A recent discovery of complicated isotope shifts of the PL 1014 meV line in Cu-containing silicon, which was made by Thewalt's group, indicates that existing models of Cu pairs are not appropriate for accounting for the luminescence center. A new structural model has been studied. First-principles calculations show that the most probable form of the complex is a four-membered complex which is composed of a substitutional Cu associated with three neighboring interstitial Cu atoms. The symmetry is C(3v). The formation mechanism of this complex is discussed. For interpreting the complicated splitting for the Γ(4) exciton peak, involvement of a non-totally symmetric mode is proposed. The pattern of splitting obtained by this model is almost in agreement with the experiment. Selection rules beyond the usual treatments are necessary to connect a specific exciton peak to the corresponding phonon.