron supply for photocatalytic H2 production;12,30 (3) hole supply for photocatalytic oxidation.31 For other mixed CdS/graphene levels, e.g. LUMO+1 and LUMO+2 (Figure 3c), electron is mostly widely delocalized over the graphene surface with two degenerate level character, i.e., LUMO and LUMO+1 of clean graphene (Figure 4).32 As it can be seen, the electron density distribution in LUMO+1 of coupled system still has the LUMO character of bare Cd4S4 cluster. Strangely, for LUMO+2, it seems that the ground-state electron is transferred directly from the HOMO of Cd4S4 cluster to the graphene CB. But, when the electron density isosurface of Cd4S4@GR is magnified, the clear LUMO character of bare cluster can be observed. The misunderstanding may be due to the fact that the electron distribution of these unoccupied orbitals only statically shows the final state after photoexcitation and electron transfer. From the above analysis, it can be concluded that the ground electron of adsorbed Cd4S4 cluster in Cd4S4@GR is first excited to the LUMO upon light adsorption, which then transfers to the CB of graphene sheet, leaving hole in the Cd4S4 cluster and to transports along graphene layer through LUMO orbital (or LUMO-1) of graphene with π* character to eventually achieve electron−hole separation at the heterogeneous interface. This process is in line with the tentative mechanism for graphenesupported CdS photocatalyst,12,13 moreover, the detailed electron separation and transport models are also presented here. In order to extend this study to more general situation, we also performed DFT calculations based on Cd4S4 cluster over periodic graphene sheet (see Computational Detail in Supporting Information). Figure S2, Supporting Information, shows electronic structure and MOs at Γ point of clean periodic graphene sheet and Cd4S4@periodic GR (c) in unit cell. We can note that the clean periodic graphene sheet has zero gap, exhibiting semimetal characteristics. The CB and VB edges are both contributed dominantly by C-2p oarbital, and the occupied and unoccupied MOs near Fermi level show the π−π stacking over the whole sheet (Figure S2a, Supporting Information). After Cd4S4 cluster adsorption on graphene sheet, the PDOS peak, centered at ∼−0.5 eV in VB bottom is
2
( ℏΓ )
1 2 L LUMO(E) = 2 π (E − E LUMO(CdS)) + 15836
2
( ℏΓ2 )
(1)
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The broadening width, ℏΓ, taken as the mean deviation of the LUMO (ads) levels, is defined as follows, ℏΓ =
∑ pi |εi − ELUMO(CdS)| i
The obtained external reorganization energy is 0.09 eV. Hence, the total reorganization energy is λ = λin + λout = 0.311 eV. The electronic coupling, VDA, can be calculating with the generalized Mulliken−Hush (GMH) model as follows:42
(2)
VDA =
where, ELUMO(CdS) is then obtained by a weighted average E LUMO(CdS) =
∑ pi εi i
⎡ (ΔG + λ)2 ⎤ 4π 3 2 ET ⎢− ⎥ | | V exp DA 4λkBT h2λkBT ⎣ ⎦
−
(10) +
where E(Cd4S4 /Cd4S4) and E(GR/GR ) are the oxidation and reduction potentials of Cd4S4 and graphene, which can be estimated from the energies of HOMO and LUMO of Cd4S4 and graphene. ΔE* means the electron excitation energy of Cd4S4 cluster (ΔE* = 2.433 eV). E(Cd4S4+/Cd4S4) is calculated to be −6.488 eV. For estimating ΔGET more accurately, the LUMO level of periodic graphene was adopted as reduction potential (4.148 eV) because the hydrogen saturation of edge carbon atom may change the true LUMO position of graphene. ΔECb is the exciton binding energy, which can be estimated with the following formula,
(5)
λ1(GR) = E(GR ) − E(GR)
(6)
λ 2(Cd4S4 ) = E(Cd4S4 ) − E(Cd4S4 +)
(7)
ECb =
Here, E(GR−) and E(GR) are the energies of the neutral GR at the anionic geometry and optimal ground-state geometry, respectively, and E(Cd4S4) and E(Cd4S4+) are, accordingly, the energies of the radical cation Cd4S4+ at the neutral geometry and optimal cation geometry. The calculated internal reorganization energy is 0.281 eV. The classical dielectric continuum models by Cornil et al. were used to calculate the external reorganization energy. Following this approach, we calculated λext as41 ⎛ 1 1 1 ⎞⎛ 1 1⎞ + − ⎟⎟⎜ − ⎟ λext = Δe 2⎜⎜ ζ0 ⎠ 2R GR R ⎠⎝ ζOP ⎝ 2R Cd4S4
(9)
ΔGCT = (E(GR/GR−) − E(Cd4S4+ /Cd4S4)) − ΔE* − ECb
(4)
where kET is the rate constant (s−1) of electron transfer from Cd4S4 to graphene, kB is the Boltzmann constant, h is the Planck constant, ΔGET is the Gibbs free energy change of intermolecular electron transfer, λ is the reorganization energy of regeneration system. VDA is the electronic coupling between the Cd4S4 cluster and graphene. The reorganization energy λ of dye molecule can be divided into inner and outer parts. The internal reorganization energy upon electron transfer consists of two terms: λ in = λ1(GR) + λ 2(Cd4S4 )
(μP − μR )2 + 4(μRP )2
