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\begin{document}

\title{REVISITING (ANTI)AROMATICITY AND CHEMICAL BOND IN PLANAR
B\textsubscript{X}N\textsubscript{X} CLUSTERS (X = 2 -- 11)}



\author[1]{Lily Arrué}%
\author[2]{Ricardo Pino-Rios}%
\affil[1]{Universidad Autonoma de Chile - Campus Providencia}%
\affil[2]{Universidad de Santiago de Chile}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\selectlanguage{english}
\begin{abstract}
The aromaticity of boron-nitrogen clusters has been revisited through a
systematic analysis using magnetic criteria. The results obtained
through Ring Current Strength (RCS) measurements indicate that
B\textsuperscript{2}N\textsubscript{2} has a strongly antiaromatic
character, even the bond pattern analysis reveals that this system is
doubly antiaromatic presenting two \selectlanguage{greek}σ- \selectlanguage{english}and two \selectlanguage{greek}π-\selectlanguage{english}orbitals of 4c-2e,
according to the Adaptive Natural Density Partitioning bond pattern
analysis (AdNDP) and z-component of the dissected Nucleus Independent
Chemical Shift (NICS\textsubscript{zz}) isolines.
B\textsubscript{4}N\textsubscript{4} and
B\textsubscript{6}N\textsubscript{6} are marginally antiaromatic
according to RCS and the bond pattern suggest four and six 8c-2e and
12c-2e delocalized \selectlanguage{greek}π-\selectlanguage{english}orbitals respectively.
B\textsubscript{3}N\textsubscript{3} and
B\textsubscript{5}N\textsubscript{5} are slightly aromatic, with a bond
pattern of three and five 6c-2e and 10c-2e \selectlanguage{greek}π-\selectlanguage{english}orbitals respectively. All
rest of the systems (x = 7 -- 11) are non-aromatic. The results show
some discrepancies with results based on the classical nucleus
independent chemical shift, which can be attributed to tensor in-plane
and core electron contributions. Finally, presented results reveal the
need to be careful with the interpretations given by this index, so it
will be necessary the use of 1D, 2D or 3D derived methodologies for a
complete and correct analysis of (anti)aromaticity.%
\end{abstract}%



\sloppy


\textbf{INTRODUCTION}

Mixed boron-nitrogen (BN) materials have been subject of both
experimental and theoretical studies in order to understand their
properties\textsuperscript{1}, such as their thermal stability for
example, hexagonal boron nitride (h-BN) are analogous to graphene and
has been used as thermally stable engineering ceramic and most recently
in optoelectronic devices\textsuperscript{2}. Additionally, BN clusters
are interesting due to their participation in formation of thin solid
films of \selectlanguage{greek}β-\selectlanguage{english}BN, that possess the particularity of scratching
diamond\textsuperscript{3}. Recently, the application of atomic clusters
as assembly blocks for the design of new materials has grown in interest
and the term ``Cluster Assembled Materials'' (CAM) has been
coined\textsuperscript{4}, so knowing the structures and electronic
properties of these clusters is of great importance\textsuperscript{5}.
B\textsubscript{x}N\textsubscript{y} clusters have been characterized
through the interaction between pulsed laser evaporation followed by
matrix infrared spectroscopy and theoretical
predictions\textsuperscript{6,7}. On the other hand,
B\textsubscript{x}N\textsubscript{x} clusters offer three-dimensional
structures that are similar to fullerene.
B\textsubscript{12}N\textsubscript{12},
B\textsubscript{76}N\textsubscript{76},
B\textsubscript{208}N\textsubscript{208}, among others, these have been
obtained through intense irradiation of boron nitride
samples\textsuperscript{8,9}. Furthermore, small clusters offer planar
structures that resemble carbon clusters\textsuperscript{10}.

Some years ago, Matxain \emph{et al} .\textsuperscript{11} carried out
an exhaustive analysis of the potential energy surface (PES) of
B\textsubscript{x}N\textsubscript{x} clusters (x = 2 -- 15) in singlet
state through Quantum Monte-Carlo calculations in order to know the
geometries of these clusters, obtaining as global minima planar
structures for x = 2 -- 11 and three-dimensional for x = 12 - 15.
Additionally, authors concluded that planar structures with 2, 3, 5, 7
BN moieties are \selectlanguage{greek}π-\selectlanguage{english}aromatic, structures with 4, 6 moieties are
antiaromatic and 8 -- 11 BN moieties are non-aromatic according to their
Nucleus Independent Chemical Shift (NICS) calculations. Results for
B\textsubscript{2}N\textsubscript{2} are counter intuitive according to
traditional electron counting rules such as H\selectlanguage{ngerman}ückel's
rule\textsuperscript{12}, which states that cyclic systems with 4n+2
(4n) electrons have an aromatic (antiaromatic) character. Along with
this, the difference in electronegativities between the B and N atoms
leads to a very different electronic distribution than typical organic
aromatic systems, leading to a reduction in aromaticity. This
characteristic has been studied in various systems such as
cyclotriphosphazenes, metallabenzenes, among
others\textsuperscript{13-16}.

