Introduction

Hematite (α-Fe2O3, hereafter Fe2O3), one of the most important transition metal oxides (TMOs), shows widespread applications, for example, corrosion, iron-cycling in geochemistry and biochemistry, dye-sensitized solar cells1, and photoelectrochemical (PEC) cells2. During the last several decades, especially, PEC water splitting has turned out to be a potential technique in alleviating the global energy issues by generating clean hydrogen fuel3,4,5. Fe2O3 is considered to be a promising photoanode material for PEC water splitting6, due to its advantages such as visible light response (bandgap of ~2.1 eV), valence band potential positive for water oxidation, long-term stability in neutral and alkaline solutions, low cost, earth-abundance, and nontoxicity7. However, the reported conversion efficiencies of solar energy into hydrogen are still left far behind its theoretical value of ~16.8%8, due in part to the low solar-to-chemical conversion efficiencies of hematite photoanodes6,8.

The low PEC efficiency for Fe2O3 was primarily assigned to its small charge carrier mobility, short charge carrier lifetime, and sluggish kinetics of oxygen evolution reaction2,9. Early studies of ex situ ultrafast transient absorption indicated that the charge recombination in Fe2O3 is ultrafast, nonradiative, and multiexponential10,11,12,13,14,15,16. Later on, the dynamics of hole charge gained ever-growing attention due to the water oxidation at Fe2O3 photoanodes deployed in PEC cells. The lifetime of photogenerated holes in Fe2O3 was reported to be about three orders of magnitude shorter than that in TiO217, which however can be extended to microseconds with electric bias by suppressing electron–hole recombination18,19,20,21,22.

Recently, the Fe2O3 polarons dynamics got special interest due to the rapid development of new experimental techniques. Polarons are formed by self-trapping charge carriers and simultaneously deforming the local lattice, thus generally causing small charge-transport ability and manifesting strong electron–phonon interaction. The concept of polarons23 was initially introduced in Fe2O3 to rationalize the abnormally low charge mobility24,25, which is about 105 times smaller than that of the conventional silicon semiconductor6,26. Experimental confirmation of electron polarons (EPs) in Fe2O3 was for the first time reported by Katz et al. by using time-resolved X-ray transient absorption spectroscopy (TAS) over Fe2O3 nanoparticles with excess electrons injected from photoexcited dye molecules27,28. After that, some groundbreaking experiments opened new avenues for exploring the roles of polarons in the excited-state dynamics of Fe2O329,30,31,32, which turn out to be key issues affecting the performance of Fe2O3 photoanodes, for example, ultrafast trapping of photoexcited charge carriers7,30,31,32,33,34 and poor device photovoltage6.

By using femtosecond extreme ultraviolet TAS, Carneiro et al. reported that the formation of polarons in Fe2O3 began within 100 fs, the formation process continued for about 2–3 ps, and the decay process lasted for more than 300 ps under several optical excitations30. Biswas et al. observed a similar process for the formation of electron and hole polarons in Fe2O3 by using femtosecond extreme ultraviolet reflection–absorption spectroscopy32. However, a timescale of 660 fs was attributed to surface trapping of the photoexcited EP formation which is demonstrated to be irrelevant to grain boundaries and surface defects and thus intrinsic to Fe2O331,32. Recently, an in situ observation of EPs re-excitation in Fe2O3 PEC cells was reported by Pastor et al.34 through using the pump–push photocurrent detection and TAS, which offers a strong argument for the formation of EP in Fe2O3 and its role in the PEC performance. A timescale of 600 fs was reported therein and attributed to the localization of delocalized electrons to the polaronic state.

On the other side, substantial efforts have been devoted to theoretical simulations on the properties of EPs and hole polarons (HPs) in Fe2O335,36,37,38. It has been demonstrated that the related properties depend on the choices of cluster or extended systems and Hartree–Fock or density functional theory (DFT)-based electronic structure methods. For example, localization of HPs on Fe or O sites or both is still in debate in both experiment39,40,41,42 and simulation37,38. In the framework of Marcus’s theory, transport of EPs and HPs in Fe2O3 and the effect of dopants were investigated by using both cluster and extended models with unrestricted Hartree–Fock, complete active space self-consistent field43,44,45,46, or DFT at the level of generalized gradient approximation (GGA), including Hubbard correction (U)26,47. Our previous work based on ab initio molecular dynamics (AIMD) simulations visualized the hopping process of an EP in Fe2O3 and uncovered the role of Si dopant in speeding up the polaron hopping48. To date, simulations on the excited-state dynamics of polarons in Fe2O3 are still unavailable, leading to a lack of insights which are fundamental for understanding the nature of excited states dynamics and thus the limitation factors related to the poor PEC performance of Fe2O3 photoanodes.

