Mathematical modeling of changes in density of near-surface ionic layers in semi-infinite metals. Equations for displacements of ionic layers

In this work, we propose a mathematical model for describing the change in the ion density of the near-surface ionic layers of a semi-infinite metal. Through averaging over the subsystem of conduction electrons, we obtain in the adiabatic approximation an effective Hamiltonian of the ionic subsystem of a semi-infinite metal, which models the effect of the "metal–vacuum" separation surface on the structure of the near-surface ionic layers. We calculate the free energy of such a model and, by its minimization, obtain an equation for finding the displacements ξm of the ionic layer m. We show that in the absence of an inhomogeneous distribution of the electronic subsystem ξm≡0.