The concept of aromaticity\textsuperscript{17}, despite not being an
experimental observable, has been of great utility to rationalize
stability, electronic structure and chemical bond among other properties
in organic and inorganic chemistry\textsuperscript{18}. There are
several criteria to rationalize aromaticity, such as the
geometric\textsuperscript{19}, electronic
delocalization\textsuperscript{20} and the magnetic
criteria\textsuperscript{21}, being the latter the latter being very
popular in recent years. In 1996, Schleyer \emph{et al} . proposed the
Nucleus independent chemical shift (NICS)\textsuperscript{22}, defined
as the negative of the isotropic magnetic shielding evaluated at the
centre of the ring of an (anti)aromatic system. This index quickly
became popular due to its ease calculation in many standard quantum
chemical software. However, its indiscriminate use has been criticized
by several authors, indicating that the validity of the NICS is limited
due to spurious contributions from the in-plane tensor components which
are not related with aromaticity\textsuperscript{23-31}.

To avoid these problems, different ways to analyse NICS have been
suggested. For instance: to compute the property 1.0 angstrom (Å) above
the molecular plane NICS(1)\textsuperscript{32}, and to evaluate the
out-of-plane component of the NICS tensor, the so called
NICS\textsubscript{zz} which has been proven to be particularly
sensitive to \selectlanguage{greek}π-\selectlanguage{english}electron delocalization\textsuperscript{33,34}. Other
strategies proposed are related to the analysis of NICS in the axis
perpendicular to the molecular plane. Stanger \emph{et al}
.\textsuperscript{35} and Sol\selectlanguage{ngerman}á \emph{et al.} \textsuperscript{36},
independently, proposed NICS scans and more recently Torres-Vega\emph{et
al} .\textsuperscript{13} proposed the FiPC-NICS strategy which allows
to obtain characteristic profiles for aromatic, antiaromatic, and
non-aromatic molecules. Another more sophisticated approaches are
related to dissected NICS approaches, bi-dimensional maps,
three-dimensional grids and quantification related to its
topology\textsuperscript{37-41}.

In this article the aromaticity of
B\textsubscript{x}N\textsubscript{x}clusters (x = 2 -- 11) has been
revisited by means of magnetic criteria of aromaticity, and chemical
bond has been analysed through Adaptative Natural Density Partitioning
(AdNDP) method\textsuperscript{42,43}. A complete analysis considering
different NICS-based strategies proposed in literature were carried out.
Additionally, ring current strengths (RCS) were computed measuring the
flow of ring current passing through interatomic surfaces according to
quantum theory of atoms in molecules (QTAIM) proposed by
Bader\textsuperscript{44-47}.

\textbf{COMPUTATIONAL METHODS}

Planar B\textsubscript{x}N\textsubscript{x} (x = 2 -- 11) clusters were
optimized at the
PBE0\textsuperscript{48}/def2-TZVP\textsuperscript{49}level of theory
using Gaussian 09 computational package\textsuperscript{50}. For the
fully optimized molecules, vibrational frequency calculations were
performed at the same level to ensure that we obtained a true minimum on
the potential energy surface. NICS\textsubscript{zz} values were
computed employing the Gauge-Including Atomic Orbital (GIAO) in gas
phase at the above-mentioned level. Ring current strength (RCS)
calculations were done using AIMAll\textsuperscript{51} software.
Chemical bond was analysed through Adaptative Natural Density
Partitioning (AdNDP), this method is a generalization of NBO method.
AdNDP recovers Lewis bonding (1c-2e lone pairs, 2c-2e two electron
bonds), additionally, localized bonds associated with (anti)aromaticity.
NICS\textsubscript{zz} scans, FiPC and NICS\textsubscript{zz}
isosurfaces and AdNDP orbitals were obtained using our own routines and
Multiwfn software\textsuperscript{52}. Visualization of
NICS\textsubscript{zz}isosurfaces and NICS\textsubscript{zz} isolines
have been plotted using Chemcraft and VisIt 2.13.0
respectively\textsuperscript{53,54}.

