Qualitative molecular orbital (MO) theory predicts that square-planar tetrasilacyclobutanetetraone D-4h-(SiO)(4) should, like D-4h-(CO)(4), have a triplet ground state, and the results of the (U)CCSD(T)-F12b/cc-pVTZ-F12//(U)-B3LYP/6-311+G(2df) calculations, reported here, confirm this expectation. Calculations at the same level of theory find that square-planar tetrasilacyclobutanetetrathione D-4h-(SiS)(4) also has a triplet ground state. However, these ab initio calculations predict that (SiO)(4) and (SiS)(4) both have a singlet state of much lower energy, with a tetrahedral. (T-d) equilibrium geometry and six, electron-deficient, Si-Si bonds. In contrast, the lowest singlet state of (CO)(4) and of (CS)(4) is calculated to prefer a D-4h to a T-d geometry. An analysis, based on the second-order Jahn-Teller effect, rationalizes the influence of the electronegativity difference between A and Y in (AY)(4) on the energy difference between a D-4h and T-d geometry. This analysis predicts that (BF)(4) and (BCl)(4), which are isoelectronic with, respectively, (CO)(4) and (CS)(4), should both prefer a T-d to a D-4h equilibrium geometry. These qualitative predictions have been confirmed by our calculations, and (BCl)(4) is known experimentally to have a T-d equilibrium geometry.