Structural Evolution and Electronic Properties of Selenium-Doped Boron Clusters SeBn0/− (n = 3–16)

A theoretical research of structural evolution, electronic properties, and photoelectron spectra of selenium-doped boron clusters SeBn0/− (n = 3–16) is performed using particle swarm optimization (CALYPSO) software in combination with density functional theory calculations. The lowest energy structures of SeBn0/− (n = 3–16) clusters tend to form quasi-planar or planar structures. Some selenium-doped boron clusters keep a skeleton of the corresponding pure boron clusters; however, the addition of a Se atom modified and improved some of the pure boron cluster structures. In particular, the Se atoms of SeB7−, SeB8−, SeB10−, and SeB12− are connected to the pure quasi-planar B7−, B8−, B10−, and B12− clusters, which leads to planar SeB7−, SeB8−, SeB10−, and SeB12−, respectively. Interestingly, the lowest energy structure of SeB9− is a three-dimensional mushroom-shaped structure, and the SeB9− cluster displays the largest HOMO–LUMO gap of 5.08 eV, which shows the superior chemical stability. Adaptive natural density partitioning (AdNDP) bonding analysis reveals that SeB8 is doubly aromatic, with 6 delocalized π electrons and 6 delocalized σ electrons, whereas SeB9− is doubly antiaromatic, with 4 delocalized π electrons and 12 delocalized σ electrons. Similarly, quasi-planar SeB12 is doubly aromatic, with 6 delocalized π electrons and 14 delocalized σ electrons. The electron localization function (ELF) analysis shows that SeBn0/− (n = 3–16) clusters have different local electron delocalization and whole electron delocalization effects. The simulated photoelectron spectra of SeBn− (n = 3–16) have different characteristic bands that can identify and confirm SeBn− (n = 3–16) combined with future experimental photoelectron spectra. Our research enriches the geometrical structures of small doped boron clusters and can offer insight for boron-based nanomaterials.


Introduction
Clusters are composed of several to thousands of atoms or molecules whose properties depend on their size and shape. Clusters are ideal model systems for correlating microscopic structure and macroscopic properties of substances, and cluster research is of great significance to deeply understand the laws of matter transformation. Research of structure and properties of clusters can offer insight for the design and manufacture of new materials and new devices at the atomic level. Boron clusters can induce polycentric chemical bonds and adopt several interesting structures with meaningful properties [1][2][3][4][5][6]. Experimental and theoretical research has shown that B n − (n < 38) have quasi-planar or planar structures [7,8], and neutral B n have quasi-planar, planar, wheel shaped, tubular structures or other structures [1,5,[9][10][11]. In 2014, the experimental finding of cage-type all-boron cluster (borospherene) [12] B 40 − has given rise to a lot of attention on boron clusters [13][14][15][16][17][18][19][20][21]. In 2015, researchers synthesized borophene on the Ag (111) base [22], and the structural unit of borophene is a B 7 cluster. In 2021, researchers synthesized borophene crystal, which was hydrogenated with hydrogen atoms [23], and it is very stable and comparable to graphene. Interestingly, the basic unit of hydrogenated borophene happens to be a hydrogenated B 7 cluster also. The experimental findings of B 40 − and borophene offer insight for the development of new boron nanomaterials and nanodevices. Research on small boron clusters is promising as a way to provide new ideas for new nanomaterials and nanodevices.