\textbf{RESULTS AND DISCUSSION}

\textbf{Quantifying aromaticity according to ring current strength (RCS)
and NICS\textsubscript{zz} based descriptors}

Systems studied in this work are
B\textsubscript{x}N\textsubscript{x}clusters (x = 2 -- 11) depicted in
Fig. S1 in the supporting information. This section is aimed to the
quantification of the (anti)aromatic character of the mentioned
clusters. For this purpose, ring current strengths (RCS) were computed
and compared with different quantification strategies based on
NICS\textsubscript{zz}. RCS values were obtained by numerical
integration of the current flow through interatomic surfaces by means of
quantum theory of atoms in molecules (QTAIM) proposed by Bader. RCS
values have been widely used in aromaticity studies and are known to be
a reliable indicator of the (anti)aromatic character of both organic and
inorganic systems. According to table 1,
B\textsubscript{2}N\textsubscript{2}, present a strong antiaromatic
character with a RCS value of -13.0 nA.T\textsuperscript{-1} in clear
disagreement with Matxain \emph{et al} . results but consistent with
electron counting rules.

B\textsubscript{4}N\textsubscript{4} and
B\textsubscript{6}N\textsubscript{6}, present low negative values (-2.7
and -1.5 nA.T\textsuperscript{-1} respectively) revealing weak
antiaromaticity. On the other hand, borazine-like
B\textsubscript{3}N\textsubscript{3} present a RCS value of 3.8
nA.T\textsuperscript{-1}, in agreement with recent reported
results\textsuperscript{55}, whereas
B\textsubscript{5}N\textsubscript{5} have a RCS value 2.2
nA.T\textsuperscript{-1} revealing its weak aromatic character. The rest
of the systems (x = 7 -- 11) show values close to zero, therefore, they
are non-aromatic. Additionally, NICS\textsubscript{zz} was measurement
at 0.0 Å, 1.0 Å, 2.0 Å and FiPC (Free in plane component, where the
in-plane contributions are zero) can be seen in Fig. 1, these values
correlate quite well with the RCS, however it is necessary to be very
cautious with the interpretation. As an example, let us take the
NICS\textsubscript{zz}(1) value of B\textsubscript{5}N\textsubscript{5},
which is -0.44 ppm, this result can be interpreted as non-aromatic and
not (weak) aromatic, as indicated by its RCS value. The same behaviour
is observed for the NICS\textsubscript{zz}(2) of
B\textsubscript{4}N\textsubscript{4} (0.32 ppm) which could be
interpreted as non-aromatic, however the RCS values showed that this
system is (weak) antiaromatic.

\textbf{Table 1.} RCS (in nA.T\textsuperscript{-1}) values and
NICS\textsubscript{zz} (in ppm?) computations for the
B\textsubscript{x}N\textsubscript{x} (x = 2 -- 11) planar clusters. RCS
positive (negative values denote aromaticity (antiaromaticity), values
close to zero, nor aromatic character. Negative (Positive) values of
NICSzz descriptors states an aromatic (Antiaromatica) character, whereas
values close to zero are for non-aromatic compounds.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
B\textsubscript{x}N\textsubscript{x} & RCS & NICS\textsubscript{zz}(0) &
NICS\textsubscript{zz}(1) & NICS\textsubscript{zz}(2) &
FiPC-NICS\tabularnewline
\midrule
\endhead
B\textsubscript{2}N\textsubscript{2} & -13.0 & 16.88 & 42.08 & 3.50 &
16.01\tabularnewline
B\textsubscript{3}N\textsubscript{3} & 3.8 & -7.36 & -6.05 & -1.88 &
-6.39\tabularnewline
B\textsubscript{4}N\textsubscript{4} & -2.7 & 19.90 & 10.17 & 0.32 &
7.48\tabularnewline
B\textsubscript{5}N\textsubscript{5} & 2.2 & 4.68 & -0.44 & -1.29 &
-2.14\tabularnewline
B\textsubscript{6}N\textsubscript{6} & -1.5 & 11.36 & 6.92 & 0.47 &
3.72\tabularnewline
B\textsubscript{7}N\textsubscript{7} & -0.9 & 4.49 & 2.20 & -0.26 &
-0.35\tabularnewline
B\textsubscript{8}N\textsubscript{8} & -0.6 & 6.09 & 4.34 & 0.50 &
1.49\tabularnewline
B\textsubscript{9}N\textsubscript{9} & -0.3 & 3.52 & 2.47 & 0.21 &
0.33\tabularnewline
B\textsubscript{10}N\textsubscript{10} & -0.3 & 3.65 & 2.89 & 0.46 &
0.72\tabularnewline
B\textsubscript{11}N\textsubscript{11} & 0.1 & 2.63 & 2.11 & 0.35 &
0.37\tabularnewline
\bottomrule
\end{longtable}

When we compare it with NICS based descriptors at 0, 1 and 2 \selectlanguage{ngerman}Å above the
plane, we can see that the first two do not correlate with RCS values
(See Fig. S2 in SI), this behaviour can be attributed to contributions
in the NICS plane and also to contributions from the core electrons of
electronegative atoms. It is for this reason that NICS(2) presents a
good correlation with the RCS values because the interference at this
height is expected to be close to zero. These results confirm that one
must be careful in the assignment of (anti)aromaticity using this index.
The following sections are intended to perform an exhaustive qualitative
analysis of the (anti)aromaticity of these clusters using different
strategies proposed in the literature.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Fig. 1.} Comparisons between ring current strength (RCS) values
and NICS\textsubscript{zz}based descriptors performed at PBE0/def2-TZVP.

