Probing the Structural Evolution and Stabilities of Medium-Sized MoB

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Probing the Structural Evolution and Stabilities of Medium-Sized MoB Clusters Peifang Li, Xindi Du, Jingjing Wang, Cheng Lu, and haihua chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05759 • Publication Date (Web): 09 Aug 2018 Downloaded from http://pubs.acs.org on August 10, 2018

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The Journal of Physical Chemistry

Probing the Structural Evolution and Stabilities of Medium-Sized MoBn 0/− Clusters Peifang Li,† Xindi Du,† Jing Jing Wang,‡,¶ Cheng Lu,∗,‡,§ and Haihua Chen∗,∥ †

College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao 028043, China Department of Physics, Nanyang Normal University, Nanyang 473061, China ¶ Education College of Information Technology, Hubei Nomal University, Huangshi 435002, China § Department of Physics and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States ∥ Department of Basic Education, Qinghai University, Xining 810016, China ‡

Supporting Information ABSTRACT: The intriguing electronic bonding properties of transition-metal-doped boron clusters have made them the subject of increased attention. However, the structures and stabilities of boron clusters doped with Mo remain elusive, and reports on Mo-doped boron clusters in the literature are still rare. Here, medium-sized MoBn 0/− (n = 10−20) clusters were investigated by utilizing the unbiased CALYPSO structure searching method with subsequent DFT optimization at the PBE0/Mo/LANL2DZ/B/6-311+G(d) level. Three types of geometries were found for the ground-state structures of the MoBn 0/− (n = 10−20) clusters: half-sandwich, drum-like and tubular. Furthermore, the stability of the ground-state structures was quantified and analyzed based on three effective criteria. The simulated photoelectron spectra served as electronic "fingerprints" of the clusters for comparison with experimental spectra. Subsequent molecular orbital and adaptive natural density partitioning analyses revealed that the enhanced stability of MoB18 resulted from strong interactions between the 4d orbitals of the Mo atoms and the 2p orbitals of the B atoms, as well as the B−B σ bonds in the B18 shell.

1. INTRODUCTION

As a prototypical electron-deficient element, boron and its compounds have very different chemistries and attracted considerable research activities in recent years. 1–5 Bulk boron is chiefly composed of cage-like structural units due to its electron deficiency. 6,7 However, experimental and theoretical studies have demonstrated that ground-state boron clusters are prone to forming planar or quasi-planar structures owing to their capacity to participate in both localized and delocalized bonding. 8 The ground-state structures remain planar or quasi-planar up to 36 atoms (B36 − ) for anionic boron clusters, 9–11 20 atoms (B20 ) for neutral clusters 12 and 16 atoms (B16 + ) for cationic clusters. 13 Very recently, Wang and coworkers showed that the transition from 2D to 3D fullerene-like structures occurs at approximately 40 boron atoms (B39 − 14 and B40 − 15 ) for negatively charged boron clusters. These fullerene-like boron clusters are referred to as borospherenes. Shortly afterwards, cage-like B39 + clusters were observed as a new member of the borospherene family. 16 Doping with a single metal atom will create a new avenue for boron clusters to become novel ligands or building blocks for forming new nanostructures. An experimental and theoretical study of Al-doped Bn clusters found two umbrella-type structures Al2 + [B7 3− ] and Al+ [B8 2− ]. 17 In addition, the doping of metal atoms into B3 − clusters has been theoretically predicted to form stable M+ [B3 − ] (M = Li−Cs) ionic complexes. 18 More interestingly, beautiful transition-metal-centered boron molecular wheels of TM©Bn Q (TM = V, Nb, Ta, Co, Ru), 19,20 which are monocyclic boron rings with a transition metal atom inside, have been experimentally observed. In addition, over the past few years, many studies on transition-metal-doped boron clusters have been reported. The Wang group observed a half-sandwich-type structure for Co/RuB12 − clusters 21 in 2014 as well as Co-centered

