The expression of equilibrium single-bond interatomic distance, d(M-X), of any M-X bond (homonuclear or heteronuclear, ionic, covalent, or metallic) (Ganguly, J. Am. Chem. Sec. 1995, 117, 2655) in terms of core-atomic lengths is examined in terms of the constraints of an atom-bond transition. These include the following: (i) a description of bonding components of the hydrogen molecule that are applicable to all bonds; (ii) the use of a universal equilibrium chemical potential, mu(univ) = 0; (iii) spin-charge conversion and a justification for the choice of valence s electron orbital radius as the core length; (iv) an examination of the atom-bond transition in terms of Thomas-Fermi screening models applied to the insulator-metal transition; (v) bond lengths and direction of polarity; (vi) bond energy of the hydrogen molecule and the maximum excitonic binding energy as the limiting values of the standard heats of formation per X atom in MXn compound in gas and solid phase. The importance of valence s electron orbital radius, r(s), as a relevant core atomic length in atom-bond transition and in determining ionicity is indicated.