In recent years, researchers have studied abundant doped boron clusters, and they mainly focused on doping a single metal atom in boron clusters of different sizes. Metal-atom-doped boron clusters can induce new geometrical configuration and properties [15,[17][18][19][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. For example, anionic B 20 − and B 22 − have a quasi-planar structure [7,39]. However, single alkali-metal-atom-doped LiB 20 − , NaB 22 − , and KB 22 − display a double-ring configuration [25,40]. Co and Rh atom-doped boron clusters MB 12 (M = Co and Rh) can lead to the quasi-planar B 12 form, a semi-sandwich configuration [3,24]. Neutral B 24 has a double-ring configuration [39], while TiB 24 and ScB 24 have a cage configuration and three-ring tubular structure, respectively, after adding one Sc or Ti atom [41,42]. Anionic B 24 − has a quasi-planar structure [7], while TiB 24 − and VB 24 − have a cage configuration after adding one Ti or V atom [43]. In addition, the LiB 40 , NaB 40 , or KB 40 cage is promising for application to the field of nonlinear optics [18]; the ScB 40 or TiB 40 cage is promising for application to the field of hydrogen storage [15,17,19]; Co atom-doped CoB 12 − and Rh atom-doped RhB 12 − can improve chemical activity [27]; Co atom-doped CoB 40 is promising for application to molecular devices [26]; and the metal-atom-doped boron clusters ReB n − (n = 3 [29][30][31][32][33][34][35][36][37]44,45]. However, nonmetallic-atom-doped boron clusters have been poorly studied. In particular, the structural evolution of boron clusters after addition of a single nonmetallic atom is rarely studied. Similar to B 7 , small boron clusters with doping are promising as the structural units of borophene and other boron nanomaterials. Selenium is one of the essential microelements in the human body and has obvious inhibitory effects on tumors. The Se atom can combine with metal atoms, such as Cd and Zn, to form semiconductor clusters or quantum dots [46,47]. These materials exhibit a variety of unique optical and electronic properties, which can be further applied in imaging and diagnosis of biological systems [48,49]. Se doping of boron clusters is promising to be a useful strategy to further increase the diversity of structural forms and to affect the properties of boron clusters. Therefore, the theoretical research of Se atom-doped small boron clusters can enrich new structures and new properties of boron clusters, and can also provide theoretical guidance for the synthesis of nanomaterials, such as borophene. Herein, to demonstrate the structural evolution of Se-doped SeB n 0/− (n = 3-16), extensive geometric configurations were generated and predicted, using the particle swarm optimization (CALYPSO) approach [50] in combination with the density functional theory method PBE0 [51].

Structures and Electronic Properties
Five low-energy structures of SeB n 0/− (n = 3-16) are shown in Figures S1-S28, and the lowest energy structures of SeB n 0/− (n = 3-16) are displayed in Figures 1 and 2. The results indicate that the low-energy structures of SeB n 0/− (n = 3-16) trend to form planar or quasi-planar structures. Interestingly, the ground state configuration of SeB 9 − is three-dimensional mushroom shaped. Early theoretical and experimental research found that most of the small neutral boron clusters are quasi-planar or planar, and all small anionic boron clusters are quasi-planar or planar structures. Figures 1 and 2 and the research results indicate that, after adding a Se atom, some of the lowest energy configurations of SeB n 0/− (n = 3-16) have a skeleton of pure boron clusters, such as SeB n (n = 3-5, 7-8, [10][11][12][13][14]16) and SeB n − (n = 3-5, 7-8, [10][11][12][13][14]16) [52,53]. As can be seen in Figures 1 and 2, except for SeB n − (n = 5, 6,9), each Se atom is connected to two boron atoms to form a three-ring. The lowest energy configurations of SeB n 0/− (n = 3-5) have planar structure, and the Se atom is attached to the boron atoms of the pure boron cluster B n 0/− (n = 3-5) [52]. The lowest energy configurations of SeB 6 0/− and SeB 13 0/− have quasi-planar  [52]. For SeB 7 0/− , SeB 10 0/− , and SeB 12 0/− , the lowest energy configurations of neutral clusters and corresponding anionic clusters have similar structure, and the Se atoms of SeB 7 , SeB 10 , and SeB 12 are connected to the pure quasiplanar B 7 , B 10 , and B 12 clusters, respectively. However, the Se atoms of SeB 7 − , SeB 10 − , and SeB 12 − are connected to the pure quasi-planar B 7 − , B 10 − , and B 12 − clusters, which leads to the planar SeB 7 − , SeB 10 − , and SeB 12 − , respectively [52]. The lowest energy structures of SeB 8 0/− have same planar structure, and the Se atom of SeB 8 is connected to the pure planar B 8 cluster. However, the Se atom of SeB 8 − is connected to the pure quasi-planar B 8 − cluster, which leads to the planar SeB 8 − . The pure B 9 0/− have same planar wheel-shape structure [52]. However, doping of Se atom causes the anionic SeB 9 − to become a threedimensional mushroom-shaped structure (with C 6V symmetry) and causes the neutral SeB 9 to become a boat-shaped structure. The lowest energy structures of SeB 11 0/− have similar structure, and the Se atom of SeB 11 is connected to the pure planar B 11 cluster, which leads to the slight structural change. However, the Se atom of SeB 11 − is connected to the pure planar B 11 − cluster [52]. The lowest energy configurations of SeB 14 0/− have same planar structure, the lowest energy configurations of SeB 16 0/− have same quasi-planar structure, and the Se atoms are connected to the pure planar B 14 0/− clusters and pure quasi-planar B 16 0/− clusters, respectively [52,53]. The lowest energy configurations of SeB 15 0/− have quasi-planar structure and exhibit two axially chiral isomers, and they are different from the ground-state configurations of pure boron cluster B 15 0/− . Similar to pure B 7 clusters, planar and quasi-planar Se-doped boron clusters are promising as the structural units of boron nanomaterials, which can be synthesized further into borophene.
