Photoinduced Carrier Dynamics at the Interface of Pentacene and

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Photoinduced Carrier Dynamics at the Interface of Pentacene and Molybdenum Disulfide Xiao-Ying Xie, Xiangyang Liu, Qiu Fang, Wei-Hai Fang, and Ganglong Cui J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b04728 • Publication Date (Web): 16 Aug 2019 Downloaded from pubs.acs.org on August 19, 2019

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The Journal of Physical Chemistry

Photoinduced Carrier Dynamics at the Interface of Pentacene and Molybdenum Disulfide Xiao-Ying Xie, Xiang-Yang Liu, Qiu Fang,∗ Wei-Hai Fang, and Ganglong Cui∗ Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China E-mail: [email protected]; [email protected] Abstract Understanding of photoinduced interfacial carrier dynamics in organic-transition metal dichalcogenides heterostructures is very important for the enhancement of their potential photoelectronic conversion efficiencies. In this work we have used density functional theory (DFT) calculations and DFT-based fewest-switches surface-hopping dynamics simulations to explore the photoinduced hole transfer and subsequent nonadiabatic electron-hole recombination dynamics taking place at the interface of pentacene and MoS2 in pentacene@MoS2 . Upon photoexcitation the electronic transition mainly occurs on the MoS2 monolayer, which corresponds to moving an electron to the MoS2 conduction band. As a result, a hole is left in the valence band. This hole state is energetically lower than certain occupied states of the pentacene molecule; thus, the interfacial hole transfer from MoS2 to pentacene is favorable in energy. In terms of nonadiabatic dynamics simulations, the hole transfer time to the HOMO-1 state of the pentacene is estimated to be about 600 fs; but, the following hole relaxation process from HOMO-1 to HOMO takes much longer time of ca. 15 ps due to the large energy gap between HOMO-1 and HOMO. Moreover, our results also show that the subsequent radiationless recombination process between the hole transferred to the pentacene molecule and the remaining electron on the MoS2 CBM needs about 10.2 ns. The computational results

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shed important mechanistic insights on the interfacial carrier dynamics of mixed-dimensional pentacene@MoS2 . These insights could help to design excellent interfaces for organic-TMDs heterostructures.

Introduction Two-dimensional transition metal dichalcogenides (TMDs) have recently witnessed significant progress due to their unique electric, optical, and mechanical properties. 1–14 These TMDs, together with various zero- and one-dimensional organic or inorganic materials, can form mixeddimensional heterostructures, which are of immense importance in optoelectronic applications such as light-emitting diodes, photodetectors, and photovoltaic devices as a result of their unique electronic band structures. 15–35 Among these mixed-dimensional heterostructures, TMDs heterojunctions with uniform and ultrathin organic films progress rapidly because of their benefits in photovoltaics, chemical sensors, and catalysts. 36–42 As one of the most studied TMDs, molybdenum disulfide (MoS2 ) has been intensively studied experimentally and theoretically because its optoelectronic properties can be easily tuned by varying the number of stacked layers and the assembling patterns. 43–56 Recently, mixed-dimensional heterojunctions based on organic pentacene film and monolayer MoS2 have been experimentally verified as a promising useful optoelectronic device as photoresponsive field-effect transistors, photodetectors, photovoltaics, and related optoelectronic technologies because electronic properties of these heterojunctions can be modulated by introducing interfacial charge transfer between organic molecules and TMDs. 57–63 The ultrafast exciton dissociation and slow carrier recombination processes play an important role in enhancing photoresponsive performance. Homan et al. have deposited an organic pentacene film on a homogeneous monolayer MoS2 surface by the chemical vapor deposition (CVD) method. 16 Subsequently, they have studied the photoinduced interfacial charge transfer and electron-hole recombination kinetics at the interface of the pentacene@MoS2 heterostructure using time-resolved transient absorption spec-

