Quaternion symmetry in relativistic molecular calculations: The Dirac-Hartree-Fock method

A symmetry scheme based on the irreducible corepresentations of the full sy mmetry group of a molecular system is presented for use in relativistic cal culations. Consideration of time-reversal symmetry leads to a reformulation of the Dirac-Hartree-Fock equations in terms of quaternion algebra. Furthe r symmetry reductions due to molecular point group symmetry are then manife sted by a descent to complex or real algebra. Spatial symmetry will be rest ricted to D-2h and subgroups, and it will be demonstrated that the Frobeniu s-Schur test can be used to characterize these groups as a whole. The resul ting symmetry scheme automatically provides maximum point group and time-re versal symmetry reduction of the computational effort, also when the Fock m atrix is constructed in a scalar basis, that is, from the same type of elec tron repulsion integrals over symmetry-adapted scalar basis functions as in nonrelativistic theory. An illustrative numerical example is given showing symmetry reductions comparable to the nonrelativistic case. (C) 1999 Ameri can Institute of Physics. [S0021-9606(99)31637-8].