The photoluminescence (PL) spectrum of Cu-containing silicon has a sharp zero-phonon (ZP) peak at 1.014 eV. The luminescence center corresponding to this peak is called Cu PL and is known to have the local C 3v symmetry. A recent measurement by ultrahigh-resolution PL spectroscopy revealed that the Cu PL center is a Cu 4 complex. Later, it was shown, by first-principles calculations, that the structure was Cu (s) Cu 3(i) , that is, a complex composed of three interstitial Cu (i) atoms around a substitutional Cu (s) atom. This complex (called C-type) has the desired symmetry.However, in this study, we show that the lowest-energy structure is different. The tetrahedral structure Cu 4 , called T -type, has the lowest energy, with the value being 0.26 eV lower than that of C-type. Between these two types, there is an energy barrier of 0.14 eV, which allows C-type to exist in a metastable state. Details of the electronic properties of the T -type complex are given, by comparing with C-type and other isovalent complexes such as Li 4 . Whereas the Cu 4 tetrahedron is incorporated in silicon in a manner compatible with the tetrahedral network, it also has its own molecular orbitals that exhibit a metallic characteristics, in contrast to other complexes. The ZP of the PL spectrum has been unambiguously ascribed to the backflow mode of the Cu 4 tetrahedron.