Weak Donor−Acceptor Interaction and Interface Polarization DefinePhotoexcitation Dynamics in the MoS2/TiO2 Composite: Time-Domain Ab Initio SimulationYaqing Wei,† Linqiu Li,‡ Weihai Fang,† Run Long,*,† and Oleg V. Prezhdo‡

†College of Chemistry, Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, Beijing NormalUniversity, Beijing, 100875, People’s Republic of China‡Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

*S Supporting Information

ABSTRACT: To realize the full potential of transition metal dichalcogenides interfacedwith bulk semiconductors for solar energy applications, fast photoinduced chargeseparation, and slow electron−hole recombination are needed. Using a combination oftime-domain density functional theory with nonadiabatic molecular dynamics, wedemonstrate that the key features of the electron transfer (ET), energy relaxation andelectron−hole recombination in a MoS2−TiO2 system are governed by the weak van derWaals interfacial interaction and interface polarization. Electric fields formed at theinterface allow charge separation to happen already during the photoexcitation process.Those electrons that still reside inside MoS2, transfer into TiO2 slowly and by thenonadiabatic mechanism, due to weak donor−acceptor coupling. The ET time dependson excitation energy, because the TiO2 state density grows with energy, increasing thenonadiabatic transfer rate, and because MoS2 sulfur atoms start to contribute to thephotoexcited state at higher energies, increasing the coupling. The ET is slower than electron−phonon energy relaxation becausethe donor−acceptor coupling is weak, rationalizing the experimentally observed injection of primarily hot electrons. The weakvan der Waals MoS2−TiO2 interaction ensures a long-lived charge separated state and a short electron−hole coherence time. Theinjection is promoted primarily by phonons within the 200−800 cm−1 range. Higher frequency modes are particularly importantfor the electron−hole recombinations, because they are able to accept large amounts of electronic energy. The predicted timescales for the forward and backward ET, and energy relaxation can be measured by time-resolved spectroscopies. The reportedsimulations generate a detailed time-domain atomistic description of the complex interplay of the charge and energy transferprocesses at the MoS2/TiO2 interface that are of fundamental importance to photovoltaic and photocatalytic applications. Theresults suggest that even though the photogenerated charge-separated state is long-lived, the slower charge separation, comparedto the electron−phonon energy relaxation, can present problems in practical applications.

KEYWORDS: MoS2−TiO2 composites, photocatalytic and photovoltaic devices, electron transfer and electron−hole recombination,energy relaxation, nonadiabatic molecular dynamics, time-domain density functional theory

TiO2 has been considered one of the most promisingphotovoltaic and photocatalytic materials for solar energy

conversion and environmental purification.1−5 As a wide bandgap semiconductor, TiO2 is only able to operate underultraviolet light irradiation. To improve the photovoltaic andphotocatalytic efficiencies, it is crucial to decrease its band gapin order to make the material active in the visible and near-infrared regions of the solar spectrum. Compared to thetraditional doping, interfacing TiO2 with other materials such asmolecular chromophores,6,7 semiconductor quantum dots,8−12

nanoscale carbon,13−15 and two-dimensional transition metaldichalcogenides,16−19 carries many advantages, including largereduction of the TiO2 bandgap and avoiding chargerecombination centers. Recently, the unique electronic andmechanical properties of MoS2 and other transition metaldichalcogenides, compared to the earlier photosensitizers, haveattracted significant attention.20 MoS2 is nontoxic, environ-

mentally friendly and earth-abundant, making it suitable for abroad range of applications. By itself, MoS2 has negligiblephotocatalytic activity due to inefficient photoinduced chargeseparation. Bulk MoS2 starts absorbing at the indirect bandgapof ∼1040 nm.21 Monolayers of transition metal dichalcogenidesare direct bandgap semiconductors that are optically activestarting at near-infrared or visible photon energies.22,23 Assemiconductors, they are more suitable than metallic graphenefor light-emitting and photovoltaic applications.24−28 Compo-sites of MoS2 monolayers with TiO2 combine the comple-mentary advantages of the two semiconductors, allowing one toobtain high photocatalytic activity and solar power conversionefficiency under visible-light irradiation.17,18,21,22,27 Treating

