Structural Evolution of Small-Sized Phosphorus-Doped Boron Clusters: A Half-Sandwich-Structured PB15 Cluster

The present study is a theoretical investigation into the structural evolution, electronic properties, and photoelectron spectra of phosphorus-doped boron clusters PBn0/− (n = 3–17). The results of this study revealed that the lowest energy structures of PBn− (n = 3–17) clusters, except for PB17−, exhibit planar or quasi-planar structures. The lowest energy structures of PBn (n = 3–17), with the exceptions of PB7, PB9, and PB15, are planar or quasi-planar. The ground state of PB7 has an umbrella-shaped structure, with C6V symmetry. Interestingly, the neutral cluster PB15 has a half-sandwich-like structure, in which the P atom is attached to three B atoms at one end of the sandwich, exhibiting excellent relative and chemical stability due to its higher second-order energy difference and larger HOMO–LUMO energy gap of 4.31 eV. Subsequently, adaptive natural density partitioning (AdNDP) and electron localization function (ELF) analyses demonstrate the bonding characteristics of PB7 and PB15, providing support for the validity of their stability. The calculated photoelectron spectra show distinct characteristic peaks of PBn− (n = 3–17) clusters, thus providing theoretical evidence for the future identification of doped boron clusters. In summary, our work has significant implications for understanding the structural evolution of doped boron clusters PBn0/− (n = 3–17), motivating further experiments regarding doped boron clusters.


Introduction
It is well known that boron is a naturally abundant element, and scientists have been exploring the properties and applications of boron, boron compounds, and their derivatives [1][2][3][4][5].With the successive discoveries of fullerene C 60 , carbon nanotubes, and graphene [6][7][8], carbon nanomaterials have attracted considerable attention and become a dynamic field of research; similarly, as a neighbor of carbon, boron has also received significant attention from researchers.Boron compounds exhibit intrinsic electronic defects, as well as the ability to form an outstanding number of multicenter bonds, which endow them with rich structural features and chemical properties [9][10][11][12][13][14].The groundbreaking discovery of borospherene [15] in 2014 sparked extensive research on boron clusters [16][17][18][19][20][21][22].Over the past two decades, a great deal of theoretical and experimental research has focused on the geometric structure and electronic characteristics of bare boron clusters [23].It is generally believed that bare boron clusters exhibit planar or quasi-planar geometric shapes over a large range of sizes.One of the most important discoveries is the planar B 36 − cluster [24], a highly stable cluster with central hexagonal vacancies that can be synthesized on a metal substrate to form "borophene".The experimental discoveries of borospherene and borophene provide new insights into novel boron nanomaterials and nanodevices.
Over the past decade, scientists have investigated richly doped boron clusters, with a primary focus on doping single metal atoms into boron clusters of various sizes.Metal doping is an effective method for adjusting the chemical bonds and occupied energy levels of boron clusters through the addition of metal elements, thereby changing their physicochemical properties.Doping metal atoms into boron clusters can lead to the formation of new geometric configurations and chemical properties, such as ring-like, sandwich-like, tube-like, and cage-like structures [17,19,20,[25][26][27][28][29][30][31][32][33][34].Following the doping of single alkali metal atoms into the quasi-planar structures of B 20 − and B 22 − [35], species including LiB 20 − , NaB 22 − , and KB 22 − exhibit bi-ring structures [33,36].Quasi-planar B 12 − clusters, upon doping with single transition metal atoms of Co, Rh, or Ta, exhibit halfsandwich structures [10,37,38].Doping with single transition metal atoms can modify the bi-ring tubular B 24 into cage-like boron clusters (TiB 24 , VB 24 , and MnB 24 ) and tri-ring tubular doped boron clusters (ScB 24 ) [39][40][41], or convert quasi-planar B 24 − into cage-like boron clusters (TiB 24 − , CrB 24 − , and VB 24 − ) [35,42].Compared with metal-doped boron clusters, there is relatively little research on the doping of boron clusters with non-metal atoms [43][44][45][46][47].In particular, there have been few studies on the structural evolution of boron clusters with the addition of phosphorus atoms.The recently reported P-doped boron cluster P 2 B 12 +/0/− has the same cage structure, with D 3h symmetry [46].The theoretical study of phosphorus-doped small boron clusters is of great significance for the discovery of new structures and properties of boron clusters.In this study, the effect of P-atom doping on the structure and electronic properties of boron clusters B n 0/− (n = 3-17) was investigated through employment of the particle swarm optimization (CALYPSO) method [48] and the density-functional theory method PBE0 [49].