boron molecular drum CoB16 − clusters. 22 Subsequently, Jian et al. 23 determined that there are two modes of RhB18 − clusters, i.e., a drum-like structure and a quasi-planar structure, and both were observed experimentally. In 2017, Li and coworkers observed a unique tubular molecular rotor and a perfect D10d nano-drum serving as the global minimum and the minor isomer of TaB20 − , respectively. 24 Medium-sized manganese-doped boron clusters, MnBn Q (n = 10−20, Q = −/0/+), have been systematically investigated using ab initio calculations. 25 Although numerous studies on transition-metal-doped boron clusters have been reported, investigations into Mo-doped boron clusters are still rare. Lv et al. 26 observed a stable high-symmetry D3h cage MoB24 cluster using first-principles density functional theory (DFT). Another theoretical study reported the formation of small MoBn (n = 5−11) clusters. 27 A systematic investigation of the ground-state geometries, corresponding electronic properties and structural evolution of medium-sized Mo-doped boron clusters is of crucial importance. In this work, the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) searching method and accurate DFT calculations were applied to study MoBn 0/− (n = 10−20) clusters. Furthermore, we simulated the PES of anionic clusters to provide predictive information for future investigations. Moreover, the inherent stabilities of the global minima were discussed. Chemical bonding analyses were then carried out to gain further understanding of the stabilization mechanism. 2. COMPUTATIONAL DETAILS

Global minimum searches for the structures of MoBn 0/− (n = 10−20) clusters were performed using the particle swarm optimization (PSO) algorithm in the CALYPSO code. 28–30 CALYPSO method has been successfully applied in various systems 31–35 owing to its ability to predict the most stable structure by relying

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solely on information pertaining to chemical composition. It is a leading method in current structure prediction field. Structural predictions of the MoBn clusters were performed over a size range of n = 10−20; for each cluster size, we followed 50 generations to acquire the converged structures, and each generation contained 30 structures. Among the approximately 1000 isomers, the top 50 energetically low-lying isomers were selected and re-optimized, if within 3 eV of the lowest-lying structure, using the Gaussian 09 package. 36 The subsequent optimizations were performed using the DFT method with the PBE0 functional. 37 The LANL2DZ basis set 38–40 was used for the Mo atom, and the 6-311+G(d) basis set 41 was used for the B atom. In the geometry optimization process, different spin multiplicities, up to sextets and quintets for the neutral and anionic clusters, were considered. The vibrational frequencies were checked to make sure that all the clusters possess real frequency values and driving the isomer to a local minimum. Timedependent density functional theory (TD-DFT) 42 was utilized to simulate the photoelectron spectra of the anionic MoBn clusters. Adaptive natural density partitioning (AdNDP) 43 bonding analyses were implemented in the Multiwfn 3.3.8 program package 44 to gain further insight into the bonding nature. 3. RESULTES AND DISCUSSIONS 3.1. Geometrical structures and photoelectron spectra. The ground-state structures and the low-lying isomers of neutral MoBn (n = 10−20) clusters, along with the relative energies, are exhibited in Figure 1 (the corresponding anionic species are exhibited in Figure 2. Each isomer of the neutral cluster is labeled na, nb or nc (na− , nb− or nc− for the anionic species), where n denotes the number of B atoms, and a, b and c indicate the structures in increasing energetic order alphabetically. For clarity, the side elevations of these structures are illustrated in Figure S1 and Figure S2 and the Cartesian coordinates of the ground-state structures are listed in Table S1 (see SI). The corresponding point group symmetry and electronic state are given in Table 1. As shown in Figure 1 and Figure 2, all of the structures possess substantially high point symmetry, except for 10b, 12b− , 15c− , 17c− and 18a− . The ground-state geometries of the small MoBn 0/− (n = 10−15) clusters are found to be half-sandwich-type structures, while the large species with n ≥ 16 are drum-type and tubular structures. The global minimum structures of both anionic and neutral MoB10 − MoB15 possess halfsandwich-type structures, where the Mo atom is half surrounded by the Bn moiety. For 10a/a− , the B10 moiety is quasi-planar with two B atoms surrounded by an eight-membered outer ring. In addition, the subsequent MoBn 0/− (n = 11−15) cluster can be considered the result of adding a new B atom to the inner boron atom or the peripheral ring of the Bn−1 moiety of the smaller MoBn−1 0/− cluster. In detail, the B11 fragment in the ground-state structures of MoB11 0/− is created by adding a B atom to the inner two boron atoms of B10 , forming a triangle; 12a/b− can be considered the result of adding a B atom to the outer ring of the B11 fragment; 13a/a− is formed by adding a B atom to the inner triangle of B12 ; there is one more B atom in the peripheral ring of 14a/b− than in 13a/a− ; and B15 of 15a/a− is a ten-membered peripheral ring with a pyramid inside it. Likewise, all the structures of 16a/a− − 20a/a− are drum-type structures, where the Mo atom is located inside the drum, with the notable exception of the tubular 19a/a− structure, which can be considered two additional B atoms capped on the Mo-centered B drum. 16a/a− , 18a− and 20a/a− are beautiful drum-type structures; 17a/a− and 18a are distorted bowl-shaped structures. The structural evolution of the nb/b− structures is similar to that of the ground-state structures. The small nc/c− structures tend to be quasi-planar and then tend to form half-surrounded and all-surrounded structures. It

