Strain energies are related to energy changes for processes that open rings into chains. In the earlier papers of this series, we introduced an s-homodesmotic reaction which converts rings into chains while preserving the valence environment around each atom and conserving bond types. In this paper, we report geometry optimized ab initio SCF MO calculations for (NH)(n) rings and H(NH)(m)H chains performed with the 6-31G** basis set at RHF and MP2 levels of theory. We use these results to calculate strain energies for (NH)(n) rings as energy differences for s-homodesmotic reactions. The bond type and valence environment conservation properties of these reactions allow at least some of the effects of basis set and electron correlation errors to cancel as differences are taken between calculated energies of products and reactants. We find that for (NH)(n) the strain energy is a maximum for n = 4, as it is for the series S-n and O-n. For the cycloalkanes, (CH2)(n), ring strain is greatest for n = 3. The (NH)(n) strain energies are smallest for n = 5 and 6 and large again for n = 7 and 8. We rationalize the relative energies of different ring conformations in various ring classes on the basis of the gauche effect, a preference for conformations in which lone pairs of electrons on adjacent atoms are approximately 90 degrees apart.