Specific features of the calculation of the density matrix of crystals in the Hartree-Fock nonlocal exchange method

It was shown that a direct use of the theory of special points, developed p reviously for calculating the electron density and local exchange potential s, can lead to the violation of the idempotent property of the density matr ix and can give rise to a nonphysical divergence when the nonlocal exchange potential is accounted for. A scheme of interpolation of the density matri x over the Brillouin zone in the reciprocal space was proposed to overcome these difficulties. The electron structures of diamond, rutile, and MgO ide al crystals were calculated by the Hartree-Fock and CNDO methods. The conve rgence of the results with increasing the number of special points in the B rillouin zone was analyzed, and the efficiency of the proposed modification of the special point theory was illustrated. The idempotent property of th e density matrix was verified quantitatively.