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troscopies. 16 The analysis of fractional amplitudes of the MoS2 decay processes shows that some of the hole generated as a result of electronic transition transfer from MoS2 to pentacene and the remaining one are trapped within the MoS2 monolayer owing to surface defects available. 16 Moreover, several different time constants are obtained upon irradiation at 535 nm. The fastest time constant of ca. 670 fs is assigned to the carrier trapping process of the MoS2 monolayer. The time constant of ca. 6.7 ps is suggested to be from the interfacial hole transfer from MoS2 to pentacene. The 5.1 ns time constant is assigned to be the nonradiative electron-hole recombination process. 16 However, these assignments could need further examination through theoretical simulations. On the other hand, in order to optimize various optoelectrical performances of this mixeddimensional pentacene@MoS2 heterojunction, it is also necessary to gain in-depth insights on the photoinduced carrier transfer dynamics at the interface between the organic pentacene molecule and the MoS2 monolayer. Theoretical calculations and dynamics simulations play an important role for rationalizing the underlying mechanism of photoinduced interfacial hole transfer processes at the atomistic level. However, as best as we know, there are no corresponding computational studies reported yet. Herein we have for the first time carried out combined static electronic structure calculations as well as developed fewest-switches surface-hopping nonadiabatic dynamics simulations to explore the dynamics of excited carriers at the interface of pentacene and MoS2 . 16 The present results revise recent experimental assignments and meanwhile shed some important light on the thermodynamical and dynamical properties related to the interfacial carrier dynamics at the pentacene@MoS2 interface.

Methods Nonadiabatic Dynamics Method Nonadiabatic dynamics simulations are carried out using the fewest-switches surface-hopping method in the framework of DFT proposed by Prezhdo and coworkers. 64–67 The time-dependent DFT with the Kohn-Sham orbitals maps an interacting many-body system onto a system of non3



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interacting particles where electron density of the latter fully equals to that of the former. In such situation, the time-dependent charge density ρ (r, t) of the interacting system is expressed by a set of time-dependent Kohn-Sham orbitals ψ p (r,t) 68–72

ρ (r, t) =

Ne

2

∑ ψp (r, t) .

(1)

p=1

The electron density evolution is governed by a set of single-electron evolution equations of Kohn-Sham orbitals ψ p (r,t) 71,73–77

i¯h

∂ ψ p (r,t) = Hˆ (r; R) ψ p (r,t) ; p = 1, 2, . . . , Ne . ∂t

(2)

If expanding a time-dependent Kohn-Sham orbital in terms of adiabatic Kohn-Sham orbitals ϕk (r; R) calculated from DFT calculations along adiabatic molecular dynamics trajectories

ψ p (r,t) = ∑ ck (t) ϕk (r; R)

(3)

k

one can thus obtain a set of equations of motion for the expanding coefficients c j (t)

i¯h

( ) ∂ c j (t) = ∑ ck (t) εk δ jk − i¯hd jk ∂t k

(4)

where εk is the energy of the kth adiabatic state (i.e. MOs for molecules) and d jk is the nonadiabatic coupling between adiabatic states j and k. The former is directly obtained from density functional theory calculations and the latter is calculated numerically, through a finite difference method, as overlaps of adiabatic states j and k at times t and t + △t: ⟩ ⟨ ⟩ ⟩ ⟨ ∂ ϕk (r; R) | | ϕ ϕ (t + △t) − ϕ ϕ (t) (t) (t + △t) j j k k d jk = ϕ j (r; R) ≈ ∂t 2△t ⟨

(5)

in which ϕ j (t) and ϕk (t + △t) are electronic wavefunctions of adiabatic states j and k at times t and t + △t, respectively. From this equation, once the overlap matrix of MOs at t and t + △t time steps is acquired, the computation of nonadiabatic couplings becomes straightforward. This 4


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overlap matrix of MOs can be further constructed using the molecular coefficient matrices and the overlap matrix between atomic orbitals (AOs) at both t and t + △t time steps. These latter quantities can be exported with CP2K after some minor modification. Previous algorithms are primarily implemented with plane wave basis sets in VASP and Quantum Espresso; 67,78,79 while, we have implemented this nonadiabatic dynamics method with Gaussian basis sets in CP2K. 28,35

Charge Transfer Analysis To estimate charge transfer from one fragment to another one in nonadiabatic dynamics simulations, we have developed an efficient density-matrix-based method. We first define a density matrix D in terms of atomic orbitals χµ Dµν i (t) = pi (t)χµ i χν∗i

(6)

in which pi (t) is the time-dependent occupation number of the ith adiabatic state calculated based on the above expanding coefficients ci (t); and χµ i is the µ th atomic orbital coefficient of the ith adiabatic state. Similar to the Mulliken charge analysis, 80 we then redefine a population matrix P using density matrix D and atomic overlap matrix S

Pµν i = Dµν i Sµν .