Geometric Configurations
Early theoretical and experimental studies found that anionic boron clusters with an atomic numbers less than 37 always maintain quasi-planar or planar structures; however, while some neutral boron clusters do have quasi-planar or planar structures, others have tube or cage-like structures.The structures of boron clusters change after atom doping.In order to facilitate understanding via visualization, the low-lying isomers of PB n 0/− (n = 3-17), along with their corresponding relative energy values, are displayed in Figures S1-S30, and the lowest energy structures of PB n 0/− (n = 3-17) are depicted in Figures 1 and 2. Clear structural diagrams show that the lowest-lying energy structures of PB n − (n = 3-17) clusters have planar or quasi-planar structures, except for PB 17 − .The lowest energy structures of PB n (n = 3-17) are planar or quasi-planar, with the exceptions of PB 7 , PB 9 , and PB 15 .As can be observed in Figures 1 and 2, after the addition of the P atom, most boron clusters remain virtually unchanged from their corresponding bare boron cluster forms, such as PB n (n = 3-6, 8, 10, 12) and PB n − (n = 3, 5-8, 10-16) [23,50,51].In order to further discuss the structural changes of boron clusters, we also compared their structures after replacing a boron atom with a phosphorus atom, and without replacing the boron atom.Compared with the bare boron clusters B n 0/− (n = 4-18), the structures of most PB n−1 0/− (n = 4-18) clusters changed, except for those of PB 3 − , PB 3 , PB 4 , and PB 5 (which remained almost similar to those of B 4 − , B 4 , B 5 , and B 6 , respectively); that is, the structures of the bare boron clusters changed due to the replacement of one atom with a P atom.The lowest energy configurations of PB n 0/− (n = 3, 5, 6, 8) are planar structures, with the P atom attached to the boron atoms of the bare boron clusters B n 0/− (n = 3, 5, 6, 8) [50].The lowest-lying energy structures of PB n 0/− (n =10, 12) are quasi-planar, similar to the ground-state structures of their corresponding bare boron clusters, B 10 0/− and B 12 0/− , with the addition of a phosphorus atom bonded to the boron atoms.PB 10 − has a chiral symmetrical structure.Likewise, the planar clusters PB 4 , PB 7 − , PB 11 − , PB 13 − , and PB 14 − , as well as the quasi-planar cluster PB 16 − , have similar structures to those of their corresponding bare boron clusters [23,50].However, the ground-state structures of the planar PB 4 − and quasi-planar PB 11 , PB 13 , and PB 16 clusters are different from their corresponding bare boron clusters due to the action of the P atom.can provide a theoretical basis for the design of highly stable boron-based nanomaterials.In addition, the quasi-planar structure of B15 becomes the three-dimensional half-sandwich-shaped structure of PB15 after P atom doping; thus, studying the structures and characteristics of PB15 is crucial to understanding the structural laws of doped nonmetallic boron clusters.In summary, the study of PB7 and PB15 is of great significance for the discovery of new stable boron-based nanomaterials.

Relative Stabilities
To analyze the relative stabilities of the lowest energy level of PBn 0/− (n = 3−17), we calculated the average binding energy (Eb) and the second-order energy differences (∆ 2 E) of the clusters using the following formulas, where n represents the number of boron atoms, and E is the total energy of the corresponding atom or cluster.The calculation results obtained using Equations ( 1)-( 3) are plotted in Figure 3.The formulas are as follows: The planar wheel-shaped structure of B 9 becomes the three-dimensional structure of PB 9 with the doping of a P atom; the anion cluster B 9 − , with a similar structure, changes from the planar wheel to the double-chain planar structure of PB 9 − .The lowest energy configurations of PB 14 and PB 17 have quasi-two-dimensional structures, and PB 17 − has a three-dimensional cage-shaped structure.It is important to note the specific behaviors of PB 7 , PB 9 − , and PB 13 .For the PB 9 − cluster, at the PBE0/6-311+G(d) level, the double-chain planar structure (Figure S14a) is more stable than the planar structure (Figure S14b), with an energy gap of 0.17 eV.At the higher level, CCSD(T)/6-311+G(d)//PBE0/6-311+G(d)+ZPE (zero-point energy corrections), both structures are almost degenerate in regards to energy, each with a tiny energy gap (that is, the planar structure (Figure S14b) is more stable than the double-chain planar structure (Figure S14a), with an energy gap of 0.01 eV).We consider the double-chain structure as the lowest energy structure of PB 9 − ; the same is true for the PB 7 and PB 13 clusters.It is worth mentioning that the umbrella-like structure found in PB 7 is also the lowest energy structure in many metal-doped boron clusters, such as LiB 7 , BeB 7 0/− , BeB 8 0/− , and MgB 8 [52][53][54].Research shows that the low-valent actinide(III) boron clusters AnB 7 (An = Pa, U, Np, and Pu), with umbrella-shaped structures, exhibit high electronic stability and can be obtained in the gas phase at room temperature [55].Similarly, the neutral cluster PB 7 also has an umbrella-shaped structure, with C 6v symmetry.Therefore, in this study, we will highlight the umbrella-like structure of PB 7 , which can provide a theoretical basis for the design of highly stable boron-based nanomaterials.In addition, the quasi-planar structure of B 15 becomes the three-dimensional half-sandwich-shaped structure of PB 15 after P atom doping; thus, studying the structures and characteristics of PB 15 is crucial to understanding the structural laws of doped nonmetallic boron clusters.In summary, the study of PB 7 and PB 15 is of great significance for the discovery of new stable boron-based nanomaterials.

