The general analytic expression for S₄‐symmetry‐invariant potential functions of tetra‐atomic homonuclear molecules

The potential energy of a homonuclear X 4 molecule is an invariant of the atom permutation group S 4 acting on the internal coordinates of X 4 . It is shown by means of invariant theory that six algebraically independent invariants and five additional invariants are required to express the general invariant function for this group. Explicit expressions for these 11 invariants are given.