## 3 Results and Discussions  
As shown in Table 1, the hydrogen atom had the lowest energy compared with the H\({}_{2}\) molecule case for all three adsorption sites considered. Thus, in the following, we will focus exclusively on the H adsorbed case. The most stable configuration was the hydrogen located at the site s1 with the adsorption energy of 1.19 eV. It was found that after the structural relaxation, all three initial adsorption sites transformed to the same final configuration. Namely, the adsorbed hydrogen cleaved one hydrogen atom from the hydrocarbon chain and a H\({}_{2}\) molecule was formed, fleeing away from the hydrocarbon chain. Thus, one dangling bond was left on the carbon atom in the chain, which caused the nearby carbon and hydrogen atoms in the chain to distort slightly. The adsorption energy of the final state was \(-0.15\) eV. The negative value means the final state formed with H\({}_{2}\) was more stable than the initial state of the hydrocarbon chain and the isolated H atom. The bond lengths and bond angles of the carbon atoms with the dangling bonds in the chain varied substantially during the process. Compared to the intact case (1.52 A), the bond length between the carbon atoms shrank about 0.05 A, to 1.47 A. The bond length between the carbon atom with the dangling bond and the left hydrogen atom also reduced slightly. These reductions of bond lengths can be ascribed to the enhanced charge density in the C-C and C-H bond area. In the process, the bond angle of C-C-C, in which the center atom is the carbon atom with the dangling bond, also changed from 113.6\({}^{\circ}\) to 120.8\({}^{\circ}\), deviating much more from the regular tetrahedron angle (109.28\({}^{\circ}\)). The shortening of bond length and expansion of bond angle indicates that the characteristic of a C-C double bond had emerged. The ability of the incident H atom to cleave one hydrogen atom from the chain can be seen intuitively by the charge-density difference, calculated by the charge density of \begin{table}
\begin{tabular}{c c c c} \hline  & & **E\({}_{\textbf{a}}\) (eV)** & \\ \cline{2-4}  & **s1** & **s2** & **s3** \\ \hline H & 1.19 & 2.87 & 2.86 \\ H\({}_{2}\) & 2.39 & 4.61 & 5.56 \\ \hline \end{tabular}
\end{table} 
Table 1: The adsorption energies of an infinitely long hydrocarbon chain with one H and H\({}_{2}\) adsorbed at s1, s2, and s3 sites in the supercell, respectively. Figure 1: (Color online) (**a**) Stereogram of an infinitely long hydrocarbon chain with one H atom adsorbed at different sites. The two dotted lines show the borders of the supercell along the \(z\) direction. (**b–d**) are enlarged views of the adsorption sites of s1, s2, and s3, respectively. The blue, pink, and red balls denote the carbon, hydrogen, and the adsorbed H or H\({}_{2}\), respectively. a H atom adsorbed at site s1 minus the charge density of the pristine hydrocarbon chain (Figure 2a). For comparison, the charge density difference of the H\({}_{2}\) molecule adsorbed is given in Figure 2b. Figure 2a shows that the charge depletes in the C-H bond region, while in the H-H bond region, the charge accumulates. This charge transfer weakens the C-H bond and leads to the bond breaking eventually. While for the case of the H\({}_{2}\) molecule, the strong H-H bond in the H\({}_{2}\) molecule makes the splitting of the molecule hard. Therefore, Figure 2b shows that there is no obvious charge depletion in the C-H bond region. In Figure 2b, the left side of the charge distribution of the H\({}_{2}\) molecule changes slightly because of the attraction of the hydrogen atom in the hydrocarbon chain. Table 1 shows that the adsorption energies of the H adsorbed at all three sites are positive, indicating that the states of the H located at these sites were less stable than the state of the H far away from the chain.