# Grain Boundary--A Route to Enhance Electrocatalytic Activity for Hydrogen Evolution Reaction
## 3 Results and Discussion
### Origin of GB-Enhanced HER  
Although Au(110) is not a traditional active catalyst for the hydrogen evolution reaction [20], it becomes a great activity catalyst for the HER by forming grain boundaries, as stated above. The improved HER activity is ascribed to the H* binding energy caused by the GBs in the Au electrocatalyst. As the strength to bind H* is inherently decided by the underlying electronic structure of the catalyst itself, we focus on the differences in atomic and electronic structures, which may provide good guidance. The density of states (DOS) is calculated to understand the interaction between the H atoms and Au GB sites and, thus, to gain an insight into the different HER activities of the GB sites. Only the 5\(d\)-projected DOS of Au atoms is presented because Au 5\(d\) orbitals decide the formation of H\(-\)Au bonds. Figure 7 shows the Au 5\(d\) orbital-projected DOS (PDOS) onto s1, s2 and s5 on Au(110) with GBs. The 5\(d\)-PDOS of the flat Au(110) with H* is also presented for comparison. Compared with the GB-free Au(110), the peak positions and shapes of Au(110) with GBs vary. The variation in the H* binding strength for different GBs sites can be explained by a \(d\)-band model, in which the \(d\)-band center (\(\epsilon_{\rm d}\)) is correlated with the adsorption energy of the adsorbate by considering either the adsorbed H* state by itself or the energy-level realignment in the HER process [32]. As previously mentioned, neither a too strong nor a too weak binding strength is suitable for HER, and an appropriate \(\epsilon_{\rm d}\) can ensure an appropriate strength of the H\(-\)Au bond and catalytic activity for the HER. The value of \(\epsilon_{\rm d}\) can be calculated by  
\[\varepsilon_{d}=\frac{\int_{-\infty}^{+\infty}E\times DOS(E)dE}{\int_{-\infty }^{+\infty}DOS(E)dE} \tag{7}\]  
Considering the dominant role of \(d\)-states under the Fermi level in the H* binding process, we integrated the domain of the Au 5\(d\) states below the Fermi energy to obtain an effective \(\varepsilon_{\rm d}\). As seen in Figure 7a, the \(\varepsilon_{\rm d}\) values for s1, s2 and s5 around the GBs are calculated to be \(-\)3.38 eV, \(-\)3.08 eV and \(-\)3.47 eV, respectively, higher than the GB-free Au(110) surface (\(-\)4.05 eV). That is, GBs indeed allow \(\varepsilon_{\rm d}\) to shift up toward the Fermi energy on the Au(110) surface. It is well known that a higher \(d\)-band center corresponds to stronger adsorption [32]. Consequently, the upper shift of \(\varepsilon_{\rm d}\) suggests that the sites near GBs have a larger H* binding strength and, thus, a lower U\({}_{\rm L}\) in comparison with the clean Au surface. To quantitively evaluate the relationship between HER activity and the electronic structure of Au(110) GBs, we present the trend in U\({}_{\rm L}\)(H*) on different GB sites as a function of \(\varepsilon_{\rm d}\) in Figure 7b. We can see that \(\varepsilon_{\rm d}\) exhibits an approximately linear relationship with U\({}_{\rm L}\) with \(r=0.84\), suggesting that the sites just at the GBs are superior to the sites near the GBs. In fact, GBs feature disorder of the atomic arrangement, where under-coordinated atoms exist; we can also elucidate the origin of GB-assisted HER from a geometrical point of view. By considering the environment of their neighboring atoms, we use the concept of the bond-energy-integrated coordination number (\(\overline{\text{CN}}^{d}\)) proposed by us [33,34]. \(\overline{\text{CN}}^{d}\) can differentiate the surface sites in HER activity.