INTRODUCTION
Mixed boron-nitrogen (BN) materials have been subject of both experimental and theoretical studies in order to understand their properties1, 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 devices2. Additionally, BN clusters are interesting due to their participation in formation of thin solid films of β-BN, that possess the particularity of scratching diamond3. 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 coined4, so knowing the structures and electronic properties of these clusters is of great importance5. BxNy clusters have been characterized through the interaction between pulsed laser evaporation followed by matrix infrared spectroscopy and theoretical predictions6,7. On the other hand, BxNx clusters offer three-dimensional structures that are similar to fullerene. B12N12, B76N76, B208N208, among others, these have been obtained through intense irradiation of boron nitride samples8,9. Furthermore, small clusters offer planar structures that resemble carbon clusters10.
Some years ago, Matxain et al .11 carried out an exhaustive analysis of the potential energy surface (PES) of BxNx 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 π-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 B2N2 are counter intuitive according to traditional electron counting rules such as Hückel’s rule12, 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 others13-16.
The concept of aromaticity17, 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 chemistry18. There are several criteria to rationalize aromaticity, such as the geometric19, electronic delocalization20 and the magnetic criteria21, being the latter the latter being very popular in recent years. In 1996, Schleyer et al . proposed the Nucleus independent chemical shift (NICS)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 aromaticity23-31.
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)32, and to evaluate the out-of-plane component of the NICS tensor, the so called NICSzz which has been proven to be particularly sensitive to π-electron delocalization33,34. Other strategies proposed are related to the analysis of NICS in the axis perpendicular to the molecular plane. Stanger et al .35 and Solá et al. 36, independently, proposed NICS scans and more recently Torres-Vegaet al .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 topology37-41.
In this article the aromaticity of BxNxclusters (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) method42,43. 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 Bader44-47.