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C: Energy Conversion and Storage; Energy and Charge Transport

Effect of Oxidation State on Charge Carrier Lifetimes in B,N Co-Doped Graphene Oxide Quantum Dots Peng Cui J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04567 • Publication Date (Web): 04 Aug 2018 Downloaded from http://pubs.acs.org on August 9, 2018

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The Journal of Physical Chemistry

Effect of Oxidation State on Charge Carrier Lifetimes in B,N co-doped Graphene Oxide Quantum Dots Peng Cui* Department of Materials Science and Engineering, Rutgers University, Piscataway, New Jersey 08901, USA.

Abstract: Graphene oxide is an outstanding photocatalyst used in the water-splitting reaction. However, the oxidation-reduction state causes unstable photocatalytic efficiency. Electronic structure calculations combined with nonadiabatic molecular dynamics is an effective tool to decipher the catalytic nature in such materials, especially regarding their intrinsic electronic properties. In this work, we performed ab initio nonadiabatic molecular dynamics to investigate the phonon-mediated charge relaxation and recombination dynamics in oxidized, partially oxidized and reduced graphene oxide quantum dots (GOQDs). The relaxation dynamics, such as symmetry and relaxation time, depend on the excitation levels and oxidation states. The partially oxidized and reduced GOQDs exhibit asymmetric relaxations at higher excitation levels, in which the partially oxidized GOQD exhibits a faster electron decay, while the reduced GOQD exhibits a faster hole decay. At lower excitation levels, the electron decay is faster in oxidized and reduced GOQDs, while the hole decay is faster in partially oxidized GOQDs. Oxidation and partial oxidation bring the occupied and unoccupied localized states into the band gaps of GOQDs. In particular, oxidation leads to faster hole trapping, while partial oxidation leads to faster electron trapping.

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1. Introduction Graphene quantum dots (GQDs) are an outstanding archetype of the carbon dot family and have drawn great attention for the past several years. With high charge carrier mobilities,1 quantum confinement effects,2-3 excellent thermal/chemical stabilities3 and strong photoluminescence emissions,4 GQDs make these classes of materials particularly useful in a wide variety of applications, such as in light emitting diodes,5 solar cells6 and biotags.7 Heteroatom doping provides a means to tune the intrinsic properties of GQDs, offering new opportunities for modulating the electronic and optical properties of GQDs. Substituting carbon atoms with foreign atoms breaks the lattice symmetry, which opens up the band gap and induces local charges into the graphene lattice. The dopant atom, having a different electronegativity with respect to carbon atom, brings different conductivity into the graphene lattice and is beneficial to catalyze hydrogen and oxygen evolution reactions for water splitting. For example, boron doping induces p conductivity into the graphene lattice, which can be used to catalyze the oxygen evolution reaction, while nitrogen doping induces n conductivity into the graphene lattice, which can be used to catalyze the oxygen evolution reaction. Recently, more advanced synthetic routes have been established to combine multiple dopants leading to B-N,8 S-N,9 and P-N10 co-doped GQDs. Codoped GQDs have exhibited improved catalytic activities compared to those of single-doped GQDs. Graphene oxide quantum dots (GOQDs) are a derivative of GQDs and are the most popular among GQD materials. They can be easily prepared by the oxidation/exfoliation of graphite, 4 they exhibit a tunable electric conductivity, and they are soluble in water, making them suitable for wet chemistry applications. The edges of GOQDs are capped with oxygen-containing functional groups, such as a C-O covalent bond, which disturbs the π-electron delocalization of the graphene lattice and reduces the sp2 domain size. The oxygen-containing functional group brings p-type conductivity into the graphene lattice, making them suitable for the hydrogen evolution reaction. Moreover, GOQDs can be doped with a nitrogen atom, which brings n-type conductivity into the graphene lattice; therefore, an overall water splitting scheme involving both hydrogen and oxygen evolution reactions can coexist in the same molecular system 2 (Figure 1). The large, accessible surface makes the GOQD an effective medium for photocatalytic water splitting. The GOQDs can be prepared by the electrochemical etching of an electrode made of graphene. 11 To incorporate the 2 ACS Paragon Plus Environment

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dopant atoms into GOQDs the molecular dopant precursor is added to the aqueous electrolytic medium.11 The oxidation of C-C bonds and substituting the carbon atoms by B and N atoms are completed via electrochemical cycling. The oxygen functional group is decorated at the edges of the GOQDs, which is confirmed by the XPS measurements that indicate a BO 2 bond component centered at 399.2 eV in the GOQDs. Adding NaBH4 can reduce the oxygen functional groups in B, N co-doped GOQDs, which correlates to an increase in chemical activity. 11 Based on the different reduced forms of GOQDs, Marco et al. proposed three categories of B, N co-doped GOQD in which the oxygen, boron and nitrogen atoms are introduced to mimic locally the active site, and their locations in GOQDs are justified by XPS measurements (Figure 2). Here, the oxygen atom represents the oxygen functional group. The concentration of dopant atoms and oxygen functional groups are close to the experimental values. 11 Their proposed models successfully predicted the reaction energy barriers that well match with the experimental results. Thus, in this study, we adopted their models to study the charge relaxation and electron-hole recombination dynamics in GOQDs. During the photocatalytic reaction, the photogenerated charges participate in the chemical reaction after relaxing to the bottom of the conduction band (CB) or valence band (VB). The charge transfer efficiency from a GOQD to the targeted reactant is determined by the shape of the density of state (DOS), electron-phonon coupling, and electronic decoherence in the GOQD. GOQDs also reduce the reaction barrier between the reactant and the product, thus accelerating the chemical reaction. Marco et al. 11 calculated the free energy barriers at different intermediate reaction stages in the GOQD-catalyzed oxygen reduction reaction (ORR) and proposed that the selectivity of the 2e- and 4e- transfer pathways depends on the oxidation state of the GOQDs. However, the phononmediated charge relaxation and electron-hole recombination in GOQDs remain largely unexplored. Adiabatic Density Functional Theory (DFT) computations only give the Gibbs free energy barrier between the reactant and the product, which cannot reveal the catalytic nature of graphene oxide materials, especially the phonon-mediated charge relaxation. When the charge carrier is initially generated in GOQDs, it undergoes a relaxation process in the conduction band (CB) or valence band (VB) of the GOQDs. These photocharges participate in either nonadiabatic recombination or charge transfer processes when they reach the band edges. The symmetric or asymmetric relaxation of electron and hole is crucial for the catalytic efficiencies of the GOQDs. If the electron and hole reach the band edges on the same time scale, i.e., symmetric relaxation, the nonadiabatic 3 ACS Paragon Plus Environment


