Key role of antibonding electron transfer in bonding on solid surfaces

The description of the chemical bond between a solid surface and an atom or a molecule is the fundamental basis for understanding a broad range of scientific problems in heterogeneous catalysis, semiconductor device fabrication, and fuel cells. Widespread understandings are based on the molecular orbital theory and focused on the degree of filling of antibonding surface-adsorbate states that weaken bonding on surfaces. The unoccupied antibonding surface-adsorbate states are often tacitly assumed to be irrelevant. Here, we show that the unoccupancy of those antibonding surface-adsorbate states is related to antibonding electron transfer: Electrons that would occupy these antibonding states are transferred to the lower-energy Fermi level. This antibonding electron transfer leads to an energy gain, which plays a critically important role in controlling the trends of bond formation on surfaces that are often inhomogeneous and defective. This finding is illustrated from the first-principles study of hydrogen adsorption on ${\mathrm{MoS}}_2$ surfaces. A clear linear relationship between the energies of antibonding electron transfer and hydrogen adsorption is identified. Active sites of hydrogen evolution reaction on ${\mathrm{MoS}}_2$ are found to originate from the in-gap states induced by sulfur vacancies or edges. The emerging picture is general and suited for both metal and semiconductor surfaces. It also offers a physically different explanation for the well-known $d$-band model for hydrogen adsorption on transition-metal surfaces.

Figure 1

Schematic diagram for the surface-adsorbate interaction. The $E_{\text{X}}$ is the center of gravity (in energy) of the active surface states participating in bonding-antibonding with the adsorbate states centered at $E_{\text{A}}$. The $E_{\sigma }^{*}$ and $E_{\sigma }$ are centers of the unoccupied antibonding states and the occupied bonding states, respectively. ${\mathrm{\Delta }}_{\text{a}}$ and ${\mathrm{\Delta }}_{\text{b}}$ are the shifts of the antibonding and bonding energy centers from $1/2(E_{\text{X}}+E_{\text{A}})$, respectively. The ${\mathrm{\Delta }}_{\text{r}}$ is the distance from $E_{\sigma }^{*}$ to the Fermi level ($E_{\text{F}}$) of the system after adsorption.

Figure 2

(a) The projected $d$-DOS of the surface Mo atom near the S vacancy before hydrogen adsorption. (b) The band structures of ${\mathrm{MoS}}_2$ with 3.125% sulfur vacancies before H adsorption. The in-gap states induced by the S vacancy are highlighted in the colors red (occupied) and blue (unoccupied). (c) Same as (b) but with hydrogen adsorbed at one S vacancy. Solid (dashed) lines are for spin up (spin down). (d), (e) The projected Mo $d$-DOS and H $s$-DOS, which are bonded to each other. (f) The COHP for the Mo-H bond. Bonding interaction to the right and antibonding interaction to the left. Dotted lines in (a)–(f) are the Fermi energy ($-5.4\mathrm{eV}$) after hydrogen adsorption.

Figure 3

(a) Calculated hydrogen adsorption energy ($\mathrm{\Delta }{E}_{\text{ad}}$) at different sites shown in panels A–G. The black solid line is the fitting to all data points with correlation coefficient $\left|R\right|=0.97$. The red and blue dashed lines are the fitting to cases A–D and to cases E–G, respectively. (b) Integrated COHP (iCOHP) up to the Fermi level. Yellow and blue bars (below zero) are the bonding contributions; red and cyan bars (above zero) are the antibonding contributions. (c) Calculated antibonding state center ($E_{\sigma }^{*}$), bonding-state center ($E_{\sigma }$), and their differences. The energies are in eV and relative to the vacuum level, which is set to zero. The black diamond symbols are the net bonding-antibonding contributions. Cases A–D: H-S binding; cases E–G: H-Mo binding. Case B is for ${\mathrm{MoS}}_2$ in the $1T$ phase and others are for ${\mathrm{MoS}}_2$ in the $1H$ phase. The gray shaded area in (a) marks the Gibbs free energy of hydrogen adsorption ranging from about $-0.25$ to 0.25 eV, where the sites can be catalytically active.