Here μRP is the transition dipole moment, and μR (μP) is the permanent dipole moment of initial (final) state of Cd4S4@GR. ΔERP is the excitation energy of Cd4S4 cluster. μRP is calculated to be 0.761 eV. For initial state of Cd4S4@GR, the Cd4S4 cluster is assumed to have no interaction with graphene, that is to say, the orbitals of two species have no perturbation from each other. In the initial Cd4S4@GR, Cd4S4 cluster and graphene maintain their independent symmetries. Hence, permanent dipole moment of initial Cd4S4@GR state (μR) is 0 D. μP is calculated to be 3.941 D. In the final state of optimized Cd4S4@GR (Figure S3, Supporting Information), we can see that the dipole moment direction of Cd4S4@GR in final state is from Cd4S4 cluster to graphene. Finally, the calculated VDA is 0.438 eV. The ΔGET can be estimated with the Rehm−Weller equation43
(3)
where, pi an εi indicate the adsorbate portion of ith MO for Cd4S4 cluster and its corresponding MO energy, respectively. The estimated electron-transfer time is obtained from the lifetime broadening through τ(fs) = 658/ℏΓ (meV). Herein, the calculated ELUMO(ads) and ℏΓ are −2.67 and 0.02 eV, respectively. Finally, the estimated electron transfer time is 32.9 fs. In the Newns-Anderson approach, the electronic coupling between QD and graphene is assumed to be strong. However, the intermolecular electronic coupling is weak between Cd4S4 cluster and graphene. Within the weak electronic coupling limit, the nonadiabatic electron transfer rate of QD to semicondcutor could be given by well-known Marcus theory.40 kET =
μRP ΔE
−
1 e2 4πε0 ζsR
(11)
The free Gibbs change ΔGET is −0.127 eV, indicating the intermolecular electron transfer is thermodynamically favorable. Finally, the interfacial electron transfer rate is 2.01 × 1015 s−1. The electron transfer obtained by adiabatic and non adiabatic methods is much faster than reported CdS/graphene complex with a picosecond time scale.13 The difference of electron transfer time may result from smaller QDs size adopted here and the dephasing effect of QDs,44,45 as the dephasing becomes prominent in the experiment because of small energy gap between CdS QDs and tremendous graphene sheet. Meanwhile, dephasing slows down with the increasing QDs cluster size, the dephasing for the small clusters (Cd4S4 cluster) leads to the different electron transfer rate between theoretical and experimental data.46
(8)
where RCd4S4, RGR, R, ζOP, and ζ0 are donor radii, acceptor radii, the distance between the centers of the donor and acceptor, and optical and zero-frequency dielectric constants of the surrounding media, respectively. Considering the single-atom layer in graphene, we use the calculated equivalent radius of single carbon atom (2.03 Å). The calculated RCd4S4 and R are 4.36 and 5.26 Å, respectively. Herein, we chose water as the solvent for CdS/GR nanomaterials (ζOP= 1.78 and ζ0= 80).11
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CONCLUSION In summary, our work presents the theoretical studies on graphene-supported CdS nanomaterials to examine the interfacial electron−hole mechanism and predicts the charge separation and recombination rates. Our calculated results show that upon visible light adsorption, the ground electron of Cd4S4 15837
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cluster in Cd4S4@GR is first promoted to the excitated state, which then injects into graphene CB and transports along graphene layer through π* orbitals to achieve interfacial electron−hole separation. Newns-Anderson and Marus theories are used to estimate the electron transfer rate occurring at the heterogeneous interfacial. Our work not only confirms the tentative mechanism of CdS−graphene hybrid nanomaterials, but provides the detailed process of interfacial charge separation and electron transport model for collection at the atomic scale in these nanometrials.
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ASSOCIATED CONTENT
S Supporting Information *
The computational details for Cd4S4@periodic graphene, configuration of bare Cd4S4 cluster, and complete data for excitated states. 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: (X.L.)
[email protected]; (J.Q.)
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The research is supported by the National Natural Science Foundation of China (21176052, 21076051). Cunku Dong thanks the support from the Joint Educational Ph.D. Program of Chinese Scholarship Council (CSC). All calculations made use of the high performance computing facilities of Harbin Institute of Technology. We thank Dr. Yusheng Cao (Department of Physics, HIT) for the support for Marcus theoretical computation.
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REFERENCES
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