True or false? Order is not uniquely defined in symmetry adapted perturbation theory

It is often stated in reviews of the theory of intermolecular interactions that one of the weaknesses of symmetry adapted perturbation theory is that order in the perturbation is not uniquely defined. The statement is false. It is based on a misinterpretation of a commutator relationship which intertwines the antisymmetrizer, the unperturbed Hamiltonian and the perturbation. Correctly interpreted, the commutator relation can be combined with the perturbed eigenproblem to eliminate from the perturbation expansion terms which contribute zero in infinite order when the perturbation is turned on fully and to sum selected terms to infinite order in the expansion parameter. A surprising consequence of including exchange symmetry by means of the commutator relation is that order in the expansion parameter is not-the same as order in the perturbing potential. (C) 2002 Elsevier Science B.V. All rights reserved.