Efficient symmetry treatment for the nonrelativistic and relativistic molecular Kohn-Sham problem. The symmetry module of the program ParaGauss

We describe a general strategy for exploiting spatial symmetry in density functional (DF) calculations of molecules and clusters, following the implementation in the parallel DF program PARAGAUSS. Point group elements are defined via a quaternion parametrization. Symmetrized irreducible bases of vector and projective representations as well as Clebsch-Gordan coefficients are constructed with the help of the eigenfunction method. We discuss the symmetrization of molecular orbitals for nonrelativistic and scalar relativistic DF calculations and molecular two- and four-component spinors for relativistic DF calculations that account for spin-orbit interaction. In addition, we present a strategy to symmetrize spinors simultaneously according to a double group and the corresponding point group. In relativistic DF calculations, this approach allows full exploitation of the symmetry of spin-free operators, e.g., in the numerical integration of the exchange-correlation potential.