The GDIM hamiltonian is a general expression for partitioning the polyatomic hamiltonian into atomic and diatomic fragments. The partitioning is determined by a set of arbitrary functions of nuclear coordinates called the G-functions, or GnPQ. The set of GnPQ is a useful mathematical device for fitting GDIM potentials. It will be good and useful if the GnPQ can also be physically interpreted. This work presents a conceptual interpretation of GnPQ in terms of the perturbation of (PQ)n, the PQ fragment in the polyatom described by the nth valence bond structure. The GDIM hamiltonian Hn is interpreted as being formulated in terms of effective perturbed diatomic hamiltonians GnPQHe,nPQ, He,nPQ being the unperturbed electronic hamiltonian (without the nuclear repulsion) of diatomic molecule (PQ)n. The GnPQ is understood as an effective perturbation factor associated to (PQ)n, it defines a series of perturbed electronic energy levels with energies E˜i(PQ, n) = GnPQEi(PQ, n), Ei(PQ, n) being eigenvalues of He,nPQ. The GDIM polyatomic energy may then be seen as synthesized from explicitly perturbed diatomic energies E˜i(PQ, n). An idealized valence state energy value for the (PQ)n including both excitation and distortion effects is proposed as a linear combination of the E˜i(PQ, n). This leads to a simple conceptual formula for GnPQ in terms of the conventional DIM valence state energy value and a distortion energy correction to this value. An opinion is expressed, that the GnPQ may be a priori modelled to introduce some distortion energy contribution equivalent in effect to correcting the basis set deficiencies related to the use of frozen atomic functions. The perturbation interpretation also leads to the derivation of physically motivated equivalence and dissociation limits constraints for GnPQ. These constraints are applied to formulating sets of distinguishable GnPQ each written as a polynomial expansion. Subsequent minimal basis calculations on H32+ (three ionic structures) and H3 (two covalent structures) produced near chemical accuracy 3D potentials with five or four parameters.
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