Figure 1. Optimized low-energy structures of MoBn clusters (n = 10−20). The ground state is labeled “a”. The relative energies of each isomer are presented in eV along with the symmetries. The green spheres represent Mo atoms.

should be noted that charge has little influence on the ground-state structure of the MoBn 0/− clusters, with the exception of MoB12 , MoB14 and MoB18 . Although the atomic arrangements are similar, there are some deformations in 11a− and 18a− due to the acquisition of an electron. The acquisition of an electron also changes the energetic order of MoB10/12/14/18/19 : switching 10b to 10c− , 12a to 12b− , 14a to 14b− , 18a to 18b− , 19b to 19c− and vice versa. To understand the electronic properties of MoBn 0/− (n = 10−20) clusters, the simulated photoelectron spectra (PES) of the anionic MoBn clusters, obtained by TD-DFT, are shown in Figure 3. Previous studies have provided convincing proof of the reliability of our results. 45–48 Among these, the theoretical simulations and the experimental PES of the TaB20 − cluster, 48 which is a similar species to our MoBn clusters, are depicted in Figure 3. As displayed in Figure 3, the spectral features are labeled X, A, B, etc. In each spectrum, the X peak denotes the transition from the anionic ground state to the neutral ground state, and the other (A, B, etc.) peaks indicate transitions to the excited state of the neutral complexes. The VDE of MoB10 − is approximately 2.44 eV. After the first peak, there are two peaks between 3 and 4 eV. There are three major peaks (X, A, and B) of the simulated spectrum of MoB11 − and the VDE is approximately 2.94 eV, where the first peak X located. The PES of MoB12 − shows a compact spectral pattern, and the VDE is ap-


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The Journal of Physical Chemistry Table 1. Electronic states, symmetries, average binding energies Eb (eV) and HOMO−LUMO energy gaps Egap (eV) of MoBn 0/− (n = 10−20) clusters

n 10 11 12 13 14 15 16 17 18 19 20

Sta. 1 A1 2 ′ A 1 A1 2 ′′ A 1 ′ A 4 B1 1 A1 2 ′ A 1 A1 2 ′ A 1 A1

MoBn Sym. Eb C 2v 5.35 Cs 5.37 C 3v 5.44 Cs 5.45 Cs 5.42 C 2v 5.39 C 2v 5.47 Cs 5.48 C 2v 5.54 Cs 5.49 C 10v 5.49

Egap 2.10 2.18 3.16 2.51 2.48 1.83 1.95 1.78 3.21 2.22 2.57

Sta. 2 A2 1 ′ A 2 ′′ A 1 ′ A 2 ′ A 1 A1 2 A1 1 ′ A 2 A 1 ′ A 2 ′′ A

MoBn − Sym. Eb C 2v 5.38 Cs 5.44 Cs 5.45 Cs 5.49 Cs 5.48 C 2v 5.50 C 2v 5.52 Cs 5.54 C1 5.59 Cs 5.54 D10d 5.55

Egap 1.92 2.41 2.16 1.89 1.85 2.90 1.38 1.96 1.64 1.78 2.53

Figure 2. Optimized low-energy structures of MoBn − clusters (n = 10−20). The ground state is labeled “a− ”. The relative energies of each isomer are presented in eV along with the symmetries. The green spheres represent Mo atoms.

