Critical evaluation of HOMA and MBL as local aromaticity
| Naoko Nishina
| Jun‐ichi Aihara
Department of Environmental and Life
Sciences, School of Food and Nutritional
Sciences, University of Shizuoka,
Department of Chemistry, Faculty of
Science, Shizuoka University, Shizuoka,
Jun‐ichi Aihara, Department of
Chemistry, Faculty of Science, Shizuoka
University, Oya, Shizuoka 422‐8529,
The harmonic oscillator model of aromaticity (HOMA) index is an excellent
structural indicator of aromaticity. We found that HOMA values for internal
benzene rings in large pericondensed polycyclic aromatic hydrocarbons are
often overestimated because of the local aromaticity of adjacent benzene rings.
The occurrence of this phenomenon was confirmed by comparing the HOMA
with the corresponding SSE(LA) values; SSE(LA) is a graph‐theoretical index
of local aromaticity not disturbed by the aromaticity of the adjacent benzene
rings. Mean bond length values were likewise assessed by comparing them with
the corresponding HOMA and SSE(LA) values.
bond resonance energy (BRE), degree of environmental aromaticity (DEA), harmonic oscillator model
of aromaticity (HOMA), mean bond length (MBL), polycyclic aromatic hydrocarbon (PAH),
superaromatic stabilization energy (SSE)
1 | INTRODUCTION
In general, different benzene rings in a polycyclic
aromatic hydrocarbon (PAH) molecule are different in
the degree of local aromaticity. In fact, many local aroma-
ticity indices have been proposed for characterizing
individual benzene rings in PAHs.
sextet rule has long been used for the empirical prediction
of local aromaticity and reactivity of closed‐shell
Sextet rings in a Clar formula represent the
locations of highly aromatic benzene rings. As pointed
out by Solà et al,
most local aromaticity indices so far
proposed indeed reproduce the locations of sextet rings
in the Clar formula
; Clar's sextet formulas are simple
and practical in this sense. However, it is true that most
of local aromaticity indices are more or less disturbed by
the local aromaticity of adjacent benzene rings.
As a very simple index of local aromaticity, consider
the mean bond length (MBL), defined as a mean value
of the 6 CC bond lengths in a given benzene ring.
All inner CC bonds in PAHs are shared by 2 aromatic
benzene rings. Thus, 6 CC bonds that form the central
benzene ring in coronene (1 in Figure 1) must be inten-
sified not only by the aromaticity of the benzene ring
but also by that of the 6 adjacent benzene rings. As a
result, it is highly probable that the MBL value calcu-
lated using the lengths of these π‐bonds more or less
overestimates the local aromaticity of the central ring.
Most other local aromaticity indices must have essen-
tially the same difficulty. This problem has not come
to light because we are not accustomed to dealing with
large PAHs and nanographenes that contain internal
As will be seen later, we defined a new local aromatic-
ity index, SSE(LA), which is almost free from this type of
overestimation or ambiguity.
SSE(LA) is a kind of
superaromatic stabilization energy (SSE) modified to esti-
mate the degree of local aromaticity (LA) for benzene
rings in PAHs. SSE(LA) arises from all circuits that
enclose the benzene ring in question; it does not take into
account the stabilization due to length‐6 circuits chosen
along the adjacent benzene rings.
This quantity can
Received: 13 August 2017 Revised: 26 September 2017 Accepted: 26 September 2017
J Phys Org Chem. 2018;31:e3783.
Copyright © 2017 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/poc 1of10