\textbf{Evaluation of NICS changes along the main molecular axis}

In this part, discussion starts analysing FiPC-NICS strategy, proposed
as a simplification of Stanger scans proposal. This strategy assumes of
that in-plane components are more sensitive to local induced fields
arising from the core and localized (lone pairs and bonding) electrons.
Local magnetic fields should be of short-range which means that they
should decay in small spatial intervals. In contrast, the out-of-plane
component is expected to highlight the induced magnetic field, as is the
case of aromatic and antiaromatic system. According to this strategy,
one can classify an aromatic (antiaromatic) system if it has a convex
(concave) slope, while a non-aromatic system behaves linearly. Fig. 2
shows that B\textsubscript{3}N\textsubscript{3} and
B\textsubscript{5}N\textsubscript{5} can be classified as aromatic while
B\textsubscript{2}N\textsubscript{2},
B\textsubscript{4}N\textsubscript{4} and
B\textsubscript{6}N\textsubscript{6} are antiaromatic in agreement with
our RCS values. The rest of the systems (x = 7 - 11) present a linear
behaviour revealing its non-aromatic character. Additionally, is
important to identify the distance where the in-plane components of NICS
becomes zero. This distance for B\textsubscript{2}N\textsubscript{2} and
B\textsubscript{3}N\textsubscript{3} are 1.7 and 1.1 \selectlanguage{ngerman}Å respectively. The
difference between distances are attributed to the local contributions
of the core electrons, being greater for
B\textsubscript{2}N\textsubscript{2} due to the electronegativity of
nitrogen atoms and a smaller ring size. For the rest of the systems, the
distance increases systematically from 1.2 Å for the
B\textsubscript{4}N\textsubscript{4} to 2.7 Å for the
B\textsubscript{11}N\textsubscript{11}. However, the increase in ring
size and the non-aromatic character of the clusters makes contributions
greater than 1.2 Å negligible (less than 1.0 ppm).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Fig. 2.} Plots of the NICS\textsubscript{in-plane} vs.
NICS\textsubscript{out-of-plane} for BxNx clusters (x = 3 -- 11).

Complementary, NICS\textsubscript{zz}-scans are showed in Fig. 3,
measurements were carried out at center of the ring and above up to 5 \selectlanguage{ngerman}Å.
Through these plots it is possible to see the long-range effects
characteristic of (anti)aromatic systems.
B\textsubscript{3}N\textsubscript{3} is the only system which presents
long-range negative values characteristic for aromatic systems.

For B\textsubscript{5}N\textsubscript{5}, no long-range effects are
observed, in disagreement with the RCS values which classify it as
weakly aromatic, but in agreement with the NICS\textsubscript{zz}values.
Recently, Cina pointed out that when NICS values moves from negative to
positive regions are good candidates for NICS failures which is the case
of this cluster\textsuperscript{56}. Additionally, this system presents
two minimum values of -7.4 ppm and -6.8 ppm at 0.0 and 1.4 Å
respectively, this may be due to local contributions from core
electrons, these local contributions have been studied and are important
in similar systems such as borazine\textsuperscript{57}.

On the other hand, B\textsubscript{2}N\textsubscript{2},
B\textsubscript{4}N\textsubscript{4} and
B\textsubscript{6}N\textsubscript{6} present positive long-range values
which is consistent with their antiaromatic character, while aromatic
(According RCS calculations) B\textsubscript{5}N\textsubscript{5} and
B\textsubscript{7}N\textsubscript{7} present small short-range. The rest
systems have very low values due to the contributions of the core
electrons.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Fig. 3.} NICS\textsubscript{zz} (ppm) vs. distance (in Angstrom)
at PBE0/def2-TZVP level

\textbf{Evaluation of NICS\textsubscript{zz} Isosurfaces}

A three-dimensional analysis to assess the anisotropic effects of
NICS\textsubscript{zz} was carried out, providing more insights
regarding the (anti)aromaticity of the
B\textsubscript{x}N\textsubscript{x} clusters.
NICS\textsubscript{zz}isosurfaces are depicted in Fig. 4. The presence
of long-range diatropic regions inside the rings are indicative of their
aromatic character. This can be observed in
B\textsubscript{3}N\textsubscript{3} where diatropic zones are located
at the center and, additionally, located in nitrogen atoms due to the
contributions of core electrons. The opposite effect can be seen
B\textsubscript{2}N\textsubscript{2},
B\textsubscript{4}N\textsubscript{4} and
B\textsubscript{6}N\textsubscript{6}, where strong paratropic long-range
zones are located at the center of these rings, denoting their
antiaromatic character. Along with this, the diatropic zones located in
the nitrogen atoms are also observed.