(7)

Finally, we can obtain the ath atomic charge through summing all basis functions µ belonging to that atom and all involved adiabatic states i ( Pa = ∑ i

))

( 1 ∑ Pµν i + 2 µ ∈a,ν ∈a

∑

µ ∈a,ν ∈a /

Pµν i +

∑

µ ∈a, / ν ∈a

Pµν i

;

(8)

It should be noted that if only an atomic orbital belongs to the ath atom, only half of Pµν i is used, as shown by the second term. This approximation has been adopted in the traditional Mulliken charge analysis method. 80 Accordingly, the total charge on a fragment A is the sum of all atomic

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charges belonging to that fragment

PA =

∑ Pa.

(9)

a∈A

It can also be reformulated as

PA = ∑ pi (t)PAi

(10)

i

in which ( PAi =

∑

a∈A

(

∑

µ ∈a,ν ∈a

χµ i χν∗i Sµν

1 + 2

))

∑

µ ∈a,ν ∈a /


+

∑

µ ∈a, / ν ∈a


(11)

In such case the differentiation of PA is written as

dPA = d(∑ c∗i (t)ci (t)PAi ) = ∑ (d (c∗i ci ) PAi + c∗i ci dPAi ) i

(12)

i

where the first term has variational occupations for adiabatic states i ; the second term has constant adiabatic state occupations but changeable charge population. These two contributions actually correspond to nonadiabatic and adiabatic electron transfers, respectively. The former is mainly caused by state hoppings between different adiabatic states and the latter is primarily originated from changes of adiabatic states induced by atomic motions. Finally, it should be noted that Gaussian basis sets are used in simulations, so molecular coefficients χµ i are real numbers. The expanding coefficients ci (t) of adiabatic states in a time-dependent orbital are complex numbers, but they are not used in the above equations; instead, their ci (t) c∗i (t) products are used for calculating the time-dependent occupation number pi (t) of the ith adiabatic state, which is a real number.

Simulation Details The pentacene@MoS2 heterojunction model is constructed using a periodic 6 × 6 supercell of the MoS2 monolayer on which a pentacene molecule is located. In this mode a vacuum layer of 25.0 6


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˚ is used to avoid the arbitrary interaction between the two slabs along the direction perpendicuA lar to the MoS2 monolayer plane. Geometry optimizations and ground-state molecular dynamics calculations are performed using the DFT method implemented in the Vienna ab initio simulation package (VASP5.4). 81 The Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation is used to treat the electronic exchange-correlation interaction. 82 In order to describe the core-valence electron interaction the projector augmented-wave (PAW) method with a cutoff energy of 400 eV is utilized. 83 Since the simulated system is large, only gamma point is used in the periodic DFT calculations. The long-range dispersion interaction of Grimme with the Becke-Johnson damping is used in all the DFT calculations. 84,85 On the basis of the optimized structure, the pentacene@MoS2 heterojunction system is first heated to 300 K through 1 ps canonical molecular dynamics simulations; then, a 5 ps microcanonical molecular dynamics is carried out to prepare trajectories for the following nonadiabatic dynamics simulations. These molecular dynamics simulations are carried out with time step of 1 fs. Nonadiabatic dynamics simulations are carried out using our own developed algorithm and package. 28,35 All required data are calculated using the DFT method implemented in the CP2K package in which a mixed gaussian and plane waves (GPW) basis set with a cutoff of 750 Ry is used. 86–88 The PBE functional together with the built-in DZVP-MOLOPT-SR-GTH basis sets and Goedecker-Teter-Hutter (GTH) pseudopotentials are used. 82,89–93 The empirical dispersion correction method of Grimme is used to describe the van der Waals interaction. 84 Similarly, gamma point is used in these calculations. The phonon analysis is carried out at the PBE level. The HSE06 functional 94,95 with the auxiliary density matrix method 96 is used to calculate accurate density of states (DOS) and projected DOS (PDOS). 100 initial structures with coordinates and velocities are randomly generated from the above 5 ps microcanonical dynamics simulation. For each structure 1000 nonadiabatic dynamics realizations are prepared. So, totally, we prepare 100*1000 trajectories for 2 ps nonadiabatic dynamics simulations. 97–99 Both state-515 and state-516 are chosen as the starting adiabatic hole states according to calculated electronic transition energies and oscillator strengths. A total 11 adiabatic states i.e. from state-510 to state-520 are included in the