In this work, we aim to establish the mechanism for the dynamic processes of EP formation and EP interactions with free holes or HPs in Fe2O3 leading to nonradiative charge losses, which are rarely simulated because such simulations require advanced simulation methodologies49. In order to address these issues, we designed a scheme to access the timescale for the formation of small EPs in Fe2O3. This scheme is made up of a series of ab initio AIMD simulations with the initial structure for each simulation randomly sampled from the AIMD trajectory of pure Fe2O3 and meanwhile addition of an extra electron as a perturbation in charge density. The simulations show that EP formation is adiabatic with ultrafast electron motion at the timescale less than 15 fs, reasonably agreeing with the recent experiments30,31,32,34. Nonadiabatic molecular dynamics (NA-MD)50,51 simulations combined with time-dependent density functional theory (TDDFT)52,53,54 in the Kohn–Sham formulation were performed to study nonradiative recombination of EPs with photogenerated holes. Two types of recombination were considered, i.e., recombination of an EP with a delocalized hole in Fe2O3 with an electron, Si, or Ti atom doping and recombination of an EP with a localized hole in Fe2O3 with constrained electron and hole excitation. Our results show that EP recombination with delocalized hole takes place on about 5 ps, which is faster by a factor of about 20 than EP recombination with localized hole that proceeds more than 110 ps, which is in good agreement with the recent experiment30. The occurrence of long-lived EPs is attributed to the weak NA coupling and fast loss of coherence. This study offers us new insights of excited-state dynamics of polarons in Fe2O3 which are distinct from those in rutile TiO249, and provide a concept for designing high-performance TMOs photoanodes from the viewpoint of polaron dynamics.

Results and discussion

To explore the excited-state dynamics of EPs in Fe2O3, two types of EP models were considered. Model I contains only an EP, which was obtained via either electron injection (e@EP) or foreign Si and Ti atom doping (Si@EP, Ti@EP), as shown in Fig. 1a, b. Si and Ti dopants were considered here because of the capability of donating an electron and the popularity in improving water oxidation at Fe2O3 photoanodes2,55. Model II contains simultaneously an EP and a localized hole, i.e., a small HP. Upon photoexcitation, the photoexcited electron and hole in Fe2O3 experience the delocalized states first, as shown in Fig. 1c and detonated as photon@DS, and then rapidly relax to the more stable localized states and form the EP and HP (photon@EP&HP), as shown in Fig. 1d.

Fig. 1: Structures of two types of polarons in Fe2O3.
figure 1

EP localized at an Fe site in Fe2O3 with (a) injection of an excess electron, defined as e@EP, and (b) Si or Ti doping, defined as Si@EP or Ti@EP. Photoexcited electron and hole in Fe2O3 of (c) delocalized states, defined as photon@DS, and (d) localized states, defined as photon@EP&HP for which a dashed orange circle highlights the HP localized at a Fe atom (green) and its six coordinating O atoms (blue). Fe3+, Fe2+, O2−, and dopant atoms were depicted in brown, cyan, red, and carmine, respectively, and the isosurfaces of electron and hole charge densities are shown in purple and cyan.

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Geometric and electronic structure of EPs at 0 K

