[en] The ground and some excited O⁺ (J=O, T=O positive parity) energy levels of closed-shell nuclei are examined, in an oscillator basis, using matrix techniques. The effect of states outside the mixed (O+2(h/2π)ω). model space in ⁴He (namely configurations at 4(h/2π)ω excitation) are taken into account by renormalization using the generalized Rayleigh-Schroedinger perturbation expressions for a mixed multi-configurational model space, where the resultant non-symmetric energy matrices are diagonalized. It is shown that the second-order renormalized O⁺ energy spectrum is close to the corresponding energy spectrum obtained by diagonalizing the O+2+4(h/2π)ω ⁴He energy matrix. The effect, on the ground state and the first few low-lying excited O⁺ energy levels, of renormalizing certain parts of the model space energy matrix up to second order in various approximations is also studied in ⁴He and ¹⁶O. It is found that the low-lying O⁺ energy levels in these various approximations behave similarly in both ⁴He and ¹⁶O. (author)