The adsorption energy of Li or K atoms on a GeC sheet is influenced by several factors, including the electronic structure, bonding interactions, and surface reactivity of the materials involved. If the adsorption energy is higher at other sites, the Li or K atom will preferentially adsorb at those locations rather than the hexagon center.
The preference for Li to be adsorbed on top of Ge can be attributed to a couple of reasons. Firstly, Ge is less electronegative than C, indicating a lower affinity for electrons. In contrast, Li is a highly electropositive metal, resulting in a stronger electrostatic interaction between Li and Ge compared to Li and C. This stronger interaction leads to a higher adsorption energy for Li on Ge compared to Li on C.
Another contributing factor is the atomic size. Ge is larger in size compared to C, while Li is a relatively small atom. The larger atomic size of Ge provides a larger surface area for interaction with Li, resulting in a stronger adsorption energy. On the other hand, the smaller size of C may lead to weaker interactions with Li.
Considering these factors, it is likely that the preferable adsorption site for Li or K atoms is on top of the Ge atom, which helps explain the behavior observed in your system.