Naphtho-homologated DNA bases have been recently used to build a new type of size-expanded DNA known as yyDNA. We have used theoretical techniques to investigate the structure, tautomeric preferences, base-pairing ability, stacking interactions, and HOMO-LUMO gaps of the naphtho-bases. The structure of these bases is found to be similar to that of the benzo-fused predecessors (y-bases) with respect to the planarity of the aromatic rings and amino groups. Tautomeric studies reveal that the canonical-like forms of naphthothymine (yyT) and naphtho-adenine (yyA) are the most stable tautomers, leading to hydrogen-bonded dimers with the corresponding natural nucleobases that mimic the Watson-Crick pairing. However, the canonical-like species of naphtho-guanine (yyG) and naphtho-cytosine (yyC) are not the most stable tautomers, and the most favorable hydrogen-bonded dimers involve wobble-like pairings. The expanded size of the naphtho-bases leads to stacking interactions notably larger than those found for the natural bases, and they should presumably play a dominant contribution in modulating the structure of yyDNA duplexes. Finally, the HOMO-LUMO gap of the naphtho-bases is smaller than that of their benzo-base counterparts, indicating that size-expansion of DNA bases is an efficient way of reducing their HOMO-LUMO gap. These results are examined in light of the available experimental evidence reported for yyT and yyC.