Received: January 12, 2017Revised: June 4, 2017Published: June 6, 2017

Letter

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MoS2 with oxidizing organic molecules or metallic nano-particles greatly increases the luminescence efficiency,25,29

which reflects favorably on the performance of MoS2 inoptoelectronic device applications because of extended excited-state lifetime.A number of recent experimental efforts have focused on

synthesis and characterization of hybrid MoS2−TiO2 nano-composites, demonstrating promising photovoltaic propertiesand enhanced photocatalytic stability against photocorro-sion.17,18,21,22,27,30,31 However, different experiments showconflicting data on the energy alignment and direction ofelectron transfer (ET) in these systems.17,18,30 King andcoauthors demonstrated photoexcited (PE) “hot” electroninjection from MoS2 into TiO2 as the basis for photo-electrochemical activity and photocurrent enhancement inMoS2−TiO2 composites.18 Zhang et al. obtained time-resolveddiffuse reflectance spectra and suggested a reverse energy bandalignment between MoS2 and TiO2. They reported electroninjection from TiO2 into MoS2 on a picosecond time scale.17

Other experiments showed formation of a type-II hetero-junction between MoS2 and TiO2, in which MoS2 acts as theelectron donor materials,18 which is in agreement with theHSE06 calculation.32 To our knowledge, the time scales of thephotoinduced electron injection from MoS2 into TiO2 and ofthe electron−hole recombination at the interface have not beenmeasured yet. In comparison, the rates of electronic energyrelaxation inside MoS2 are well-known. Multiple papers reportseveral hundred femtosecond relaxation times.33−35 Thesubstantial promise of the MoS2−TiO2 nanocomposites forsolar energy applications, combined with the contradictoryexperimental results, provide us with a strong motivation toinvestigate the fundamental mechanisms of the chargeseparation, energy relaxation, and electron−hole recombinationin this material. To interpret the experimental data, resolve thecontroversies, predict the yet-to-be-measured rates, provide adetailed understanding of the complex interplay betweenvarious dynamical processes, and ultimately formulate practicalguidelines, we perform ab initio time-domain simulations.Our simulations show that the donor−acceptor interaction at

the MoS2/TiO2 interface is significantly weaker than atinterfaces of TiO2 with other sensitizers, including molecularchromophores,36,37 semiconductor quantum dots,38,39 gra-phene,40 hybrid organic/inorganic perovskites,41 and evenmetallic particles,42 because of the outstanding chemicalstability of the MoS2 layer. This factor determines the keyfeatures of the photoinduced dynamics at the MoS2/TiO2interface. In particular, the injection of the electrons photo-generated inside MoS2 is slower than the electron−phononenergy relaxation. As a result, the electrons can become trappedon MoS2 defects and only “hot” electrons can be injectedefficiently, rationalizing the experiment.18 The injection occursby the nonadiabatic mechanism that acts in the weak couplinglimit. The energy dependence of the ET time and efficiencyarises from the dependence of the nonadiabatic injection rateon the density of TiO2 acceptor states, which increases withenergy. Additional energy dependence stems from contribu-tions of S atoms to the MoS2 conduction band (CB) at higherenergies. Such contributions bring the donor state densitycloser to the TiO2 acceptor, increasing the coupling. Incontrast, once the charge separation is achieved, the weakMoS2−TiO2 interaction guarantees a long-lived charge-separated state and a very short electron−hole coherencetime. Finally, polarization of the MoS2/TiO2 interface creates

the possibility of charge separation already during thephotoexcitation process. The electron dynamics couple toboth out-of-plane and in-plane vibrations of MoS2, as well aspolar Ti−O modes. The lower frequency out-of-plane modesmodulate the donor−acceptor separation and coupling, whilethe higher frequency phonons create larger nonadiabaticcoupling. Higher-frequency phonons play a more importantrole during the electron−hole recombination process, because asingle quantum of a higher-frequency phonon can accept alarger fraction of electronic energy lost during the recombina-tion.The nonadiabatic molecular dynamics (MD) simulation of

the photoinduced electron-vibrational dynamics in the MoS2−TiO2 system is carried out using classical path approximation tothe fewest-switching surface hopping technique (FSSH)43

implemented within the time-dependent Kohn−Sham theory.44

A quantum decoherence correction45 is added to FSSH tostudy the electron−hole recombination, because it is a slowprocess taking place across a wide energy gap. The techniquehas proven reliable, as applied to study the photoinduceddynamics in a broad range of systems, including TiO2 interfacedwith molecular chromophores,36,37,46,47 wet-electron,48 semi-conducting quantum dots,39 graphene,40 metallic nanopar-ticles,42 and perovskites,41 as well as at heterojunctions of MoS2with MoSe2,

49 polymer with carbon nanotube,50 polymer withquantum dot,51 and other systems.52−57 The method andsimulation details are described in the Supporting Information(SI). A more detailed description is presented in our previouspublications.58−61

