Efficient symmetry treatment for the nonrelativistic and relativistic molecular Kohn–Sham problem. The symmetry module of the program ParaGauss Original Research Article

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.