The formation of small polarons in Fe2O3 is sensitive to the Fe–O bond length48,56. The calculated average Fe3+–O bond length is 2.04 Å in the pure Fe2O3, which was elongated to 2.11, 2.13, and 2.11 Å for the average Fe2+–O bond length during polaron formation in e@EP, Si@EP, and Ti@EP, respectively, associated with the reduction of an Fe3+ ion to an Fe2+ ion and lattice expansion. The Fe2+-O bond elongation by ~0.08 Å is consistent with the previous investigations35,36. For photon@EP&HP, photoexcitation induces the redox reaction in Fe2O3, giving rise to the average Fe2+-O bond length of 2.12 Å and Fe4+–O bond length of 1.99 Å due to the larger radius of Fe2+ than Fe3+ and the smaller radii of Fe4+ and O− than Fe3+ and O2−. The computed magnetic moment on an Fe3+ ion in the pure Fe2O3 is 4.14 μB. After electron injection and Si or Ti doping, an Fe3+ ion is reduced to an Fe2+ ion with the local magnetic moments decreased to 3.62 μB in e@EP, 3.67 μB in Si@EP and 3.64 μB in Ti@EP. For photon@EP&HP, the magnetic moment of an Fe3+ ion is reduced to 3.63 μB of an Fe2+ ion which is assigned to the EP and to 3.70 μB of an Fe4+ ion which is attributed to the HP, while the changes in the magnetic moments of the six O atoms coordinating the Fe4+ ion are relatively small. The calculated magnetic moments of the Fe2+ ions agree well with the previous report48, and the change in the magnetic moment of Fe4+ relative to Fe3+ is similar to that obtained using the PBE0 functional with low fraction of the exact exchange37. To determine the location of the EP site, we calculated the total energies of all possible EP sites in the Si- and Ti-doped Fe2O3 supercell and compared their energy difference with respect to the most stable EP, as shown in Supplementary Fig. 1. The same Fe ion was chosen for the e@EP.

Figure 2 shows the projected density of states (PDOS) and charge densities of the valence band maximum (VBM), conduction band minimum (CBM) and polaron states of pure Fe2O3, e@EP, photon@DS and photon@EP&HP. For pure Fe2O3, the VBM and CBM are composed primarily of O 2p and Fe 3d orbitals, respectively, see Fig. 2a. For e@EP, the EP occurs as a mid-gap state with the electron charge localized at an Fe site and the VBM remains delocalized over majority of the supercell, see Fig. 2b. Similarly, Si and Ti doping also lead to localized EPs and delocalized VBMs36,48,57, as shown in Supplementary Fig. 2. Following photoexcitation of pure Fe2O3, electrons in the VB would be promoted into the CB. Figure 2c shows a pair of delocalized CBM electron and VBM hole. Driven by electron-vibrational interaction, the delocalized electron and hole further decay and form a pair of stable EP and HP accompanied with local lattice distortion. As shown in Fig. 2d, the EP is localized at an Fe site and the HP is resided around another Fe site and the six O atoms next to it, which is similar to the recent theoretical simulation of Fe2O3 by using the HSE functional with 12% of exact Exchange38. The enlarged PDOS shown in Supplementary Fig. 3 shows that the EP and HP states are dominated by the Fe-d orbital and the hybridized Fe-d and O-p orbitals, respectively, agreeing well with the charge density analysis.

Fig. 2: Electronic structures for two type of polarons in Fe2O3 and the corresponding charge recombination processes.
figure 2

Projected DOS for (a) pure Fe2O3, b e@EP, c photon@DS, and (d) photon@EP&HP. The insects indicate the charge densities of the VBM and CBM state in (a), the VBM and EP state in (b), the VBM and CBM state in (c), and the EP and HP state in (d). Analyses are focusing on the spin-up component in which polarons are present in the defective systems. Schematic potential energy surfaces for describing two type of charge recombination processes of (e) the EP and the delocalized hole at VBM in e@EP and (f) the EP and HP in photon@EP&HP. Note that the photoexcitation and subsequent electron trapping by EP in (e) are hypothetical processes which are represented by the dashed line (photoexcitation) and circles (electron and hole), but they are simulated processes in (f) by using ΔSCF and are represented by the solid line and circles.

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AIMD simulations of EP formation dynamics

The experiment confirmed that EPs can be formed in Fe2O3 by electron injection from photoexcited dye molecules58. However, how the EP was formed in Fe2O3 at atomistic level remains unclear yet. According to our previous work48, the transition of the local magnetic moment on an Fe ion from ~4.1 to 3.6 μB corresponds to the electron transfer from Fe3+ to Fe2+, thus demonstrating the EP formation. Figure 3a shows two types of EP formation in the current AIMD simulations, i.e., instantaneous EP formation in most cases and delayed EP formation in few cases. The possibility of the two types of EP formation is summarized in Fig. 3b. The former arises due to the initial structures with appropriate Fe–O bond lengths to accommodate EPs. However, the latter conveys an important message that the EP formation proceeds with the added electron changing from a delocalized meta-stable state to a localized stable state. This process is adiabatic with the timescale of sub-15 fs, which is ultrafast in relation to the EP recombination (see below). We notice that the formation time is shorter than the values from two experimental reports30,34. The discrepancy can be attributed to the hot electron relaxation within the CB which was not considered here. The hot electron relaxation is a common process in experiments where electrons in the VB were pumped with 400 nm light to the CB34. According to our previous report, the process took about 100 fs to the CBM although the specific values depended on the initial state above CBM59. Taking this situation in mind, the current simulations agree well with the experiments30,34. For more details of the EP formation in Fe2O3, refer to Supplementary Fig. 4. The calculated energy to re-excite the EP to the delocalized state within CB is about 1.08 eV and agrees well with a previous report34, which is much larger than the thermal energy at room temperature (kBT = 0.025 eV). The ultrafast EP formation by self-trapping of free electrons reduces charge carrier mobility and is expected to be detrimental to PEC water oxidation. As reported recently, re-excitation of EPs in Fe2O3 by near-IR light correlates well with the improvement in photocurrent of Fe2O3 photoanodes34. Consequently, retarding the self-trapping process or re-exciting EPs to the CB may be alternative strategies to alleviate the ultrafast EP formation and improve the water oxidation at Fe2O3 photoanodes.

