Ground-state energy of many-electron systems from x-ray-scattering cross sections

In the nonrelativistic limit and for a purely electrostatic Hamiltonian, an exact relation between the ground-state energy of a crystal and the x-ray-scattering cross section has been derived which allows us to distinguish static from dynamical (exchange and correlation) contributions. With the use of this relation and the corresponding one valid in the case of an isolated atom, it is possible to calculate the cohesive energy of a crystalline substance. Available x-ray cross-section data have been used to calculate the cohesive energy of Be, Si, Al, and Cu. In the case of Be, agreement of calculated cohesive energy with the thermochemical value is obtained if exchange and correlation contributions are included. For the other solids, a substantial disagreement increasing with atomic number has been evidenced. Poor agreement of calculated cohesive energies with thermochemical values is presumably to be attributed to a lack of sufficiently comprehensive sets of measured cross sections.