Understanding the Mechanism of Plasmon-Driven Water Splitting: Hot Electron Injection and Near Field Enhancement Effects

Utilizing plasmon-generated hot carriers to drive chemical reactions has currently become an active area of research in solar photocatalysis at the nanoscale. However, the mechanism underlying exact transfer and the generation dynamics of hot carriers, and the strategies used to further improve the quantum efficiency of the photocatalytic reaction still deserve a further look. In this work, we perform a nonadiabatic excited-state dynamics study to depict the correlation between the reaction rate of plasmon-driven water splitting (PDWS) and the sizes of gold particles, the incident light frequency and intensity, and the near-field’s spatial distribution. Four model systems, H2O and Au20@H2O separately interacting with the laser field and the near field generated by the Au nanoparticle (NP) with a few nanometers in size, have been investigated. Our simulated results clearly


Introduction
Plasmonic metal (typically Au, Ag, and Cu) nanoparticles (MNPs) have extremely important applications in many fields due to their characteristic optical properties 1-3 such as localized surface plasmon resonance (LSPR). When the incident light induces the collective oscillation of metal free electrons, LSPR occurs in those MNPs. 4,5 However, this coherent electron oscillation can dephase quickly by nonradiative decay, [6][7][8][9] generating electron-hole pairs with higher energy in non-equilibrium state (i.e., hot carriers) at the timescale of 1-100 fs. 10 During dephasing, the collective dipole moment decreases along with the near-field interaction and scattering probabilities, with the incident energy converted into a hot carrier distribution. 1,11 When molecules are adsorbed on the metal nanostructure surface, the hot electrons can be transferred to the empty states of adsorbates before thermalization and create a transient negative ion (TNI). [12][13][14][15] With the response of molecular geometry, TNI moves on the excited-state potential energy surface, and therefore their reactive capability is mediated. The plasmon-induced photochemical reactions have different properties from thermal activation, and have the potential to efficiently convert solar energy into chemical energy. 2,8,16 In general, there exist two pathways for hot electron transfer, the conventional indirect transfer and the recently proposed direct transfer. 14,[17][18][19] In indirect electron transfer process, 20 hot electrons are first generated in the plasmonic metal nanoparticle, then inject into the adsorbate. For direct electron transfer, 18,21 in the presence of empty hybridized orbitals due to the strong metal-adsorbate coupling, chemical interface damping 22,23 can induce the plasmon dephasing directly and generate nonthermalized electrons in the empty hybridized orbitals. The plasmon-induced hot carrier transfer has been utilized to foster various photochemistry processes, such as the dissociation of H 2 , 24-26 N 2 , 27 and O 2 , 28,29 CO 2 reduction, 15,30 water splitting [31][32][33] and organic transformations. 34 The solar photocatalytic water splitting is a promising method for hydrogen production. This process usually take place in metal-semiconductor heterojunctions where plasmons enhance photoconversion in the semiconductor via three mechanisms, including light trapping, hot electron/hole transfer, and plasmon-induced resonance energy transfer. 16,35 The solar water splitting in a Schottky-free junction has been recently found by Robatjazi et al., 36 who observed large photocurrents as a result of direct injection of hot electrons from plasmonic Au NP to molecules. Many theoretical works started to explore the mechanism by investigating the effect of laser intensity and frequency on photocatalytic activity. For example, Meng's group 31 simulated the H 2 O splitting dynamics on Au nanosphere using TDDFT/Ehrenfest dynamics scheme and found the strong correlation between laser intensity, hot electron transfer, and reaction rates. Zhang et.al. 25 focused on the H 2 dissociation induced by Au spheres and found that the dissociation rate of H 2 was closely related to the molecular initial positions. In above two works, the Au particles were identified by the Jellium spheres. The Jellium model is the simplest physical model for the valence electrons, it replaces the real geometry of the metal ionic core by a featureless positively charged background in a finite volume and treats only delocalized electrons explicitly in the mean-field approximation, such as the Hartree-Fock or the local density approximations. The jellium model neglects the lattice structures of metal spheres, and hardly describes the interaction between the metal and adsorbates, and the effect of lattice's vibration. Furthermore, the LSPRs of MNPs are largely dependent on the MNP's shapes and sizes. It is essential to involve those effects in describing plasmon-mediated chemical reactions.
