Theoretical Design of Novel Boron-Based Nanowires via Inverse Sandwich Clusters

Borophene has important application value, boron nanomaterials doped with transition metal have wondrous structures and chemical bonding. However, little attention was paid to the boron nanowires (NWs). Inspired by the novel metal boron clusters Ln2Bn − (Ln = La, Pr, Tb, n = 7–9) adopting inverse sandwich configuration, we examined Sc2B8 and Y2B8 clusters in such novel structure and found that they are the global minima and show good stability. Thus, based on the novel structural moiety and first-principles calculations, we connected the inverse sandwich clusters into one-dimensional (1D) nanowires by sharing B−B bridges between adjacent clusters, and the 1D-Sc4B24 and 1D-Y2B12 were reached after structural relaxation. The two nanowires were identified to be stable in thermodynamical, dynamical and thermal aspects. Both nanowires are nonmagnetic, the 1D-Sc4B24 NW is a direct-bandgap semiconductor, while the 1D-Y2B12 NW shows metallic feature. Our theoretical results revealed that the inverse sandwich structure is the most energy-favored configuration for transition metal borides Sc2B8 and Y2B8, and the inverse sandwich motif can be extended to 1D nanowires, providing useful guidance for designing novel boron-based nanowires with diverse electronic properties.


INTRODUCTION
Boron-based materials were found wide applications in the fileds of emissions, supercapacitors, optical absorptions, photodetectors, etc. (Xu et al., 2013;Sussardi et al., 2015;Akopov et al., 2017;Carenco et al., 2013;Tian et al., 2019). Unlike the extensive attention on carbon clusters such as fullerenes and carbon fibers, boron clusters and materials are relatively less studied by scientists. However, there is much space and potential to develop boron-based nanomaterials.
Boron shows a strong tendency to form multi-center-two-electron bonds (mc-2e) in both polyhedral molecules and bulk isotopes (Wang, 2016;Jian et al., 2019;Lipscomb, 1977;Alexandrova et al., 2006) due to its electron deficiency. Therefore, boron clusters have the characteristic of electron delocalization bonding with some delocalized electronic structures and unique aromaticity . In the past two decades, the structure and chemical bonding of bare boron clusters have been studied by combining experimental and theoretical methods Pan et al., 2019), and planar clusters, nanotube-like cluster structures, graphenelike boron spheres and fullerene-like boron spheres have been found (Kiran et al., 2005;Piazza et al., 2014;Li et al., 2014;Bai et al., 2019;Zhai et al., 2014). Also due to the characteristic of electron deficiency, boron can be doped with metal to form different kinds of metal boride structures. Boron has formed a large number of important boride materials, ranging from superconducting MgB 2 and superhard transition metal borides to borides with extremely high thermal conductivity (Nagamatsu et al., 2001;Chung et al., 2007).
As the 5th element adjacent to carbon in the periodic table, ring and cage boron clusters have poor stability due to their electron-deficient properties. However, the introduction of transition metals can greatly improve the stability of boron clusters. Transition-metal-doped boron clusters have led to a new direction of boron nanomaterials, such as the metal-centered aromatic borometallic wheels and tubular metal-centered drums (Romanescu et al., 2011;Popov et al., 2015;. On the other hand, assembling boron clusters by doping them with different types of atoms is a potential way to change properties. For example, CoB 18 and RhB 18 planar clusters have been found, which makes it possible to dope metal with borographene . Wang and Boldyrev's joint research group have reported a variety of neutral or charged planar wheel clusters centered on supercoordination transition metals M©B n (M Fe, Co, Nb, Ru, Rh, Ir, Ta; n 8-10) (Romanescu et al., 2011).
Recently, Wang's experimental group and Li's theoretical group jointly observed several new metal boron clusters Ln 2 B n − (Ln La, Pr, Tb; n 7-9) with an inverse sandwich structure Chen et al., 2019). It is found that these clusters have the double aromatic properties of π and σ bonding contributions, showing high stability and symmetry, and the magnetization of B 8 ring is high. The study provides a novel pattern for the design of new lanthanide borides, and a few inverse sandwich complexes were proposed Cui et al., 2020;Shakerzadeh et al., 2020;Xiao et al., 2021). A few questions arise naturally: Would the transition metal borides adopt the inverse sandwich structure in a stable manner? Can the inverse sandwich structure motif be extended to periodic nanomaterials, like designing the super stable 1D-P 10 nanowire and 2D-P 8 N 2 nanosheet based on all pentagon containing P 8 clusters Dong et al., 2021)? Thus, in this work, by means of first-principles calculations, we examined the stability of M 2 B 8 (M Sc and Y) clusters with the inverse sandwich structure, and extended the inverse sandwich moiety to design novel boron-based nanowires (NWs). The constructed 1D-Sc 4 B 24 and 1D-Y 2 B 12 NWs show good stability, and the former/later one is a semiconductor/metal. Our theoretical work successfully extended the inverse sandwich moiety to the 1D crystals, which is helpful to design novel boron-based nanowires with diverse electronic properties.