recombination is able to compete with charge transfer, which decreases the photocurrents. On the other hand, the asymmetric relaxation promises efficient charge transfer at the conduction band maximum (CBM) and the valence band maximum (VBM),12 which benefits the hydrogen and oxygen evolution reactions for water splitting. As such, unraveling the details of charge relaxation as well as electron-hole recombination provides insight about the catalytic nature of GOQDs, which is helpful for the chemical modification of their electronic structures to improve their catalytic efficiencies. The conventional DFT methods invoke the Born-Oppenheimer (BO) approximation, in which a crossover between electronic-level is ignored, therefore the electronic transition mediated by the nuclear motion cannot be properly described with BO approximation. Particularly in graphene, the BO approximation fails due to the phonon-induced renormalization of electronic properties. 13 Thus, to fully incorporate electron-electron interaction and electron-phonon coupling effects into the charge relaxation dynamics, one needs to carry out ab initio nonadiabatic molecular dynamics (NAMD). For example, Nie et al. reported that the carrier cooling in the few-layer MoS 2 mainly occurs through the carrier-carrier scattering and carrier-phonon scattering, and they predicted that the two processes occur on the time scales of 40 fs and 0.5 ps in the few-layer MoS 2, respectively, based on their NAMD results, which well match with the experimentally measured nonthermal carrier cooling time scales.14 In addition, the phase randomization in the electronic wave function causes the decoherence of quantum superpositions. 15 Inducing the decoherence effect into FSSH is particularly important for accurately describing nonradiative electron-hole recombination since the nonradiative decay across bandgap typically takes longer than the electronic transitions between the neighboring energy states in the conduction band (CB) and valence band (VB) for most nanomaterials. Especially for GQDs, including decoherence is essential for obtaining correct electron-hole recombination time due to the quantum size effects on bandgaps. There exists a variety of NAMD methods that can be used to model the carrier relaxation and charge transfer dynamics in condensed matter system, such as surface-hopping, 15-16 ab initio multispawning (AIMS),17 hydrodynamic nonadiabatic dynamics,18 Bohmian dynamics19-20 and meanfield nonadiabatic dynamics through exact decomposition of electron-nuclear motion. 21-22 Compared to the other NAMD methods, the surface-hopping algorithm selects the electronic potential surfaces to steer nuclear trajectories at each time step of molecular dynamics, and the 4 ACS Paragon Plus Environment

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decoherence can be resolved in an ad-hoc fashion.15 In particular, Tully fewest switched surface hopping (FSSH),16,

23

which determines the spawning of electronic potential surfaces by a

stoichiometric procedure carried out at each molecular dynamics step, can efficiently explore the nuclear phase space and significantly reduce the computational cost compared to the other methods. This method (FSSH) has been further developed by Prezhdo’s group and is combined with classical path approximation, which can be used to simulate the condensed phase systems that contain up to hundreds of atoms.12,

14-15, 23-26

In a previous work,27 we used this method to

investigate the charge transfer dynamics of black dye functionalized Cd 33Se33 QDs and correctly predicted the hole transfer from black dye to Cd33Se33 QDs. There have been a few theoretical reports about the charge transfer, relaxation and recombination dynamics of graphene materials. Jaeger et al.

12

investigated the electron-hole

nonradiative recombination of pristine GQDs. Long et al. 28 investigated the photoinduced charge separation at the graphene-TiO2 interface. Wang et al. 29 used the PYXAID code24 to simulate the photoexcited electrons in chevron-type graphene nanoribbons. However, we have not found any report about the photoinduced carrier relaxation and electron-hole recombination of GOQDs, especially with respect to different oxidation states. As such, in the present work, we simulate the electron and hole relaxations as well as their recombination in B, N co-doped GOQDs with different oxidation states to provide some insight about the catalytic nature of GOQD. Our work can be used as the guidance for designing the electronic structures of such class of materials to improve their catalytic efficiencies.

2. Computational Details The overall simulation consists of the electronic structure calculation and the adiabatic molecular dynamics (MD).14, 24-26 The electronic structure calculation was carried out using single-point DFT to obtain the Kohn-sham orbital energies at each MD time step; afterward, the electronic amplitudes are evolved on the fly by solving the time-dependent Schrödinger equation (see supplemental information, part A for details). The 𝑁 × 𝑁 dimensional nonadiabatic coupling vector matrix were obtained at each MD time step by employing the time derivative approach. 30 To propagate the electronic amplitudes, one needs to construct an initial Hamiltonian matrix using the nonadiabatic coupling vectors and Kohn-sham orbital energies; see the right side of eqn.(6) in supplemental information, part A. The slope of the Hamiltonian matrix is calculated between each 5 ACS Paragon Plus Environment


