The ‘‘primitive’’ wave function in the theory of intermolecular interactions

The concept of the primitive wave function for a supermolecule consisting of interacting subsystems is critically analyzed. The distinction between formal and genuine primitive functions is stressed. The concept of uniformly complete basis sets as contrasted to simply complete basis is introduced. Primitive basis sets are defined and shown not to be uniformly complete for the expansion of the supersystem wave function while ’full supersystem basis sets’ are. The conditions are specified under which a supersystem wave function can be decomposed into its ’primitive components’ corresponding to different partitions of the electrons among the subsystems. These primitive components satisfy the Schrödinger equation asymptotically. The matrix representation of the Hamiltonian (both the full supersystem Hamiltonian H and the zeroth order Hamiltonian Ho) in terms of these partitions is analyzed. It is shown that in the standard application of RS-perturbation theory to intermolecular forces (the polarization approximation) the limiting processes λ→1 and R→∞ do not commute, that the λ-series is not uniformly convergent with respect to R and that the wave function to any finite order in λ is genuinely primitive. The symmetrized polarization approximation is justified for the ’coasymptotic ground state’ in certain cases and a ’symmetrized polarization approximation with shifted eigenvalues’ is proposed that connects the lowest eigenvalue of Ho with the physical ground state. A justification of simplified schemes in the region of ’small exchange’ is given and alternative perturbation schemes are discussed. Finally the use of the primitive function in variational treatments is outlined. One advantage is that a genuinely (not a formally) primitive function is uniformly expandable in a primitive basis set.