Fig. 3: Ultrafast electron polaron formation in Fe2O3.
figure 3

a Evolution of the interested Fe magnetic moment in the first 20 fs of the AIMD simulation on each structure which was prepared by adding an electron in the snapshot sampled from the trajectory of pure Fe2O3. More details can be found in Supplementary Fig. 4. b Probability of the two types of EP formation derived from the 39 AIMD simulations. “instantaneous” means an EP was formed at the first step of the AIMD simulation and “delayed” means after a period of time an EP was formed.

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NA-MD simulations of EP recombination dynamics

In the current NA-MD simulations, the initial state for the first type of EP recombination is the excited state composed of an EP and a VBM hole, see Fig. 2e. This initial state was prepared by assuming photoexcitation of an electron from the VBM to the CBM with a hole remained at the VBM in Fe2O3 containing an EP, corresponding to the e@EP, Si@EP, and Ti@EP systems. The charge distribution of the EP and VBM in each ground state was shown in the inset of Fig. 2b for e@EP and Supplementary Fig. 2 for Si@EP and Ti@EP. In the second type of EP recombination, the initial state corresponds to the excited state composed of an EP and an HP (photon@EP&HP), see Fig. 2f. In this case, the initial state was prepared using ΔSCF by photoexcitation of an electron from the VBM to the CBM of pristine Fe2O3 ground state followed by interacting with lattice, leading to formation of an EP and an HP. The charge distribution of the EP and HP of this excited state is shown in the inset of Fig. 2d.

Electron-vibrational interaction

Nonradiative charge recombination correlates with electron-vibrational interactions. Figure 4a, b shows time evolution of the energies of all the states involved in the EP recombination processes. The energies of the EP and HP states for photon@EP&HP fluctuate more violently than those of the EP and VBM states for e@EP, suggesting stronger electron-vibrational interactions in the former system. The coherence between the pairwise states was further inspected by unnormalized autocorrection functions (un-ACF) of the phonon-induced fluctuation in the energy gaps, i.e., EP-HP for the photon@EP&HP and EP-VBM for the e@EP, as shown in Fig. 4c. Generally, larger initial value, slower and more asymmetric decay of un-ACF favor faster dephasing60,61, especially the initial value62. The elastic charge−phonon scattering is responsible for the phonon-induced loss of coherence within the electronic subsystem, which is determined by the pure-dephasing function of the optical response theory63. Fits of the pure-dephasing functions derived by integrating the un-ACFs with the Gaussian function of exp (−0.5(t/τ)2) lead to the pure-dephasing times τ of 3.62 and 4.84 fs for the photon@EP&HP and e@EP, respectively, as shown in Fig. 4d. Inelastic charge phonon scattering creates NA coupling and accommodates the excess energy lost during EP recombination. To identify the phonon modes that couple to the electronic transition, Fourier transforms of the un-ACF of the phono-induced fluctuations in the energy gap of EP-VBM of e@EP and EP-HP of photon@EP@HP were computed. Figure 4e exhibits multiple low-frequency phonon modes in the photon@EP&HP, which correspond to the infrared- and Raman-active vibrational modes observed experimentally64. The sum of them surmounts the high-intensity major peak around 550 cm−1 in the e@EP that is similar to the vibrational mode occurring in Fe2O3 with an oxygen vacancy59, driving faster pure-dephasing.

