Density Matrix of Crystals in the Hartree-Fock Method

Density Matrix of Crystals in the Hartree-Fock Method... 

In practical calculations of the band structure of crystals by the Hartree-Fock method, the one-electron density matrix Prr (k) in the reciprocal space can be calculated only for a rather small finite set of special points (see Sect. 4.2). Let us consider such a set of special points kj, j = 1,2,..., Nq. Then, in the calculation of the density matrix of the infinite crystal the integration over the BriUouin-zone volume Vg is changed by the sum over the special points chosen... 

The unrestricted and restricted open-sheU Hartree-Fock Methods (UHF and ROHF) for crystals use a single-determinant wavefunction of type (4.40) introduced for molecules. The differences appearing are common with those examined for the RHF LCAO method use of Bloch functions for crystalline orbitals, the dependence of the Fock matrix elements on the lattice sums over the direct lattice and the Brillouin-zone summation in the density matrix calculation. The use of one-determinant approaches is the only possibility of the first-principles wavefunction-based calculations for crystals as the many-determinant wavefunction approach (used for molecules) is practically unrealizable for the periodic systems. The UHF LCAO method allowed calculation of the bulk properties of different transition-metal compounds (oxides, perovskites) the qrstems with open shells due to the transition-metal atom. We discuss the results of these calculations in Chap. 9. The point defects in crystals in many cases form the open-sheU systems and also are interesting objects for UHF LCAO calculations (see Chap. 10). 

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