adjacent time steps. The Hamiltonian matrix of the next time step can be constructed using the Hamiltonian matrix of the current time step as well as the slope of the matrix. A first order finite difference method is used to propagate the electronic amplitudes to the second time step. Afterward, the second order finite difference method is used to propagate the electronic amplitudes in order to increase the numerical accuracy. The time step for propagating the electronic amplitudes is 1 attosecond. The adiabatic molecular dynamics is carried out with the Verlet algorithm. The nuclear trajectories are dominated by the thermal fluctuations of the system such that the single electron or the single hole in the conduction band or the valence band has a minimum effect on the propagation of nuclear trajectories. Such classical approximation is introduced into FSSH to largely reduce the computational cost.23 The upwards or downwards trajectory hops are replaced by multiplying a Boltzmann factor with the hopping probability, which greatly reduces the upwards hops to achieve the same effect as the original velocity rescaling scheme in FSSH to conserve the total energy. To simulate the electron-hole recombination, we adopted the two-band model based on the decoherence induced surface-hopping (DISH) algorithm. 15 This is done by resetting the electronic amplitude to 0 (lower state) or 1 (upper state) when the coherent time step is equivalent to the collapse time,31 which is determined by comparing the current time step with a random number sampled from the Poisson distribution with the characteristic time given by the pure-dephasing function. The details regarding the pure dephasing function are provided in supplemental information, part B. The electronic structure and molecular dynamics calculations were carried out with the VASP software package32-35 with the hybrid PBE1 functional.25 The cutoff of the plane-wave basis is 500 eV. The interaction between core and valence electrons are treated with the projector augmented wave (PAW) potentials.36 The computation of the NA coupling vector matrix and the propagation of electronic amplitudes were carried out with a self-written nonadiabatic surface-hopping package. The simulation was performed in the simulation boxes containing oxidized B, N co-doped GOQDs (GOQDox), partially oxidized B,N co-doped GOQDs (GOQDpox) and fully reduced B-doped GOQDs (GOQDre), respectively. Each nitrogen dopant is linked only to two sp2 carbon atoms (pyridine N). Depending on the oxidation state, each boron atom can be bonded directly to two oxygen atoms or one oxygen atom and one nitrogen atom or three carbon atoms. A vacuum layer of ten angstroms was added on each side of the molecule to avoid the spurious self-interaction. The structure relaxation was carried out until the force on each atom was smaller than 10 -3 eV/Å. 6 ACS Paragon Plus Environment

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Then, the system was brought up to 300 K through repeated velocity rescaling to reach thermal equilibrium. 3.2 ps molecular trajectories with 1 fs atomic time steps were produced. The first 500 fs of molecular dynamics were used to prepare the initial ensemble configurations of the NAMD calculations. To ensure the convergence of the NAMD results, we re-ran the same simulation by increasing initial configurations to the first 800 fs of molecular dynamics. However, there was no noticeable difference between the two runs, indicating that 500 fs was sufficient for preparing the initial conditions for the NAMD calculations.

3. Role of Carrier-carrier Scattering and Carrier-phonon Scattering on Charge Relaxation The carrier-carrier scattering and carrier-phonon scattering govern the charge carrier relaxation in the VB and the CB.37-38 The carrier-carrier scattering is due to the collision between electrons or holes, which results in the electrons or holes scattered into the unoccupied states and redistributed in VB and CB. At the earlier times of charge relaxation, the transformation from an extremely nonequilibrium distribution to an equilibrium distribution of charge carriers as well as the dynamic screening results in a sharp decline of relaxation energy,39 in which carrier-carrier scattering plays a dominant role. Subsequently, carrier-phonon scattering governs the relaxation, in which the electron or hole is scattered off the lattice vibration. However, if the charge carrier is excited to the energy level near the band edge, the initial electronic state is only coupled with a few other electronic states that were very close to the energy equilibrium, resulting in a slow energy decay (as shown in Figure 4 (c)) at the beginning of relaxation dynamics. Carrier-carrier scattering depends on the electron-electron interaction, 40-42 which is represented by the exchange-correlation energy term in PBE1 functional. Even though the adiabatic Kohnsham basis is employed in our NAMD simulation, the effect of electron-electron interaction is fully included in the obtained Kohn-sham orbital energy. Consequently, the effect of electron scattering is included in the energy observables of NAMD. To characterize the electron scattering effect one can use the nonadiabatic (NA) coupling vector and DOS. The DOS represents the number of electronic states at each energy level and is obtained at each time step of the molecular dynamics. The more number of electronic states there are on each energy level, the more collisions between electrons it suggests. The shapes of the DOS are asymmetric for the three systems, which have slightly higher densities in VBs than in CBs; see Figure 4 (g) ~(i). The NA coupling vectors 7 ACS Paragon Plus Environment


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govern the changes in electronic amplitudes through the equation of motion for electronic system (eqn. (6) in supplemental information, part A). Multiplying the electronic amplitude by its complex conjugate gives the electronic population, i.e., the occupation number of the molecular orbital. The orbital relaxation energies are obtained by multiplying the occupation numbers of the molecular orbitals with the Kohn-sham orbital energies. As such, the effect of electron scattering is included in the relaxation energy. The NA coupling vector describes the electronic transitions during a very short period, i.e., 1fs in our case. During such a short period, the electron scattering plays a dominant role in manipulating the relaxation since the phonon-mediated carrier relaxation typically takes longer than the electron scattering-mediated carrier relaxation due to the slow nuclear motion.14 A larger DOS and NA coupling vector suggest a stronger carrier-carrier scattering, resulting in a faster carrier relaxation. This can be understood in another perspective, the DOS and the square of the NA coupling vectors are proportional to the decay rate according to Fermi’s golden rule,43 therefore the larger NA coupling vectors and DOS give rise to a faster charge relaxation. To characterize the NA coupling strength, the averaged NA coupling vectors between pairs of the first, second and third nearest adiabatic states are computed using, 31 〈𝑑