The current study focuses on the interplay between thephotoinduced ET, energy relaxation, and electron−holerecombination at the MoS2/TiO2 interface and explores thefactors responsible for the enhancement of the visible lightphotocatalytic and photovoltaic activity reported experimen-tally. Figure 1a depicts the energy diagram of the interface. Anabsorbed photon promotes an electron from the MoS2 groundstate located within the TiO2 band gap to an excited state thatis in resonance with the TiO2 CB. The hot electron injects fromMoS2 into TiO2. The injection process competes with energydissipation into lattice vibrations. In the presence of defects in

Figure 1. (a) Energy diagram for the photoinduced electron injection,relaxation, and recombination processes. An absorbed photonpromotes an electron from the MoS2 valence band (VB) locatedwithin the TiO2 band gap into the MoS2 conduction band (CB) that isin resonance with the TiO2 CB. Electron injection into TiO2 isaccompanied by electron−phonon energy losses. Once the electronhas relaxed to the bottom of the TiO2 CB, it can return to the MoS2 byrecombining with the hole. (b) ET mechanisms. The photoexcitedelectron can be transferred adiabatically by passing over a transitionstate barrier (curved red arrow). The transfer can proceed non-adiabatically, hopping between donor and acceptor states (downwardblue arrow). Photoexcitation can promote the electron directly fromthe donor ground state to an acceptor excited state (upward greenarrow).

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MoS2, the energy dissipation can lead to electron trapping,preventing charge separation. Once inside TiO2, the injectedelectron relaxes to the bottom of the TiO2 CB. On a muchlonger time scale, the electron residing inside TiO2 recombineswith hole left in MoS2.The ET process can occur by three mechanisms (Figure 1b),

which have substantially different dependence on systemproperties, such as density of donor and acceptor states,strength of donor−acceptor coupling, and temperature.Adiabatic ET requires strong donor−acceptor interaction. Anenergy fluctuation drives the system along the reactioncoordinate and across a transition state. Nonadiabatic ETdoes not require strong donor−acceptor interaction and can beultrafast even for weak coupling if the density of acceptor statesis high. Typically, as the distance between the donor andacceptor species increases and the donor−acceptor couplingdecreases, adiabatic ET becomes insignificant, and ET proceedsby the nonadiabatic mechanism. Charge transfer can takealready during the photoexcitation process if the ground andexcited electronic states overlap, and the optical selection rulesare satisfied, for example, the transition dipole moment is large.Understanding the ET mechanism is important for bothfundamental reasons and practical applications.Geometric and Electronic Structure of the MoS2−TiO2

Interface. The MoS2−TiO2 interfacial geometry and separa-tion characterize the strength of the interfacial interaction,whereas the interaction determines the rate and mechanisms ofthe ET processes, as well as the efficiency of ET in competitionwith energy relaxation. The left panels of Figure 2 shows thetop and side view of the system relaxed at 0 K, Figure 2a,c. Arepresentative geometry taken from the MD trajectory at 300 Kis shown in Figure 2b,d. As temperature increases, theinterfacial structures change slightly and the donor−acceptorinteraction remains virtually the same. The situation is differentfrom the graphene−TiO2 system in which significantly strongerdonor−acceptor binding was observed at room temperature.40

The largest scale motion observed in the current system isassociated with displacements of bridging oxygen atoms on theTiO2 surface and MoS2 monolayer sliding with respect to TiO2.The separation between MoS2 and the TiO2 surface increases8.5% from 2.948 Å at 0 K to the canonically averaged value of3.205 Å at 300 K. The increasing MoS2−TiO2 distance servesto decrease the donor−acceptor coupling strength, facilitatingnonadiabatic ET.In order to test the validity of the classical path

approximation, we compared the changes in the optimizedgeometries for the ground and excited electronic states withthermally induced atomic fluctuations in the ground state andobserved that the fluctuations were a factor of 3−6 greater thanthe optimized geometry changes. The excited state wasdescribed by the δ-SCF calculation, also known as constrainedDFT, in which an electron was promoted across the bandgap.The S−Mo bond lengths for the ground and excited states were2.447 and 2.447 Å, while the O−Ti bond lengths were 1.952and 1.954 Å. In comparison, the bond lengths averagedcanonically at room temperature were 2.450 Å for S−Mo and1.958 Å for O−Ti. Electron−phonon interaction in chargedTiO2 facilities formation of polaron.62−64 Polaron is formedafter electron injection and relaxation, and therefore, it shouldnot affect the early time dynamics simulated here. Polaroncreates a trap state within the TiO2 bandgap and can affectelectron−hole recombination.Figure 2e,f shows examples of PE states with lower and

higher energy. Near the CB edge, the MoS2 CB is formed bythe 4d electrons of Mo atoms. Therefore, the PE has density inthe middle plane of MoS2. At higher energies, S atoms startcontributing to the MoS2 CB, and the state density appears inall three MoS2 planes. By extending their density from the Moplane to the S atoms, higher energy donor states create strongerdonor−acceptor coupling, leading to faster ET. Both lower andhigher energy PE states delocalize significantly onto the TiO2substrate. At the same time, the orbitals responsible for the