In this work, we investigate the dynamic process of water splitting driven by Au cluster and NPs with a few nanometers in size under femtosecond laser pulse. We explore the related mechanisms of H 2 O splitting and hot electron injection, and reveal the relationships between the reaction rate and the incident light intensity and frequency, and NP's sizes. The real-space real-time TDDFT/Ehrenfest dynamics schemes is adopted. Four model systems, H 2 O and Au 20 @H 2 O interacting with the laser field and the near field generated by different sized NPs, have been investigated. The water molecule is assumed to bind with one of the vertexes of Au 20 . Au 20 has a tetrahedral structure and is highly stable and chemically inert. 37,38 The tetrahedral Au20 is a fragment of the face-centered cubic lattice of bulk gold with a small structural relaxation, a unique molecule with atomic packing similar to that of bulk gold. 38 For H 2 O and Au 20 @H 2 O systems, their electronic degrees of freedom were treated quantum mechanically within the real-space real-time implementation of time-dependent density functional theory (TDDFT), while their nuclei were handled classically.
Currently, it is still a great challenge to describe the excited-state dynamics of the hybrid system of molecule-MNPs with large sizes without using the jellium approximation to the MNPs. Here, we thus divide the nanosized tetrahedron into two parts: the tetrahedral cluster Au 20 and the residue, where Au 20 is described by TDDFT and the interaction of the residue to Au 20 @H 2 O is identified by the near field to which Au 20 @H 2 O is subjected. The near field is obtained by the numerical solution of Maxwell's equations using the classical computational electrodynamics finite-difference time-domain (FDTD) technique. With this regard, the interaction of metal-molecule is described at the atomic level and the strong near-field enhancement effect of NPs can also get involved.

Theoretical and computational details
The real-space real-time TDDFT calculations reported in this work are carried out using the open-source OCTOPUS code (version 9.2). [39][40][41] The simulation grid is localized spherically around each atom with a radius of 8.00 Å, and the grid point is set to be 0.20 Å which is considered as the balance of simulation accuracy and time consumption.
where v f ield (r, t) describes the time-dependent electric field acting on the system, {ϕ i }(i = 1, 2, ..., N ) are the occupied Kohn-Sham orbitals,ĥ is the Fock operator and n is the one-electron density. R α stands for the coordinate of the nucleus labeled α, m α for its mass, and F α for the force exerted on it.
The laser field is assumed to polarize along the +z direction with the function form: , where |E 0 max | denotes the amplitude of external electric field, ω 0 is the excitation frequency, t 0 = 6.60 fs is the center of Gausstype laser and τ = 1.60 fs is the width of laser pulse. When the water molecule is in the proximity of the nanosized Au tetrahedron, the field E(r, t), interacted with Au 20 @H 2 O, includes the incident laser field ⃗ E 0 (t) and the scattered field ⃗ E sca (r, t) generated by the truncated tetrahedron (Au 20 is cut off from this nanosized tetrahedron). This inhomogeneous near field can be expressed as is the spatial function that represents the non-uniform distribution of fields and E t (t) is the temporal function which matches the incident laser pulse. In order to describe the non-uniformity of the enhanced near-field, we need to obtain the expression of the spatial function E s (r). In this work, we applied fifth-order polynomial to fit the spatial function E s (r) , r represent the coordinate of the space grid and a i are the fitting parameters.
The classical electromagnetic simulations to the Au NPs are performed using the FDTD++ package. 49,50 The Maxwell's equations are solved using Yee's algorithm. 51,52 Considering that Au 20 is a fragment of the face-centered cube lattice of bulk gold, or a part of the whole large-sized tetrahedron, we choose the shape of Au NP to be tetrahedral. The other reason for our choice is that we know that a weak laser field can induce an intensive near field near the apex of Au tetrahedron, even when the size of NP is small. The dielectric function of Au tetrahedron is describe by Drude-Lorentz model 53 in the form of The parameters of dielectric function are shown in Table 1. 54 The cubic simulation box with a side length of 40.00 nm and a grid size of 0.20 nm is adopted in all FDTD calculations. We use the geodesic Levenberg-Marquardt (LM) algorithm 47,48 to fitting the FDTD field into a polynomial function which can be read in every TDDFT time step.We note that the current FDTD method is a classic electromagnetic model, the quantum size effect in Au NPs is ignored, which can be accounted for by the nonlocal hydrodynamic model. 55,56 The neglecting of the quantum effect may bring some errors to the field enhancement. For a metal tetrahedron with the side length longer than 3 nm, however, its quantum size effect seems not so obvious. 57 The excited-state population is computed by using orbital projections. The occu- and the normalization condition is 3 Results and discussion  The OH bond near the apex of Au 20 is prone to breaking firstly, attributed to the initial structural arrangement. As Figure 1 shows, we set one of H atom of H 2 O to bind with Au atom in the apex of Au 20 and the other to be away from the apex. With this structural arrangement, the symmetry of H 2 O breaks down. As the MO of No. 125 in Figure   1(c) shows, the wavefunction overlap between two OH bonds of H 2 O and Au 20 will be different, indicating that their ability to accept electrons will be different. With this regard, the asymmetric dissociation appears in PDWS process.
