{'fraction_non_alphanumeric': 0.03284160654678583, 'fraction_numerical': 0.023689027673091417, 'mean_word_length': 4.5088967971530245, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Dissociation of hydrogen molecules on the clean and hydrogen-preadsorbed Be(0001) surface

Using first-principles calculations, we systematically study the potential energy surfaces and dissociation processes for hydrogen molecules on the clean and hydrogen-preadsorbed Be(0001) surfaces. It is found that the most energetically favored dissociation channel for H2 molecules on the clean Be surface is at the surface top site, with the minimum energy barrier of 0.75 eV. It is further found that after dissociation, hydrogen atoms do not like to cluster with each other, as well as to penetrate into subsurface sites. For the hydrogen-preadsorbed Be(0001) surface, the smallest dissociation energy barrier for H2 molecules is found to be 0.50 eV, which is smaller than the dissociation energy barrier on a clean Be(0001) surface. The critical dependence of the dissociation energy barriers for H2 molecules on their horizontal distances from the preadsorbed hydrogen atom is revealed. Our studies well describe the adsorption behaviors of hydrogen on the Be(0001) surface.

These two channels also have the lowest energy barriers for the dissociation of H 2 among the twelve adsorption channels. Herein, the dissociation of H 2 molecules on the clean Be (0001) surface is different from on the clean Mg(0001) surface, where the bri-y channel is the most energetically favored dissociation channel 5,7 . Besides, it is interesting to find from Fig. 2(d) that the minimum energy paths along the top-x(y) and z channels have a cross point at the molecular height of 1.64Å, which means that the H 2 molecule would firstly orients perpendicular, and then rotates to be parallel to the Be surface during its dissociation process. to H 2 is important for the dissociation of H 2 . The bond length (d H−H (TS)) and molecular height of H 2 (h H 2 (TS)) at the corresponding transition states are also included in Table   I. Although the interactions between H atoms and the Be(0001) surface have long been studied, our results concerning the dissociation energy barrier and minimum energy paths are still meaningful.