In B\textsubscript{5}N\textsubscript{5}, diatropic zones in nitrogen
atoms and above the molecular ring are observed, however it is possible
to see paratropic values at the centre of the ring, this characteristic
pattern has been observed in non-aromatic organic systems including
cyclopropane and cyclohexane\textsuperscript{58}. The rest of the
systems present diatropic regions located in the nitrogen atoms and
short range paratropic zones in the center of the ring, characteristic
of its non-aromatic nature.

\textbf{Hosted file}

\verb`image4.emf`  available at \url{https://authorea.com/users/316479/articles/446619-revisiting-anti-aromaticity-and-chemical-bond-in-planar-bxnx-clusters-x-2-11}

\textbf{Fig. 4.} NICS\textsubscript{zz} isosurfaces for
B\textsubscript{x}N\textsubscript{x} clusters (x = 3 -- 11) at +/- 4 ppm
isovalue. Blue color represents negative (diatropic) values and red
color represent positive (paratropic) values.

In order to gain more insights about the (anti)aromaticity patterns in
``problematic'' B\textsubscript{2}N\textsubscript{2} and
B\textsubscript{5}N\textsubscript{5}, dissected
NICS\textsubscript{zz}isolines have been obtained which allows us to
observe in detail the contributions of the core, \selectlanguage{greek}σ \selectlanguage{english}and \selectlanguage{greek}π \selectlanguage{english}electrons,
results are shown in Fig. 5. In the case of
B\textsubscript{2}N\textsubscript{2}, core electron contributions to
NICS\textsubscript{zz} present small diatropic short-range values.
Surprisingly, \selectlanguage{greek}σ-\selectlanguage{english}electron contributions present unexpected paratropic
long-range pattern which resembles antiaromatic compounds, whereas
\selectlanguage{greek}π-\selectlanguage{english}electron contributions shows to an antiaromatic pattern, concluding
that this cluster is doubly antiaromatic.

\textbf{Hosted file}

\verb`image5.emf`  available at \url{https://authorea.com/users/316479/articles/446619-revisiting-anti-aromaticity-and-chemical-bond-in-planar-bxnx-clusters-x-2-11}

\textbf{Fig. 5.} Isolines of dissected NICS\textsubscript{zz} for
B\textsubscript{2}N\textsubscript{2} and
B\textsubscript{5}N\textsubscript{5}clusters.

Isolines of
B\textsubscript{5}N\textsubscript{5}NICS\textsubscript{core,zz}, have
not negligible long range diatropic values according to the isosurface
of NICS\textsubscript{zz} previously shown, where the diatropicity is
located nitrogen atoms. Contributions of \selectlanguage{greek}σ-\selectlanguage{english}electrons present short-range
paratropic values in the center of molecular plane as seen in the
NICS\textsubscript{zz} isosurface of
B\textsubscript{5}N\textsubscript{5}. The contributions of \selectlanguage{greek}π-\selectlanguage{english}electrons
show long-range pattern that allows us to say that this cluster is
weakly \selectlanguage{greek}π-\selectlanguage{english}aromatic in agreement with RCS values.

\textbf{Analyzing bonding pattern of
B\textsubscript{x}N\textsubscript{x} clusters via Adaptative Natural
Density Partitioning (AdNDP)}

For a more detailed analysis regarding the aromaticity and chemical bond
in B\textsubscript{x}N\textsubscript{x} clusters, AdNDP was performed,
representative cases (antiaromatic, aromatic and non-aromatic) are shown
in Fig. 6 and Fig. 7, the remaining systems can be seen in the
supporting information.

The bonding pattern for B\textsubscript{2}N\textsubscript{2} (Fig. 6)
starts with four 2c-2e B-N \selectlanguage{greek}σ \selectlanguage{english}bonds, it is necessary to note that the
bonds are polarized towards N atoms mainly due to their high
electronegativities regarding B atoms. In addition, two \selectlanguage{greek}σ- \selectlanguage{english}and two \selectlanguage{greek}π-
\selectlanguage{english}delocalized 4c-2e bonds fullfilling electron counting rules which
confirms their doubly aromatic character.