proximately 2.88 eV. For MoB13 − , there are three major peaks, and the first peak (X) corresponds to a VDE of 2.69 eV. The simulated spectrum of MoB14 − is crowded with six peaks, and the X peak is located at approximately 3.04 eV. In contrast, the spectrum of MoB15 − is sparse, and the X peak, located at 3.42 eV, is far from the A peak. A sparse spectral pattern with four sharp bands is observed for MoB16 − , whose VDE is 3.17 eV. For the simulated spectrum of MoB17 − , the first two peaks are somewhat weak, the X peak is similar to the A peak, and the X peak is located at approximately 3.29 eV. The X peak in the spectrum of MoB18 − is bifurcated, and the VDE is approximately 3.27 eV. There are five peaks in the spectrum of MoB19 − , whose VED is 3.24 eV. The simulated spectrum of MoB20 − presents a sparse spectral pattern with a VDE of 3.30 eV. 3.2. Relative Stabilities. The average binding energy (Eb ) is an effective criterion for the thermodynamic stability of a cluster, and the Eb values of the MoBn 0/− (n = 10−20) clusters are determined as follows: Eb (MoBn ) = [nE(B) + E(Mo) − E(MoBn )]/(n + 1)

− − Eb (MoB− n ) = [nE(B) + E(Mo ) − E(MoBn )]/(n + 1)

(1) (2)

where E is the energy of the matching cluster or atom. The value of Eb as a function of cluster size n is shown in Figure 4 and listed in Table 1. A large Eb value indicates high chemical stability. As shown in Figure 4(a), the Eb curve of neutral MoBn clusters lies be-

Figure 3. Calculated photoelectron spectra of MoBn − (n = 10−20) clusters, along with the simulated (blue) and experimental (red) photoelectron spectra 24,48 of the anionic TaB20 − cluster.

low the curve of the anionic clusters, which means that the anions are thermodynamically more stable. For both anionic and neutral clusters, the value of Eb gradually increases with increasing cluster size n, implying that larger clusters form more easily than do smaller clusters. In addition, when n = 18, there is an obvious outlier in both the neutral and anionic curves, which means that the alternative is a local optimum. The second-order difference in the energy (∆2 E), which is a more sensitive parameter for reflecting relative stability, can be calculated for the ground-state geometry of the MoBn 0/− clusters as follows: ∆2 E(MoBn ) = E(MoBn−1 ) + E(MoBn+1 ) − 2E(MoBn )

ized in Figure 4(b). It is well known that for a given cluster, a maximum ∆2 E relative to its immediate neighbors indicates enhanced stability. Figure 4(b) demonstrates that the neutral MoB12 , MoB16 , and MoB18 clusters, as well as the anionic MoB11 − , MoB13 − , MoB16 − and MoB18 − clusters, are obviously more stable than their neighbors.


(3)

− − − ∆ E(MoB− (4) n ) = E(MoBn−1 ) + E(MoBn+1 ) − 2E(MoBn ) 2 0/− The ∆ E values of the ground-state MoBn clusters are visual2


As a reflection of the energy cost for an electron jumping from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO), the energy gap (Egap ) can also elucidate the stability of the clusters. High Egap values imply high chemical stability. The Egap curves for the ground-state MoBn 0/− (n = 10−20) clusters are shown in Figure 4(c), and the values are listed in Table 1. Three distinct local maxima can be observed for the MoB12 , MoB18 , and MoB15 − clusters, suggesting that these clusters are more stable than the other clusters. Consequently, by combining the foregoing analysis of Eb , ∆2 E, and Egap , we can determine that the neutral MoB18 clusters can be viewed as “magic" cluster that is thermodynamically stable. 3.3. Chemical Bonding Analysis. According to the comprehensive analysis of the electronic properties of the MoBn 0/− clusters, the neutral MoB18 cluster is chemically inert and has a large Egap (3.21 eV). To further understand of the bonding properties of the molybdenum-doped boron clusters, the molecular orbital (MO) and AdNDP analyses of MoB18 , which is chosen as a representative sample, are presented in Figure 5 and Figure 6, respectively. The pictorial MOs near the HOMO and the corresponding energy levels of MoB18 are shown in Figure 5. The LUMO is formed primarily by the 4d atomic orbital (AO) of Mo and the σ B−B bonds of the B18 component. For the occupied MOs of MoB18 , HOMO, HOMO-4, HOMO-5, HOMO-6 and HOMO-9, which are σ + π hybrid orbitals, are formed from the Mo 4d and B 2p AOs. HOMO3 and HOMO-8 are also σ + π hybrid orbitals but are predomi-

