It appears that many problems associated with analytic expansions of the Dirac equation can be computationally avoided by judicious selection of basis sets for the large and the small component spinors, as shown in chapter 2. Practical methods of generating reliable and economic basis sets for relativistic SCF calculations are developed. Basis sets obtained by the method for the first and second row atoms are given in chapter 2, and the quality of the basis set is discussed. With the correct selection of the basis sets, virtual orbitals in RSCF calculations become very similar to those in nonrelativistic calculations implying that relativistic virtual orbitals can be used in electron correlation calculations in the same manner as the conventional nonrelativistic virtual orbitals. An improved method of generating fitted relativistic basis sets for the third and fourth row atoms is discussed in chapter 3. Compared to the conventional basis sets, the new ones, produced by the present method, are more appropriate for the descriptions of the relativistic effects on chemical properties.
Procedures performing relativistic SCF (RSCF) calculations for linearmolecules having open-shell configurations are developed in chapter 4. The present method is a straightforward extension of the previous RSCF calculation method for closed shell systems and is a relativistic analog of the restricted Hartree-Fock method. The formalism is described for configurations with one open shell, and some other cases which can be treated by the present method are discussed. The success of relativistic SCF calculations for open-shell molecules provides us an alternative calculation method for spin-orbit coupling in molecules. When each fine state is calculated variationally using the Dirac Hamiltonian, independent of other fine states, the difference of total energies between fine states becomes the spin-orbit splitting. Compared to the conventional perturbational method, the new one is variati...