METHODS
The comprehensive genetic algorithm (CGA) (Zhao et al., 2016) combined with the DMol 3 program (Delley, 1990;Delley, 2000) was used to search the global minimum of Sc 2 B 8 and Y 2 B 8 clusters. The low-energy clusters generated by CGA were further optimized using density functional theory (DFT) implemented in the Vienna Ab initio Simulation Package (VASP) code (Kresse and Furthmuller, 1996;Kresse and Hafner, 1993;Kresse and Hafner, 1994). The exchange and correlation functional are defined by the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional (Perdew et al., 1996). The k points of the geometric optimization and the molecular dynamics simulation were set to 1 × 7 × 1 and 1 × 3 × 1. The phonon spectra were calculated by VASP and Phonopy codes (Togo and Tanaka, 2015). Thermal stability was assessed at 300 and 500 K based on first-principles molecular dynamics [FPMD simulations conducted at the DFT level using a canonical ensemble having a constant number of atoms, volume with the temperature controlled by the Nosé-Hoover thermostat (Martyna et al., 1992;Kresse and Hafner, 1993)], and temperature (NVT) with 1 fs time steps for a total simulated time duration of 5 ps. The band structures of the designed nanowires were calculated by PBE and Heyd-Suseria-Ernzerhof (HSE06) hybrid functional (Heyd et al., 2003). To predict the clusters and nanowires in a more reliable manner, we also considered the PBE + D2 approach (Bučko et al., 2010). Almost no difference was found between the PBE-D2 and PBE structures and cohesive energies.

Structure, Stability and Magnetic Properties of Sc 2 B 8 and Y 2 B 8 Clusters
Based on the inverse sandwich structure of La 2 B 8 − , we optimized the neutral transition metal boron clusters of the same configuration-Sc 2 B 8 and Y 2 B 8 clusters (the two Sc/Y atoms locate symmetrically to the two sides of the B 8 ring). In As shown in Supplementary Figure S1, the two vibrational spectra have simple vibration modes due to the high symmetry, and no negative mode was found, indicating the stability of these two clusters. In the Sc 2 B 8 cluster, the intensity peaks of 144 and 752 cm −1 can be assigned to Sc−B bond and B−B bond vibrations, respectively. The sharp asymmetric oscillations in the Y 2 B 8 cluster are at 149 and 721 cm −1 , indicating the vibration modes of the Y−B bond and the B−B bond, respectively. At the same time, a FPMD simulation lasting for 5 ps was performed for both clusters at room temperature (300 K). The annealed structures well remain the original inverse sandwich configuration, as shown in Supplementary Figure S2, which also suggests the good stability of the Sc 2 B 8 and Y 2 B 8 clusters adopting inverse sandwich structure.
Furthermore, CGA was used to generate low-energy isomers of Sc 2 B 8 and Y 2 B 8 clusters. The four low-lying structures, and an isomer, which can be viewed as the B-centered B 7 ring sandwiched by two Sc/Y atoms, were presented in Supplementary Figure S3, and the inverse sandwich configuration for both Sc 2 B 8 and Y 2 B 8 clusters is the most stable one (0.69-1.34 eV lower than the other four low-energy isomers at PBE-D2 level of theory). In particular, the CCSD(T) test computations also support the PBE-D2 results that the inverse sandwich structures are much lower in energy than other isomers. Thus it is feasible to synthesize the inverse sandwich Sc 2 B 8 and Y 2 B 8 clusters in experiments.
Additionally, we examined the dissociation of inverse sandwich M 2 B 8 (M Sc, Y) clusters. For the first M dissociation (M 2 B 8 → M + MB 8 ), the reaction is endothermic by 2.11 and 2.08 eV, respectively for M Sc and Y; and for removing the second M (MB 8 → M + B 8 ), it is also an endothermic reaction with the energy input of 2.37 and 2.17 eV for M Sc and Y, respectively. The highly endothermic dissociations of M from B 8 , indicate reaction barriers are >2 eV. Meanwhile, when the M atoms were put 5 Å from the B 8 center, it will be optimized to the energetically favored inverse sandwich structure. The above results as summarized in Supplementary Figure S4 again confirmed that the M 2 B 8 (M Sc, Y) clusters with inverse sandwich configuration are highly stable.
Besides, we further explored magnetic properties of the global minimum structures. Three magnetic configurations were compared, namely, antiferromagnetic (AFM), ferromagnetic (FM) and nonmagnetic (NM) states. We set the energy value of NM as 0 eV and all other energy values as their relative differences. Our calculations revealed that both Sc 2 B 8 and Y 2 B 8 clusters are nonmagnetic ( Table 1).

