Structural variations of the well-known guanine quartet (G4) motif in nucleic acid structures, namely substitution of two guanine bases (G) by two adenine (A) nucleobases in mutual trans positions, are discussed and studied by density functional theory (DFT) methods. This work was initiated by three findings, namely (1) that GA mismatches are compatible with complementary pairing patterns in duplex-DNA structures and can, in principle, be extended to quartet structures, (2) that GA pairs can come in several variations, including with a N1 protonated adeninium moiety (AH), and (3) that cross-linking of the major donor sites of purine nucleobases (N1 and N7) by transition metal ions of linear coordination geometries produces planar purine quartets, as demonstrated by some of us in the past. Here, possible structures of mixed AGAG quartets both in the presence of protons and alkali metal ions are discussed, and in particular, the existence of a putative four-purine, two-metal motif.Electronic supplementary materialThe online version of this article (10.1007/s00775-017-1507-7) contains supplementary material, which is available to authorized users.