To obtain the information of products of water splitting, we compute the Hirshfeld Next we examine the dependence of the dissociation rate on the laser intensity and frequency. The dissociation rate of H 2 O molecule is defined as the inverse of time required for the first OH bond length to reach 2.00 Å. As shown in Figure 3a, initially, the splitting rate increases linearly as E 0 max increases from 1.80 V/Å to 2.20 V/Å. A maximum rate appears at 2.20 V/Å. When the field intensity is further increased, the rate doesn't change obviously. To get insight on this phenomenon, we plot the time-evolution of OH bond length at E 0 max = 2.80 V/Å in Figure 3c, and find that both of two OH bonds are dissociated at this case. The intensive laser field can drive two OH bonds to break one after another though the reaction rate doesn't change obviously. As the light field increases from 1.80 V/Å to 2.80 V/Å, there is a transition from water splitting to water fragmenting, and the dissociation rate of OH bond even decreases.
To unveil the possibility of water fragmentation, we perform a calculation of absorption spectra of Au 20 @H 2 O with the varied laser intensity. Figure S4 in SI shows the calculated results. We observe that as the field intensity continuously increases, the intensities of high-energy absorption bands with excitation energies ≥ 2.9 eV decrease and their peak locations blue-shift while the intensities of low-energy absorption bands continuingly increase. These phenomena manifest that the intensive laser fields couple with the system Au 20 @H 2 O nonlinearly. 64 The decrease of the high-energy absorption and the integrated energy shift are attributed to the absorption saturation and the field dressing during the excitation. The appearing and continuing increasing intensity of low-energy bands confirms that the multiphoton absorption occurs. This nonlinear coupling between the system and laser field definitely affects the dynamics of water splitting and may lead to the water fragmentation. Figure 3b shows that the splitting rate varies with the laser frequency. The maximum rate appears at ω 0 = 2.95 eV, not at 3.20 eV, indicating that more hot electrons are transferred when the frequency of the incident field matches the energy gap between Fermi-level and AB orbital, namely, the hot electrons injection mechanism in water splitting reaction follows the direct one. 11,25

Electronic/Nuclear dynamics of nanosized tetrahedron@H 2 O
To simulate the plasmon-induced water splitting reaction with Au particle at the nanometer scale with mixed TDDFT/FDTD method, we firstly calculate the time-dependent spatial inhomogeneous scattering field generated by the truncated Au tetrahedron via FDTD++ package, then describe the time evolution trajectory dynamics of Au 20 @H 2 O system under the intensive near field by TDDFT/Ehrenfest scheme. With this treatmen- t, the hot electron injection is assumed to always appear around the interface between the metal cluster and the adsorbate, and the different sized NP provides the near field with different intensity to which Au 20 @H 2 O is subjected, as Figure 4 shows. bond oscillates at a certain frequency, and there is no sign of splitting. These numerical simulations suggest that the near field can enhance the reaction rate of water splitting and one can adjust the size of metal NP to control the plasmon-assisted photochemistry via field enhancement effect. However, without the injection of hot electrons, the water splitting reaction will not take place, which highlights the decisive factor to drive the water splitting.
To show the field enhancement effect, we calculate the absorption spectra and near fields of the truncated Au tetrahedrons with different side lengths of 2.88 nm, 4.32 nm, and 5.76 nm in Figure S5 and Figure  The near field decays rapidly with the surface separation as Figure S6 shows. To have a clear picture on the effect of the near field's inhomogeneity on the water splitting, we perform the TDDFT/Ehrenfest dynamics of Au 20 @H 2 O interacted with the real near field generated by the truncated Au tetrahedron with L=2.88 nm and the uniform electric field taken from the center of mass of Au 20 @H 2 O generated by the same NP, respectively.