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nonadiabatic dynamics simulations. The time steps for nuclear and electronic propagations are set to 1.000 and 0.001 fs, respectively. For the nonadiabatic electron-hole recombination process, the prepared 5 ps trajectory may not be long enough. Therefore, we sequentially iterate the previous 5 ps trajectory three times resulting into a 15 ps trajectory. This procedure has been widely used in previous studies by Prezhdo and coworkers. 99,100 Oscillator strengths between Kohn-Sham orbitals can be directly output by CP2K. Empirical quantum decoherence correction (0.1 a.u.) of Granucci et al. is used in surface-hopping dynamics simulations. 101 The present work is focused on exploring the photoinduced interfacial charge transfer dynamics while the excitonic effects are not considered. All reported dynamical results are averaged over all prepared trajectories. More detailed techniques can be found in previous work. 28,35

Figure 1: (left) PBE+D3 optimized pentacene@MoS2 structure (0 K) and (right) one snapshot extracted from canonical molecular dynamics simulations (300 K). Also shown is the distance of the pentacene center to the MoS2 surface.

Results and Discussion Firstly, we have constructed three pentacene@MoS2 heterojunction models with one pentacene molecule (see Figs. 1 and S1) adsorbed on the monolayer MoS2 surface. These heterojunctions 8


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share similar DOS and PDOS and should thus have close charge transfer dynamics (see Figs. 2 and S2-S4). However, the pentacene@MoS2 heterojunction with a parallel pentacene molecule is the most stable and we thus focus on its charge transfer dynamics (see Table S1). In the parallel model, the adsorption energy is estimated to be 1.60 eV at the PBE+D3 level (2.11 eV with HSE06), which is consistent with the results reported by Shen and Tao. 59 This similar adsorption for organic chromophores on semiconductors has been observed in recent works. 28 At this adsorption configuration, both molecular pentacence and monolayer MoS2 are essentially planar. The inter˚ at 0 K, close distance between pentacene and MoS2 is calculated at the PBE+D3 level to be 3.31A ˚ predicted in recent theoretical work. 59 Upon heated to 300 K, the pentacence@MoS2 hetto 3.4 A erostructure does not change visibly except a larger inter-distance between pentacence and MoS2 , ˚ at 300 K at the same computational level. We have also calculated the which is increased to 3.44 A corresponding root mean square deviation (RMSD) values of bond lengths in pentacene and MoS2 fragments of the pentacene@MoS2 heterostructure at 300 K compared with those at 0 K according to √

σ=

1 N ∑ (Xi − Xi0)2 N i=1

in which N is the total number of covalent chemical bonds, Xi is the bond length of the ith chemical bond at 300 K, and Xi0 is the corresponding value of the ith chemical bond at 0 K (i.e. optimized minimum-energy structure, see Fig. 1). The calculated RMSD values for the pentacene and MoS2 ˚ respectively. In-depth analysis of specific chemical bonds in moieties are 0.0613 and 0.0229 A, pentacene reveals that the structural distortion of the C-C chemical bonds is more remarkable than ˚ that of the C-H chemical bonds at 300 K (RMSD: 0.0685 vs. 0.0450 A). Relative energies of involved band states are very important for qualitatively understanding the hole transfer dynamics at the interface of pentacence and MoS2 ; thus, we have employed the HSE06 method to calculate the corresponding density of states (DOS) and projected DOS (PDOS) at 0 and 300 K. The former corresponds to the minimum-energy structure and the latter does

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Figure 2: (top) DOS and PDOS of pentacene@MoS2 at (left) 0 K and (right) 300 K calculated by the HSE06 functional; (bottom) the contribution of the MoS2 (orange) and pentacene (blue) fragments to each adiabatic state. The relevant results calculated at PBE+D3 level are also shown in Fig. S2.

