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

Abstract

A symmetry scheme based on the irreducible corepresentations of the full symmetry group of a molecular system is presented for use in relativistic calculations. Consideration of time-reversal symmetry leads to a reformulation of the Dirac-Hartree-Fock equations in terms of quaternion algebra. Further symmetry reductions due to molecular point group symmetry are then manifested by a descent to complex or real algebra. Spatial symmetry will be restricted to D2h and subgroups, and it will be demonstrated that the Frobenius-Schur test can be used to characterize these groups as a whole. The resulting symmetry scheme automatically provides maximum point group and time-reversal symmetry reduction of the computational effort, also when the Fock matrix is constructed in a scalar basis, that is, from the same type of electron 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. © 1999 American Institute of Physics.