Fig. 4: Electron-vibrational interaction for e@EP and photon@EP&HP.
figure 4

Evolution of the orbital energies of (a) the localized EP and delocalized VBM states for e@EP and (b) the localized EP and HP states for photon@EP&HP, (c) unnormalized autocorrelation functions derived from the two energy gaps, (d) pure-dephasing functions, and (e) influence spectra of EP-VBM for e@EP and EP-HP for photon@EP&HP.

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Figure 5a, b shows that time evolution of the energies of the EP and VBM states for the Si@EP and Ti@EP. The energy of the EP states fluctuates slightly more violently than that of e@EP, see Fig. 4a. Fourier transforms of the un-ACF of the fluctuation in the EP-VBM energy gap characterize the vibrational modes participating in the EP recombination, see Fig. 5c, d. The infrared- and Raman-active vibrational modes observed experimentally64 appeared for Si@EP and Ti@EP as well, which are similar to those in photon@EP&HP but activate more phonon modes with low intensities due to symmetry breaking induced by dopants. The high-frequency modes around 600 cm−1 dominate the influence spectra and lead to strong NA coupling. The presence of multiple phonon modes leads to fast loss of coherence, corresponding to the pure-dephasing times of 4.55 and 4.51 fs for Si@EP and Ti@EP, respectively, see Fig. 5e, f, which are very close to 4.84 fs for e@EP. The similar pure-dephasing times of the Si@EP and Ti@EP systems are attributed to the similar spectral densities, see Fig. 4e.

Fig. 5: Electron-vibrational interaction for Si@EP and Ti@EP.
figure 5

a, b Evolution of the orbital energies of the EP and VBM states, (c, d) influence spectra, (e, f) pure-dephasing functions for Si@EP and Ti@EP.

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Nonradiative charge carrier recombination

Population evolution of EP states in the four models is shown in Fig. 6, and fitting the decay curves to the exponential function, P(t) = exp(−t/τ), gives the recombination time τ. The recombination between the EP and HP state is estimated to proceed about 110 ps, in good agreement with the lifetimes reported in recent experiments16,30. The recombination time is about 26 times larger than the time of 4.2 ps between the EP and VBM state for e@EP, greatly prolonging the lifetime of EPs. The recombination times of 5.1 and 5.6 ps for Si@EP and Ti@EP are slightly longer than that for e@EP, consistent with the experimental observation in ref. 14 that the charge carrier dynamics in Ti-doped Fe2O3 are slightly slower than in the unintentionally doped sample. The charge recombination rate depends on the NA coupling, energy gap and dephasing time which are summarized in Table 1 for the four systems. The average NA coupling between the EP and HP state is 1.61 meV, which is significantly smaller than 8.40, 7.50, and 6.90 meV between the relavent pairwise electronic states for e@EP, Si@EP, and Ti@EP, respectively. Besides, the larger fluctuation in the energy gap between the localized EP and HP state gives rise to a shorter decoherence time than in the other three systems. The weaker NA coupling and faster decoherence effect contribute mainly the slower EP recombination dynamics with the HP despite the energy gap is slightly smaller.

Fig. 6: Population of polaron states for e@EP, Si@EP, Ti@EP, and photon@EP&HP.
figure 6

Note the different scales of the time axes for e@EP, Si@EP and Ti@EP, and photon@EP&HP.

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Table 1 Canonically averaged energy gap, pure-dephasing time, average absolute NA coupling, and electron–hole recombination time for the electron–hole recombination in Fe2O3.
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The simulations greatly extend understanding of the EP generation and recombination dynamics in Fe2O3 toward the PEC water oxidation. The localized EPs recombine fast with the delocalized VBM holes, accumulation of which is expected to be substantial for water oxidation at photoanodes. In contrast, photoexcitation upon Fe2O3 generates simultaneously localized EPs and HPs which create weak NA coupling and fast decoherence between the two states, leading to slow charge recombination and prolonged EP lifetime. These findings disobey the intuition that small polarons facilitate the electron–hole recombination and offer a piece of evidence which directly support the conclusions of the extreme ultraviolet spectroscopy experiments which indicated prolonged polarons lifetimes upon photoexcitation of Fe2O331. Generally, small polaronic states should be avoided in transition metal oxides for solar energy conversion, and some methods may be worth having a try, such as excitation energy increasement30, co-doping65, and formation of multinary oxides34. Very recently, the concept of self-trapped exciton was proposed to rationalize the Auger recombination in Fe2O366,67,68, which is however beyond the scope of this work.

