Brillouin's theorem in Roothaan's open-shell SCF method

The underlying assumptions of Roothaan's symmetry-restricted SCF method for open-shell systems are considered. A ‘restricted Brillouin's theorem’ is formulated and applied in a discussion of total energy discontinuities arising in restricted SCF calculations of systems which exhibit Jahn-Teller instability, such as the tetrahedral 2 T 2 state of CH4 +.