IV. DIFFUSION, PENETRATION AND DISTRIBUTION OF DISSOCIATED HYDROGEN ATOMS
The PES cut for one H atom on the Be(0001) surface is also calculated to study its diffusion characters. Our calculated PES is shown in Fig. 4(a), with the energy path crossing the four high-symmetry surface sites shown in Fig. 4(b). One can see that the hcp and fcc hollow sites are two minimum energy locations for the H atom, while the bridge site is the saddle point in the diffusion pathway, and the top sites are maxima of the PES. As shown in Fig. 4(b) the energy barrier for one H atom to diffuse from the hcp (fcc) to fcc (hcp) hollow site is 0.35 (0.28) eV, which is very small and can be easily overcome at room temperatures. So after dissociation, the H atoms will easily diffuse around on the Be(0001) surface.
As has been pointed out, the adsorption of H atoms energetically prefers the surface hollow sites at low coverage on the Be(0001) surface 19 . We then study the penetration of H atoms from these surface hcp and fcc hollow sites to the subsurface sites. There are three different kinds of high-symmetry subsurface sites. The octahedral site (octa) lies just underneath the on-surface fcc site, and one tetrahedral site (tetra) lies below the on-surface hcp site. A second tetrahedral site (tetra*) is located directly below a first-layer metal atom.
However, the direct hydrogen penetration into the tetra* site from the on-surface adsorption without bypassing the other subsurface sites is very unfavorable, since this site is located beneath a surface Be atom. So the penetration into the tetra* site will not be discussed.
And our calculated results for penetrations into the other two subsurface sites are shown in Figs. 5(a) and (b) respectively. It is clearly shown in Fig. 5  atom to penetrate through the Be surface is larger than 1.5 eV. As shown in Fig. 5(b), for subsurface adsorption, the H atom will stay at the octa site. However, the energy barrier from on-surface fcc hollow site to subsurface octa site is as large as 1.25 eV. In addition, the subsurface adsorption state is much less stable than the on-surface adsorption state at the fcc hollow site, and the energy barrier for the H atom to penetrate from subsurface back to on-surface site is very small (∼ 0.07 eV). So after dissociation, the H atoms have a much larger probability to stay on the clean Be(0001) surface than penetrating into the subsurface sites.
After the systematic studies on the diffusion and penetration energy barriers, we then analyze the distribution properties for the dissociated H atoms. Since the penetration of atomic H is found to be very hard, and the subsurface adsorption is always less stable than on-surface adsorption, we will mainly discuss the distribution for on-surface adsorption of H atoms. And we focus on the total energy calculation for the adsorption system of dissociated H atoms at different hollow sites. Figures 6(a), (b) and (c) respectively shows three different   The preadsorbed H atom is set at a surface hcp hollow site, since it is the most energetically favored adsorption site for H atoms at low coverage 19 . And in order to compare the adsorption of H 2 molecules near to and away from the preadsorbed H atom, a 3 × 3 supercell with 9 Be atoms at each monolayer is adopted, with the k-points grid for integrations over the Brillouin zone changed to be 7 × 7 × 1. Our structural model for the hydrogen-preadsorbed Be(0001) surface is shown in Fig. 7, with the considered high symmetry sites respectively denoted as T1∼T5, B1∼B3, F1∼F2 and H1∼H2. Since a H 2 molecule has different possible orientations while adsorbing at each high symmetry sites, we here use for example, T1-x to represent for the adsorbing channel of a H 2 molecule orienting along the x (i.e., [1120]) direction at the T1 site.
Among all the calculations, we find no molecular adsorption states of H 2 on the hydrogenpreadsorbed Be(0001) surface. The calculated 2D-PES cuts for the H1-x, T2-y, B3-y and T3-x channels are respectively shown in Figs. 8(a), (b), (c) and (d). As shown in Fig. 8(a), the dissociation energy barrier for a H 2 molecule directly on the precovered H atom is 3.61 eV. Since the dissociation energy barrier for a H 2 molecule at the hcp hollow site of a clean Be(0001) surface is only 1.28 eV as been listed in Table I, the preadsorbed H atom actually makes the dissociation of H 2 molecule on top of it much harder. Moreover, as shown in Fig. 8(b), the dissociation energy barrier for a H 2 molecule around the preadsorbed H atom along the T2-y channel is 1.70 eV. In comparison with the energy barrier of 0.75 eV for a H 2 molecule at the top site of a clean Be(0001) surface, the dissociation of a H 2 molecule becomes harder too around a preadsorbed H atom. However, when the H 2 molecule is enough far away from the preadsorbed H atom, the dissociation energy barrier can be lower   H 2 molecules on their horizontal distances from the preadsorbed hydrogen atom is clear. The dissociation energy barrier for H 2 molecules along other adsorption channels are summarized in Fig. 9(b), from which the lowering down of the dissociation energy barrier with increasing d 0 is also very clear. However, the increasing of the dissociation energy barrier with very large d 0 is unseen because of the limitation of our cell size.

VI. CONCLUSIONS
In conclusion, we have systematically investigated the dissociation of H 2 molecules on the clean and hydrogen-preadsorbed Be(0001) surfaces by using the DFT methods. And our paper perfectly describes the dissociation behaviors for H 2 molecules on the Be (0001) surface.
From the calculated 2D PES cuts for H 2 molecules on the clean Be(0001) surface, we have found that surface top-x, y channels are the most energetically favorable dissociation channels, and the lowest dissociation energy barrier is 0.75 eV for the adsorbing H 2 molecules.
Besides, the dissociation of H 2 along the bri-y channel is also very probable to happen with the energy barrier of 0.91 eV. During our calculations, we have also found that the dissociation energy barrier for H 2 at the hcp hollow sites is always smaller than at the fcc hollow sites on the clean Be(0001) surface.
For the dissociated hydrogen atoms, we have revealed that the diffusion energy barrier is as small as 0.35 eV, while the penetration energy barrier is as large as 1.25 eV, so the dissociated H atoms can easily diffuse around on the Be(0001) surface without penetrating into the subsurface sites. We have also revealed that the adsorption structure with uniform distributions of dissociated hydrogen atoms always has a lower energy.
Based on these studies, we have then further calculated the 2D PES cuts for H 2 molecules on the hydrogen-preadsorbed Be(0001) surface, which shows that the dissociation energy barriers for H 2 molecules depend critically on their horizontal distances from the preadsorbed hydrogen atom. The dissociation of H 2 molecules directly on the preadsorbed hydrogen atom is very hard, but the lowest dissociation energy barrier for H 2 on the hydrogen-preadsorbed Be surface is 0.25 eV smaller than that on a clean Be surface.