The geometry-based HOMA (Harmonic Oscillator Model of Aromaticity) index, has been defined more than thirty years ago [1] and reformulated in 1993 [2] to describe quantitatively π-electron delocalization in strongly conjugated aromatic systems [3]. This reformulated index applied recently [4] to simple acyclic systems has led to some expected results: the HOMA values are close to zero or even negative showing that π-electrons are considerably less delocalized in these acyclic molecules than in reference systems applied for HOMA.

In majority of simple acyclic compounds, weakly delocalized by hyperconjugation (e.g., aldehydes, ketones, imines), or n-π conjugation (e.g., amides, amidines, guanidines), one part of atoms occurs in sp³ state of hybridization and the other one in sp² state of hybridization. This dramatically differs from situation in majority of aromatic compounds, where solely sp² atoms form pi-electron system and mainly π-π conjugation takes place (e.g., benzene, naphthalene, antracene, pyridine, pyrimidine). The n-π conjugation is only possible for five-membered systems (e.g., pyrrole, furan, thiophene).

Taking these hybridization state and resonance conjugation differences into account, the reference CX single and double bond lengths were defined for the geometry-based HOMED (Harmonic Oscillator Model of Electron Delocalization) index in order to describe properly π-electron delocalization in acyclic systems containing C, N, O and/or S atoms. We propose to use the HOMED abbreviation for the modified index, based on the old HOMA idea, to distinguish it from the HOMA index defined for strongly delocalized aromatic systems. The HOMED index applied to keto-enol, imine-enamine, amide-iminol, thione-thiol, thioamide-thioiminol systems describes better the π-electron delocalization for individual tautomers than the HOMA index.

Acknowledgments. Ab initio calculations were carried out at the Interdisciplinary Center for Molecular Modeling (ICM, Warsaw).

[1] J. Kruszewski, T. M. Krygowski, Tetrahedron Lett. 1972, 3839.

[2] T. M. Krygowski, J. Chem. Inf. Comput. Sci. 1993, 33, 70.

[3] T. M. Krygowski, M. K. Cyrański, Chem. Rev. 2001, 101, 1385.

[4] E. D. Raczyńska, W. Kosińska, B. Ośmiałowski, R. Gawinecki, Chem. Rev. 2005, 105, 3561.

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