We obtain the lifetime of state D ∼ 1 A ′ and F ∼ 1 A ′ by applying the simulation from each specific adiabatic surface. Thousands of trajectories are performed with different initial condition and then we can collect the numbers of undissociated trajectories at each time t as N(t). Finally, the lifetime τ is obtained through an exponential fitting on N(t) versus t as: N t = N 0 exp ⁡ ⁡ − t / τ .

The state D ∼ 1 A ′ is believed to be unstable due to the strong non-adiabatic coupling with the lower state of B ∼ 1 A ′ at the bending geometry. Several experimental studies have reported slightly diverging results. Steinkellner etal [18] obtained a value of 60 ± 50 fs with a large uncertainty using an ultrafast two-photon experiment in 2004. Then Yuan etal [19] estimated the lifetime of D ∼ 1 A ′ to be 13.5 fs from the bandwidth value of a two-photon spectrum. In the present study, as shown by Figure 1A, the dissociation lifetime for D ∼ 1 A ′ state is determined to be near 124 fs. The relatively short lifetime of 13.5 fs by Yuan etal [19] is within the lower limit of 60 ± 50 fs by Steinkellner etal [18] while the present value of 124 fs is near the upper limit of that. Present study may slightly overestimate the lifetime of D ∼ 1 A ′ state because other non-adiabatic processes (e.g. Coriolis couplings) may also lead to the dissociation thus reduce the dissociation lifetime. More theoretical and experimental works are required to accurately determine the lifetime of D ∼ 1 A ′ state. It should be noticed that, at the first 50 femtoseconds, the counts in Figure 1A is flat. This is caused by our simulation algorism: in first tens of femto-seconds, most trajectories cannot reach the defined dissociation conditions (e.g. OH bond length larger than a threshold value), so they are not regarded as ‘dissociated’.

The lifetime of F ∼ 1 A ′ state had been determined by Yang etal [6] to be as long as 1000 ± 300 fs using the time-resolved photo-electron spectroscopy (TRPES). They suggested a weak non-adiabatic traisition from F ∼ 1 A ′ to D ∼ 1 A ′ , followed by dissociation from the D ∼ 1 A ′ surface as discussed above. However, in our last study [10], we suggested that the long lifetime should come from the long-time for symmetry-breaking process by analysing the PESs corresponding to such process. As shown in Figure 1B, the lifetime of F ∼ 1 A ′ is determined to be about 770 fs with our semi-classical simulation which is in good agreement with the TRPES results of Yang etal [6]. So our initial suggestions are well supported by the present simulation.

In previous theoretical studies, researchers mainly focus on part of the dissociation channels. e.g., for H + OH dissociation channel, Jiang etal [20] studied the rotational and vibrational distributions of the OH fragment, Zhou etal [8] studied the effect of spin-orbit couplings on the rotational distributions of OH fragment. For H₂+O channel, the only theoretical study was performed by van Harrevelt etal [21], in which the rotational and vibrational distributions of H₂ were obtained, a 10% ratio for the H₂+O channel was found which was in good accordance with earlier experimental results t [22]. For the three body channels, no specific theoretical studies are published. In a recent study, Chang etal [7] found a quite large ratio of the three-body channel at short wavelengths (near 100 nm, 12.34 eV).

Here we perform a simulation containing all three channels with the full-dimensional PESs obtained in our last work [10]. A key point is the determination of the initial surface. In the present study, we perform the simulation from all the excited 1 A ′ states and the numbers of the trajectories from each surface are determined as: N i ∝ D 1 i R e 2 / ω 1 i 2 . (4)

Here N i is the number of the trajectories from the ith (i > 1) 1 A ′ surface, and D 1 i R e and ω 1 i are the transition dipole moments and vertical excitation energy at the equilibrium geometry from 1 A ′ to i 1 A ′ . Such approximation is based on a vertical excitation from the ground state to the ith excitation state. Then the photon energy of each trajectory is determined as: E p = U i q t = 0 + ∑ α 1 2 m α q ˙ α t = 0 2 − E 0 (5)

E p and E 0 are the photon energy and the zero-point energy of ground state, respectively. U i is the PES of the ith surface. q t = 0 and q ˙ α t = 0 correspond to the initial coordinates and velocities of each atom. Totally, hundreds of thousands of trajectories are performed, and the channel ratios are obtained and shown in Figure 2.

