First-principles calculation of the energy of compressed calcium

The energy of a calcium crystal with a simple cubic lattice as a function of the ratio (t/U) between two internal parameters of the Hubbard model has been calculated using the Hubbard model for the s bands, equations of motion, and direct algebraic method. The electronic spectra have been calculated for the 4s band of the crystal in two principal symmetry directions of the first Brillouin zone. The calculations have been performed at temperatures T ₁ = 0 K and T ₂ = 1000 K. All calculations have been carried out for different interaction energies U of s electrons, one angle, and their different concentrations n in the range 0 ≤ n ≤ 2. The calculations have demonstrated that the dependences of the energy and electronic spectra in this compressed state are very smooth. The occupation of the Ca 4s band is in good agreement with the results of the pioneering calculations of compressed Ca (and a number of other metals), which were carried out by Gandel’man and his colleagues in the Wigner-Seitz spherical cell approximation. It has been shown that the performed analysis accurately reproduces the data obtained on the superconductivity in terms of the Bardeen-Cooper-Schrieffer theory if the 4s band is half-occupied.