Quaternionic formulation of the two-component Kohn-Sham equations and efficient exploitation of point group symmetry

The quaternionic formulation of the time-reversal invariant quasirelativistic Kohn-Sham equations with exact Hartree-Fock exchange leads to hypercomplex one-component equations with half of the dimension compared to the original two-component problem. The combination of the quaternionic equations with point group symmetry exploitation for D_2h and its subgroups by construction of corepresentations leads to quaternionic, complex, or real algorithms depending on the structure of the point group. In this work, the quaternionic approach with point group symmetry exploitation of the relativistic four-component Dirac-Hartree-Fock theory by Saue and Jensen [J. Chem. Phys. 111, 6211 (1999)] will be adopted to the quasirelativistic two-component Kohn-Sham scheme for closed-shell systems. The implementation in the program system TURBOMOLE is applied to the large lead cluster Pb₅₆ as a test case.