This work continues the study of graphene lattice properties based on the hydrogen-like atom model. The relevance of this topic does not dry out due to the not fully understood mechanism of conduction of such fine structures of carbon and the processes of emission from their surface. To describe the properties of the lattice, a modification of the BrandtKitagawa approach with screened ions, proposed by us earlier, is used. In the cold lattice approximation, this model assumes that the three bond atoms oriented along the bond lines belong to the screening shell of the ion. And only one valence electron determines the ground state of the lattice atom and the inhomogeneous angular distribution of its field. In this work, it is proposed to take into account the Coulomb interactions of the electrons of the outer shell of the atom with its own ion and its immediate environment. For this, a modification of the electron density distribution of the screening shell has been developed taking into account its Coulomb interaction with the electron of a hydrogenlike atom. The problem of the parameters of the ground state of a lattice atom is solved numerically using a variational approach. In numerical experiments, the interaction parameters of a weakly bound electron with an ion are obtained. It is also shown that, for an isolated carbon atom, taking into account the Coulomb interaction of the electron with the screening shell of the ion makes it possible to calculate the ionization potential of the ground state with good accuracy. The proposed numerical technique leads to adequate results for calculating the ionization potential for all light atoms from Li to Ne.