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to a randomly chosen snapshot structure from the first-principles canonical molecular dynamics simulations. Fig. 2 shows the HSE06 calculated DOS and PDOS. Obviously, both HOMO and HOMO-1 of the pentacene molecule, referred to as 519 (HOMO) and 518 (HOMO-1) in Fig. 2, are located between the valence band maximum (VBM) and the conduction band minimum (CBM) of the MoS2 monolayer. For example, HOMO is 1.450 [1.546] eV higher than VBM, and 0.743 [0.540] eV lower than CBM at 0 [300] K at the HSE06 level. HOMO-1 is much closer to VBM than HOMO (see Fig. 2 for their relative energies). In contrast, LUMO of the pentacene molecule, referred to as 561 (LUMO) in Fig. 2, is much higher than CBM of the MoS2 monolayer, 0.920 eV at 0 K vs. 0.818 eV at 300 K at the HSE06 level. From the above results, the HOMO-LUMO energy gap of the pentacene molecule is predicted to be 1.663 eV at the HSE06 level at the minimumenergy structure. In parallel, the VBM-CBM energy gap of the MoS2 monolayer is estimated to be 2.193 eV at the HSE06 level. Moreover, as discussed above, the studied pentacene@MoS2 system is a type-II heterostructure. According to the calculated HOMO and CBM energies, the band gap is thus estimated to be 0.743 eV at the HSE06 level. In order to explore the interfacial effects on the band gaps of pentacene and MoS2 moieties in pentacene@MoS2 , we have calculated the DOS and PDOS of isolated pentacene and MoS2 in Fig. S7. The HOMO-LUMO energy gap of the pentacene molecule and the VBM-CBM energy gap of the MoS2 monolayer are separately estimated to be 1.689 and 2.201 eV at the HSE06 level, respectively, which are close to 1.663 and 2.193 eV in pentacene@MoS2 . This also demonstrates that the interfacial interaction between pentacenec and MoS2 is small so that their band gaps do not change visibly from isolated ones to their pentacene@MoS2 heterostructure. In order to explore the photoinduced interfacial hole transfer dynamics, we have first explored the electron transition upon photoirradiation in the Franck-Condon region. At the HSE06 level, there are four primary electron transitions with large oscillator strength, i.e. state-516 to state-520 (2.23 eV, f:0.60734), state-516 to state-521 (2.23 eV, f: 0.60376), state-515 to state-520 (2.24 eV, f: 0.60978), and state-515 to state-521 (2.24 eV, f: 0.60955). The computed electron excitation energies, 2.23 and 2.24 eV, are in good agreement with experimentally measured 2.04 eV for the

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Figure 3: Spatial distributions of six adiabatic states from states 515 to 520 involved in the interfacial hole transfer and the electron-hole recombination dynamics of pentacene@MoS2 calculated at HSE06 level. See spatial distributions calculated at PBE+D3 level in Fig. S6. pentacene@MoS2 heterojunction. As a result, upon electron transition, an electron will occupy either state-520 or state-521 and a hole will be produced in either state-515 or state-516. Further examination on these four electron and hole states reveals that they are all mainly localized within the MoS2 monolayer. As mentioned above, state-519 (HOMO) and state-518 (HOMO1) are primarily from the pentacene molecule, so the photoinduced interfacial hole transfer from state-515 and state-516 to state-518 and state-519 should be thermodynamically favorable because the former ones are lower than the latter ones in energy. This could qualitatively explain why the interfacial hole transfer is observed in recent experiments. 16 In contrast, the interfacial electron transfer could be difficult in this situation because the excited electron stays in CBM of the MoS2 monolayer and hopping to higher electron states is energetically inefficient. Nevertheless, high excitation energy can populate higher electron states that can benefit the interfacial electron transfer, which is however beyond the present work. Thereby, we mainly focus on studying the interfacial hole transfer from the MoS2 monolayer to pentacene in this work. Fig. 3 shows the spatial distribution of six states involved in the interfacial hole transfer between pentacene and MoS2 . The state-519 (HOMO) and state-518 (HOMO-1) states are obvious 12


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Figure 4: Time-dependent energies of selected adiabatic states i.e. from states 515 to 520 that are mainly involved in the interfacial hole transfer and the electron-hole recombination dynamics of pentacene@MoS2 calculated at PBE+D3 level.

π character and nearly completely localized on the pentacene molecule. The state-517 (CBM), state-520 (VBM), state-515, and state-516 states are mainly from the MoS2 monolayer but their character are distinct from each other. The state-517 (CBM) is mainly composed by the dz2 orbitals of the Mo atoms; while, both state-515 and state-516 are primarily from the dxy and dx2 −y2 orbitals of the Mo atoms (see Table S2). From computed DOS and PDOS in Fig. 2, it is clear that state-515, state-516, and state517 that are mainly located on the MoS2 monolayer are very close to state-518 (HOMO-1) but a litte far away from state-519 (HOMO) on pentacene. This situation is also observed in the 2 ps dynamics simulations in Fig. 4, in which state-515, state-516, and state-517 (VBM) that belong to the same valence band of the MoS2 monolayer are slightly below state-518 (HOMO-1) but much lower than state-519 (HOMO). In addition, the time-dependent evolution of the above states shows that state-520 (CBM), state-518 (HOMO-1), and state-519 (HOMO) only fluctuate and do not cross any other states. By contrast, state-515, state-516, and state-517, due to belonging to 13



