Dirac density matrix, equations

The ground-state wavefunction corresponding to this noninteracting system is then a single Slater determinant i(x) of the lowest occupied orbitals i(x) of the Kohn-Sham differential equation. The Dirac [15] single-particle density matrix y,(r, r ) that results from this Slater determinant is... 

The TDHF equation of motion for the singleelectron density matrix (eq A4 in Appendix A) was first proposed by Dirac in 1930. This equation has been introduced and explicitly applied in nuclear physics by Ferrel. °° The TDHF description was widely used in nuclear physics in the 50—... 

In this paper we present the first application of the ZORA (Zeroth Order Regular Approximation of the Dirac Fock equation) formalism in Ab Initio electronic structure calculations. The ZORA method, which has been tested previously in the context of Density Functional Theory, has been implemented in the GAMESS-UK package. As was shown earlier we can split off a scalar part from the two component ZORA Hamiltonian. In the present work only the one component part is considered. We introduce a separate internal basis to represent the extra matrix elements, needed for the ZORA corrections. This leads to different options for the computation of the Coulomb matrix in this internal basis. The performance of this Hamiltonian and the effect of the different Coulomb matrix alternatives is tested in calculations on the radon en xenon atoms and the AuH molecule. In the atomic cases we compare with numerical Dirac Fock and numerical ZORA methods and with non relativistic and full Dirac basis set calculations. It is shown that ZORA recovers the bulk of the relativistic effect and that ZORA and Dirac Fock perform equally well in medium size basis set calculations. For AuH we have calculated the equilibrium bond length with the non relativistic Hartree Fock and ZORA methods and compare with the Dirac Fock result and the experimental value. Again the ZORA and Dirac Fock errors are of the same order of magnitude. 

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