Abstract
Bilayer graphene (BLG) exhibits distinct physical properties under external influences, such as torsion and structural defects, setting it apart from monolayer graphene. In this study, we explore the synergistic effects of carbon vacancies, in conjunction with phosphorus dopants, across BLG, focusing on their impact on structural, magnetic, electrical, and hydrogen adsorption properties. Our findings reveal that the substitutional doping of a phosphorus atom into a single carbon vacancy in a graphene layer induces substantial structural distortion in BLG. In contrast, doping phosphorus into a double vacancy maintains the flat structure of graphene layers. These distinct layer structures affect the electron distribution and spin arrangement, leading to varied electronic configurations and intriguing magnetic behaviors. Furthermore, the presence of abundant unsaturated electrons around the vacancy promotes the capture and bonding of hydrogen atoms. Hydrogen adsorption on BLG results in substantial orbital hybridization, accompanied by significant charge transfer. The calculated Gibbs free energies for hydrogen adsorption on BLG range from -0.08 to 0.09 eV, indicating exceptional catalytic activity for the hydrogen evolution reaction. These findings carry implications for optimizing the properties of graphene layers, making them highly desirable for applications such as catalysis.