Application of the Extended HOMED (Harmonic Oscillator Model of Aromaticity) Index to Simple and Tautomeric Five-Membered Heteroaromatic Cycles with C, N, O, P, and S Atoms

Abstract

The geometry-based HOMA (Harmonic Oscillator Model of Aromaticity) descriptor, based on the reference compounds of different delocalizations of n- and π-electrons, can be applied to molecules possessing analogous bonds, e.g., only CC, only CN, only CO, etc. For compounds with different heteroatoms and a different number of CC, CX, XX, and XY bonds, its application leads to some discrepancies. For this reason, the structural descriptor was modified and the HOMED (Harmonic Oscillator Model of Electron Delocalization) index defined. In 2010, the HOMED index was parameterized for compounds with C, N and O atoms. For parametrization, the reference molecules of similar delocalizations of n- and π-electrons were employed. In this paper, the HOMED index was extended to compounds containing the CP, CS, NN, NP, PP, NO, NS, PO, and PS bonds. For geometrical optimization of all reference molecules and of all investigated heterocompounds, the same quantum–chemical method {B3LYP/6-311+G(d,p)} was used to eliminate errors of the HOMED estimation. For some tautomeric systems, the Gn methods were also employed to confirm tautomeric preferences. The extended HOMED index was applied to five-membered heterocycles, simple furan and thiophene, and their N and P derivatives as well as for tautomeric pyrrole and phosphole and their N and P derivatives. The effects of additional heteroatom(s) in the ring on the HOMED values for furan are parallel to those for thiophene. For pyrroles, aromaticity dictates the tautomeric preferences. An additional N atom in the ring only slightly affects the HOMED values for the favored and well delocalized NH tautomers. Significant changes take place for their rare CH forms. When intramolecular proton-transfer is considered for phosphole and its P derivatives, the PH tautomers seem to be favored only for 1,2,3-triphosphole/1,2,5-triphosphole and for 1,2,3,5-tetraphosphole. For other phospholes, the CH forms have smaller Gibbs energies than the PH isomers. For phosphazoles, the labile proton in the favored form is linked to the N atom. The PH forms have smaller HOMED indices than the NH tautomers but higher than the CH ones.

Push–Pull Effect on the Gas-Phase Basicity of Nitriles: Transmission of the Resonance Effects by Methylenecyclopropene and Cyclopropenimine π-Systems Substituted by Two Identical Strong Electron Donors

“…The HOMA and HOMED procedures are analogous, although their parametrizations (α and R o ) are different. For example, the HOMA and HOMED descriptors are equal to unity for aromatic benzene and s-triazine; however, zero is not the same in the HOMA and HOMED scales-HOMED = 0 for the Kekulé structure of benzene with non-delocalized C-C and C=C bonds [54], similar to the original HOMA, whereas HOMA = 0 for the hypothetical structure of benzene with moderately delocalized C-C and C=C bonds [50]. In HOMED(0), the bond lengths of ethane and ethene were taken for the C-C and C=C bonds in the Kekulé structure of benzene, whereas those of 1,3-butadiene were used for the hypothetical structure of benzene in HOMA(0).…”

“…In both cases, C-N in methylamine and C=N in methylimine were employed for the reference single and double bond lengths, respectively. The differences in zero on the two HOMA and HOMED scales lead to some discrepancies between the HOMA and HOMED values for heterocompounds [54]; hence, it is recommended that the HOMA index be used for the delocalized systems containing the same types of bonds, e.g., hydrocarbons, while the HOMED index should be used for any π-π, n-π, or σ-π delocalized heterocompounds [51,54,57,58]. In this study, the HOMA index (α = 257.7 and R o = 1.388) [50] was applied for cyclic fragments containing only CC bonds, while the HOMED index was applied for selected fragments with CC and CN bonds.…”

“…To quantitatively describe changes in electron delocalization for simple neutral and cyano N protonated derivatives, the geometry-based HOMED index [51,54] has been applied. Based on the geometries, optimized at the DFT1 level, HOMEDs have been calculated for selected fragments using equation (3) and parameters from Table S4 (SM).…”

Purine tautomeric preferences and bond-length alternation in relation with protonation-deprotonation and alkali metal cationization

“…The structural HOMED (harmonic oscillator model of electron delocalization) indices [66][67][68] were determined on the basis of the calculated structures for the isomeric forms of the entire purine molecule (HOMED10, ten bonds), for their imidazole (HOMED5, five bonds) and pyrimidine (HOMED6, six bonds) fragments, as well as for the monocyclic molecules of imidazole and pyrimidine derivatives using Eq. (1).…”

On the aromaticity of uracil and its 5-halogeno derivatives as revealed by theoretically derived geometric and magnetic indexes

“…The number of delocalized electrons could be determined according to Hückel's formula 4n + 2, where n = 1 for benzene. There are two commonly used theoretical indexes of aromaticity, the geometric one (HOMA, and closely related parameters, derived from structural dimensions [11][12][13][14]) and magnetic [7,9,15,16] (NICS). For benzene, HOMA is close to 1.…”