Density, degeneracy, delocalization-based index of aromaticity (D3BIA)

Abstract

A aromaticidade tem sido exaustivamente discutida e continua sendo um tema misterioso. Nesse trabalho é proposto um novo índice de aromaticidade chamado índice baseado na densidade-degenerescência-deslocalização ou, simplesmente, D 3 BIA, numa tentativa de lançar nova introspecção sobre esse tema. Esse índice é baseado na teoria de átomos em moléculas (AIM) e, de certa forma, é suportado pela teoria dos spins acoplandos (SC). A aromaticidade diminui com o número de heteroátomos na molécula aromática, pois a degenerescência diminui, e diminui com o aumento do tamanho do anel do composto aromático porque desfavorece a sobreposição dos estados monoeletrônicos. A relação entre planaridade do anel, sua densidade eletrônica e aromaticidade é também observada. A interação atrativa da ressonância de 6 elétrons π no diânion ciclobutadieno compensa sua interação repulsiva carbono-carbono enquanto no seu parente dicatiônico a ressonância de 2 elétrons π é insuficiente para contrabalancear sua interação repulsiva e adota uma estrutura não-plana.Aromaticity has been exhaustedly discussed for several years and it remains as a misterious issue. In this work it is proposed a new index of aromaticity named density, degeneracy and delocalization-based index of aromaticity or simply D 3 BIA in an attempt to cast new insight and perspective over this theme. This index is based on AIM (atoms in molecules) theory and it is somewhat supported by SC (spin-coupled) theory. Aromaticity decreases as the number of heteroatoms in the aromatic molecule increases since degeneracy decreases and it decreases as the ring size of an aromatic compound increases because it disfavors overlap of single-electron states. The relation between planar structures, electron density and aromaticity is also observed. The attractive interaction of 6π-electron resonance in cyclobutadiene dianion compensate its carbon-to-carbon repulsive interaction while in its dicationic parent the 2π-electron resonance is insufficient to counterbalance its carbon-to-carbon repulsive interaction and it adopts a puckered structure.Keywords: delocalization index; degeneracy; ring density; aromaticity IntroductionIn the nineteenth century benzene was the pivot of the aromatic empiricism. However, for cyclobutadiene both theories gave completely different results. 8,11Hückel's MO study predicted the stability of other aromatic compounds and zero stability for conjugated cyclic systems such as cyclobutadiene. Many different magnetic criteria have appeared so far, based on magnetic shielding or ring current. 20Within MO theory, the aromatic character of benzene is explained through delocalized orbitals. Nevertheless by using the spin coupled valence bond theory (SCVB), Gerratt et al. 21 established that all the six π electrons of benzene are localized and symmetrically distorted towards neighboring carbon atoms on each side and possess the same energy and shape. Other studied aromatic molecules have similar features. 22Within the description SCVB, the stability of aromatic syst...

On the basicity and π-electron delocalization of ‘hexaazabenzene’ N6 – Quantum-chemical studies

“…Mandado et al investigating various azines, concluded that aromaticity of azines decreases with the number of N atoms in the ring [23]. Similar order of aromaticity was reported by Dong et al [24] and Firme et al [25]. Divergent conclusions were derived by Sola et al [26].…”

Latin American contributions to quantum chemical topology

“…In 2007, Firme et al introduced D3BIA, an aromaticity index based on the delocalization index of QTAIM, defined as where RDF is the ring density formula, DIU is the delocalization index uniformity and δ is a measure of the degeneracy of atoms in the examined aromatic as explained next. RDF is defined depending on the molecular system, where is the average of the eigenvalues associated with the eigenvectors of H ( r BCP ) that point to the ring critical point (RCP) or cage critical point (CCP).…”

“…For instance Si 6 H 6 and benzene display the same degree of degeneracy, δ = 1 as opposed to pyridine, pyrazine, 1,3,5‐triazine, 1,2,4‐triazine showing values of 0.83, 0.67, 0.50, and 0.33, respectively …”

“…In 2007, Firme et al [44] introduced D3BIA, an aromaticity index based on the delocalization index of QTAIM, defined as…”

“…For instance Si 6 H 6 and benzene display the same degree of degeneracy, δ = 1 as opposed to pyridine, pyrazine, 1,3,5-triazine, 1,2,4-triazine showing values of 0.83, 0.67, 0.50, and 0.33, respectively. [44] Firme et al [45] used the D3BIA index and the nucleus-independent chemical shift (NICS) to study the electronic structure of bisnoradamantenyl and bisnoradamantanyl cations and some of their derivatives. The D3BIA and NICS indicators display a linear correlation for the examined species.…”