Relative Stabilities
To analyze the relative stabilities of the lowest energy level of PB n 0/− (n = 3−17), we calculated the average binding energy (E b ) and the second-order energy differences (∆ 2 E) of the clusters using the following formulas, where n represents the number of boron atoms, and E is the total energy of the corresponding atom or cluster.The calculation results obtained using Equations ( 1)-( 3) are plotted in Figure 3.The formulas are as follows: E b represents the inherent stability of the cluster, in that a larger value of E b denotes higher relative stability.As evidenced in Figure 3, the E b values of PB n 0/− (n = 3−17) are gradually increasing with the increase in the boron atom number n, indicating that the cluster becomes more and more stable.Furthermore, the E b values of the anions are overall more sizable than those of the corresponding neutral ions; thus, we can infer that the anion clusters of PB n − (n = 3−17) are more stable than their corresponding neutral clusters, and that the excess electrons enhance the stability of the P-doped boron clusters.∆ 2 E is an important indicator of relative stability and can provide valuable insights into the stability of the clusters.In Figure 3, the second-order difference of the peaks found in n = − are relatively more stable than their adjacent clusters.
The energy difference E gap between HOMO and LUMO is an indicator of chemical stability.A larger E gap value for a cluster implies that the electrons are more difficult to excite from HOMO to LUMO, which indicates that the corresponding structures are chemically inert.As can be seen in Figure 3, two obvious E gap peaks are found in PB 7 (

Chemical Bonding Analysis
Through a comprehensive stability analysis of all of the clusters detailed in the previous section, we inferred that PB7 and PB15 show chemical stability, due to their high Egap values.We analyzed the charge populations of PB7 and PB15 (see Figure S33).Different from the metal elements in metal-doped boron clusters, which can undergo one or more electron transfers, the phosphorus atom in PB7 or PB15 transfers less than one electron.To further understand the electronic properties and stability of the closed-shell clusters PB7 and PB15, the AdNDP method was used to analyze their chemical bonding characteristics.The AdNDP method is an extension of the popular natural bond orbital (NBO) analysis, which can be used to analyze localized and delocalized multicenter bonds.We quantitatively analyzed the bonding properties of PB7 and PB15 using the AdNDP method, and the results are depicted in Figures 4 and 5.In Figure 4, we clearly observe six two-center twoelectron (2c-2e) σ bonds around the peripheral B atoms of the PB7 cluster.In addition, there are three 8c-2e σ bonds and three 8c-2e π bonds in PB7, which together support the plane of the cluster and enhance the stability of PB7.As can be seen in the Figure 4, the contribution of the P atom to the 8c-2e π bonds is greater than its contribution to the 8c-2e σ bonds.The delocalized σ and π bonds give rise to double aromaticity and fulfill the Hückel 4N + 2 rule with N = 1.
For PB15 (Figure 5), there is one lone pair on the P atom, and three 2c-2e σ bonds cover the B-P bond attached to the P atom.These three 2c-2e σ bonds are formed by three