\textbf{Hosted file}

\verb`image6.emf`  available at \url{https://authorea.com/users/316479/articles/446619-revisiting-anti-aromaticity-and-chemical-bond-in-planar-bxnx-clusters-x-2-11}

\textbf{Fig. 6.} AdNDP bonding pattern for doubly antiaromatic
B\textsubscript{2}N\textsubscript{2}. ON = occupation number

The bonding pattern of B\textsubscript{3}N\textsubscript{3} is slightly
different, 1c-2e corresponding to N-lone pairs are localized, in
agreement with NICS\textsubscript{zz} isosurface showed previously where
local diatropic zones are found. Additionally, 2c-2e corresponding to
B-N \selectlanguage{greek}σ \selectlanguage{english}bonds are localized. Finally, three 6c-2e delocalized \selectlanguage{greek}π \selectlanguage{english}bonds are
found fulfilling H\selectlanguage{ngerman}ückel's rule, which indicates an aromatic compound.
This pattern is similar to all remaining aromatic and antiaromatic
B\textsubscript{x}N\textsubscript{x} (x = 3 -- 6) clusters (See Fig. S4
-- S6 in the SI). The bonding pattern for non-aromatic
B\textsubscript{7}N\textsubscript{7} cluster presents fourteen 2c-2e \selectlanguage{greek}σ
\selectlanguage{english}bonds. The lone pair of nitrogens can no longer be located, so the
pattern reveals 14 \selectlanguage{greek}π \selectlanguage{english}bonds in agreement with bond equalization for
non-aromatic B\textsubscript{x}N\textsubscript{x} clusters. This same
pattern is observed for clusters with x = 8 -- 11 BN moieties (See Fig.
S6 -- S9 in SI).

\textbf{Hosted file}

\verb`image7.emf`  available at \url{https://authorea.com/users/316479/articles/446619-revisiting-anti-aromaticity-and-chemical-bond-in-planar-bxnx-clusters-x-2-11}

\textbf{Fig. 7.} AdNDP bonding pattern for aromatic
B\textsubscript{3}N\textsubscript{3} and non-aromatic
B\textsubscript{7}N\textsubscript{7}.ON=occupation number

\textbf{CONCLUSIONS}

A complete analysis of the (anti)aromatic character of
B\textsubscript{x}N\textsubscript{x} clusters (x = 2 -- 11) has been
performed according to magnetic criteria of aromaticity through ring
current strength (RCS) analysis, 1D, 2D, 3D
NICS\textsubscript{zz}descriptors and AdNDP analysis. The RCS values,
FiPC strategy and NICS\textsubscript{zz}-3D-grids patterns show that the
B\textsubscript{2}N\textsubscript{2} cluster is anti-aromatic.
Additionally, the isolines of dissected NICS\textsubscript{zz} and the
bond pattern according to AdNDP reveal that this cluster is doubly
anti-aromatic, showing paratropic long-range regions in \selectlanguage{greek}σ- \selectlanguage{english}and
\selectlanguage{greek}π-\selectlanguage{english}contributions and delocalized \selectlanguage{greek}σ- \selectlanguage{english}and \selectlanguage{greek}π-\selectlanguage{english}bonds complying with the
electron counting rules. For the case of
B\textsubscript{3}N\textsubscript{3} and
B\textsubscript{5}N\textsubscript{5} clusters, the
NICS\textsubscript{zz}-based strategies show patterns that suggest an
aromatic character, in line with this, the AdNDP results show three
delocalised 3c-2e bonds and five delocalised 5c-2e bonds for the
B\textsubscript{3}N\textsubscript{3} and
B\textsubscript{5}N\textsubscript{5} respectively. For the latter, the
NICS\textsubscript{zz} 3D grids show paratropic contributions in the
center of the ring that can be attributed to the contributions of the
core electrons of the N and B atoms, for this reason, isolines of
dissected NICS\textsubscript{zz} were obtained which show that
B\textsubscript{5}N\textsubscript{5} is non-aromatic \selectlanguage{greek}σ- \selectlanguage{english}and weakly
\selectlanguage{greek}π-\selectlanguage{english}aromatic, this is confirmed with RCS values revealing that both
clusters are weakly aromatic. The rest of the studied systems (X = 7 --
11) are non-aromatic, FiPC, NICS\textsubscript{zz} 3D-grids and RCS
calculations confirm these results. The AdNDP pattern shows that these
clusters have 2X localised \selectlanguage{greek}σ- \selectlanguage{english}and \selectlanguage{greek}π-\selectlanguage{english}bonds which explains the bond length
equalisation. Description of aromaticity using
NICS\textsubscript{zz}-based descriptors confirms its limitations even
though it has good correlations with RCS values, For example, the
results of NICS\textsubscript{zz}(0) present non-negligible positive
values for the clusters x = 7 - 11 which could be interpreted as having
a certain degree of anti-aromaticity, or the
NICS\textsubscript{zz}-scans which present patterns that could lead to
incorrect conclusions as mentioned by Cina. Finally, the use of
NICS\textsubscript{zz} descriptor to diagnose (anti)aromaticity must be
done carefully. Thus, the use of 1D, 2D or 3D tools based on
NICS\textsubscript{zz} are necessary to have a complete and appropriate
description of the aromaticity.

