Moreover, in all our subsequent simulations, the graphite surface is modeled by three atomic layers, and the sodium surface is modeled by four atomic layers. For the sodium cation adsorbing on the graphite surface, we utilize the PAW potential including 9 valence electrons (2S 2 2P 6 3S 1 ). This choice offers better convergence in the electronic structure calculations, leading to reduced runtime. For simulations involving the sodium metal surface, we employ the PAW potential with 1 valence electron (3S 1 ) for sodium, which provides sufficient accuracy and a significantly lower computational expense.