Structure and Stability of 1D Nanowires
Considering that the Sc 2 B 8 and Y 2 B 8 clusters of inverse sandwich configuration are the global minima, the inverse sandwich structural moiety might be extended to a periodic manner. Therefore, we connected the inverse sandwich clusters into 1D nanowires by sharing B−B bridges between adjacent clusters, similar to the observation of inverse triple-decker La 3 B 14 − (Chen et al., 2019). The 1D-Sc 4 B 24 and 1D-Y 2 B 12 nanowires were obtained after structural relaxation as displayed in Figure 2. For the optimized 1D-Sc 4 B 24 (Figure 2A), neither the inverse sandwich moiety of Sc 2 B 8 nor the sharing B−B bonds was clearly observed, largely due to the formation of B 4 rhombus, which is regarded as a stable unit of boron analogs. The In order to confirm the stability of the two nanowires, we first examined their thermodynamic stability by calculating the cohesive energy (E coh ). In our work, the cohesive energy is defined as equation 1, where, E 1 /E 2 is the energy of an  isolated transition metal atoms (Sc or Y)/B atom, E tot is the total energy of nanowire, n/m is the number of transition metal/B atoms. According to the above definition of cohesive energy, the larger the calculated value is, the more stable the structure is. The calculated cohesive energies of 1D-Sc 4 B 24 and 1D-Y 2 B 12 nanowires are 5.92 and 6.00 eV/atom, respectively, much larger than the E coh values of the clusters (5.35 and 5.29 eV/ atom, respectively for Sc 2 B 8 and Y 2 B 8 ). These high cohesion energies show that two 1D nanowires have good thermodynamic stability.
Then, we calculated the phonon dispersion to investigate their dynamic stability. In these phonon dispersions, no imaginary frequencies were observed (Figure 3), indicating that the two designed nanowires based on the inverse sandwich Sc 2 B 8 and Y 2 B 8 clusters are dynamically stable.
Finally, we performed FPMD simulations in order to access their thermal stability with the supercell of 112 atoms (16 transition metal atoms and 96 B atoms). The 1D-Sc 16 B 96 was annealed at 300 K for 5 ps, and the final structure retained the original B 8 rings (Supplementary Figure S5A), and the structure obtained remains intact. For the one-dimensional nanowire structure constructed by Y 2 B 8 , we conducted two 5 ps simulation at room temperature of 300 K (Supplementary Figure S5B) and 500 K (Supplementary Figure S5), respectively. The 1D-Y 16 B 96 structure still showed structural integrity under both simulation conditions. It also preserves structural integrity at 500 K in particular. The results of FPMD simulations confirm that two designed nanowires possess good thermal stability.

Magnetic and Electronic Properties
Through the above analysis of thermodynamic, dynamic and thermal stability, it is found that the two designed nanowires are stable. Therefore, we further explored the magnetic and electronic properties of the two nanowires. For the magnetic  Figure S7, FM, and NM. Our computations showed that neither 1D-Sc 4 B 24 nor 1D-Y 2 B 12 is magnetic. The relative energies of examined magnetic configurations of the two structures were given in Table 2. In addition, through the analysis of charge transfer, we found that each Sc/Y atom transferred ∼1.5/2.0 electrons to boron. The differential charge density diagrams of the two 2D nanostructures (Figure 4) showed that the electrons have delocalized bonding characteristics.
We used the PBE method to predict the electronic band structures of the two designed nanowires ( Figure 5). Compared to the metallicity of teetotum cluster Li 2 FeB 14 based nanowire (Shakerzadeh et al., 2020), the 1D-Sc 4 B 24 nanowire is a direct-bandgap semiconductor with the bandgap of 0.51 eV, while the 1D-Y 2 B 12 NW is a metal, and the p orbital of B dominates the state near the Fermi level. The commonly used PBE method usually underestimates the bandgaps. Therefore, we also used HSE06 method to calculate the electronic band structure of 1D-Sc 4 B 24 nanowire, as shown in Supplementary Figure S8

CONCLUSION
In summary, by means of first-principles calculations combined with CGA search, we found that Sc 2 B 8 and Y 2 B 8 clusters of inverse sandwich structure are the lowest-energy isomers and have good stability, and we constructed one-dimensional nanowires containing the structural moiety of the two clusters. The high stability of 1D-Sc 4 B 24 and 1D-Y 2 B 12 nanowires is confirmed by the investigation of thermodynamical, dynamical and thermal perspectives. Both 1D-Sc 4 B 24 and 1D-Y 2 B 12 nanowires are nonmagnetic; in terms of electronic behavior, the 1D-Sc 4 B 24 is semiconducting with the HSE06 bandgap of 0.85 eV, while the 1D-Y 2 B 12 is metallic. Our theoretical work not only identified the inverse sandwich configuration as the lowest-energy one for transition metal borides Sc 2 B 8 and Y 2 B 8 clusters, but also successfully extended the inverse sandwich moiety to 1D nanomaterials. Thus, it is helpful to design novel boron-based nanowires for both experimental and theoretical communities. E coh (nE 1 + mE 2 − E tot )/(n + m)

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DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.

AUTHOR CONTRIBUTIONS
CJ contributed to calculations, methodology, formal analysis, writing-original draft, and funding acquisition. ZL performed formal analysis and writing-original draft. SL performed data curation and investigation. LS and SW performed methodology, investigation, writing-original draft, and supervision, and funding acquisition. FL contributed to conceptualization, methodology, writing-review and editing, funding acquisition, project administration, and supervision.