\textbf{ACKNOWLEDGEMENTS}

R.P.-R. thank the financial support of FONDECYT Postdoctorado 3180119,
(R.P.-R.). LA thanks Universidad Andres Bello for her PhD scholarship.

\textbf{REFERENCES}

1. Wang, J.; Ma, F.; Sun, M. RSC Advances 2017, 7, 16801-16822.

2. Caldwell, J. D.; Aharonovich, I.; Cassabois, G.; Edgar, J. H.; Gil,
B.; Basov, D. N. Nature Reviews Materials 2019, 4, 552-567.

3. Pouch, J. J.; Alterovitz, S. A. Synthesis and properties of boron
nitride; Trans Tech, 1990.

4. Khanna, S. N.; Jena, P. Physical Review Letters 1992, 69, 1664-1667.

5. Jena, P.; Sun, Q. Chemical Reviews 2018, 118, 5755-5870.

6. Becker, S.; Dietze, H. J. International Journal of Mass Spectrometry
and Ion Processes 1986, 73, 157-166.

7. Seifert, G.; Schwab, B.; Becker, S.; Dietze, H. J. International
Journal of Mass Spectrometry and Ion Processes 1988, 85, 327-338.

8. St\selectlanguage{ngerman}éphan, O.; Bando, Y.; Loiseau, A.; Willaime, F.; Shramchenko, N.;
Tamiya, T.; Sato, T. Applied Physics A 1998, 67, 107-111.

9. Oku, T.; Nishiwaki, A.; Narita, I. Science and Technology of Advanced
Materials 2004, 5, 635-638.

10. Van Orden, A.; Saykally, R. J. Chemical Reviews 1998, 98, 2313-2358.

11. Matxain, J. M.; Ugalde, J. M.; Towler, M. D.; Needs, R. J. The
Journal of Physical Chemistry A 2003, 107, 10004-10010.

12. Hückel, E. Zeitschrift für Physik 1931, 70, 204-286.

13. Torres-Vega, J. J.; Vásquez-Espinal, A.; Caballero, J.; Valenzuela,
M. L.; Alvarez-Thon, L.; Osorio, E.; Tiznado, W. Inorganic Chemistry
2014, 53, 3579-3585.

14. Fernández, I.; Frenking, G.; Merino, G. Chemical Society Reviews
2015, 44, 6452-6463.

15. Fowler, P. W.; Steiner, E. The Journal of Physical Chemistry A 1997,
101, 1409-1413.

16. Engelberts, J. J.; Havenith, R. W. A.; van Lenthe, J. H.;
Jenneskens, L. W.; Fowler, P. W. Inorganic Chemistry 2005, 44,
5266-5272.

17. Kekulé, A. Bulletin mensuel de la Société Chimique de Paris 1865, 3,
98.

18. Martín, N.; Scott, L. T. Chemical Society Reviews 2015, 44,
6397-6400.

19. Krygowski, T. M.; Cyra\selectlanguage{polish}ń\selectlanguage{english}ski, M. K. Chemical Reviews 2001, 101,
1385-1420.

20. Feixas, F.; Matito, E.; Poater, J.; Sol\selectlanguage{ngerman}à, M. Chemical Society
Reviews 2015, 44, 6434-6451.

21. Gershoni-Poranne, R.; Stanger, A. Chemical Society Reviews 2015, 44,
6597-6615.

22. Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; van Eikema
Hommes, N. J. R. Journal of the American Chemical Society 1996, 118,
6317-6318.

23. Lazzeretti, P. Physical Chemistry Chemical Physics 2004, 6, 217-223.

24. Pelloni, S.; Monaco, G.; Lazzeretti, P.; Zanasi, R. Physical
Chemistry Chemical Physics 2011, 13, 20666-20672.

25. Islas, R.; Martínez-Guajardo, G.; Jiménez-Halla, J. O. C.; Solà, M.;
Merino, G. Journal of Chemical Theory and Computation 2010, 6,
1131-1135.

26. Badri, Z.; Pathak, S.; Fliegl, H.; Rashidi-Ranjbar, P.; Bast, R.;
Marek, R.; Foroutan-Nejad, C.; Ruud, K. Journal of Chemical Theory and
Computation 2013, 9, 4789-4796.

27. Torres-Vega, J. J.; Vásquez-Espinal, A.; Ruiz, L.;
Fernández-Herrera, M. A.; Alvarez-Thon, L.; Merino, G.; Tiznado, W.
ChemistryOpen 2015, 4, 302-307.

