Use of group chains to utilize molecular symmetry

1 Use of group chains to utilize molecular symmetry The relativistic Cl program DIRRCI [36] was designed to calculate RASCI wave functions and was primarily intended for calculations of states of heavy transition metals and rare earth complexes. Since these complexes are often highly symmetric it was beneficial to invest effort in the implementation of a double group symmetry scheme. This scheme will be briefly discussed below because it shows how molecular symmetry can be incorporated in correlated relativistic calculations. 

If the double group under consideration is Abelian the symmetry character of determinants is easily and uniquely determined by the direct product of all the representations of the constituent one-electron functions. For highly symmetric molecules the appropriate double group is, however, usually non-Abelian. The direct product of spinor irreps is then reducible and a linear combination of 

The final group in the chain should be Abelian and is used at the Cl level of theory, while the first and highest group can be used at the Dirac-Hartree-Fock level of theory where inclusion of non-Abelian symmetry is easier. 

The use of Abelian double group symmetry is accompanied by a change in the graphical representation of the Cl-space. The vertices of the graphs are split according to the symmetry character of the paths (determinants) that pass through it. In Fig. 2 this is illustrated for the Abelian group C3.  

All vertical arcs (connecting vertices with the same number of electrons) have zero weight. 

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