,

〉=

1 (𝑡 − 1)(𝑁 − 𝑗)

𝑑,

(1)

Where t is the number of MD steps and N is the total number of adiabatic states. The threedimensional surface plots of the NA coupling vectors for the three GOQD systems, which represents the average magnitudes of NA couplings with different colors, are also provided in supplemental Figure S2. The averaged NA coupling values decreased as the adiabatic states or excitation levels in the VB increased; see Table 1. However, the situation is different in the CB. The averaged NA coupling values increased as the number of adiabatic states for oxidized and partially oxidized GOQDs increased, yet it is opposite for reduced GOQDs. The carrier-phonon scattering depends on the electron-phonon interaction. The electron interacts with the nucleus through elastic and inelastic energy exchanges. 26 The inelastic energy exchange between an electron and a vibrational subsystem is required to accommodate the excess energies from charge carrier relaxation, leading to a detailed balance between the nuclear and electronic subsystems. On the other hand, the elastic electron-phonon interaction causes the loss 8 ACS Paragon Plus Environment

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of coherency between electronic states, which has a pronounced influence on the electron-hole recombination of QDs. The strong electron-phonon interaction gives rise to a large fluctuation of orbital energy, which can be characterized through Fourier transforms (FTs) of the orbital energies;31 see Supplemental figure S1. The integration of spectra density over vibrational frequencies describes the overall electron-phonon coupling strength. The strong electron-phonon coupling causes self-trapping,44 slowing down carrier relaxation. In addition, the electron-phonon interaction can also affect the electron-electron correlation, 44 which consequently interfere with the electron-scattering mediated charge relaxation, bringing additional relaxation channels into VB and CB.

4. Results and Discussion 4.1 Electronic Structure and Charge Carrier Relaxation in VB and CB Figure 2 shows the optimized structures of GOQDox, GOQDpox and GOQDre. The average C-C bond length is approximately 1.42 Å. Replacing the edge carbon with nitrogen decreases the bond distance due to nitrogen withdrawing electrons from carbon, i.e., 1.34 Å for the average N-C bond length compared to 1.42 Å for the average C-C bond distance. Similarly, replacing the edge carbon with oxygen also decreases the bond distance: 1.36 Å for the average C-O bond length compared to 1.42 Å for the average C-C bond length. In contrast, replacing carbon with boron expands the neighboring carbon atoms: 1.50 Å for the average B-C bond length compared to 1.42 Å for the average C-C bond distance, which is consistent with previous molecular dynamic simulation results.46 Boron forms sp2 hybridized bonding with neighboring carbon atoms. In addition, it has one empty orbital that can accept a certain amount of electrons from carbon. 47 As such, each boron atom in the GOQD is slightly negatively charged, which repels the electron shell of carbon away from boron and therefore increases the bond length. Variations of average B/N-C bond lengths indicate the change of the neighboring carbon bonding environment. In particular, these changes occur in the edge carbon atoms and therefore have a profound effect on the sp 2 domain size of the graphene lattice, which accordingly changes the quantum confinement, density of state (DOS) and electron-phonon coupling. Figure 3 (a)~(c) shows that the HOMO levels of oxidized and partially oxidized GOQDs are shifted to more negative values compared to that of reduced GOQD because the oxygen functional group induces p-type conductivity into the graphene lattice, which causes the Fermi level to shift 9 ACS Paragon Plus Environment


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to a more negative value. In addition, the oxygen functional group brings the localized π electronic state into the band gap, i.e., Lcb and Lvb, because the C-O covalent bond damages the sp 2 domain, which results in confinement of the π orbital.2 These bandgap states depend on the oxidation states of GOQDs. The full oxidation induces the occupied band gap state (Lvb) while partial oxidation induces the unoccupied band gap state (Lcb). The reduced GOQD has a clean band gap compared to the other two structures. Figure 4 shows the energy decay curves of electrons and holes. The simulated relaxation time scales well matches with the slow (10s to 100 s of picosecond) nonadiabatic relaxation of excited charge carrier.48 The initial electron and hole excitation levels are prepared in accord with the Kohn-sham formalism, the oscillation strength of which is given as, 49 𝑓 = where 𝜇

2𝑚 (𝜀 − 𝜀 ) 𝜇 3ℏ

(2)

= ⟨𝜀 |𝜇̂ |𝜀 ⟩ is the transition dipole moment, and 𝜀 , 𝜀 are the respective Kohan-sham

orbital, and 𝜇̂ is the dipole moment operator. The pair of Kohn-sham orbitals corresponding to the largest oscillation strength is chosen as the initially photoexcited electron and hole states, which can be further addressed with a Gaussian envelop function to represent the initial charge carrier distribution in the VB and the CB. Subsequently, the NAMD is carried out and the propagation of quantum wave packets is demonstrated in Figure 4 (j)-(l). In addition, we also increased the number of adiabatic states to study the dependency of the relaxation dynamics on the excitation level. The relaxation rates are obtained by biexponential fitting of the relaxation energy curves and averaging over the slow and fast components. The fast component is due to carrier-carrier scattering and the slow component is due to carrier-phonon scattering, as demonstrated in Nie et al’s work.14 The relaxation symmetry and hot carrier cooling rates are related to the oxidation states of GOQDs. Different oxidation-reduction states bring different extents of disorders into the graphene lattice, which change the confinement of sp 2 electrons and their localizations.2 The localization of sp2 electrons reduces carrier-carrier scattering, which causes a slower energy decay in the CBs of the GOQDox and GOQDpox than in that of GOQDre. Furthermore, the localized bandgap state gives rise to charge trapping and slows down the electronic transition, as shall be discussed below. The