Chemical Bonding Analysis
Through a comprehensive stability analysis of all of the clusters detailed in the previous section, we inferred that PB 7 and PB 15 show chemical stability, due to their high E gap values.We analyzed the charge populations of PB 7 and PB 15 (see Figure S33).Different from the metal elements in metal-doped boron clusters, which can undergo one or more electron transfers, the phosphorus atom in PB 7 or PB 15 transfers less than one electron.To further understand the electronic properties and stability of the closed-shell clusters PB 7 and PB 15 , the AdNDP method was used to analyze their chemical bonding characteristics.The AdNDP method is an extension of the popular natural bond orbital (NBO) analysis, which can be used to analyze localized and delocalized multicenter bonds.We quantitatively analyzed the bonding properties of PB 7 and PB 15 using the AdNDP method, and the results are depicted in Figures 4 and 5.In Figure 4, we clearly observe six two-center two-electron (2c-2e) σ bonds around the peripheral B atoms of the PB 7 cluster.In addition, there are three 8c-2e σ bonds and three 8c-2e π bonds in PB 7 , which together support the plane of the cluster and enhance the stability of PB 7 .As can be seen in the Figure 4, the contribution of the P atom to the 8c-2e π bonds is greater than its contribution to the 8c-2e σ bonds.The delocalized σ and π bonds give rise to double aromaticity and fulfill the Hückel 4N + 2 rule with N = 1.
the P atom, and the last 3c-2e σ bond is distributed on a ternary boron ring.Moreover, there are three 4c-2e σ bonds over three B4 rings, one 6c-2e σ bond attached to an internal B6 ring, and one 7c-2e σ bond over a B7 ring.On the whole, there are strong interactions between B15 and the P atom through delocalized bonds that stabilize the PB15 cluster.According to AdNDP investigations, the PB15 cluster possesses 12 delocalized σ bonds that do not satisfy spherical aromaticity [2(n + 1) 2    the P atom, and the last 3c-2e σ bond is distributed on a ternary boron ring.Moreover, there are three 4c-2e σ bonds over three B4 rings, one 6c-2e σ bond attached to an internal B6 ring, and one 7c-2e σ bond over a B7 ring.On the whole, there are strong interactions between B15 and the P atom through delocalized bonds that stabilize the PB15 cluster.According to AdNDP investigations, the PB15 cluster possesses 12 delocalized σ bonds that do not satisfy spherical aromaticity [2(n + 1) 2 rule].To further confirm the above AdNDP analysis results, we analyzed PB7 and PB15 ing the ELF method, a function that can be used to describe the localization and deloca zation of different molecular regions.The ELF results for PB7 and PB15 are shown in Figu 6, as well as in Figure S31 and Figure S32, respectively.As can be observed from Figu 6 and S31, the isosurface map of PB7 covers six peripheral B-B bonds that correspond six peripheral 2c-2e σ bonds, as well as the entire region of B and P atoms correspondi For PB 15 (Figure 5), there is one lone pair on the P atom, and three 2c-2e σ bonds cover the B-P bond attached to the P atom.These three 2c-2e σ bonds are formed by three electrons on the P atom combining with an electron of each B atom on the B 3 ring.In addition, nine 2c-2e σ bonds are distributed over the peripheral B-B bond.The seven 3c-2e σ bonds are divided into the four following groups: one 3c-2e σ bond is distributed on the inner ring triangle at the back side of the P atom, two 3c-2e σ bonds are distributed on two peripheral B 3 rings, three 3c-2e σ bonds cover the three peripheral B 3 rings behind the P atom, and the last 3c-2e σ bond is distributed on a ternary boron ring.Moreover, there are three 4c-2e σ bonds over three B 4 rings, one 6c-2e σ bond attached to an internal B 6 ring, and one 7c-2e σ bond over a B 7 ring.On whole, there are strong interactions between B 15 and the P atom through delocalized bonds that stabilize the PB 15 cluster.According to AdNDP investigations, the PB 15 cluster possesses 12 delocalized σ bonds that do not satisfy spherical aromaticity [2(n + 1) 2 rule].
To further confirm the above AdNDP analysis results, we analyzed PB 7 and PB 15 using the ELF method, a function that can be used to describe the localization and delocalization of different molecular regions.The ELF results for PB 7 and PB 15 are shown in Figure 6, as well as in Figures S31 and S32, respectively.As can be observed from Figure 6 and Figure S31, the isosurface map of PB 7 covers six peripheral B-B bonds that correspond to six peripheral 2c-2e σ bonds, as well as the entire region of B and P atoms corresponding to the 8c-2e bonds.Combining Figure S32 and Figure 6 shows that the isosurface map of PB 15 covers nine peripheral B-B bonds and three B-P bonds, which correspond to twelve 2c-2e σ bonds, as well as seven B 3 triangles that correspond to seven 3c-2e σ bonds.Additionally, the three regions around PB 15 are fatter, indicating the presence of 3c-2e and 4c-2e bonds.To further confirm the above AdNDP analysis results, we analyzed PB7 and PB15 using the ELF method, a function that can be used to describe the localization and delocalization of different molecular regions.The ELF results for PB7 and PB15 are shown in Figure 6, as well as in Figure S31 and Figure S32, respectively.As can be observed from Figures 6 and S31, the isosurface map of PB7 covers six peripheral B-B bonds that correspond to six peripheral 2c-2e σ bonds, as well as the entire region of B and P atoms corresponding to the 8c-2e bonds.Combining Figures S32 and 6 shows that the isosurface map of PB15 covers nine peripheral B-B bonds and three B-P bonds, which correspond to twelve 2c-2e σ bonds, as well as seven B3 triangles that correspond to seven 3c-2e σ bonds.Additionally, the three regions around PB15 are fatter, indicating the presence of 3c-2e and 4c-2e bonds.

