The algebraic Hamiltonian for diatomic molecules in the vibron model

A quantitative description of the higher-lying vibrotational energy levels of diatomic molecules requires going beyond the lowest-order vibron hamiltonian. A systematic expansion to higher orders which is simple to derive and apply is discussed. The essential point is that only such generators of U(4) or powers thereof, that transform under rotation as scalars can appear in the hamiltonian. Higher-order scalars are generated as the products of scalars and scalar products of vectors. The resulting expansion for the rotationally invariant hamiltonian is equivalent to that derived using the spherical tensors formalism. Applications to H₂ are described.