Energy changes for reactions that convert cyclic structures into chains can be interpreted as ring strain energies. For oxygen rings O-n, we have considered two types of reactions. One is an isogyric reaction that involves the addition of XY to O-n to produce an XO(n)Y chain. The other is the s-homodesmotic reaction in which the O-n ring is dismantled into atoms which are then inserted individually into XO(s+1)Y chains to make XO(s+2)Y chains. The parameter s specifies the length of the reference chain. We calculate energy changes for these reactions using geometry-optimized total energies of rings and chains obtained from ab initio SCF MO calculations at the RHF and MP2 levels using the 6-31G** basis set. Ring strain energies would seem to depend on the nature of the chain as well as that of the ring. In this paper, we have investigated the effect of the chain-terminating groups on the calculated strain energies of oxygen rings O-n, n 3-8. We used terminators XY HH, FF, ClCl, and HF. For the straightforward addition of XY to the ring to give an XO(n)Y chain, we find that the strain energies are highly dependent on the choice of X and Y although qualitative trends in strain energies with ring size are comparable. For the s-homodesmotic reaction, calculated strain energies are independent of X and Y for s greater than or equal to 2 and results at the RHF and MP2 levels are essentially the same. The geometry-optimized structures we obtained for XO(n)Y chains show some interesting variations in bond lengths that can be interpreted using valence models previously proposed by others. Although some chains containing three or more oxygen atoms have been reported, experimental structural data are not available with which to compare the predicted trends.