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damage of the sp2 domain also changes the coupling of electronic states to the vibronic subsystem, resulting in the decrease of carrier-phonon scatterings. The symmetry of the relaxation dynamics varies with respect to the excitation level. At the lower excitation level, the electron decay is faster than the hole decay for the oxidized and reduced GOQDs while the hole decay is faster than the electron decay for the partially oxidized GOQD. At the higher excitation level, the electron and hole decay are symmetric for oxidized GOQD, the electron decay is faster than the hole decay for the partially oxidized GOQD, and the hole decay is faster than the electron decay for the reduced GOQD. Under asymmetric relaxation, the charge carrier with a faster relaxation rate has a greater opportunity to be delivered to the targeted reactant. Therefore, at the lower excitation level, the reduced GOQD is better than the oxidized and partially oxidized GOQD to catalyze the water reduction reaction, which well matches with Marco et al. ’s study.11 However, when the electron is excited to the higher excitation level, the oxidized and partially oxidized GOQDs are better than the reduced GOQD at catalyzing water reduction reaction. The electron relaxation rate increases as the initial excitation level increases, for the oxidized and partially oxidized GOQDs; however, this is opposite for the reduced GOQD, which is consistent with their NA couplings in the CBs. At the lower excitation level, the magnitudes of the relaxation times are GOQDpox > GOQDox > GOQDre, while at the higher excitation level, the magnitudes of the relaxation times are GOQDre > GOQDpox > GOQDox. At the lower excitation level, the reduced GOQD has the fastest electron cooling due to the largest NA coupling among the three systems. The oxidized GOQD has a slower electron cooling rate than that of partially oxidized GOQD due to the reduced carrier-carrier scattering caused by the damage of sp 2 domain. At the higher excitation level, the reduced GOQD has the slowest electron cooling rate due to reduced NA coupling. The electron cooling rates of the other two systems are both increased due to increased NA couplings. The hole relaxation rate of the oxidized and reduced GOQDs becomes faster at the higher excitation level, which is opposite for the partially oxidized GOQD. In the case of partially oxidized GOQD, the hole relaxation is consistent with NA couplings, i.e., the larger NA coupling corresponds to a faster relaxation according to Fermi’s golden rule; however, it is inconsistent with NA couplings for the other two systems, which suggests the phonon-mediated charge relaxation 11 ACS Paragon Plus Environment


interferes with electron scattering mediated relaxation and changes the overall relaxation dynamics in VBs. This is verified by the FTs of orbital energies in VBs; see Supplemental Figure S1. The overall electron-phonon couplings in VBs of GOQDox and GOQDre are greater than those of GOQDpox. In addition, the spectra densities for GOQDox and GOQDre are relatively uniformly distributed among all nuclear modes (0~2000 cm-1), while the spectra densities for GOQDpox are mainly distributed among the two peaks centered around 1500 cm-1 and 250 cm-1. This indicates in the GOQDox and GOQDre that the phonons can more efficiently scatter off the carriers, which benefits the carrier relaxation. Therefore, the hole relaxation rates in GOQD ox and GOQDre are faster than those in GOQDpox due to a greater number of available nuclear modes coupled with electronic states in these two systems. The electron-phonon coupling speeds up the relaxation dynamics, which causes the divergence of the relaxation in the VB with respect to the NA couplings for reduced and oxidized GOQDs. Overall, the reduced, oxidized and partially oxidized GOQDs all have asymmetric relaxations at the low excitation levels, and in particular, the slower hole relaxation in oxidized GOQD benefits the water reduction reaction, while the slower electron relaxation in partially oxidized GOQD benefits the water oxidation reaction. The reduced and partially oxidized GOQDs show asymmetric electron and hole relaxations at the higher excitation levels, and in particular, for partially oxidized GOQD, the slower hole relaxation benefits the water reduction reaction, while for reduced GOQD, the slower electron relaxation benefits the water oxidation reaction. 4.2 Electron-hole Recombination Electron-hole recombination is another factor used to determine the charge carrier lifetime in the VB and the CB in addition to charge carrier relaxation. Fast nonradiative recombination between an electron and a hole is the primary factor causing a loss of quantum efficiency and photocatalytic efficiency of a light sensitizer. Figure 5 outlines the recombination pathways in the three systems. The direct recombination corresponds to electron-hole recombination in reduced GOQDs. The electron-hole recombination in oxidized and partially oxidized GOQDs are comprised of two subprocesses: a charge transition from the LUMO to the band gap state, i.e., electron trapping, and a charge transition from the HOMO to the band gap state, i.e., hole trapping. We further inspected the populations of charge carriers of the band gap states as well as LUMO orbitals for the three systems by re-running the 12 ACS Paragon Plus Environment