Figure 2. Top and side views of the simulation cell showing (a,c) the optimized MoS2−TiO2 geometry at 0 K and (b,d) a representative geometry at300 K. Charge densities for (e,f) photoexcited electron donor states at different energies E1 and E2, (g) electron acceptor state, and (h) hole state.The lower energy photoexcited state E1 is localized on Mo atoms, while the higher energy state E2 is localized on both Mo and S. The photoexcitedstates are delocalized between MoS2 and TiO2. The electron donor state is localized on TiO2, while the hole resides within the MoS2 monolayer.Top (i) and side (j) views of the electron energy difference reflecting charge redistribution when MoS2 and TiO2 are brought in contact in theground electronic state. Red represents electron density enhancement, while green shows electron density depletion. O atoms of TiO2 draw someelectron density from MoS2. Electron density in MoS2 adjacent to the O atoms is strongly depleted, while electron density in MoS2 between the Oatoms is strongly enhanced.

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lowest energy PE state are localized within different subsystems,Figure 2g,h. The nonadiabatic coupling between these statesdetermines the rate of the nonradiative electron−holerecombination. The coupling is small, and the recombinationis slow. This is a favorable factor, because the electron−holerecombination constitutes a major pathway for charge andenergy losses in photocatalytic and photovoltaic devices.Electrostatic interaction between TiO2 and MoS2 results in a

significant interface polarization, Figure 2i,j. The interfacial Oatoms of TiO2 draw some electron density from MoS2. Theelectron density in the MoS2 regions immediately adjacent tothe O atoms gets significantly depleted, whereas the electrondensity in the MoS2 regions between the O atoms gets notablyenhanced. The polarization happening at the interface createelectric fields that can both allow charge transfer during thephotoexcitation and facilitate subsequent charge transferdynamics in the excited state.Our calculations show that the charge separation can occur

already during the photoexcitation at the polarized MoS2/TiO2interface. This conclusion is evidenced by the delocalization ofthe initial photoexcited state onto the TiO2 acceptor. Thesurface Ti−O bonds carry significant dipole moments, and thedelocalization of the PE state between MoS2 and TiO2 allowsthe optical selection rules that are needed for a significantamount of ET to occur already during the photoexcitationprocess, cf. the direct ET mechanism in Figure 1b. In particular,the oscillator strength for the lowest energy excitation from theMoS2 HOMO into TiO2 LUMO is 0.078, indicating a 7.8%probability of photon absorption for this transition. Theoscillator strengths are several times higher for the transitions atthe energies at which MoS2 absorbs, in particular, correspond-ing to the photoexcited states E1 and E2, Figure 3a.Electron-Vibrational Interaction. Atomic motions mod-

ulate donor and acceptor state energies and coupling, thereby,creating an ensemble of initial conditions for the photo-excitation and ET processes. Moreover, atomic motions drive

the system across a transition state during adiabatic ET andgenerate the nonadiabatic coupling that is proportional to thenuclear velocity. Figure 3a presents the evolution of theenergies of the two PE states, whose charge densities are shownin Figure 2e,f. The states are chosen to have the largestoscillator strength within the ±250 meV range around 1.0 and1.5 eV above the Fermi energy. The initial conditions for thephotoinduced dynamics are sampled from these trajectories.The energy fluctuation of both PE states is on the order of 200meV. The fluctuation could produce frequent crossing betweenthe MoS2 and TiO2 states, leading to adiabatic ET. However, itcan be seen from Figure 3a that all states fluctuate in phase,indicating that adiabatic ET is not particularly efficient in thiscase. Figure 3b shows the evolution of the localization of thetwo PE states. The y-axis reflects the fraction of the PE statedensity on the MoS2 monolayer. At the lower energies, only 4delectrons of Mo atoms of MoS2 contribute to the electrondonor state, Figure 2e, and the PE state is delocalized onto theTiO2 acceptor very significantly. At the higher energies, bothMo and S atoms of MoS2 contribute, Figure 2f, and thedelocalization of the PE state onto TiO2 is smaller.Fourier transforms (FTs) of the PE energy and localization

characterize vibrational modes that couple to the electronicsubsystem, Figure 3c,d. The FTs show that both PE energy andlocalization couple primarily to low frequency motions in the200−800 cm−1 range. We can identify a number peaks toparticular modes observed experimentally in the MoS2 andTiO2 Raman spectra. The in-plane E1g phonon of MoS2 at 286cm−1 involves opposite motions of two S atoms with therespect to the central Mo atom.65 This vibration affectschemical bonding inside MoS2, partially alters MoS2−TiO2donor−acceptor coupling. The peak at 440 cm−1 might beascribed to the out-of-plane S−Mo motions. It is important forthe ET, because bridging surface oxygen atoms of TiO2 canattack Mo−S−Mo bonds at the MoS2 surface. This mode is acombination of a longitudinal acoustic (LA) mode and the first-

