Theoretical study on the formation of diamond germanium vacancy color center

•In this paper, the formation mechanism of germanium vacancy color center is calculated by first principles.•VASP software was used to calculate the adsorption and migration process of germanium on different diamond surfaces. The differential charge, Bader and magnetic moment of germanium before and after adsorption were calculated. The adsorption energy, bonding strength and migration energy of germanium on different diamond surfaces were obtained.