Dependence of the binding energy of the metal crystal lattice on the average number of conduction electrons

We establish the dependence of the electron binding energy in a separate isolated Wigner–Seitz cell of the metal crystal lattice on the average number of electrons located in this cell. The calculation is made using the modified Hellmann–Feynman theorem, which allows relating the eigenvalue of the steady-state Hamiltonian to the variation in its parameters that do not affect the degree of freedom of a system. As one of these parameters, we choose the average number of electrons in the cell. According to the calculated data, removal of 10–30% of electrons in monovalent metals leads to the crystal lattice fracture. The results obtained using the Hellmann–Feynman theorem are directly compared with the data of the jellium model.