Nowadays, electrochemical reduction of CO$_2$ has been considered as an effective method to solve the problem of global warming. The primary challenge in studying the mechanism is to determine the adsorption states of CO$_2$, since complicated metal surfaces often result in many different adsorption sites. Based on the density functional theory (DFT) calculations, we performed a theoretical study on the adsorption of CO$_2$ on the Ag electrode surface. The results show that the adsorption populations of CO$_2$ are extremely sensitive to the adsorption sites. Importantly, we found that the preferable adsorption positions are the terrace sites, rather than the previous reported step sites. The adsorption populations were found with the order of (211) > (110) > (111) > (100). Subsequently, the adsorption characteristics were correlated with the d-band theory and the charge transfers between Ag surfaces and CO$_2$.
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