Figure 5: (left) Vibrational spectrum from the Fourier transformation of the time-dependent energy of state-515 calculated at PBE+D3 level. See text for discussion. the same valence band, are very close to each other in energy. Since state-518 (HOMO-1) on the pentacence molecule is energetically close to state-517, state-516, and state-515 located on the MoS2 monolayer, the interfacial hole transfer should be allowed and expected to be efficient, as observed in recent experiments. 16 On the other hand, one can see that there is a clear band gap between both state-520 (CBM) on the the MoS2 monolayer and state-519 (HOMO) on the pentacene molecule, thus, it is natural to expect that the electron-hole recombination process is relatively slower than the interfacial hole transfer dynamics. As discussed above, both state-515 and state-516 are two main hole states. To get insights into vibrational modes that drive the energy fluctuation of these two hole states, we have done Fourier transformation on their time-dependent energies. The results for state-515 are shown in Fig. 5. The peak around 400 cm−1 has the largest amplitude, which is associated with the lowfrequency vibrational mode of the MoS2 monolayer. It corresponds to the out-of-plane motion of MoS2 and thus enhancing inter-state couplings thereby benefitting the interfacial electron-hole recombination. This is also seen in previous work. 99 The peaks around 47 and 695 cm−1 stem from the out-of-plane vibrations of the pentacene molecule. The similar results are also found for state-516 (see Fig. S8).

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Figure 6: (left) Time-dependent state populations of states from 515 to 519 and (right) the corresponding time-dependent hole amount localized on the MoS2 fragment in the nonadiabatic dynamics simulations for the interfacial hole transfer starting from state-515. Those for the state-516 are shown in Fig. S9. All these simulations are carried out based on the PBE+D3 calculated quantities. The nonadiabatic dynamics simulations are carried out to quantitatively estimate the hole transfer process from the MoS2 to pentacene moieties under the classical path approximation, which is demonstrated to be reasonably accurate for photoinduced charge transfer processes without involving large conformational changes and chemical bond-making or -breaking. 67,79,99,102,103 In CPA nuclear trajectories are predetermined and independent of electronic evolution. The algorithm is implemented with Gaussian basis sets while previous ones are primarily done with plane wave basis sets. 28,35 As mentioned above, there are two main hole states generated in the electronic excitation, i.e. state-515 and state-516; thus, we have run two sets of nonadiabatic dynamics simulations with different initial hole states. In the first one, the hole initially occupies state-515 and five states are included in the simulations, i.e. states 515-519. The left panel of Fig. 6 depicts their time-dependent state populations within 2 ps simulation time. The state population of the initially populated state-515 decreases to ca. zero in the first 500 fs. Meanwhile, the state population of the intermediate state-516 quickly increases to its maximum value at ca. 250 fs and then slowly decreases to zero at the end of 2 ps dynamics simulation. The dynamical behavior of state-517 is similar to that of state-516. The state population of state-518 monotonously grows up until it approaches ca. 0.9 at ca. 1.5 ps. Furthermore, one can see that the state population of state-519

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is slowly increased and becomes ca. 0.1 at the end of 2 ps nonadiabatic dynamics simulation process. The small increase of the state population of state-519 is obviously caused by the relatively large energy gap between it and state-518 (see Fig. 4). Concerning that state-518 and state-519 are mainly from the pentacene molecule and state-515, state-516, and state-517 are on the MoS2 monolayer, one can explore the interfacial hole transfer dynamics as shown in the right panel of Fig. 6. Through fitting the time-dependent population of the hole amount still localized on the MoS2 monolayer with a simple exponential function, the interfacial hole transfer time is estimated to be 611 fs. However, this interfacial hole transfer is mainly contributed from the population of state-518 from the MoS2 states as shown in the left panel of Fig. 6. By contrast, the hole cooling process from state-518 to state-519 within the pentacene molecule is very slow because of the large energy gap. The corresponding time is estimated to be 15 ps through fitting the state population of state-519 with a simple exponential function. It is noteworthy that there is also substantial overlap between the deep MoS2 hole state and the HOMO-2 state of pentacene (see Fig. 2); thus, the hole transfer between them is possible. However, the experimentally used wavelength of 535 nm is not enough to produce such deep MoS2 hole state. 16 As a result, the hole transfer from MoS2 to HOMO-2 is not considered in the present work. In the second set of nonadiabatic dynamics simulations, the initial hole state is state-516 and five states that are the same as those in the above dynamics simulations are also used. As shown in the left panel of Fig. S9, the state population of state-516 slowly decreases to zero at the end of 2 ps simulation; while, that of state-518 gradually increases to ca. 0.9 in the same time period. The state population of state-517 evolves like that in the first set of nonadiabatic dynamics. One can also see a very slow increase for the state population of state-519 (ca. 0.1 at the end of 2 ps simulation time). Analogously, starting from state-516, there also exists a fast interfacial hole transfer as shown in the right panel of Fig. S9. The estimated time is about 547 fs, close to 611 fs starting from state-515. Furthermore, fitting the state population of state-519 with a single-exponential function gives a time constant of 15.7 ps, which is close to the above estimated one of 15.0 ps. This much longer hole cooling process from state-518 to state-519 is also ascribed to the large