Figure 3. (a) Evolution of the energies of the photoexcited states E1 and E2 (thick black and red lines) and TiO2 conduction band states (thin bluelines). The spatial densities of E1 and E2 are shown in Figure 2e,f. (b) Evolution of the photoexcited state localizations on the MoS2 monolayer. Thelocalization of the lower energy E1 state on MoS2 is smaller and fluctuates more, compared with E2. Phonon modes that couple to the photoexcitedstate (c) energy and (d) localization. The data are obtained by computing Fourier transforms of the autocorrelation functions, shown in the insets, ofthe fluctuations of the photoexcited state energy and localization.

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order optical phonon peak A2u.40,42 The peak at 660 cm−1

might be attributed to the combination of out-of-plane A1g

motion and the LA mode of MoS2.42 The mode at 725 cm−1

might be assigned to the A1g + E1g vibrational overtone.40 The

690 cm−1 signal is seen in the rutile TiO2 Raman spectrum.32

The TiO2 modes influence the PE state energy and localization,because the PE states delocalize onto TiO2, Figure 2e,f. Besidesthe main low frequency modes, a number of weak highfrequency peaks are seen up to 2000 cm−1. These are signalsfrom overtones of the low-frequency vibrations.The autocorrelation functions (ACFs) describe how the

energy at a particular time depends on its value at earlier times.Well-correlated, periodic motions produce ACFs that oscillatebetween 1 and −1. Poorly correlated, random motions lead toACFs that decrease rapidly from 1 to 0. The ACFs of the PEstate energy and localization, insets Figure 3c,d, decay veryrapidly to 0 within 15 fs. On the longer time scale, the energyACF oscillates with a 60 fs period for quite a long time, rising toas high as half of its initial value. In contrast, the ACF of the PEstate localization recovers only 20% of its initial value. Thedifference is explained by a large number of phonon modes thatcouple to the PE state localization than energy. For instance,there are many more small, high frequency peaks in Figure 3panel d than panel c. Localization is a measure of the electronicdonor−acceptor coupling. It is more sensitive to nuclearpositions than the electronic energy.Electron Injection and Energy Relaxation. Figure 4a,b

shows the average ET dynamics for the lower and higherenergy initial states, whereas Figure 4c,d depicts the evolutionof the PE electron energy. The initial value of the ETcoordinate on the y-axis represents the contribution of theprobability of the ET event to occur already during thephotoexcitation process, that is, by the direct mechanism,Figure 1b. Such probability is smaller for state E2 and larger forE1, approaching 70% and 45%, respectively, and agreeing wellwith the state densities shown in Figure 2e,f, and the statelocalization in Figure 3b. The polar nature of the interface helpsthe ET to occur already during the photoexcitation. Theinterfacial electric field drives the electrons and holes in the

opposite directions and enables the optical selection rules thatallow charge separation to happen during the photoexcitation.The ET data were fitted with the exponential function, eq 1

τ= − −⎜ ⎟

⎛⎝

⎞⎠f t A

t( ) 1 exp

(1)

Here, τ is the ET time constant, and the constant A reflects thecontribution of the direct ET mechanism to the overall ET. Inparticular, A = 1 − f(t0), and f(t0) is the probability of the ET tooccur during the photoexcitation. The calculated electroninjection times are around 1 ps. In comparison, the electroninjection in the graphene−TiO2 system is almost an order ofmagnitude faster, because the graphene−TiO2 interaction isstronger.40 The injection at the lower energy, E1, is slower thanat the higher energy, E2. The difference is related to the factsthat the density of TiO2 acceptor states increases with energyand that the donor−acceptor interaction is stronger at E2. Theinteraction increases at the higher energy, because S atoms ofMoS2 start to contribute to the donor state, compare Figure2c,d, and the S atoms are closer to the TiO2 surface. The fasterET at the higher energy supports the experimentally observed“hot” electron injection.18 Interestingly, the charge transfercharacter of the PE state does not correlate with the injectiontime. On the contrary, the larger the charge transfer characterof the PE state is, E1 versus E2, the slower the injection of theremaining part of the electron is. The result can be attributed totwo effects, the density of acceptor states and the donor−acceptor coupling that depends on the localization of the donorstate. First, because state E2 is higher in energy than state E1,the density of the TiO2 acceptor states at the E2 energy ishigher than at the E1 energy. Consider that in Figure 3a onecan see that the density of blue lines is higher at E2 than at E1.As a result, the injection at E2 is faster. Second, the donor stateat the lower E1 energy is fully localized on the Mo atoms thatform the middle layer of MoS2, Figure 2e, whereas the donorstate at the higher E2 energy is localized on both Mo and Satoms, Figure 2f. Because the S atoms are closer to TiO2 thanthe Mo atoms, localization of the E2 state on the S atomsincreases the donor−acceptor coupling and accelerates the ET.