Molecules 2023, 27, x FOR PEER REVIEW 3 of 13 energy configurations of SeBn 0/− (n = 3-5) have planar structure, and the Se atom is attached to the boron atoms of the pure boron cluster Bn 0/− (n = 3-5) [52]. The lowest energy configurations of SeB6 0/− and SeB13 0/− have quasi-planar structure, and they are different from the ground-state structures of corresponding pure boron clusters B6 0/− and B13 0/− [52]. For SeB7 0/− , SeB10 0/− , and SeB12 0/− , the lowest energy configurations of neutral clusters and corresponding anionic clusters have similar structure, and the Se atoms of SeB7, SeB10, and SeB12 are connected to the pure quasi-planar B7, B10, and B12 clusters, respectively. However, the Se atoms of SeB7 − , SeB10 − , and SeB12 − are connected to the pure quasi-planar B7 − , B10 − , and B12 − clusters, which leads to the planar SeB7 − , SeB10 − , and SeB12 − , respectively [52]. The lowest energy structures of SeB8 0/− have same planar structure, and the Se atom of SeB8 is connected to the pure planar B8 cluster. However, the Se atom of SeB8 − is connected to the pure quasi-planar B8 − cluster, which leads to the planar SeB8 − . The pure B9 0/− have same planar wheel-shape structure [52]. However, doping of Se atom causes the anionic SeB9 − to become a three-dimensional mushroom-shaped structure (with C6V symmetry) and causes the neutral SeB9 to become a boat-shaped structure. The lowest energy structures of SeB11 0/− have similar structure, and the Se atom of SeB11 is connected to the pure planar B11 cluster, which leads to the slight structural change. However, the Se atom of SeB11 − is connected to the pure planar B11 − cluster [52]. The lowest energy configurations of SeB14 0/− have same planar structure, the lowest energy configurations of SeB16 0/− have same quasiplanar structure, and the Se atoms are connected to the pure planar B14 0/− clusters and pure quasi-planar B16 0/− clusters, respectively [52,53]. The lowest energy configurations of SeB15 0/− have quasi-planar structure and exhibit two axially chiral isomers, and they are different from the ground-state configurations of pure boron cluster B15 0/− . Similar to pure B7 clusters, planar and quasi-planar Se-doped boron clusters are promising as the structural units of boron nanomaterials, which can be synthesized further into borophene.
To further understand the stability of typical structures of SeBn 0/− (n = 3-16), we analyzed the chemical bonding of closed-shell planar SeB8, three-dimensional SeB9 − , and quasi-planar SeB12 using the adaptive natural density partitioning (AdNDP) approach. Figures 3 displays the bonding patterns of planar SeB8. For SeB8, AdNDP analyses reveal that one lone pair (Figure 3a) is found on the Se atom and eight 2c-2e σ bonds (Figure 3b) on the peripheral ring. The remaining six bonds contain three σ bonds and three π bond, which are classified into four sets ( Figure 3): one 3c-2e σ bond covers one B3 triangle, in which two of the boron atoms are connected to the Se atoms; two 4c-2e σ bonds cover two B4 rings; one 3c-2e π bond is distributed around the B-Se-B triangle; and two 5c-2e π bonds cover two B5 rings. Overall, the eight 2c-2e σ bonds, one delocalized 3c-2e σ bond, and two delocalized 4c-2e σ bonds cover the planar molecule, which renders stability to the SeB8, and the delocalized 3c-2e π bond and 5c-2e π bonds further stabilize the SeB8 cluster. Figure 4 displays the bonding patterns of SeB9 − , and there are five categories. First, there is one lone pair (see Figure 4a) on the Se atom. Then, there are two 2c-2e σ bonds on the Se-B and adjacent B-B. Third, two 2c-2e π bonds cover the Se-B symmetrically. Fourth, The harmonic frequency analysis confirmed that these lowest-energy structures are actually stable (no imaginary frequency). For closed-shell clusters, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy gaps (HOMO-LUMO energy gaps) of SeB − cluster possesses the largest HOMO-LUMO gap of 5.08 eV, which shows the superior chemical stability.
