© 2016 Elsevier B.V. All rights reserved. In previous studies, we introduced a generalized formulation for canonical transformations and spectra to investigate the concept of canonical potentials strictly within the Born-Oppenheimer approximation. Data for the most accurate available ground electronic state pairwise intramolecular potentials in H2+, H2, HeH+, and LiH were used to rigorously establish such conclusions. Now, a canonical transformation is derived for the molecular force, F(R), with H2+as molecular reference. These transformations are demonstrated to be inherently canonical to high accuracy but distinctly different from those corresponding to the respective potentials of H2, HeH+, and LiH. In this paper, we establish the canonical nature of the molecular force which is key to fundamental generalization of canonical approaches to molecular bonding. As further examples Mg2, benzene dimer and to water dimer are also considered within the radial limit as applications of the current methodology.