Intersections of the potential-energy surfaces of several dihydrides

Abstract

In the schemes for lowering the symmetry of molecules of the AH2 type we have encountered configurations characterized by two-, three-, four-, five-, and sixfold degeneracy of the terms. 1. When double degeneracy is removed, the potential can have the following forms: a) a double oblique elliptical cone, b) two intersecting planes, c) a double paraboloid of revolution, and d) a “double boat.” 2. When threefold degeneracy is removed, the possible forms are: a) two intersecting planes (with partial removal of the degeneracy), b) a double paraboloid of revolution and a plane, c) an oblique “double boat” and a plane, and d) a double oblique elliptical cone and a plane. 3. When fourfold degeneracy is removed, the possible forms are: a) a double oblique elliptical cone (with partial removal of the degeneracy), b) two intersecting planes (with partial removal of the degeneracy), c) two double elliptical cones having a common vertex, d) two “double boats” having a common vertex, and e) four paraboloids of revolution having a common vertex. 4. When fivefold degeneracy is removed, in the special case of α=π/2, the terms have the form of two double circular cones with a common vertex and a horizontal plane. 5. When sixfold degeneracy is removed, in the special case of α=π/2, the terms have the form of two double circular cones and a double paraboloid of revolution having one common vertex.