To further understand the stability of typical structures of SeB n 0/− (n = 3-16), we analyzed the chemical bonding of closed-shell planar SeB 8 , three-dimensional SeB 9 − , and quasi-planar SeB 12 using the adaptive natural density partitioning (AdNDP) approach. Figure 3 displays the bonding patterns of planar SeB 8 . For SeB 8 , AdNDP analyses reveal that one lone pair (Figure 3a) is found on the Se atom and eight 2c-2e σ bonds (Figure 3b) on the peripheral ring. The remaining six bonds contain three σ bonds and three π bond, which are classified into four sets (Figure 3): one 3c-2e σ bond covers one B 3 triangle, in which two of the boron atoms are connected to the Se atoms; two 4c-2e σ bonds cover two B 4 rings; one 3c-2e π bond is distributed around the B-Se-B triangle; and two 5c-2e π bonds cover two B 5 rings. Overall, the eight 2c-2e σ bonds, one delocalized 3c-2e σ bond, and two delocalized 4c-2e σ bonds cover the planar molecule, which renders stability to the SeB 8 , and the delocalized 3c-2e π bond and 5c-2e π bonds further stabilize the SeB 8 cluster. Figure 4 displays the bonding patterns of SeB 9 − , and there are five categories. First, there is one lone pair (see Figure 4a) on the Se atom. Then, there are two 2c-2e σ bonds on the Se-B and adjacent B-B. Third, two 2c-2e π bonds cover the Se-B symmetrically. Fourth, the peripheral B 7 ring at the top of the mushroom is characterized by six localized B−B 2c-2e σ bonds. The last six delocalized 3c-2e σ bonds cover the inner B 3 triangles at the top of the mushroom. The six localized B−B 2c-2e σ bonds and six delocalized 3c-2e σ bonds are responsible for the connection between the outer B 7 ring and the inner B atom at the top of the mushroom, which enhances the stability of SeB 9 − . Figure 5 displays the bonding patterns of quasi-planar SeB 12 . For SeB 12 , AdNDP analyses reveal that one lone pair (see Figure 5a) is found on the Se atom and ten 2c-2e σ bonds (see Figure 5b) on the peripheral ring. The remaining ten bonds contain seven σ bonds and three π bonds, which are classified into three sets ( Figure 5): one 3c-2e π bond covers B-Se-B triangle, seven 3c-2e σ bonds cover the seven inner B 3 triangles, and two 5c-2e π bonds are distributed symmetrically around the two B 5 rings. Similar to the SeB 8 , the ten 2c-2e σ bonds and seven delocalized 3c-2e σ bonds cover the quasi-planar molecule, which renders stability to the SeB 12 cluster, and the delocalized 3c-2e π bond and 5c-2e π bonds further stabilize the SeB 12 cluster. AdNDP bonding analyses revealed that the SeB 8 and SeB 12 possess three delocalized π bonds, which, quite surprisingly, satisfy the 4m + 2 Hückel rule for π aromaticity. Furthermore, SeB 8 and SeB 12 possess three delocalized σ bonds and seven delocalized σ bonds, which satisfy the 4m + 2 Hückel rule for σ aromaticity. However, the three-dimensional SeB 9 − cluster possesses two delocalized π bonds and six delocalized σ bonds, which satisfy the 4m Hückel rule for π and σ antiaromaticity.   (e)2 × 4c − 2e σ bonds (f)1 × 5c − 2e π bond (g)1 × 5c − 2e π bond ON = 1.8980|e| ON = 1.9445 |e| ON = 1.9445|e|  To describe the electron localization or delocalization of electrons, the electron localization function (ELF) [54] of the valence electrons was analyzed, as shown in Figures S29-S31. At the isosurface value of 0.60, the isosurface maps of most of the clusters are connected on the surface of the whole molecule. Yet, the isosurface diagrams of SeB 5 − , SeB 6 − , SeB 9 − , and SeB 11 − are disconnected on the surface of the whole molecule, indicating that the delocalization of the whole molecule is weaker than that of the other clusters. Figure S30 displays the ELF with the isosurface value of 0.70. The isosurface diagram of SeB 3 , SeB 3 − , SeB 4 − , SeB 9 , SeB 12 , and SeB 15 − is still connected on the surface of the whole molecule, while