Photoelectron Spectra
Photoelectron spectra (PES) is an effective approach for exploring the energy levels of valence electrons in nanoclusters.In photoelectron spectra, the positions of the peaks represent the energy differences between the initial and final electronic state after photons absorption.In order to identify the structures of the PBn − (n = 3−17) clusters, we calculated the vertical detachment energies (VDEs) of the anionic clusters and simulated the photoelectron spectra of the PBn − (n = 3−17) clusters using the time-dependent density functional theory (TD-DFT).The first few peaks of the photoelectron spectrum are commonly used

Photoelectron Spectra
Photoelectron spectra (PES) is an effective approach for exploring the energy levels of valence electrons in nanoclusters.In photoelectron spectra, the positions of the peaks represent the energy differences between the initial and final electronic state after photons absorption.In order to identify the structures of the PB n − (n = 3−17) clusters, we calculated the vertical detachment energies (VDEs) of the anionic clusters and simulated the photoelectron spectra of the PB n − (n = 3−17) clusters using the time-dependent density functional theory (TD-DFT).The first few peaks of the photoelectron spectrum are commonly used to identify boron clusters [10,15]; thus, studying the peaks on the low-binding-energy side is of significant importance.Figure 7 shows the photoelectron spectra of the PB n − (n = 3-17) clusters.According to the photoelectron spectra, the anion PB 16 − exhibits the largest first VDE value (3.88 eV, list in Table S1), while PB 4 − shows the lowest first VDE (1.78 eV).In addition, the energy gap (about 1.95 eV) between the first and second PB 6 − energy bands is the largest.
Molecules 2024, 29, x FOR PEER REVIEW 8 of 12 to identify boron clusters [10,15]; thus, studying the peaks on the low-binding-energy side is of significant importance.Figure 7 shows the photoelectron spectra of the PBn − (n = 3-17) clusters.According to the photoelectron spectra, the anion PB16 − exhibits the largest first VDE value (3.88 eV, list in Table S1), while PB4 − shows the lowest first VDE (1.78 eV).
Partially anionic boron clusters doped with P atoms have similar structures to those of the corresponding bare boron clusters; however, a comparison of their photoelectron spectra revealed that the addition of a phosphorus atom results in large changes in the photoelectron spectra of most clusters (except for PB11 − ) [23,50].For instance, the doped P  The first peaks of the photoelectron spectrum (except for those of PB ).The second peak of PB 5 − comes from the third VDE (4.01 eV) and the fourth VDE (4.05 eV).For PB 11 − , the second peak comes from the third VDE (3.74 eV).Furthermore, peaks with higher binding energies are derived from the separation of electrons from lower molecular orbitals.
Partially anionic boron clusters doped with P atoms have similar structures to those of the corresponding bare boron clusters; however, a comparison of their photoelectron spectra revealed that the addition of a phosphorus atom results in large changes in the photoelectron spectra of most clusters (except for PB 11 − ) [23,50].For instance, the doped P atom causes the first peaks of PB  7, all photoelectron spectra are different, which indicates that the addition of P atoms not only alters the geometric structure of the clusters, but also leads to changes in their electronic structures.In summary, it is of great significance to study the peaks at the low-binding-energy side, as these simulated spectra may be used as fingerprints with which to identify PB n − (n = 3-17) structures in the future.