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simulation with two band states using decoherence induced surface hopping: electronic transitions from the HOMO to the Lvb state (HOMO/Lvb) and from the HOMO to the Lcb state (HOMO/Lcb) for hole trapping, and electronic transitions from the LUMO to the Lcb state (LUMO/Lcb) and from LUMO to Lvb state (LUMO/Lvb) for electron trapping (Figure 6). The population decay in the LUMO orbital for reduced GOQDs proceeds faster than the other two systems, followed by oxidized GOQDs, and lastly partially oxidized GOQDs, which is consistent with their NA couplings and dephasing time scales (Table 2). The populations of the LUMO/L vb increase noticeably faster than that of the HOMO/Lvb, indicating a faster electron transition from the CB edge than that from the VB edge, which suggests a faster electron trapping than hole trapping in oxidized GOQDs (Figure 6b). In contrast, the populations of the HOMO/Lcb increase noticeably faster than that of the LUMO/Lcb suggesting a faster hole trapping for partially oxidized GOQDs (Figure 9c). Therefore, the hole trapping constitutes the fast decay channel in partially oxidized GOQDs, while the electron trapping constitutes the fast decay channel in oxidized GOQDs for electron-hole recombination. The simulated electron and hole trapping times are on the order of 10 s of a picosecond, which are much shorter than the 186 ms of charge trapping time of GQDs reported elsewhere.49 This is expected, since the result reported therein corresponds to a larger sized GQD, ca. 3~4 nm, than that of the GOQDs in our study. Reducing the dimension of graphene increases the carrier-carrier scattering and decreases the charge trapping times. During its synthesis, the graphene lattice is easily oxidized due to air exposure. Previous studies of electrochemical oxygen reduction show that the oxidation of GQDs represses their catalytic efficiencies. Since the oxidation of graphene is sometimes unavoidable, it is important to have long-lived charge carriers in the VB and the CB to improve the total number of charge carriers participating in the reaction. The asymmetric relaxation is essential for the survival of electron and hole carriers such that they cannot efficiently recombine with one another. On the other hand, the fast charge carrier tapping induced by the bandgap states is detrimental for the carrier mobilities. Therefore, it is quite beneficial to remove or at least alleviate it in graphene-based materials. In particular, the faster electron trapping in oxidized GOQD can be resolved by interfacing with an electron-extracting layer or adding chemical functionalization with electron-conducting materials, which introduce additional shallow trap states into the band gap and alleviates the fast electron trapping (Figure 5). Similarly, the faster hole trapping in partially oxidized GOQD can be resolved by interfacing with a hole-extracting layer or adding chemical functionalization with hole 13 ACS Paragon Plus Environment


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conducting materials, which alleviates the fast hole trapping. One example of illustrating our point can be found in the recent study of the relaxation dynamics of hematite, 31 in which the shallow and deep trap states jointly modulate the charge carrier lifetimes and participate in the electronhole recombination process during the charge relaxation dynamics, offering additional controllability of charge transfer efficiencies from the GOQD to the targeted reactant. 4.3 Effect of Nuclear-Induced Decoherence on the Bandgap States During charge relaxation, the phase randomization in electronic wavefunction causes the electronic decoherence. If the dephasing rate is faster than the quantum transition rate, the coherency between two electronic states is broken, slowing down the electronic transition. In particular, the decoherence between the band edge and the band gap states results in a slow charge trapping. The slower charge trapping increases the carrier mobility, resulting in a higher photocurrent. This charge trapping can be tuned by confining the electronic wave functions either via reducing the dimension of graphene or changing the edge functionalization. 50 To study the charge trapping, we need to calculate the dephasing time first. The dephasing time can be obtained by fitting the pure dephasing function by a combined Gaussian and exponential function; see Figure 7. 𝑓(𝑡) = 𝐴𝑒𝑥𝑝 −

𝑡 𝑡 + (1 − 𝐴) exp − 𝜏 2𝜏

(3)

The first term at the right-hand side, i.e., the Gaussian component, describes the slow decay of the dephasing curve. The second term, the exponential component, describes the fast decay of the dephasing curve. The pure dephasing time is calculated by averaging the times in Gaussian and exponential components, and the data are summarized in Tables 2 and 3. The pure dephasing function can be obtained by integrating the autocorrelation function (ACF) of the energy gap fluctuation. The definition of the autocorrelation function and the pure dephasing function can be found in Zhou et al.

31

and is also provided in the supporting information, part B. The computed

non-normalized autocorrelation functions (u-ACFs) for the selected pairs of electronic states are presented in Figure 8. In general, a larger initial value and a slower, more asymmetric decay of the u-ACFs lead to faster dephasing.24, 51 In particular, the initial value of the u-ACFs determines the dephasing rates, assuming the decay rates of the electron-nuclear pairs are comparable. 52


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Figure 8 show that the initial value of u-ACF for the LUMO/Lvb in the oxidized GOQD is less than those initial values of u-ACF for reduced and partially oxidized GOQDs; in addition, the decay of u-ACF is much faster than those of the other two structures, which gives rise to the longest dephasing time - 566 fs. The u-ACF for the LUMO/Lcb of partially oxidized GOQDs and HOMO/Lvb of oxidized GOQDs are more asymmetric than the others; in addition, the decay of uACF for the LUMO/Lcb is slightly faster than that for the HOMO/Lvb, both of which contribute to faster dephasing of HOMO/Lvb for oxidized GOQDs and LUMO/Lcb for partially oxidized GOQDs (Table 2). The fast dephasing in the LUMO/Lcb and the HOMO/Lvb leads to electron trapping and hole trapping, respectively, which gives rise to the slow electron decay and hole decay near the band edges, as mentioned above. The dephasing time scale of the HOMO/LUMO for reduced GOQD is 280 fs, which is shorter than that of the LUMO/Lvb for oxidized GOQDs and the HOMO/Lcb for partially oxidized GOQDs but greater than that of the LUMO/Lcb for partially oxidized GOQDs and the HOMO/Lvb for oxidized GOQDs. The electron-phonon interaction causes the dephasing. 45 The higher frequency nuclear modes correspond to the breakdown of BO approximation 54 since the electrons do not have enough time to reach the instantaneous ground state with respect to the nuclear motion, which results in the larger NA coupling vectors, i.e., ⟨𝜑 (𝑥; 𝑹)|∇𝑹 |𝜑 (𝑥; 𝑹)⟩ ∙ 𝑹̇. The larger NA couplings cause a faster electron-hole recombination, which corresponds to slower electronic decoherence due to the lack of sufficient time for electron-phonon interaction due to the fast nuclear motion. In contrast, the lower frequency nuclear modes correspond to the faster electronic decoherence due to sufficient electron-phonon interaction. To obtain those nuclear modes coupled with electronic states, one can perform an FTs of the normalized autocorrelation function. Fourier transforms of the normalized ACFs provide the vibrational frequencies contributing to the decay of the ACFs. Figure 9 shows that the dominant peak of reduced GOQDs is centered around 1250 cm -1, matching well with the referenced infrared vibrational modes.55 In addition, there are two secondary peaks with much lower intensities: one above 1500 cm -1 and another one below 500 cm1