To summarize, the excited-state dynamics of EPs in Fe2O3 have been systematically investigated by using both AIMD and NA-MD simulations. The elaborately designed AIMD simulations establish the adiabatic mechanism of the EP formation which is ultrafast with a timescale of sub-15 fs. Taking into account the process of hot electron relaxation in the CB, the EP formation time agrees well with the experiment. Electron injection, Si, or Ti doping generate localized EPs in Fe2O3, while photoexcitation generates pairwise localized EPs and HPs. The different nature of the polarons affect notably the electronic structure and recombination dynamics. The NA-MD simulations show that recombination of an EP with a delocalized VBM hole gives rise to the short EP lifetime while recombination between pairwise localized EP and HP extends significantly the EP lifetime. The reason is ascribed to the weaker NA coupling and faster loss of coherence in the latter case. The current work establishes the mechanisms of excited-state dynamics of EPs in Fe2O3, advances our understanding of the EP formation and recombination dynamics, and provides the knowledge of rational design of high-efficiency TMOs photoanodes.

Methods

AIMD simulations of EP formation dynamics

To access the timescale of an EP formation in Fe2O3, a method combining AIMD simulations with a perturbation in charge density were proposed. The procedure was described as follows. First, a nuclear trajectory for pure Fe2O3 in equilibrium at room temperature was generated by running an AIMD simulation. Then, a number of structures were sampled randomly from the trajectory, including the atomic coordinates and velocities. Finally, a series of AIMD simulations were carried out with those initial structures each of which an electron was added into. The sudden injection of a foreign electron into the Fe2O3 lattice was thus deemed as a perturbation in the charge density of pure Fe2O3.

NA-MD simulations of EP recombination dynamics

NA-MD simulations of EP recombination process were carried out by the mixed quantum-classical dynamics methodology implemented within the time-dependent DFT in the Kohn–Sham (KS) representation52. ΔSCF was used to promote one electron from the VBM to the CBM to prepare the initial EP-HP state of photoexcited Fe2O3 which offers a simple method to describe the excited state in the condensed phases. The details about TDDFT procedure were shown in Supplementary Methods. The mixed quantum-classical approach treated lighter and faster electrons quantum mechanically, while described the heavier and slower nuclei classically. The classic path approximation (CPA)69 is used to accelerate the calculation because CPA has been justified in condensed matter systems, in which the nuclear dynamics were steered by thermal fluctuations, and a single-electron excitation had little effect on the geometric structures and electronic dynamics. In order to test the validity of the CPA, we compared the changes in the geometries of Fe2O3 (Fig. 1d) induced by a delocalized electron and hole (Fig. 1c) with thermally induced atomic fluctuations in the ground state, and observed that the average Fe–O bond length is 1.967 in the excited state vs 1.966 Å in the ground-state geometries with negligible change of 0.001 Å, while the thermal fluctuations increased the Fe–O bond length to 1.972 Å. The thermal fluctuations show the bond length change a factor of 6 greater than the optimized geometry changes upon photoexcitation, indicating that the CPA was reasonable for the systems under investigation. Decoherence-induced surface hopping (DISH) algorithm70 was introduced to rescale the nuclear velocity in the direction of the gradient NA coupling vector, 〈ϕi | ∇R | ϕj〉, after a quantum hop. When the decoherence time was significantly shorter than the quantum transition time, it strongly affects the transitions especially for carrier recombination across large bandgap. The approach has been applied to study excited state dynamics in metal oxides59,71,72.

Simulation details

Geometry optimization and electronic structure calculations were carried out by using the VASP code within the framework of spin-polarized density functional theory73. To access the EP formation time in Fe2O3, an AIMD trajectory of 10 ps was generated first. Then, an electron was added in 39 snapshots chosen randomly from the thermally equilibrated portion of the trajectory to perform a new AIMD simulations with each lasting for 200 fs. Geometry optimization for the four EP structures were done first at 0 K and then heated to 300 K with repeated velocity rescaling for 2 ps. Four AIMD trajectories with each lasting 4 ps were generated in the microcanonical ensemble with the time step of 1 fs. Based on these trajectories, the NA-MD simulations were performed by using the Python eXtension for Ab initio Dynamics code50,51 with 5000 stochastic realizations of the surface hopping algorithm which guarantees good statistical convergence. For more details on the NA-MD method, one can refer to the original works50,51,74. More details of the simulation are shown in Supplementary Simulation Details.