16


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energy gap between state-518 and state-519. Furthermore, we have found that the nonadiabatic contribution plays a major role for the interfacial hole transfer between the MoS2 monolayer and the pentacene molecule (see Figs. S10).

Figure 7: Time-dependent electron-hole recombination amount in nonadiabatic dynamics simulations calculated at PBE+D3 level. See text for discussion. In addition to the interfacial hole transfer dynamics, we have also explored the interfacial electron-hole recombination dynamics. In this case, the excited electron occupies state-520 on the MoS2 monolayer and the hole occupies state-519 on the pentacene molecule. In terms of the calculated state population in Fig. 7, one can estimate the nonadiabatic electron-hole recombination time to be about 10.2 ns, which is on the same timescale with experimentally measured 5.13±0.44 ns. 16 The difference between experimenal and theoretical data could be ascribed to the fact that the realistic pentacene@MoS2 heterostructure in experiments is more complex than the used model in which defect effects are not considered and only one pentacene molecule is considered. Our dynamics simulations are carried out using DFT-based surface-hopping approach (see above). Electron and hole states are expanded in terms of DFT calculated band states and the excitonic effect is not explicitly considered. TD-DFT and GW-BSE electronic structure methods could capture such 17



effects but their calculations are still expensive for periodic systems. Excitonic interaction is usually strong in molecular systems. 104 Our studied recombination process takes place at the interface between pentacene and MoS2 and the excitonic interaction is thus expected to have very small effects on the process. In addition, the classical path approximation works well 28,35,67,79,99,102,103 for the electron-hole recombination process because the relevant ground- and excited-state structures ˚ see spatial superposition in Fig. S11). Finally, are highly similar to each other (RMSD: 0.0072 A; long-time nonadiabatic simulations are still very expensive for periodic material systems. The extrapolation of short-time dynamics is a compromising approach. In spite of some uncertainties, it is expected to give reasonably accurate results. The extrapolation is based on time-dependent probability populations of electron or hole on involved states. Sometimes involved states do not really cross each other, there remain hopping probabilities based on which time-dependent probability populations are calculated. This strategy has been extensively used by Prezhodo and coworkers for estimating recombination rates in a lot of materials simulations. 99,100,105–107 Alternatively, the semiclassical Marcus model is a good choice to calculate long-time recombination rate constants and will be considered in our future works. 108 Furthermore, the present simulation is focused on individual interfacial hole transfer and recombination processes. The exploration of the yield of each relaxation process is interesting but beyond the present scope.

Correlation with Previous Works Time-resolved absorption spectra of pentacene@MoS2 upon 535 nm photoexcitation revealed several time constants that are assigned to different photoinduced carrier relaxation processes. 16 As demonstrated in recent experiments this excitation wavelength mainly excites the MoS2 moiety and the contribution from the pentacene one is negligible. The fastest decay time constant of ca. 670 fs is directly assigned to the intrinsic carrier trapping within MoS2 in the pentacene@MoS2 heterojunction compared with that in MoS2 -only film. The present dynamics simulations resolve the experimental assignment and give new insights. The interfacial hole transfer from MoS2 to pentacene is estimated to be 611 and 547 fs from the shallow MoS2 hole states i.e. state-515 and 18