Computation Details
In this paper, the geometrical structure searches for the neutral and anionic clusters of PB n 0/− (n = 3-17) were performed using CALYPSO, an efficient and reliable method for searching for geometrical cluster configurations which has been successfully applied to the study of both boron clusters and doped boron clusters [25,27,33,36,40,54,[56][57][58][59].CALYPSO 5.0 software generates 70% of the structure in each generation, and the remaining 30% is formed randomly.When the size of a boron atom is in the range of n = 3-10, nearly 100-1200 isomers are initially obtained for each cluster.The number of isomers increases with the number of boron atoms; when n = 11-14, there are approximately 2000 isomers for each cluster, and when n = 15-17, the number of isomers increases to 2500.

Conclusions
In this work, the ground state structures of P-doped boron clusters PB n 0/− (n = 3-17) were identified using the CALYPSO method.In addition, the bonding properties of PB 7 and PB 15 were discussed, based on AdNDP and ELF analyses, and the photoelectron spectra of the anionic clusters were also calculated.The conclusions can be summarized as follows:

Figure 3 .
Figure 3. Average binding energy (E b ), second-order energy differences (∆ 2 E), and HOMO-LUMO gaps (E gap ) of doped boron clusters PB n 0/− (n = 3−17).Red represents the neutral cluster, blue represents the anion cluster, and n represents the number of boron atoms in the cluster.

Figure 4 .
Figure 4. AdNDP analysis of PB7.ON is the occupation number, and the yellow ball is the P atom.

Figure 4 .
Figure 4. AdNDP analysis of PB 7 .ON is the occupation number, and the yellow ball is the P atom.

Figure 4 .Figure 5 .
Figure 4. AdNDP analysis of PB7.ON is the occupation number, and the yellow ball is the P atom.

Figure 5 .
Figure 5. AdNDP analysis of PB 15 .ON is the occupation number, and the yellow ball is the P atom.

Molecules 2024 ,Figure 5 .
Figure 5. AdNDP analysis of PB15.ON is the occupation number, and the yellow ball is the P atom.

( 1 )
The lowest-lying energy structures of PB n − (n = 3-17) clusters, except for PB 17 − , exhibit planar or quasi-planar structures.The lowest energy structures of PB n (n = 3-17) are planar or quasi-planar, with the exceptions of PB 7 , PB 9 , and PB 15 .The lowest energy structure of PB 7 has an umbrella-like structure, with high symmetry (C 6V ), and the ground-state configuration of PB 10 − exhibits a chiral symmetric structure.(2) The lowest energy structures of the neutral ion PB 15 have a half-sandwich structure, and they possess relatively high ∆ 2 E and E gap values, indicating that they possess superior relative and chemical stability.(3) AdNDP bonding analysis and ELF analysis further verified the stability and validity of the lowest energy structures of PB 7 and PB 15 .(4) The PB n − anionic clusters (n = 3-17) exhibit different photoelectron spectra on their low-binding-energy sides, which can provide a theoretical basis for the identification of doped boron clusters.Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules29143384/s1,Figures S1-S30: Low-lying isomers of doped boron clusters PB n 0/− (n = 3-17); Figure S31: Electron localization function (ELF) of PB 7 with the isovalue set to 0.59; Figure S32: Electron localization function (ELF) of PB 15 with the isovalue set to 0.7; Figure S33: Charge population of PB 7 and PB 15 ; Table S1: The first VDE values of bare B clusters and P-doped boron clusters.
about 5.11 eV) and PB 15 (about 4.31 eV), implying that the neutral clusters PB 7 and PB 15 exhibit better chemical stability than that of the other clusters.Therefore, combining ∆ 2 E and E gap analyses proved that PB 15 has a high relative and chemical stability.Additionally, due to the PB 7 cluster having the largest values of E gap , as well as a special umbrella structure, we chose these clusters as examples through which to analyze chemical bonding in P-doped boron clusters.
5.11 eV) and PB15 (about 4.31 eV), implying that the neutral clusters PB7 and PB15 exhibit better chemical stability than that of the other clusters.Therefore, combining ∆ 2 E and Egap analyses proved that PB15 has a high relative and chemical stability.Additionally, due to the PB7 cluster having the largest values of Egap, as well as a special umbrella structure, we chose these clusters as examples through which to analyze chemical bonding in P-doped boron clusters.
3 − , PB 6 − , and PB 13 − to move 0.63, 0.54, and 0.34 eV, respectively, towards the low-binding-energy side.At the same time, the first peaks of .41,0.1, and 0.49 eV, respectively, to the high-binding-energy side.As can be seen from Figure