## 3 Results and Discussions
Reaction coordinate describes the process of an incident H atom approaching the hydrocarbon chain along the \(x\)-direction and fleeing away by detaching a hydrogen atom from the hydrocarbon chain and forming a H\({}_{2}\) molecule. Zero coordinate is set as the position of the H atom residing at the s1 position mentioned in Table 1.  
To further understand the cross-linking, partial densities of states (DOSs) of the carbon atom with the dangling bond before and after the cross-linking are given in Figure 5 for the R2 configuration. In the initial state, the p\({}_{x}\) hardly interacts with other three orbitals, while s, p\({}_{x}\), and p\({}_{y}\) hybridize to each other and form sp\({}^{2}\) orbital. The unoccupied states above the Fermi level (E\({}_{\text{F}}\)) indicate the existence of the dangling bonds. After structural optimization, the recombination of carbon orbitals makes the three p orbitals mix well with each other. The unoccupied states are pushed downward and filled. Above, we considered the H dissociation and cross-linking of infinitely long hydrocarbon chains. Now, a finitely long alkane molecule, icosane (C\({}_{20}\)H\({}_{42}\)), is taken as an example, to observe what will happen in an experiment. The calculated binding energy shows that the incident H atom residing at the two ends of the C\({}_{20}\)H\({}_{42}\) was more stable than at the position in the middle part of the molecule by 0.15 eV in energy. In the simulation of R2 configuration for C\({}_{20}\)H\({}_{42}\) molecules, cross-linking also occurred as expected. Especially, the two C\({}_{20}\)H\({}_{42}\) molecules can align'shoulder-to-shoulder' (as shown in Figure 4a) or 'head-to-head' (seen Figure 4c). The energy of the 'head-to-head' alignment is found to be about 0.85 eV lower than the'shoulder-to-shoulder' one because in the latter case, the neighboring H atoms of the two molecules repel each other, resulting in the system unstable relatively. In the 'head-to-head' mode, the cross-linking caused the two C\({}_{20}\)H\({}_{42}\) molecules to connect and form a longer molecule C\({}_{40}\)H\({}_{82}\), as illustrated in Figure 4d. We could see from it that the charge also accumulated in the bond region. [PERSON] et al. found that by bombarding frozen methane molecules, much longer hydrocarbon molecules containing at least 13 atoms were detected [41]. While [PERSON] et al. investigated ion-irradiated water-ice mixtures and found C\({}_{2}\)H\({}_{6}\) could be yielded by CH\({}_{4}\) dimerization [42]. Our calculations indicate that hydrogen bombardment can also lead to the polymerization, thus benefit the formation of long chain hydrocarbon molecules. These results are important to understand the synthesis mechanism of complex organic molecules from quite simple hydrocarbon molecules in organic chemistry and astrophysics. The'shoulder-to-shoulder' cross-linking may also happen when the dangling bonds are in the middle of C\({}_{20}\)H\({}_{42}\) molecules instead of at the two ends of the molecules. Although the dangling bond is easier to form at the ends of the molecules, the incident H atom may have a large probability to hit the H atom located in the middle part of the target molecules, especially for long molecules. Thus, for longer hydrocarbon molecules,'shoulder-to-shoulder' cross-linking may occur more easily. In experimental work dis  
Figure 5: (Color online) The partial densities of states (DOSs) of the carbon atom with one of its connective hydrogens removed in the initial (**a**) and relaxed (**b**) structures for the R2 configuration. played for Dotriacontane C\({}_{32}\)H\({}_{66}\), the'shoulder-to-shoulder' cross-linking made the thin film form perpendicular to the substrate and enhanced the mechanical properties of the film [12]. For shorter molecules, longer molecules can be fabricated through the 'head-to-head' cross-linking mode. However, we must emphasis the preference of the cross-linking mode highly depends on the experimental conditions, such as the arrangement of the molecules.