nantly composed of B p AOs of the peripheral B atoms. HOMO-1, HOMO-2 and HOMO-7 feature σ bonds derived from the mixing of the Mo d AOs with the B p AOs. Based on the analyses described above, there is pd hybridization between the Mo 4d AOs and B 2p AOs. Moreover, the interactions between the Mo atom and the B18 moiety stabilize the C 2v structure of MoB18 . We performed a chemical bonding analysis of the MoB18 cluster using the AdNDP method, which interprets the bonding of a cluster in accordance with n-center two-electron (nc−2e) bonds (1 ≤ n ≤ total number of atoms of the system). As depicted in Figure 6, the MoB18 cluster contains fourteen localized bonds and eighteen delocalized bonds, ordered by occupation number (ON) ranging from 1.76 to 2.00∣e∣. The fourteen localized bonds are all 2c−2e σ bonds on the peripheral B18 tube of the B18 moiety, and their ONs are 1.76−1.84∣e∣. Among the eighteen delocalized bonds, there are six 2c−2e σ bonds on the peripheral B18 moiety. The twenty σ bonds in the B18 shell contribute to the high stability of the B18 periphery. The remaining bonds mainly describe the interaction between the Mo atom and B18 fragment. The eight nc−2e (n = 4−11) σ bonds are formed from the 4dz2 AO of Mo and the 2p AOs of the (n−1) B atoms in the B18 moiety. As shown in the bottom row of Figure 6, the 16c−2e and 17c−2e σ bonds (ON = 2.00∣e∣) are dominated by the 4d AO of Mo atom. Finally, the 18c−2e σ bond and 19c−2e π bond visualize both the σ and π interactions between the Mo atom and the entire B18 shell. Hence, all of the bonds above lead to the substantial stabilization of the C 2v symmetry of the MoB18 cluster.

Figure 5. Molecular orbitals and energy levels of the neutral MoB18 cluster.

4. CONCLUSIONS

Figure 4. Size dependence of the averaged binding energies Eb , the secondorder energy differences ∆2 E and the HOMO−LUMO energy gaps Egap for the lowest energy MoBn 0/− (n = 10−20) clusters.

In summary, we investigated the geometric and electronic properties of medium-sized MoBn 0/− (n = 10−20) clusters using the unbiased CALYPSO structure searching method coupled with DFT optimizations. Three categories for the ground-state structures of both neutral and anionic MoBn clusters were obtained: half-sandwich structures for 10 ≤ n ≤ 15, drum-type structures for 16 ≤ n ≤ 20 except n = 19, and a tubular structure for n = 19. The simulated PES provides predictive information for future investigations based on our reliable calculations. The inherent stabilities of the groundstate structures of both the neutral and anionic MoBn clusters were also studied systemically. Based on the relative stability analyses, MoB18 was chosen as a representative for chemical bonding analysis. Furthermore, chemical bonding analysis of the MoB18 cluster revealed that the 4d orbitals of the Mo atom and the 2p orbitals of


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Figure 6. AdNDP chemical bonding analysis of the neutral MoB18 cluster. ON denotes the occupation number.

the B atoms, as well as the B−B σ bonds in the B18 shell, contribute to the stabilization of the C 2v MoB18 cluster.

∎ ASSOCIATED CONTENT Supporting Information

The side elevations of optimized low-energy structures of MoBn 0/− (n = 10−20), molecular orbitals and AdNDP results of neutral MoB15 cluster. This material is available free of charge via the Internet at http://pubs.acs.org.

∎ AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected] (L.C.). *E-mail: [email protected] (C.H.). Notes The authors declare no competing financial interest.

∎ ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 11304167, 11604175 and 21671114), the 973 Program of China (No. 2014CB660804), the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase No. U1501501), the Program for Science & Technology Innovation Talents in Universities of Henan Province (No. 15HASTIT020), and the Science and Technology Plan Projects of Qinghai province (No. 2014-ZJ-942Q). Parts of the calculations were performed using the Cherry Creek Supercomputer of the UNLV’s National Supercomputing Institute.

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Probing the Structural Evolution and Stabilities of Medium-Sized MoB

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