Structure, stability, and electronic properties of singly and doubly transition metal doped boron clusters B14M

An examination of the first-row transition metal doped boron clusters, B14M (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) in the neutral state, is carried out using DFT quantum chemical calculations. The lowest-energy equilibrium structures of the clusters considered are identified at TPSSh/ 6-311+G(d) level. It is found that the structural patterns of doped species evolve from exohedrally capped quasi-planar structure B14 to endohedrally doped double ring tubular when M goes from Sc to Cu. The B14Ti and B14Fe turn out to be remarkable species due to their enhanced thermodynamic stabilities with larger average binding energies. Their electronic properties can be understood in terms of the density of state (DOS). 


Introduction
There has been considerable interest in the boronbased clusters as endorsed by a large number of experimental and theoretical investigations in the last decades. This is due to not only their novel physical and chemical properties but also their promising abilities for new technological applications. The structural landscape of small pure boron clusters up to B20, provided by many studies [1], is now clearly determined for both neutral and charged states. It reveals that from the size B17 + to B20 + , the cations favor a double ring tubular structure [2], whereas anionic and neutral clusters are more stable in the planar form [3,4] except for the neutral B14. The B14 is an extraordinary size during the growth mechanism of small bare boron clusters since it is the smallest all-boron fullerene [5], whereas the dicationic state B14 2+ was found as the first double-ring (DR) boron cluster [6]. The DR structure emerges from a superposition of two Bk strings leading to a tube B2k. The most stable structure of neutral B20, having the very high stability in comparison with the other isomers, is the most well-known all-boron double ring [7], among the others B18 2+ [6], B22 2+ [8], B24 [9], etc. For the neutral state of pure boron clusters Bn, however, the DR structures only exist at the sizes n ≥ 20. The DR tube achieves double aromaticity [10][11][12] by the classic Hückel (4N + 2) rule for both π electrons (radial electrons) and σ electrons (tangential electrons). It can be thus rationalized for the enhanced stability of the DR structure.
They are expected to become the potential candidates as dopants in clusters due to the interaction between these impurities and host electrons and may alter both electronic and geometrical structures and thus generate the doped cluster possessing the novel physicochemical properties [13,14].
Numerous theoretical and experimental studies reported that doping one transition-metal atom on small boron clusters leads to the formation of the wheel-type structures, detected at the sizes of 8 ≤ n ≤ 10, in which the impurity M tends to be encapsulated at the center of the Bn rings [15][16][17][18][19][20].
For the sizes of Bn with n > 10, numerous geometrical patterns of boron clusters doped with a transition metal were found, such as the leaf-like, pyramid-like, umbrella-like, or metallo-borophene structures [21][22][23]. Remarkably, our previous study indicates that the iron-doped B14Fe and B16Fe are stabilized DR tubes, whereas B18Fe and B20Fe are stabilized fullerenes [24]. Most recently, our systematic investigation on singly and doubly nickel-doped boron clusters reveals that from the size n = 14, the Ni impurities cause stronger effects, and the most stable isomers BnNim thus favor the shape of the related DR tubular boron structures [25]. The formation and high thermodynamic stability of boron clusters doped with both Fe and Ni certify the use of transition-metal atoms as impurities to generate various growth paths leading to larger boron clusters possessing peculiar 3D structures, such as tubes, cages, or fullerenes [26].
Although some studies on transition-metaldoped boron clusters have been carried out, the investigations on metal-doped boron clusters, in particular at the sizes n > 10, are insufficient. There are still some boron clusters doped with 3d transition metals that have not been systematically examined yet. Only a few BnMm clusters, with M being a transition metal, such as Sc, Ti, Fe, Co, and Ni, were reported in the recent past [25,27,28].
Motivated by that, we set out to operate a theoretical study on the boron clusters doped with a transition metal atom B14M, where M is a firstrow transition metal ranging from Sc to Cu, using density functional theory (DFT) calculations. We thoroughly identify the geometries of the most stable structures and, thereby, explore their exciting possibilities of structural evolution as well as determine their electronic configuration and energetic parameters.

Computational Methods
In consideration of the reliability tests obtained from many earlier reports on boron-based clusters [8,24,25,[27][28][29], we have used the hybrid TPSSh functional in conjunction with the 6-311+G(d) basis sets as implemented in the Gaussian 09 package [30] for all calculations in this work. The search for energy minima is conducted using two diverse approaches. First, all possible structures of BnMm clusters are generated using a stochastic algorithm [31]. In addition, initial structures of

Lower-lying isomers of B14M clusters
The shapes of the equilibrium structures of the B14M clusters detected, their spin states, and DFT relative energies are shown in Fig. 1 and Fig. 2.
Because of a large number of isomers located on the potential energy surfaces of the clusters

Relative stabilities of B14M
Like in previous studies on various clusters [25,32,33], the relative stabilities of B14M species considered can be evaluated on the basis of the average binding energy per atom (Eb), which is conventionally defined as follows: Furthermore, the average binding energy of pure boron neutral B15 with the same number of atoms is also determined for comparison with Eb(B14M): where

Density of states of B14Ti and B14Fe
The