Ab initio and DFT calculations have been carried out to search for the simplest neutral singlet species with double planar tetracoordinate carbons (dptCs) [the "simplest" means the species containing the least number (six) and types (two) of atoms]. Under the restrictions to the possible models (M1-M4) with dptCs and to the singlet electronic states, the B3LYP/6-31+G* scanning on the candidates, C2E4 (E = the second- and third-row main group elements), only led to two minima (D-2h C2Al4 and C-2h C2Be4) with stable DFT wave functions. The extensions to the heavier elements after the fourth row in the IIA and IIIA groups revealed that the D-2h C2E4 (E = Ga, In, and Tl) are also minima with dptCs but C2Ca4 (C-2h) is a first-order saddle point. Extensive explorations at the DFT level on their potential energy surfaces (PESs) further confirmed that the D-2h C2E4 (E = Al, Ga, In, and Tl) are the global minima, but the C-2h C2Be4 is a local minimum. The optimizations at the MP2 level distorted the D-2h C2E4 (E = Ga, In, and Tl) slightly and the distortion energies are less than 0.02 kcal/mol. The C2E4 (E = Al, Ga, In, and Tl) with dptCs are 18.0, 18.3, 13.4, and 12.2 kcal/mol energetically more favorable than their nearest isomers, respectively, at the CCSD(T)//MP2 level with aug-cc-pVTZ for C and Al and aug-cc-pVTZ-PP for Ga, In, and Tl basis set. The substantial energy differences suggest their promise to be experimentally realized. The strong peak on the C2Al4- component in the time-of-flight mass spectrum from laser vaporization of a mixed graphite/aluminum may relate to the D-2h C2Al4 global minimum. The analyses of the electronic structures Of C2Al4 (D-2h), CAl42- (D-4h) and CAl5+(D-5h) indicates that the C-2 moiety in C2Al4 is the equivalence of carbon centers in CAl42- and CAl5+ and unveils the reasons for their stability. The electronic structures Of C2Al4 and ethene are compared. On the one hand, an Al atom functions like an H atom because the eight more valence electrons Of C2Al4 than C2H4 OCCUPY four nonbonding orbitals and are not effectively utilized for bonding. On the other hand, an Al atom is different from an H atom because an Al atom has p electrons available for peripheral bonding around the C-2 moieties in C2Al4, which further rationalize the origins for C2E4 to achieve double ptCs.