We consider the decay widths of ψ to η (η') γ and the mixing parameters between η (η') and ηC in the framework of the SU(3)C quark-gluon model. We calculate them in the lowest order perturbation in quark-gluon coupling constant under the assumptions: (i) Among the initial and final quark-antiquark bispinors, only those components which exhibit the transformation property of observed particle under the Lorentz group contribute to the processes, (ii) thus obtained bispinor in the final state is identified with the pseudoscalar field with two possible choices of the proportionality constant, and (iii) the divergence in the integral with respect to the Feynman parameter should be removed by the introduction of binding energy in the parent charm-anticharm system. The formulae for these two processes contain the four parameters: The overlap of quark wave functions in ηC, the quark-gluon coupling constant at the mass of η, that at the mass of η', and the mass of charm-quark MC. The solutions are obtained by comparing the formulae with the phenomenological values of mixing parameters and the data on Γ (ψ to η (η') γ). It is pointed out that, for the decay widths, the contribution of the photon emission from the internal charm-quark line is larger than that from the external charm-quark line. The predictions for Γ (ηC to 2 γ) and Γ (Υ to η γ, η' γ, ηC γ) are made.