Figure 4. Average ET dynamics starting in state (a) E1 and (b) E2. The solid black, dashed blue, and dotted red lines represent the total, adiabatic,and nonadiabatic electron transfer, respectively. The y-axis intercept represents the charge transfer character of the photoexcitation.

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Similarly to the graphene−TiO2 and Au20−TiO2 systems,40,42

the ET is proceeded primarily by nonadiabatic mechanism, andthe adiabatic ET contribution is very small. Nondiabatic ET isthe primary mechanism because of the weak donor−acceptorcoupling and high density of acceptor state.Parallel to transferring from MoS2 into TiO2 the PE electron

undergoes energy relaxation through the (quasi-)continuousmanifolds of MoS2 and TiO2 electric states by coupling tophonons. Figure 4c,d shows the evolution of the PE electronenergy starting at states E1 and E2. The data are fitted by theGaussian, eq 2

τ= + − ⎜ ⎟

⎛⎝⎜

⎛⎝

⎞⎠

⎞⎠⎟E t E t B

t( ) ( ) exp 0.50

2

(2)

In the current fit, τ is the energy relaxation time scale, E(t0) isthe initial energy, and the amplitude B is determined by theenergy range included in the calculation. The calculated timescales agree well with the experimental showing that theelectronic energy relaxation in MoS2 occurs within severalhundred femtoseconds.34 Our simulations show that the ET isslightly slower than the energy relaxation. This would not havebeen a problem in practical applications, because MoS2 hadcontained no defects. Because the MoS2 conduction bandmaximum (CBM) is only slightly higher than the TiO2CBM,18,32 which is even a matter of debate,17 defects inMoS2 constitute trap states. Because the electron energy lossoccurs on a time scale that is similar to the ET time, oneexpects trapping of the PE electron. This finding agrees withthe experimental observation that only sufficiently “hot”electrons can be injected from MoS2 into TiO2. Although thecalculated ET time difference between state E1 and E2 is small,other factors should be taken into account. First, the electron−phonon relaxation time is shorter than the electron injectiontime, indicating that electrons that are not sufficiently “hot” andwould relax before they can inject. Second, the donor−acceptorcoupling is stronger for the higher energy electrons. Comparethe densities of the MoS2 states shown in Figures 2e,f. Thelower energy state (Figure 2e) is localized on Mo atoms ofMoS2. At the same time, the higher energy state (Figure 2f) islocalized on both Mo and S atoms. Because the S atoms arecloser to TiO2, the donor−acceptor coupling is stronger for“hotter” electrons. Finally, the density of TiO2 acceptor states ishigher at higher energies, that is, for “hotter” electrons,facilitating faster injection. The last argument in generic to allinterfaces involving TiO2. However, the first and secondarguments are quite unique for the current type of systems. Thesituation is notably different for the graphene−TiO2 system,

40

in which the energy relaxation is substantial slower than theelectron injection over a broad range of photoexcitation energy.The electron−phonon energy relaxation occurs on similar timescales in graphene−TiO2 and MoS2−TiO2, however, theinjection is much faster in the former, because the donor−acceptor interaction is stronger. In particular, the MoS2 electronnear the CBM is localized on Mo atoms and is separated fromTiO2 by S atoms that create a tunnelling barrier. No suchbarrier is present in the case of graphene. Additionally,graphene−TiO2 chemical bonding is stronger than in thecurrent system.Around 70% and 45% of the photoexcited electron resides in

TiO2 for states E1 and E2, respectively, agreeing with Figure 3b.The empty circles show exponential fits, eq 1, of the total ETdata. The remaining ET proceeds primarily by the nonadiabatic

mechanism. The ET is faster for E2 than E1 because of a largerdensity of acceptor states at the higher energy. Energyrelaxation starting in state (c) E1 and (d) E2. The Gaussianfits, eq 2, shown by the empty circles, give the energy relaxationtimes. ET is slower than energy relaxation due to weak donor−acceptor coupling.