the isosurface diagrams of other clusters are broken on the partial regions of the molecule, indicating that the delocalization of SeB 3 , SeB 3 − , SeB 4 − , SeB 9 , SeB 12 , and SeB 15 − is stronger than that of the other clusters. Figure S31 displays the ELF with the isosurface value of 0.80, in which the isosurface maps of some clusters are disconnected and there are no connected regions. The isosurface maps of SeB 3 , SeB 3 − , SeB 6 , SeB 7 , SeB 7 − , SeB 9 − , SeB 12 , and SeB 15 − show that there is still some connected area on the surface of molecule, indicating that the local delocalization of these clusters is stronger than that of other clusters. Quite specially, the isosurface diagram of SeB 9 − is still connected on the peripheral B 7 ring at the top of the mushroom. ELF analyses further confirm these observations based on the AdNDP analyses, such as the contributions from the valence electrons of the SeB 12 were partitioned in Figure S31. Isosurface maps of the SeB 12 ( Figure S31) cover eight peripheral B-B bonds and two B-Se bonds that correspond to ten peripheral 2c-2e σ bonds, and they cover seven B 3 triangles that correspond to seven 3c-2e σ bonds. Isosurface maps on the two B 5 ring are fatter due to another two 5c-2e π bonds.  To describe the electron localization or delocalization of electrons, the electron ization function (ELF) [54] of the valence electrons was analyzed, as shown in Figur S31. At the isosurface value of 0.60, the isosurface maps of most of the clusters a nected on the surface of the whole molecule. Yet, the isosurface diagrams of SeB5 − SeB9 − , and SeB11 − are disconnected on the surface of the whole molecule, indicati the delocalization of the whole molecule is weaker than that of the other clusters. S30 displays the ELF with the isosurface value of 0.70. The isosurface diagram o SeB3 − , SeB4 − , SeB9, SeB12, and SeB15 − is still connected on the surface of the whole mo while the isosurface diagrams of other clusters are broken on the partial regions molecule, indicating that the delocalization of SeB3, SeB3 − , SeB4 − , SeB9, SeB12, and S stronger than that of the other clusters. Figure S31 displays the ELF with the iso value of 0.80, in which the isosurface maps of some clusters are disconnected an are no connected regions. The isosurface maps of SeB3, SeB3 − , SeB6, SeB7, SeB7 − , SeB9 − and SeB15 − show that there is still some connected area on the surface of molecule, i ing that the local delocalization of these clusters is stronger than that of other c Quite specially, the isosurface diagram of SeB9 − is still connected on the peripheral at the top of the mushroom. ELF analyses further confirm these observations based AdNDP analyses, such as the contributions from the valence electrons of the SeB  Figure S32 shows the isosurface diagram of the spin density of the open-shell clusters, and spin density can reveal the distribution of unpaired electrons. Figure S32 shows the spin density diagram with an isosurface value of 0.002, in which green represents alpha electrons and blue represents beta electrons. Figure S32 shows that the unpaired single electrons are mostly alpha electrons, and there are a small number of beta electrons on B atoms. Most of the unpaired alpha electrons are distributed on the B atoms; only a small portion of the unpaired alpha electrons are distributed on the Se atom. The spin density can reflect chemical reactions or adsorption to a certain extent. The single electrons of these clusters are mostly alpha electrons and are basically on the B atoms. The B or Se atoms with single alpha electrons can pair with free radicals or small molecules with beta single electrons to form new covalent bonds. In addition, these spin features are expected to produce interesting magnetic properties, which will further lead to potential applications in molecular devices.