. For the HOMO/Lvb of oxidized GOQDs, the dominant peak is centered around the lower

frequency mode that is below 500 cm-1, resulting in the shortest decoherence time. The secondary peak is centered around 1350 cm-1, corresponding to the Raman D band.54 In addition, there are a few other peaks centered around 1650 cm-1, 1100 cm-1 and 650 cm-1 with much lower intensities. 15 ACS Paragon Plus Environment


For the LUMO/Lvb of oxidized GOQDs, the dominant peak is centered around 1125 cm -1, and the secondary peak is centered around 1500 cm-1. There are a few other lower frequency peaks below 500 cm-1. Compared to those of the other two systems, the LUMO/Lvb of oxidized GOQDs has more number of peaks with moderately high intensities, which are distributed above 1000 cm -1, leading to the longest decoherence time. For the partially oxidized GOQDs, the dominant peak of the LUMO/Lcb is centered around 1650 cm-1, corresponding to the Raman G band,54 and there are a couple of secondary peaks between 1000 cm-1 and 1500 cm-1 and below 500 cm-1. For the LUMO/Lcb of GOQDs, the dominant peak is centered around 1350 cm -1, corresponding to the Raman D band. The electron-phonon interaction causes energy gap fluctuations and provides the driving force for nonadiabatic transitions. The presence of an energy gap state opens up the additional nonadiabatic decay channel inside the band gap. Due to the decoherence of electronic transitions from the band edge to the band gap state, the presence of the band gap state introduces quantum interference to the phonon-mediated electron-hole recombination dynamics, offering additional controllability of charge carrier lifetimes.

5. Conclusion In this work, we performed a nonadiabatic molecular dynamics investigation to study the phonon mediated charge relaxation and recombination in reduced, oxidized and partially oxidized GOQDs. The characteristics of relaxation dynamics depend on the oxidation state. At high excitation levels, only full oxidation presents a symmetric relaxation in GOQDs, while partial oxidation opens up a faster electron decay channel, and the reduction opens up a faster hole decay channel in GOQDs. At low excitation levels, the oxidized and reduced GOQDs have faster electron decay than hole decay. The carrier-carrier scattering induced by NA couplings have a dominant effect on electron relaxations in GOQDs; however, the electron-phonon coupling interferes with carrier-carrier scattering, leading to a divergence of relaxation rates with respect to the NA couplings in the valence band. Moreover, the partial oxidation leads to faster hole trapping than electron trapping, while full oxidation leads to faster electron trapping than hole trapping. These charge trapping states are detrimental to charge carrier mobilities in GOQDs. Therefore, based on our simulation results, we propose to hybridize GOQDs with a charge extracting layer or chemically functionalize it with electron or hole conducting materials, which inserts more electronic states inside the 16 ACS Paragon Plus Environment

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bandgap and induces additional relaxation pathways into the electron-hole recombination. Overall, our work reveals the relaxation and recombination dynamic processes in reduced, oxidized and partially oxidized GOQDs, which, to some extent, provide insight about the catalytic nature in such classes of materials. Supporting Information Time dependent density functional theory and nonadiabatic molecular dynamics (NAMD), autocorrelation Function, Fourier transforms, pure dephasing time, Fourier transforms of orbital energies and three-dimensional surface plots of average magnitudes of nonadiabatic coupling vectors. AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected]

Acknowledgement Peng is grateful for the support of the Qiqihar University for providing the computational facilities with the calculations carried out in this work.

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Figure 1. Scheme of GOQD as photocatalyst for water oxidation and reduction reactions.



(b)

(a)

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(c)

Figure 2. Structures of (a) GOQDre, (b) GOQDox, and (c) GOQDpox, optimized at 300 K. Grey color represents the carbon atom, pink color represents the boron atom, light grey color represents the hydrogen atom, red color represents the oxygen atom and green color represents the nitrogen atom.


GOQDre

4 3 2 1 0 -1 -2

LUMO HOMO

0

1000

2000

3000

(c)

GOQDox

(b) Energy (eV)

(a) Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3 2 1 0 -1 -2 -3

GOQDpox

4 Energy (eV)

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Lvb

3 2

Lcb

1 0 -1

0

1000

2000

3000

0

Time (fs)

Time (fs)

Lcb

Lvb

1000

2000

3000

Time (fs)

HOMO

LUMO

GOQDre

GOQDox

GOQDpox

Figure 3. Time-dependent orbital energies for (a) GOQDre, (b) GOQDox and (c) GOQDpox, and molecular orbital plots for the HOMO, LUMO and band gap states (Lcb and Lvb). Edge oxidation induces the occupied (Lvb) and the unoccupied (Lcb) band gap states into GOQDox and GOQDpox, respectively. The fermi level is shifted to 0.