Electron−Hole Recombination. The photoinducedcharge separation promotes an electron from MoS2 intoTiO2, leaving a hole inside MoS2. The electron can escape intoTiO2 bulk, while the hole remains confined within the two-dimensional MoS2 next to TiO2. If the electron returns to theMoS2/TiO2 interface, it can recombine with the hole, leading tolosses in conversion of absorbed photons into electrical currentor chemical activity. The electron−hole recombination processproceeds exclusively by the nonadiabatic mechanism, because itinvolves quantum transition across a large energy gap. Whenthe energy gap is large, the system is in the inverted Marcusregion. In this case, the system needs to cross over a transitionstate that appears on the opposite side of the parabolas, relativeto the transition state for the regular Marcus region. Reachingthe transition state in the inverted region requires a very largeenergy fluctuation. A nonadiabatic transition avoids the need toreach the inverted region transition state. During thenonadiabatic transition the electronic energy is depositeddirectly into vibrational modes, away from the transition state.Participation of phonon modes is particularly important in

the present case, because the phonons have to accommodatethe energy lost by the electron during the nonadiabatictransition to the ground state. Figure 5a presents the FT of the

ACF of the energy gap between the electron and hole stateswith the ACF shown in the inset. The influence spectrumshows a significant contribution from higher frequencyvibrations in the 600−800 cm−1 range. In comparison, theelectron couples more strongly to lower frequency modesduring the injection process, Figure 3c,d. The strongest peakseen in Figure 5a is very close to the 650 cm−1 mode of rutileTiO2.

66 The second main peak at 800 cm−1 is associated withthe high-frequency polar longitudinal optical phonon of TiO2

Figure 5. (a) Fourier transforms of the autocorrelation function of theCBM−VBM energy gap, identifying the phonon modes responsiblefor the electron−hole recombination. (b) Electron−hole recombina-tion dynamics. The small circles show the linear fit representing theinitial stage of exponential decay, eq 3. The insets of (a,b) present theautocorrelation and pure-dephasing functions for the CBM−VBMenergy gap. The dephasing function is fitted by a Gaussian.

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that plays a dominant role in the TiO2 polaron formation.67

These higher frequency signals are overtone combinations ofthe lower frequency phonons. These high-frequency modesinvolve vibrations of polar Ti−O bonds that respondelectrostatically to the charge transfer. The lower frequencypeaks are close to the 255 cm−1 and Eg 450 cm−1 modes ofrutile TiO2.

40,42 Similarly to the ACFs shown in Figure 3c,d, thecurrent ACFs exhibits an initial decay followed by multiplerecurrences because the electronic subsystem couples stronglyto relatively few phonons.Both elastic and inelastic electron−phonon scattering play

important roles in the electron−hole recombination process.Inelastic scattering results in energy transfer from the electronicsubsystem to vibrations. Elastic scattering destroys coherenceformed between the initial and final states of the electron−holerecombination process. Loss of coherence affects the transitionrate, as exemplified by the quantum Zeno effect.52 Elasticelectron−phonon scattering manifests itself as pure-dephasingin optical measurements. Its typical time scale is within 100 fsfor condensed phase systems.38,41,42,49 The decoherence-correction is needed for the FSSH simulation of theelectron−hole recombination process, because recombinationproceeds across a wide energy gap.38,41,42,49 Rossky et al.initially introduced the decoherence correction for relaxation ofthe hydrated electron from the first excited to the ground statewith a large energy gap on the order of 1 eV.68

The pure-dephasing time for the electron−hole is computedusing the optical response theory, as detailed in the SI. Thecalculated pure-dephasing function is shown in the inset ofFigure 5b. The 4 fs time constant is obtained by Gaussianfitting. The pure-dephasing is very fast, because the two statesforming the quantum superposition are localized entirely ondifferent subsystems, Figure 2g,h. As a result, the fluctuations ofthe energies of the two states are not correlated and proceedwith a large relative amplitude. Typically, fast coherence lossleads to slow quantum dynamics.52

The evolution of the population of the charge separated stateduring the electron−hole recombination process is shown inFigure 5b. Because pure DFT functionals, including that ofPerdew−Burke−Ernzerhof (PBE),69 underestimate energygaps, the PBE gap value was scaled to 0.7 eV obtained usingthe HSE06 hybrid DFT functional,70,71 which is in agreementwith the previous HSE06 calculation,32 Figures S1−S3. Therecombination data were fitted by the short-time, linearapproximation to the exponential decay

