Schrödinger Perturbation Formalism for Exchange Interactions between Atoms or Molecules

A Schrödinger perturbation expansion is developed for exchange interactions between atoms or molecules, starting from a complete, orthonormal set of symmetrized basis functions. The unperturbed Hamiltonian $H_0$ and the perturbation $H^{\prime }$ are defined in such a way that they are separately permutation-invariant. First- and second-order results are compared with those obtained by Eisenschitz and London for non-orthonormal basis functions, and with those derived from a Brillouin expansion.