GOQDox

3

(a)

2 Relaxation energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3

e28.7 ps

CBM+4 CBM+17

1

54.5 ps

0

(d)

(b) 41.5 ps

2

CBM+4 CBM+8

191 ps

23.6 ps VBM-6 VBM-11 0

1000

2000

(c) 134 ps

2

CBM+2 CBM+9

41.7 ps

(f) 88.1 ps

-1 -2

-3 -4

3.71 ps 0

(e)

-2

-3

GOQDre

71.4 ps

-1

-2

3

1

1 0

h+

-1

-4

GOQDpox

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102 ps

VBM-6 VBM-11 0

1000

2000

-3 -4

VBM-6 VBM-12 0

1000

2000

Time (fs)

Time (fs)

Time (fs)

24.3 ps

(g)

(h)

(i)

(j)

(k)

(l)

Initial excitation levels h+

e-

Figure 4. The upper panel are energy relaxation curves with different initial excitation levels, (a)(f). The middle panel are the time-dependent DOS, (g)-(i). The lower panel demonstrates the propagations of quantum wave packets, (j)-(l).


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Figure 5. Schematic illustration of electron-hole recombination pathways in reduced, oxidized and partially oxidized GOQDs. In the case of oxidized GOQDs, the electron trapping occurs earlier than in hole trapping due to the larger NA couplings and longer dephasing time, while in the case of partially oxidized GOQDs, the hole trapping occurs earlier than electron trapping due to the longer dephasing time. Chemical functionalization or interfacing with a charge extracting layer introduces an additional charge trapping state and additional tunability in charge carrier relaxation dynamics and their lifetimes.



(a)

0.98 GOQDpox GOQDox GOQDre

0.97 0.96 0

500 1000 1500 2000 2500

0.03 Population

0.99

LUMO/Lvb HOMO/Lvb

0.02

GOQDox

0.01 0.00

0.06

(b)

HOMO/Lcb LUMO/Lcb

0.05 Population

1.00 Population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.04

(c)

0.03 GOQDpox 0.02 0.01

0

Time (fs)

500 1000 1500 2000 2500 Time (fs)

0.00

0

500 1000 1500 2000 2500 Time (fs)

Figure 6. Population decay of reduced, oxidized and partially oxidized GOQDs in direct electronhole recombination, electron trapping and hole trapping. (a) are the populations of the LUMO orbitals for reduced, oxidized and partially oxidized GOQD. (b) are the population increase of the hole trapping states for the oxidized GOQD. (c) are the population increase of the electron trapping states for the partially oxidized GOQD.


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Figure 7. Pure dephasing functions () derived from the u-ACFs of the energy gap fluctuations for the selected pairs of states for GOQDre, GOQDox and GOQDpox.



0.006

GOQDre HOMO/LUMO

0.004 Cu(eV2)

0.004 0.002 0.000

HOMO/Lvb LUMO/Lvb

0.006

GOQDox

0.002 0.000

0.002 0.000

-0.002

-0.002

-0.002

-0.004

-0.004

-0.004

0

100 200 300 400 500 600 Time (fs)

0

100 200 300 400 500 600 Time (fs)

HOMO/Lcb GOQDpox LUMO/Lcb

0.004 Cu(eV2)

0.006

Cu(eV2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0

100 200 300 400 500 600 Time (fs)

Figure 8. Unnormalized autocorrelation functions (u-ACFs) of the energy gap fluctuations for the selected pairs of states for (a) GOQDre, (b) GOQDox and (c) GOQDpox.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Spectra density (arb.units)

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HOMO/LUMO (b)

(a) GOQDre

0

HOMO/Lvb (c) LUMO/Lvb

GOQDox

500 1000150020002500 0 -1

Frequency (cm )

500 1000 1500 2000 2500 0 -1

Frequency (cm )

HOMO/Lcb LUMO/Lcb

GOQDpox

500 100015002000 2500 3000 Frequency (cm-1)

Figure 9. Fourier transforms of the normalized ACFs of energy gap fluctuations for the selected pairs of states for (a) GOQDre, (b) GOQDox and (c) GOQDpox.



Page 30 of 33

Table 1. Averaged NA Coupling Vectors (units in meV) for Electron and Hole Relaxation. GOQDre electron relax hole relax GOQDox electron relax hole relax GOQDpox Electron relax Hole relax

number of adiabatic state 3 (0 ~ 0.79 eV) 10 (0 ~ 2.54 eV) 7 (0 ~ 1.12 eV) 13 (0 ~ 2.18 eV)

38.3 21.5 17.8 15.2

/ 15.5 14.7 12.2

/ 13.8 15.2 11.8

5 (0 ~ 1.04 eV) 18 (0 ~ 2.73 eV) 7 (0 ~ 1.39 eV) 12 (0 ~ 2.13 eV)

6.28 9.02 11.2 10.1

3.85 6.96 9.32 8.65

2.40 6.05 8.09 8.01

5 (0 ~ 1.41 eV) 9 (0 ~ 2.11 eV) 7 (0 ~ 1.42 eV) 12 (0 ~ 2.28 eV)

6.63 12.4 11.3 10.1

5.25 8.11 8.29 8.11

1.26 6.78 9.05 8.25


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Table 2. Fitting parameters of dephasing curves.

A 𝜏 𝜏

GOQDre LUMO/HOMO 0.10 730 230

GOQDox HOMO/Lvb LUMO/Lvb 0.37 0.21 34 556 233 568


GOQDpox LUMO/Lcb HOMO/Lcb 0.66 0.85 294 300 177 210


Page 32 of 33

Table 3. Average energy gaps, pure-dephasing times, average absolute NA couplings, recombination times for the selected pairs of states in the electron-hole recombination processes. GOQDre LUMO/HOMO energy gap (eV) 1.53 dephasing time (fs) 280 NA couplings (meV) 1.65 recombination (ps) 12

GOQDox HOMO/Lvb LUMO/Lvb 1.11 0.74 160 566 1.84 2.66 82 50


GOQDpox LUMO/Lcb HOMO/Lcb 0.64 1.24 254 287 4.61 2.02 71 11

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