Within the framework of the quantum-statistical functional and the Ritz method, the
the problem of finding the surface energy per unit area and work function electrons of a
metal flat surface with a inhomogeneous dielectric coating, taken into account in the
approximation of a continuous medium. For a uniform coating, the calculated values are
insensitive to the selection one-parameter functions for an electronic profile, but
sensitive to the gradient series of kinetic energy non-interacting electrons. Calculations
are performed for Al, Na and the comparison with the calculations by the Kohn-Shem
method is made. Analytically the connection between the theory of the Ritz method for
inhomogeneous coatings and calculations by the Kohn-Shem method work function of
electrons for metal-dielectric nanosandwiches. As it turned out, the influence
inhomogeneous coating on the characteristics of the metal surface can be scaled down to
a uniform coverage case. The possibility of using the obtained results in various
experimental situations are discussed.