Determination of the Bond Energies for the Series O2–O2+ through O2–O10+

Equilibrium constants for the reactions O₂ + O_2n⁺ = O_2n+2⁺, $\text{n\hspace{0.17em}=\hspace{0.17em}1–8}$ , have been determined mass spectrometrically. The fraction of the O₄⁺–O₁₂⁺ ions which dissociate in the spectrometer is computed theoretically. It is found that a signicant fraction of the O₁₀⁺ and O₁₂⁺ ions dissociate in this region. The equilibrium constants are corrected for this and other phenomena. Rotational entropies are computed for the theoretical structures of these complexes. Vibrational entropies are used to estimate weak mode vibrational frequencies. By extrapolation of the enthalpy data to 0°K, the bond energies are found to be $D_0({\mathrm{O}}_2–{\mathrm{O}}_2^{+}{\text{\hspace{0.17em}=\hspace{0.17em}10.53\hspace{0.17em}±\hspace{0.17em}0.10, D}}_0({\mathrm{O}}_2–{\mathrm{O}}_4^{+}{\text{)\hspace{0.17em}=\hspace{0.17em}6.51\hspace{0.17em}±\hspace{0.17em}0.07, D}}_0({\mathrm{O}}_2–{\mathrm{O}}_6^{+}{\text{)\hspace{0.17em}=\hspace{0.17em}2.56}}_{\text{−0.06}}^{\text{+0.16}}{\mathrm{,\; D}}_0({\mathrm{O}}_2–{\mathrm{O}}_8^{+}{\text{)\hspace{0.17em}=\hspace{0.17em}2.43}}_{\text{−0.09}}^{\text{+0.06}},\mathrm{and}{D}_0({\mathrm{O}}_2{\mathrm{–O}}_{10}^{+}{\text{)\hspace{0.17em}=\hspace{0.17em}2.0}}_{\text{−0.6}}^{\text{+0.4}}\mathrm{kcal}/\mathrm{mole}$ . The $D_e({\mathrm{O}}_2–{\mathrm{O}}_{\text{2n}}^{+})$ for $\text{n\hspace{0.17em}=\hspace{0.17em}3–5}$ obtained by correcting $D_0({\mathrm{O}}_2–{\mathrm{O}}_{\text{2n}}^{+})$ for zero‐point energy differences are in reasonable agreement with the values computed by a classical electrostatic model. The vibrational entropy of O₄⁺ at 298°K is found to be 9.93 e.u. This is in good agreement with the theoretical value of 10.21 eu obtained from the theoretical (semiempirical SCF MO) potential surface. Various models are used to analyze the equilibrium constant data to determine the model dependence of the derived quantities. The ${\mathrm{\Delta H}}_n{\mathrm{°,\; \Delta S}}_n\mathrm{°,}\mathrm{and}{D}_0({\mathrm{O}}_2–{\mathrm{O}}_{\text{2n}}^{+})$ values are only weakly dependent on the assumed geometry and weak mode vibrational frequency distribution of the O_2n⁺. On the basis of the $D_e({\mathrm{O}}_2–{\mathrm{O}}_{\text{2n}}^{+})$ values for O₈⁺–O₁₂⁺, it is tentatively concluded that the frequencies for the O₆⁺ base cluster in O₈⁺–O₁₂⁺ are close to those of free O₆⁺. The experimental data are not accurate enough to prove this hypothesis.