  All symmetry allowed couplings between the 4f^2-electron ground state doublet
of trivalent praseodymium in PrRu4P12 and PrFe4P12 and displacements of the
phosphorus, iron or ruthenium ions are considered. Two types of displacements
can change the crystal lattice from body-centred cubic to simple orthorhombic
or to simple cubic. The first type lowers the point group symmetry from
tetrahedral to orthorhombic, while the second type leaves it unchanged, with
corresponding space group reductions Im3 --> Pmmm and Im3 --> Pm3 respectively.
In former case, the lower point-group symmetry splits the degeneracy of the
4f^2 doublet into states with opposite quadrupole moment, which then leads to
anti-quadrupolar ordering, as in PrFe4P12. Either kind of displacement may
conspire with nesting of the Fermi surface to cause the metal-insulator or
partial metal-insulator transition observed in PrFe4P12 and PrRu4P12. We
investigate this scenario using band-structure calculations, and it is found
that displacements of the phosphorus ions in PrRu4P12 (with space group
reduction Im3 --> Pm3) open a gap everywhere on the Fermi surface.