As shown in Figure 2, at low photon energy (near 9 eV), most trajectories lead to the H + OH(X) channel. As the photon energy increases the ratio of H + OH(X) channel reduces rapidly and the ratios of other channels rise. H + OH(A) channel corresponds to the dissociation on B 1 A ′ surface: as the photon energy increases, the ratio of H + OH(A) channel rises to the maximum at near 10.7 eV. This may due to the fact that at higher photon energy, competition between three-body and H₂+O channel can take place. The H₂+O channel also rises with the photon energy increases from 9 eV and reaches the maximum at about 11.2 eV. It should be noted that, at about 10.2 eV, the H₂+O channel ratio is close to 10%, this is in good agreement with the ones presented by the theoretical results of van Harrevelt etal [21] and the experimental ones of Slanger etal [22]. The three-body dissociation of water molecule is an important way to generate the oxygen atom, and was discovered by both dissociative electron attachment [23] and photodissociation [7] experiments, but the mechanisms are different because the PESs of H₂O molecule and its anion are quite different. In present result, the ratio of three-body channel reaches the first maximum of about 22% at near 10 eV, and reduces to below 10% at 10.6eV. Such reduction may come from the competition of the H + OH(A) and H₂+O channel. After that, the ratio of the three-body channel increases rapidly. A quite large value of 62% ± 12% of such channel is determined near 12 eV. In the recent experimental study by Chang etal [7], the ratios considering only H + OH and three-body channels are obtained, and a value of near 85% at 102 nm photon wavelength (12.15 eV) was presented. In present study, if we also exclude the H₂+O channel, the ratio of three-body channel can be determined as near 78% ± 15% at 12 eV. Such value is within the range of the experimental ones by Chang etal [7].

In recent experimental work of Chang etal [3], the photo dissociation of water at wavelength ranging from 102.67 to 112.81 nm (10.99—12.08 eV), corresponding to the H₂+O channel, was studied. The H₂+O (¹S) channel was observed and the vibrationally excited H₂ molecule was mostly populated. This is surprising because the H₂+O (¹S) channels correspond to the fourth 1 A ′ surface at the asymptotic region and there exist a rather high energy barrier to overcome on this surface as shown in Figure 3B. In our last work [10] and the theoretical study in Chang etal [3], it was pointed out that the system can follow a non-adiabatic reaction path which corresponds to an avoid crossing zone between D ∼ 1 A ′ and 4 t h 1 A ′ (two OH bonds near 3.4 bohr and HOH angle near 45°), after such non-adiabatic transition, the system falls into a well which leads to the hot vibration of H₂ fragment. In present study, we also found few numbers of trajectories leading to the H₂+O (¹S) channel. A typical trajectory for the H₂+O (¹S) channel is shown in Figures 3A,B not only with the geometry movement but also the adiabatic state transition processes. Just as illustrated in our last study [10], the system oscillates for several cycles on the bending and symmetric stretching coordinates, but when the system transit to D ∼ 1 A ′ surface and the two OH bonds enlarge to near 2.6 bohr, at the HOH angle of 180°, the length of the two OH bonds will not shorten or elongate for a while and the system will keep staying at the D ∼ 1 A ′ surface. The main movement then is the contraction of HOH angle from 180 ° to near 60 °. Then the system moves to the avoid crossing between D ∼ 1 A ′ and fourth 1 A ′ and transit to fourth 1 A ′ which leads to the H₂+O (¹S) channel.