Valence bonds in elongated boron clusters

Abstract

A well-defined class of planar or quasi-planar elongated boron clusters, of type B q2 713n , serves as a basis to identify the valence bond picture of delocalized boron networks. The origin of the series is the B 2 7 cluster, which exhibits r-aromaticity. The cluster generating step is the repetitive expansion by three boron atoms in the direction of elongation. Specific electron counting rules are obtained for p-bonding, peripheral r-bonding and multicenter inner r-bonding. A valence bond structure is introduced which explains the remarkable regularity in the bonding pattern. The analysis supports 4c-2e bonds as an alternative to the common 3c-2e bonds. The results are validated by symmetry induction and ab initio calculations. K E Y W O R D S boron clusters, computational chemistry, induction method, multicenter bonding 1 | I N TR ODU C TI ONThe recent literature reports on a wide variety of planar and bowl shaped boron clusters. Proposed structures are usually based on theoretical calculations, but for some cases structures could be confirmed by photoelectron or infrared spectroscopy [1] on clusters produced by laser evaporation. [2][3][4] A further special feature of some clusters which are shaped like two concentric rings is the almost barrierless rotatory motion of the inner ring with respect to the outer ring. [5] This motion has been compared to a Wankel motor at the molecular scale. [6] In view of the rich variety of shapes and properties, which challenges accepted concepts of chemical bonding, boron is said to be the new carbon. As opposed to carbon, it is known to adopt multicenter bonds which have to be accomodated in a proper theoretical scheme. [7][8][9] To build a consistent valence bond picture that would apply to all these clusters, a gradual approach is required based on a well-defined set of structures. For this, we chose the particular family of the so-called elongated boron clusters. The aim is to obtain a set of rules that rationalize the electronic structure calculations on a series of structures extending from B 2 7 to B 22 28 . [10][11][12][13][14][15][16][17][18] Int J Quantum Chem. 2018;118:e25575.

Structure, stability and bonding of the leapfrogB240,±1,±2

“…The results from the AdNDP analysis of the leapfrog clusters 3 and 4 are in accordance with those obtained by Arvanitidis et al [28] who reported that boron elongated clusters prefer 2c 2e bonds at their periphery. However, AdNDP analysis alone is not sufficient and cannot be used as the sole argument to support a given distribution of the σ electron density of any system.…”

“…The data as reported in Table 3 respectively. The reverse counting principle is followed, as used earlier in Arvanitidis et al [28] and Patouossa et al [29] Even though their minimum geometries are of C 2v symmetry, performing AdNDP analysis in high point group such as D 2h or C 4v is justified by the fact that if an electron distribution holds in the covering group, it should necessarily be obeyed in the subgroups, while the opposite is not true. [28,29] The dianion B Γ MO = Γ π + Γ σ = 9A g + 2B 1g + 2B 2g + 6B 3g + A u + 7B 1u + 7B 2u + 3B 3u ð16Þ in which the contribution of π-orbitals has the global symmetry.…”

“…In our recent study on the ring current in B 50 , we reported a generic scheme based on leapfrog principle [27] that may be used to build a family of leapfrog boron clusters, in particular the leapfrog B 24 . The valence bonds in elongated and planar boron disks were investigated in detail by Arvanitidis et al [28] and Patouossa et al [29] Moreover, it has been demonstrated that π molecular orbitals (MOs) in the elongated and disk-like boron clusters follow the models of an electron confined to a rectangular box and a disk, respectively. [30][31] In the same context, this study presents for the first time the structure and relative stabilities of two leapfrog B 24 0,±1,±2 isomers in different charge states.…”

“…The distribution of valence σ-bonds in leapfrog B 24 boron clusters is analyzed using density functional theory (DFT), group theory, and adaptive natural density partitioning analysis (AdNDP). These techniques were already applied successfully to several boron clusters [28,[31][32][33] and yielded electron counting rules that govern the distribution of inner σ-electrons in boron clusters. The present study shows that a quasiplanar leapfrog B 24 is more stable than the bowl shape and appears to be experimentally viable as it competes with the most stable quasiplanar boron cluster with pentagonal holes reported by Boldyrev et al [26] 2 | COMPUTATIONAL METHODS…”

Overlap of Radial Dangling Orbitals Controls the Relative Stabilities of Polyhedral BnHn–x Isomers (n = 5–12, x = 0 to n – 1)

“…A similar possibility exists for flat structures as well. 43 The effect of overlap of radial dangling orbitals formed after removal of H atoms from polyhedral boranes in shaping the cluster geometries is quantitatively studied in this article for polyhedral B n H x clusters, by varying the sizes from 5 to 12 and x ≤ n. The topology of the polyhedron decides the angular direction of the dangling radial orbitals and therefore must determine the structural transition points from 3D to 2D geometries upon removal of H atoms. The corresponding Sidoped boron clusters, being isolobal to the BH units, have also been studied by varying the cluster sizes.…”