τ τ= − ≈ −⎜ ⎟

⎛⎝

⎞⎠y t

t t( ) 1 exp

(3)

producing τ = 1.23 ns. This electron−hole recombination timeis slower than the times reported for TiO2 sensitized with aPbSe quantum dot38 and a gold nanoparticle42 in particularbecause loss of coherence is faster in the present case. A total of1.23 ns is close to the time of electron−hole recombination inCH3NH3PbI3−TiO2, in which decoherence is also fast.41 Ourcalculations emphasize the importance of quantum coherencein electron-vibrational dynamics. Generally, decoherenceshould be slow during charge separation49 and fast duringcharge recombination. Such situation would be most beneficialfor enhancing of photovoltaic and photocatalytic activity.Concluding Remarks. The qualitative conclusions ob-

tained in this work rely on the MoS2/TiO2 interactionproperties, such as the donor−acceptor coupling strength,electric fields formed at the interface, alignment of valence and

conduction bands of the donor and the acceptor, and donorand acceptor state densities. Replacing MoS2 with anothertransition metal dichalcogenide should preserve these proper-ties, and therefore the qualitative conclusions obtained in thiswork should be general to related interfaces althoughquantitative difference are expected.The electron−phonon relaxation time can depend on the

number of MoS2 layers, which will affect the density of electronand phonon states, and dielectric screening. The ET can beaccelerated by increasing the donor−acceptor coupling bychemistry. For instance, defects or dopants within MoS2 canfacilitate covalent-type bonding between MoS2 and TiO2. Atthe same time, the key electronic properties of MoS2 should bepreserved, and therefore the defect/dopant concentrationshould be small. The rate of electron−hole recombinationcan be decreased by allowing the positive and negative chargestravel away from each other. The injected electron can diffuseinside TiO2. The hole remaining inside MoS2 can be distancedfrom the electron by increasing the number of MoS2 layers.Increasing the number of layers should also increase thedielectric screening and decrease the Coulomb interaction,extending the lifetime of the charge separated state.In summary, we have performed an ab initio nonadiabatic

molecular dynamics study of photoinduced electron transfer,energy relaxation and electron−hole recombination dynamicsat the MoS2/TiO2 interface. We have established themechanism for each process and have characterized the keyelectronic states and phonon modes taking part in the carrierdynamics. The obtained time scales agrees well with theavailable experiments. The interaction between MoS2 and rutileTiO2 (110) surface is van der Waals at both zero and roomtemperatures, resulting in weak donor−acceptor coupling. Thedelocalization of the PE electron from MoS2 onto TiO2,combined with the polar nature of the MoS2/TiO2 interface,creates a high probability of ET to occur already during thephotoexcitation. Electrons generated inside MoS2 transfer intoTiO2 slowly, compared to similar systems. The ET mechanismis nonadiabatic due to the weak donor−acceptor coupling andhigh density of acceptor states. Both coupling and acceptorstate density increase with energy. In particular, the couplingincreases because S atoms start contributing to the CB states.The electron−phonon energy relaxation is slightly faster thanthe electron injection, creating unfavorable conditions forcharge separation in the presence of MoS2 defects that createelectron traps. The electronic subsystem couples to relativelyhigh frequency polar phonons that create large nonadiabaticcoupling, because they interact with the electronic subsystemelectrostatically and have high velocities. The electron−holerecombination across the MoS2/TiO2 interface is slow, takingover 1 ns. The recombination requires a long time because thedonor−acceptor interaction is weak, purely van der Waals, andbecause quantum coherence loss is very rapid, 4 fs, deceleratingquantum dynamics. The high probability of charge separationduring photoexcitation and a particularly slow electron−holerecombination create favorable conditions for high photo-catalytic and photovoltaic activities of MoS2−TiO2 compositesreported experimentally. At the same time, the rapid electron−phonon energy relaxation relative to the ET creates isdetrimental, because it can lead to charge trapping, Thefundamental insights generated by the reported simulationsprovide guidelines for rational design of novel and efficientsystems interfacing two-dimensional transition metal dichalco-

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genides with bulk semiconductors for visible-light photo-catalysis and photovoltaics.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.nano-lett.7b00167.

Theoretical methodology and densities of states of theMoS2/TiO2 system obtained using PBE, PBE+U andHSE06 density functionals (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: runlong@bnu.edu.cn.

ORCIDWeihai Fang: 0000-0002-1668-465XOleg V. Prezhdo: 0000-0002-5140-7500NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSY.Q.W. and R.L. are grateful to the National ScienceFoundation of China, Grant No. 21573022, the FundamentalResearch Funds for the Central Universities, the RecruitmentProgram of Global Youth Experts of China, and the BeijingNormal University Startup Package. W.H.F. thanks theNational Science Foundation of China, Grants 21520102005and 21421003. L.Q.L. and O.V.P. acknowledge support theU.S. National Science Foundation, Award Number CHE-1565704.

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