28. Radenkovi\selectlanguage{polish}ć, \selectlanguage{english}S.; Bultinck, P. The Journal of Physical Chemistry A
2011, 115, 12493-12502.

29. Carion, R.; Champagne, B.; Monaco, G.; Zanasi, R.; Pelloni, S.;
Lazzeretti, P. Journal of Chemical Theory and Computation 2010, 6,
2002-2018.

30. Bultinck, P.; Fias, S.; Ponec, R. Chemistry -- A European Journal
2006, 12, 8813-8818.

31. Steiner, E.; Fowler, P. W. Physical Chemistry Chemical Physics 2004,
6, 261-272.

32. Schleyer, P. v. R.; Jiao, H.; Hommes, N. J. R. v. E.; Malkin, V. G.;
Malkina, O. L. Journal of the American Chemical Society 1997, 119,
12669-12670.

33. Steiner, E.; Fowler, P. W.; Jenneskens, L. W. Angewandte Chemie
International Edition 2001, 40, 362-366.

34. Cernusak, I.; Fowler, P. W.; Steiner, E. Molecular Physics 2000, 98,
945-953.

35. Stanger, A. The Journal of Organic Chemistry 2006, 71, 883-893.

36. Jim\selectlanguage{ngerman}énez-Halla, J. O. C.; Matito, E.; Robles, J.; Solà, M. Journal of
Organometallic Chemistry 2006, 691, 4359-4366.

37. Merino, G.; Heine, T.; Seifert, G. Chemistry -- A European Journal
2004, 10, 4367-4371.

38. Báez-Grez, R.; Ruiz, L.; Pino-Rios, R.; Tiznado, W. RSC Advances
2018, 8, 13446-13453.

39. Báez-Grez, R.; Rabanal-León, W. A.; Alvarez-Thon, L.; Ruiz, L.;
Tiznado, W.; Pino-Rios, R. Journal of Physical Organic Chemistry 2018,
0, e3823.

40. Rabanal-León, W. A.; Vásquez-Espinal, A.; Yañez, O.; Pino-Rios, R.;
Arratia-Pérez, R.; Alvarez-Thon, L.; Torres-Vega, J. J.; Tiznado, W.
European Journal of Inorganic Chemistry 2018, 2018, 3312-3319.

41. Islas, R.; Heine, T.; Merino, G. Accounts of Chemical Research 2012,
45, 215-228.

42. Boldyrev, A. I.; Wang, L.-S. Physical Chemistry Chemical Physics
2016, 18, 11589-11605.

43. Zubarev, D. Y.; Boldyrev, A. I. Physical Chemistry Chemical Physics
2008, 10, 5207-5217.

44. Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon
Press, 1994.

45. Keith, T. A.; Bader, R. F. W. Chemical Physics Letters 1992, 194,
1-8.

46. Keith, T. A.; Bader, R. F. W. The Journal of Chemical Physics 1993,
99, 3669-3682.

47. Keith, T. A.; Bader, R. F. W. Chemical Physics Letters 1993, 210,
223-231.

48. Adamo, C.; Barone, V. The Journal of Chemical Physics 1999, 110,
6158-6170.

49. Weigend, F.; Ahlrichs, R. Physical Chemistry Chemical Physics 2005,
7, 3297-3305.

50. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;
Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.;
Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.;
Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.;
Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima,
T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery Jr., J. A.;
Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J.; Brothers, E. N.;
Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.;
Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi,
J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross,
J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R.
E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.;
Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador,
P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.;
Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09
2009.

51. Keith, T. A. AIMAll (Version 190213) Overland Park KS, USA, 2019
(aim.tkgristmill.com).

52. Lu, T.; Chen, F. Journal of Computational Chemistry 2011, 33,
580-592.

53. Jones, L.; Lin, L.; Chamberlain, T. W. Nanoscale 2018, 10,
7639-7648.

54. Bethel, E. W.; Childs, H.; Hansen, C. High Performance
Visualization: Enabling Extreme-Scale Scientific Insight; CRC Press,
2012.

55. Rabanal-León, W. A.; Tiznado, W.; Alvarez-Thon, L. International
Journal of Quantum Chemistry 2019, 119, e25859.

56. Foroutan-Nejad, C. Theoretical Chemistry Accounts 2015, 134, 8.

57. Islas, R.; Chamorro, E.; Robles, J.; Heine, T.; Santos, J. C.;
Merino, G. Structural Chemistry 2007, 18, 833-839.

58. Pino-Rios, R.; Cárdenas-Jirón, G.; Ruiz, L.; Tiznado, W.
ChemistryOpen 2019, 8, 321-326.\selectlanguage{english}
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