Photoelectron Spectra
Photoelectron spectroscopy in combination with theoretical calculations was used to identify the structures of size-selected boron clusters [3,12,55]. To assist with future identifications of SeB n − (n = 3-16), vertical detachment energies (VDEs) were calculated and photoelectron spectra of SeB n − (n = 3-16) were simulated with the time-dependent DFT (TD-DFT) method [12,55,56]. Figure 6 presents the photoelectron spectra of SeB n − (n = 3-16). The results indicate that SeB 3 − has the lowest first VDE, and SeB 12 − has the largest energy gap (about 1.48 eV) between the first and second peaks. The first several peaks were used to identify boron clusters [3,12]; the peaks on the low binding energy side are of great significance. The first peaks of these photoelectron spectra (except for SeB 9 − ) come from the calculated ground-state VDEs of SeB 14, 3.64, and 3.63 eV, respectively, which originate from detaching the electrons from the singly occupied molecular orbital β -HOMO-1. In addition, the peaks with higher binding energy originate from detaching the electrons from lower molecular orbitals. It is noted that some of the doped anionic boron clusters have a similar skeleton as the corresponding anionic pure boron clusters. Comparing their photoelectron spectra, the addition of the Se atom results in a great change in the photoelectron spectra [52,53]. However, the photoelectron spectra of some doped boron clusters are similar to those of the corresponding anionic pure boron clusters [52,53]. For example, compared with the photoelectron spectra of pure boron clusters, the addition of Se atoms causes the first two peaks of SeB 3 to move 0.30 eV towards the low binding energy side and causes the first two peaks of B 5 to move 0.46 eV towards the high binding energy side [52]. For SeB 4 − , SeB 8 − , and SeB 13 -, compared with the photoelectron spectra of pure boron clusters, the addition of Se atoms causes different band characteristics [52]. Compared to the photoelectron spectra of pure boron clusters, planar SeB 7 − and quasiplanar B 7 have almost the same first VDE (2.89 eV for SeB 7 -, 2.85 ± 0.02 eV for B 7 − ) [52], planar SeB 10 and quasi-planar B 10 have almost the same first VDE (3.14 eV for SeB 10 − , 3.06 ± 0.03 eV for B 10 − ) [52], and quasi-planar SeB 14 − and quasi-planar B 14 have almost the same first VDE (3.14 eV for SeB 14 − , 3.10 ± 0.01 eV for B 14 − ) [52]. For SeB 11 -, compared to the photoelectron spectra of pure boron clusters B 11 − , the addition of the Se atom causes the first peak to move 0.08 eV towards the high binding energy side and causes the second peak to move 0.25 eV towards the low binding energy side. For SeB 12 − and SeB 16 − , planar SeB 12 and quasi-planar B 12 − have similar band characteristics [52], and quasi-planar SeB 16 − and quasi-planar B 16 -have similar band characteristics [53]. Figure 6 indicates that SeB n − (n = 3-16) has different spectral features; especially the peaks at the low binding energy side can identify the SeB n − (n = 3-16). As with the discovery of other anionic boron clusters, if the photoelectron spectra of SeB n − (n = 3-16) are obtained in experiments, these simulated values can be used for the identification of SeB n − (n = 3-16). similar band characteristics [52], and quasi-planar SeB16 − and quasi-planar B16have similar band characteristics [53]. Figure 6 indicates that SeBn − (n = 3-16) has different spectral features; especially the peaks at the low binding energy side can identify the SeBn − (n = 3-16).
As with the discovery of other anionic boron clusters, if the photoelectron spectra of SeBn − (n = 3-16) are obtained in experiments, these simulated values can be used for the identification of SeBn − (n = 3-16).

Computation Details
Configuration searches of Se-doped boron clusters SeB n 0/− (n = 3-16) were performed with CALYPSO 5.0 software in combination with Gaussian 16 software. CALYPSO is a reliable cluster configuration prediction software, and it has successfully predicted boron or doped boron clusters [11,25,40,41,45,[57][58][59][60][61]. The initial structures were generated by the CALYPSO software, and then these initial structures were optimized using Gaussian 16 software at the PBE0/3-21G level for the preliminary structural search. In each generation produced by the CALYPSO software, 70% of the structures were produced by particle swarm optimization (PSO) operations, while the others were randomly generated. When cluster sizes vary from n = 3 to n = 10, nearly 100-900 isomers are initially predicted for each boron cluster of a different size. When cluster sizes vary from n = 11 to n = 16, nearly 2000 isomers are initially predicted for each boron cluster of a different size.

Conclusions
DFT combined with CALYPSO software is employed to demonstrate the structural evolution of SeB n 0/− (n = 3-16) clusters. The conclusions are summarized as follows. (1) The global minima of SeB n 0/− (n = 3-16) clusters tend to form quasi-planar or planar structures. (2) The ground-state structure of SeB 9 − is a three-dimensional, mushroomshaped, ground-state structure, and it possesses the largest HOMO-LUMO gap of 5.08 eV, which shows the superior chemical stability. (3) AdNDP bonding analyses reveal that SeB 8 is doubly aromatic, with six delocalized σ and six delocalized π electrons, whereas SeB 9 − is doubly antiaromatic, with twelve delocalized σ and four delocalized π electrons. Similarly, SeB 12 is doubly aromatic, with fourteen delocalized σ and six delocalized π electrons. (4) ELF analysis shows that SeB n 0/− (n = 3-16) clusters have different local electron delocalization and whole-electron delocalization effects.