Currently, the handling of point group symmetry in LASSCF and LASSI only supports symmetry elements that leave each fragment in place. So for instance, trans-butadiene split into two (2,2) π-orbital fragments on either end can be calculated with C_s point group but not the full C_2h point group, because the C₂ rotation permutes each fragment with the other. Symmetry elements that permute one fragment with another are mandatory for PBC-related applications such as band structures because such features represent the only rigorous way to consistently enforce a particular phase convention of the wave function.

The main obstacles here seem to be:

1. Applying a symmetry operator to an entire multielectron wave function defined in an active subspace such that it changes places with a different active subspace. Symmetry operators applied to individual orbitals are, of course, already implemented in PySCF
2. Deriving and implementing the energy derivatives with respect to symmetry-adapted unitary group generators.
3. Deriving the equations describing a symmetry-adapted LASSI model space and applying this framework to the LASSI logical scaffolding.