Relativistic Self-Consistent-Field Theory for Open-Shell Atoms. I

The formulation of a relativistic restricted multiconfigurational self-consistent-field theory for open-shell atoms is given. The relativistic Hamiltonian is the sum of the one-electron Dirac-Hamiltonian and the two-electron Coulomb-repulsion terms. The total wave function is assumed to consist of a linear combination of eigenfunctions of total operators $J^2$ and $J_z$, which are themselves assumed to be known linear combinations of Slater determinants of four-component one-electron orbitals. The applicability of the formulation derived in this first paper is limited to wave functions expanded in terms of a set of distinct Slater determinants $D_i$, which obey the three conditions. (i) Two or more "core shells" may belong to a same symmetry specy $k$ but their occupations must be similar. (ii) Distinct "peel shells" must belong to different symmetry species $k$. (iii) The symmetry species of the peel shells must be different from the symmetry species of the core shells. The most important cases are the calculations using wave functions expanded in terms of the distinct Slater determinants which arise from the ${\left(2\mathrm{}\overline{p}\right)}^n \mathrm{}\left(2p\right)\mathrm{}$, ${\left(3\mathrm{}\overline{d}\right)}^n {\mathrm{}\left(3d\right)\mathrm{}}^{n^{\prime }}$, and ${\left(4\mathrm{}\overline{f}\right)}^n {\mathrm{}\left(4f\right)\mathrm{}}^{n^{\prime }}$ configurations.