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state-516, respectively. These estimated times are close to the experimentally measured fastest relaxation time constant but this process should correspond to the interfacial hole transfer from the shallow MoS2 hole state to the energetically close HOMO-1 state of the pentacene molecule. In addition, due to the large energy gap between HOMO and HOMO-1, the hole will be trapped in HOMO-1 for a relatively long time. Therefore, the experimentally observed decay time of ca. 670 fs could correspond to the interfacial hole transfer from MoS2 to pentacene and the hole trapping in HOMO-1. Moreover, there is a fast decay process of ca. 6.7 ps for the pentacene@MoS2 heterojunction, which is experimentally ascribed to be the hole transfer from MoS2 to HOMO of the pentacene. Our simulations show that this process is related to the hole cooling process from HOMO-1 to HOMO of the pentacene. Its time constant is estimated to be 15.0 and 15.7 ps from state-515 and state-516, respectively, which are on the same time scale with the experimentally measured value. 16 Therefore, the 6.7 ps relaxation process could be associated with this hole cooling process within the pentacene as a result of the ultrafast interfacial hole transfer from the MoS2 to pentacene fragments. Finally, there is an additional decay constant of ca. 5.13 ns observed in the pentacene@MoS2 dynamics, which does not exist in the dynamics of the pure MoS2 monolayer. This time constant is experimentally suggested to be related to the nonadiabatic recombination process of the hole transferred to the pentacene molecule and the electron still on the MoS2 moiety. This assignment has been seconded by the nonadiabatic dynamics simulations, which predict that this electron-hole recombination process takes ca. 10 ns, on the same timescale with experimentally measured value. 16 The discrepancy between experiments and simulations could be caused by the fact that the pentacene@MoS2 model still deviates from realistic pentacene@MoS2 heterojunctions because about 30 nm pentacene films are used in experiments and possible MoS2 defects are not considered in the simulations. On the other hand, Shen and Tao have computationally explored the possibility of the interfacial electron transfer processes in various pentacene@MoS2 heterojunctions in terms of calculated density of states, charge density difference, etc. and concluded that the interfacial electron transfer is negligible between pentacene and 2H-MoS2 while significant between pentacene and 1T-

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Figure 8: Photoinduced interfacial hole transfer process from MoS2 to pentacene and subsequent radiationless recombination process between the hole transferred to the pentacence and the electron left on the MoS2 monolayer. See text for discussion. MoS2 . 59 This viewpoint is also seconded by the present calculations. The above analysis shows that the MoS2 CBM is much lower than the lowest unoccupied molecular orbital of the pentacene molecule, which is thus thermodynamically unfavorable. Moreover, the present results indicate that the electronic excitations with the pentacene molecule in the range of experimentally used wavelengths are much weaker than those with in MoS2 (see above). This could explain the recent experimental phenomenon that the 535 nm excitation of pentacene@MoS2 does not include any contribution from the pentacene molecule because of much weaker absorption.

Conclusion In this work we have employed both DFT-based electronic structure calculations and fewestswitches surface-hopping dynamics simulations to study the photoinduced interfacial hole transfer dynamics and subsequent nonadiabatic electron-hole recombination dynamics at the interface between pentacene and MoS2 in pentacene@MoS2 . Upon 535 nm photoirradiation, the electronic transition mainly takes place within the MoS2 moiety due to the comparably large oscillator 20


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strength. This process moves an electron to the MoS2 conduction band thereby leaving a hole in the valence band. This hole state is energetically lower than the occupied HOMO-1 state that is primarily located on the pentacene molecule; thus, the interfacial hole transfer process is favorable in energy. The time for such interfacial hole transfer to the HOMO-1 state of the pentacene is estimated to be about 600 fs, close to the experimentally measured fastest time constant of ca. 670 fs. Due to the large energy gap between HOMO and HOMO-1, the following hole relaxation within the pentacene takes much longer time, about 15 ps, which is on the same time scale with the experimentally measured time constant of ca. 6.7 ps. Moreover, the results also show that the subsequent radiationless electron-hole recombination process is about 10.2 ns. The work supplies useful mechanistic insights for the interfacial carrier dynamics of mixed-dimensional pentacene@MoS2 , which could help to design excellent interfaces for separating charge-transfer excitons of organic-TMDs heterostructures. Acknowledgment: This work has been supported by the grants NSFC 21522302 (G.C.) and NSFC 21520102005 (G.C. and W.F.). Supporting Information Available: Studied pentacene/MoS2 models, DOS and PDOS, and additional figures and tables. This material is available free of charge via Internet at http://pubs.acs.org.

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Photoinduced Carrier Dynamics at the Interface of Pentacene and

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