Modeling of the Potential Energy of Interaction of Two Atoms by Solving a System of Nonlinear Equations

In the first order of perturbation theory, it is shown that the potential energy of interaction between two atoms can be calculated by solving a system of nonlinear equations. The system of equations has been constructed both with and without regard to the Pauli principle, and the atomic form factor has been calculated using wave functions that approximate the solution of the Hartree–Fock equation for isolated nitrogen atoms. The graph of the potential energy of the interaction of two nitrogen atoms satisfactorily agrees with the known results when the Pauli principle is taken into account. It is shown that without taking into account the Pauli principle and collective oscillations of the electrons of atoms, it is not possible to obtain agreement with experiment. It is shown that the total energy of a diatomic molecule is a functional that depends on the electron density of isolated atoms.