In this case, a very weak laser field with ω 0 = 3.07 eV and E 0 max = 0.65 V/Å is applied. As Figure S7 shows, the duration of scattered field at the center of mass of Au 20 @H 2 O is much longer than the incident field, the scattered field's amplitude is magnified about three-fold so that the OH bond disassociates even with a weak laser field. Figure 6 displays the evolution of OH bonds in Au 20 @H 2 O which is interacting with the two kinds of fields, respectively. In the laser activity window, in the case with a uniform field, the change of OH bond length shows an "upward arc", while in the real near field case, it shows as a "downward arc". The near field generated from LSPR is a very short-range electromagnetic field with a strong intensity gradient which may generate gradient force to affect the molecule. 62,63 To explain why the field's spatial distribution can affect the evolution of OH bonds with the time, we compare the forces acting on H 2 O molecule in Figure S8 and Figure S9.
During the laser activity window ( from 6.60 fs to 6.84 fs), the results with the uniform field and the near field are quite dissimilar. In the uniform field, the force vectors in the XZ plane act on the H 2 O molecule are affected by the field and electron injection, and its direction and magnitude change rapidly. While in the near field, the force vectors in the XZ plane always point to the 'tips' of Au 20 , especially the force acting on O atom. It is known that this direction is also the negative gradient direction of the field. We thus suggest that the inhomogeneous near field affects the water splitting reaction through the gradient force and causes a different reaction during the field active window.

Concluding Remarks
We have presented a theoretical study on the PDWS via TDDFT/Ehrenfest nonadiabatic dynamics. By comparing the calculated results of four model systems: H 2 O and Au 20 @H 2 O separately interacting with the laser field and the near fields, we clearly reveal the microscopic mechanism of PDWS and the interface electron transfer, and the correlation of the reaction rate with the laser field frequency and intensity, the NP's sizes, and the field's spatial distribution. A multiscale scheme has been applied to describe PDWS dynamics. For H 2 O and Au 20 @H 2 O systems, its electronic degrees of freedom were treated quantum mechanically within the real-space real-time implementation of TDDFT, while their ions were handled classically. For the system with larger sized NP, we divided this NP into Au 20 + residue, where Au 20 was described by TDDFT and the truncated NP was described by FDTD.
The main conclusions are summarized as follows: (1) The electrons populated on the AB orbitals of H 2 O are mandatory to drive the OH bond breaking. The strong orbital hybridization between Au 20 and H 2 O creates the condition for photo-induced direct electron injection.
(2) The dynamic results under different laser intensity unveil that the linear dependence of reaction rate of PDWS and the incident field amplitude holds only at a relatively weak field, however the linear correlation breaks down by the participation of other reactions such as water fragmenting in the intensive field regime. The splitting rate varies with the laser frequency, and the maximum rate appears when the laser frequency matches the energy gap between the metal Fermi-level and AB orbital.
(3) To describe the effect of field enhancement induced by large-sized Au NPs, the mixed FDTD/TDDFT method is used. By dividing the large sized NP into Au 20 + Residue, the requirement of near-field enhancement and hot-electron injection in the water splitting reaction can be simultaneously satisfied. Setting the water near the apex of large-sized tetrahedron, OH bonds cab be disassociated by a very weak laser field.
(4)The intensive electric field can make two OH bonds in Au 20 @H 2 O system break successively, attributed to the nonlinear coupling between the system and the applied field. When the intensity of the incident field reaches a certain degree, the field couples with the system nonlinearly, opening the possibility of multiphoton absorption. These hot electron excited by multiphoton absorption can give important contributions in H 2 O splitting reaction.
(5) The influence of the field's spatial distribution on water splitting is significant.
The gradient force caused by the strong intensity gradient of the near field makes the distinction of force vectors in XZ plane compared to those in the uniform field case, leading to the different OH bond evolution dynamics.
This work is useful for understanding the hot electron induced reactions at ambient conditions by plasmonic excitations and can provide a reference for the development of related mixed quantum-classical method in describe the large-sized plasmonic system.

Support Information Available
The materials in SI include the DOS of isolated H 2 O molecule, the evolution of OH bond when an isolated H 2 O molecule interacts with the laser field, the time evolution of OH bonds in Au 20 @H 2 O system under the laser field with E max =1.60 V/Å and E max =1.70 V/Å), the absorption spectra of Au 20 @H 2 O vary with the intensity of incident field, the absorption spectra of Au tetrahedrons with L=2.88 nm, 4.32 nm, and 5.76 nm calculated by FDTD, the contour plot of near fields, the time evolution of the forces acted on H 2 O molecule in the XZ plane under a uniform field and the real near field, respectively.