New theoretical methods are reported for obtaining the binding energies of molecules and other atomic aggregates employing the spectral eigenstates and related properties of the constituent atoms in the absence of prior wave function antisymmetry. Calculations of the lowest-lying attractive and repulsive states of the electron pair bond as functions of atomic separation from chemical (exchange) to physical (van der Waals) binding regions illustrate the nature of the formalism and its convergence to values in accord with results obtained employing conventional methods. (C) 2002 Published by Elsevier Science B.V.