Abstract:The HOMA (Harmonic Oscillator Model of Aromaticity) index, reformulated in 1993, has been very often applied to describe π-electron delocalization for mono-and polycyclic π-electron systems. However, different measures of π-electron delocalization were employed for the CC, CX, and XY bonds, and this index seems to be inappropriate for compounds containing heteroatoms. In order to describe properly various resonance effects (σ-π hyperconjugation, n-π conjugation, π-π conjugation, and aromaticity) possible for heteroatomic π-electron systems, some modifications, based on the original HOMA idea, were proposed and tested for simple DFT structures containing C, N, and O atoms. An abbreviation HOMED was used for the modified index.

All possible twenty-three prototropic tautomers of neutral and redox adenine (nine amine and fourteen imine forms, including geometric isomerism of the exo ═NH group) were examined in vacuo {DFT(B3LYP)/6-311+G(d,p)}. The NH → NH conversions as well as those usually omitted, NH → CH and CH → CH, were considered. An interesting change of the tautomeric preference occurs when proceeding from neutral to reduced adenine. One-electron reduction favors the nonaromatic amine C8H-N10H tautomer. This tautomeric preference is similar to that (C2H) for reduced imidazole. Water molecules (PCM model) seem to not change this trend. They influence solely the relative energies. The DFT vertical detachment energy in the gas phase is positive for each tautomer, e.g., 0.03 eV for N9H-N10H and 1.84 eV for C8H-N10H. The DFT adiabatic electron affinity for the favored process, neutral N9H-N10H → reduced C8H-N10H (ground states), is equal to 0.18 eV at 0 K (ZPE included). One-electron oxidation does not change the tautomeric preference in the gas phase. The aromatic amine N9H-N10H tautomer is favored for the oxidized molecule similarly as for the neutral one. The DFT adiabatic ionization potential for the favored process, neutral N9H-N10H → oxidized N9H-N10H (ground states), is equal to 8.12 eV at 0 K (ZPE included). Water molecules (PCM model) seem to influence solely the composition of the tautomeric mixture and the relative energies. They change the energies of the oxidation and reduction processes by ca. 2 eV.

The consequences of one-electron oxidation and one-electron reduction were studied for 4-aminopyrimidine (4APM), which displays prototropic tautomerism. Since experimental techniques are incapable of detecting less than 0.1% of minor tautomers, quantum-chemical calculations [DFT(B3LYP)/6-311+G(d,p)] were carried out for all possible tautomers of neutral 4AMP and its redox forms, 4APM (+ •) and 4APM (- •). Four tautomers were considered: one amine and three imine tautomers (two NH and one CH form). Geometric isomerism of the exo = NH group was also taken into account. One-electron oxidation (4APM - e → 4APM  (+ •)) has no significant effect on the tautomeric preferences; it influences solely the composition of the tautomeric mixture. The amine tautomer is favored for both 4APM  (+ •) and 4APM. An interesting change in the tautomeric preference occurs for 4APM (- •). One-electron reduction (4APM + e → 4APM (- •)) favors the C5 atom for the labile proton. The preference of the imine CH tautomer in the tautomeric mixture of 4APM (- •) may partially explain the origin of CH tautomers in nucleobases.

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The complete tautomeric mixture consisting of nine prototropic tautomers has been studied in the gas phase at the DFT(B3LYP)/6-311?G(d,p) level for neutral, oxidized, and reduced cytosine. Rotational isomerism of the exo -OH group and geometrical isomerism of the exo =NH group have also been considered. Tautomeric conversions possible for cytosine have been compared with those for its structural models, 4-amino-and 2-hydroxypyrimidine. Effects of intramolecular interactions between neighboring groups for cytosine are analogous to those observed for model compounds. Although they are not very strong, they are sufficient to influence tautomeric equilibria and relative stabilities of individual tautomers. One-electron oxidation and one-electron reduction change tautomeric preferences. Tautomers that are rare forms for neutral cytosine become favored ones for oxidized and reduced cytosine. Aromaticity is not the main factor that dictates the tautomeric preferences. Stability of functional groups seems to be more important than full electron delocalization.