The atomic structures of TM@CNT and TM@G are shown in Fig. 1 and Figure S1-2 (Supporting Information), different transition metal atoms have been introduced into the models. One hydrogen atom was also added onto different positions of the TM@CNT and TM@G, and the adsorption geometries are fully optimized to calculate the H-atom bonding free energy (ΔGH). ΔGH serves as a good descriptor for evaluating the HER performance,46 the value is better when closer to zero. Higher ΔGH suggests weaker H-binding, while lower ΔGH indicates stronger adsorption on the catalyst. The ΔGH of the original CNTs and graphene nanosheet are very positive, it means that H atoms can hardly adsorb on the catalysts, indicating poor HER activity. However, the introduction of TM atoms led to a huge improvement in the HER performance of the catalysts. In this work, 3d group TM, such as Ti, V, Cr, Mn, Fe, Co and Ni have been systematically studied and the \(\text{∆}{\text{G}}_{\text{H}}\) of each species was calculated.
Figure 2 shows the energy step diagram of HER catalyzed by the TM@CNT and TM@G, the atomic structures of three reaction stages of hydrogen evolution are present as well. The values of ΔGH for TM@CNT (TM = Fe, Co, Ni) are very close to zero, indicating very high HER performance. Other TM@CNT catalysts with too high or too low Gibbs free energy for atomic hydrogen adsorption are not shown here. As presented in Fig. 2, the ΔGH for the C-H binding on CNTs and graphene are extremely high, i.e., 1.06 eV and 1.65 eV, respectively, which demonstrates the weak attraction between C and H atoms and poor HER electrocatalytic performances. For TM@CNT and TM@G catalysts, however, it can be greatly decreased. Especially for the TM@CNT (TM = Fe, Co, Ni), they show excellent HER performance, which is superior to that of the state-of-the-art Pt and well-known MoS2 catalysts. In addition, if the ΔGH values are ranked from high to low, (i.e., graphene > CNTs > Co@G > Fe@G > Ni@G > Co@CNT > Fe@CNT > Ni@CNT), it is obviously that the HER performance of the catalysts based on CNTs is much better than that of the graphene derived samples. This should be attributed to the most significant structural difference between CNTs and graphene: surface curvature. The high surface curvature of CNTs will bring distortion on the carbon skeleton and the charge re-distribution around the active sites,47–49 resulting in the change of adsorption energy for the hydrogen atoms, and then the HER performance.
In Fig. 3, a volcano plot is used to compare the HER activity of the TM@CNT, TM@G and the benchmark catalysts, such as Pt and MoS2. Through Eqs. (7) and (8), the calculated exchange current (i0) can be obtained using the values of ΔGH for different catalysts45. It can be found that the catalysts with positive and negative ΔGH values are scattered around the right and left legs of the volcano plot. Catalysts that have ΔGH values closer to zero are located closer to the volcano peak. Therefore, the HER performance of the catalysts can be evaluated by its i0 and ΔGH position relative to the peak of volcano curve, a closer position to the peak means a higher HER catalytic activity. It is clear that TM@CNT (TM = Ti, V, Cr) and TM@G (TM = Fe, Co, Ni) show very positive ΔGH values, it means that the adsorption of H atom is difficult to achieve. TM atoms from Ⅷ B group, such as Fe, Co and Ni, encapsulated in CNTs are ideal for the HER, particularly Ni@CNT, with the ΔGH being extremely close to the ideal zero value (Fig. 3).
Encapsulated TM atoms could greatly influence the adsorption energy of hydrogen atoms on CNTs, as demonstrated above. Figure 4 depicts the key mechanism for boosting the HER activity of CNTs. In theory, the HER catalytic activity of CNTs and graphene nanosheets with sp2 hybridization can be activated by the accumulation of electrons surrounding C atoms. The insertion of TM atoms will cause a strong electrical connection between metal and single-walled CNTs, and the stable π conjunction between carbon atoms (Fig. 4c) will be broken by electron transfer from the d orbital of TM atoms, as schematically shown in Fig. 4a. Afterward, H+ atoms are capable of accepting the accumulated electrons and H-C bonds will be formed. To further reveal the reaction mechanism, the local density of states and differential charge density of TM@CNT (TM = Fe, Co, Ni) and Ni@G are calculated, shown in Fig. 4b and Fig. 4d as well as Figure S3-5 (Supporting Information). The LDOS of Ni@CNT and pristine CNTs are present in Fig. 4b, implying the prominent DOS at the Fermi level, it is obvious that the CNTs are strongly hybridized with the filled Ni atoms, which can significantly promote the electron transfer efficiency. Meanwhile, the differential charge density for two typical systems, TM@CNT and a H atom chemisorbed on it (TM@CNT-H) are calculated based on the following equations:
$$\text{∆}\text{ρ}\text{(r) = }{\text{ρ}\text{(r)}}_{\text{TM@CNT}}\text{ - }\text{ρ}{\text{(r)}}_{\text{CNT}}\text{ - }{\text{ρ}\text{(r)}}_{\text{TM}}$$
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$$\text{∆}\text{ρ}{\prime }\left(\text{r}\right)\text{ = }{\text{ρ}\text{(r)}}_{\text{TM@CNT-H}}\text{ - }\text{ρ}{\text{(r)}}_{\text{TM@CNT}}\text{ - }{\text{ρ}\text{(r)}}_{\text{H}}$$
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Where ρ(r)TM@CNT, ρ(r)CNT and ρ(r)TM represent the calculated charge density of TM@CNT, CNTs and TM atoms, respectively, that are in the same coordinates. ρ(r)TM@CNT−H, ρ(r)TM@CNT and ρ(r)H in the system TM@CNT-H also have the same meanings. Figure 4c and Fig. 4d show the results of the charge density difference for Ni@CNT and Ni@CNT-H. From Fig. 4c, we can find that an increase in electron charge density around C atoms of CNTs, and a loss of electron charge density between the filled Ni atoms. C atoms in CNTs can easily gain electron density from the introduced Ni atoms that can disrupt the π bond between C atoms, ionize the CNTs and dramatically reduce the Gibbs free energy of H-binding. The calculation results obtained in the systems such as Co@CNT, Fe@CNT and Ni@G have the same regularity (Figure S3-5, Supporting Information).