硼基B6Al2-/0/+合金团簇结构和成键理论研究

张洁琼，王康，翟华金

（山西大学 分子科学研究所，山西 太原 030006）

0 Introduction

Boron is an electron-deficient element，and boron-based clusters have received systematic experimental and theoretical studies during the past decades［1-9］.The planarity or quasi-planarity（2D）of boron clusters［1-6］occurs in an unprecedented wide range of sizes，which is a peculiar feature that distinguishes boron from any other elements in the periodic table.The 2D boron clusters have delocalized π/σ bonding，giving rise to chemical bonding concepts of π/σ aromaticity，antiaromaticity，multifold aromaticity，and conflicting aromaticity［1-2］.Other progresses in the field include borospherenes（all-boron fullerenes）［10-12］，borophenes［13-18］，and dynamically fluxional clusters［19-23］，which are also associated to boron’s electron-deficiency.

Doping or alloying with metals is a natural way to compensate for the electron-deficiency of boronbased clusters.The Al element appears to be a promising choice for a couple of reason.First，the Al and B atoms are both valence three.Thus，an idea of“isoelectronic Al-B substitution”is of interest to pursue in physical chemistry.Second，the Al clusters are intriguing systems for all-metal aromaticity and antiaromaticity［24-26］.Third，the Al element has a lower electronegativity than B（1.61 versus 2.04），which should lead to intramolecular electron transfer from Al to B and help stabilize a boron-based system.

There have been a number of research works in binary B-Al clusters during the past 10 years.Wang，Boldyrev， and coworkers［27-29］studied a series of BnAl-（n=6～11）clusters in 2011，using the combination of anion photoelectron spectroscopy and theoretical calculations.It was revealed that isoelectronic Al-B substitution induces the planarization of quasiplanar B7-and B12-clusters［27］.However，not all boron clusters doped with Al can result in planarization.For example，Wang and coworkers［28］also obtained umbrella-like B7Al-and B8Al-clusters，suggesting that Al doping generates a diversity of boron-based clusters.The evolution of structural and physical properties of binary B-Al clusters was also investigated［30-33］.Nakajima et al.［30］experimentally studied the mass distribution of AlnBm-（n=5～30，m=1～3）clusters and revealed plausible evidence for an icosahedral Al12B-cage.More recently，Luo and coworkers［31］carried out a density-functional theory（DFT）study on BnAl（n=2～12）clusters.Lei［32］computationally studied the successive substitution of Al13cluster by B，that is，both neutral and anionic AlnBm（n+m=13）clusters.Starik and coworkers［33］theoretically investigated the different isomeric forms of AlnBm（n+m ≤ 7）clusters，including their physical and thermodynamic properties.

Obviously，current knowledge on the nature of a doping Al site in binary B-Al clusters remains insufficient.Also，there are few studies on the structural，bonding，and aromatic properties of boron clusters doped with multiple Al atoms.In this contribution，we report a theoretical study on three B-Al binary clusters in different charge-states，B6Al2-/0/+，via global-minimum（GM）searches using the Coalescence Kick （CK） algorithm［34-35］and electronic structure calculations.Chemical bonding of key structures of B6Al2-/0/+clusters is understood using the canonical molecular orbital（CMO）analysis，adaptive natural density partitioning（AdNDP）［36］，and natural bond orbital（NBO）analysis［37］.Two types of geometries are important for the clusters：inverse sandwich and molecular wheel.Neutral B6Al2cluster features 6π aromaticity，although its σ framework shows 4σ antiaromaticity.This situation leads to an unusual system with conflicting π/σ aromaticity.The anionic/cationic clusters have similar bonding，except for a 5σ/3σ electron-counting that deviates from ideal 4σ an-tiaromaticity.The doping Al site can be classified to three distinct categories，showing characters as valence three/two/one，respectively.Only one out of three categories is consistent with the idea of“isoelectronic Al-B substitution”.

1 Methods

Global structural searches of B6Al2-/0/+clusters were conducted using the unbiased CK algorithm at the B3LYP/6-31G level［38-40］，further aided by manual structural construction.These efforts serve simply to identify possible candidate geometries.About 2000 stationary points were probed on the potential energy surface for each species.The low-lying isomeric structures were then fully reoptimized at the PBE0/6-311+G（2df）level.Frequency calculations were done at the same level to ensure that all reported structures are true minima.To benchmark the energetics，the top five isomeric structures were refined at the singlepoint CCSD（T）/6-311+G（2df）//PBE0/6-311+G（2df）level［41-44］.It is considered to offer the ultimate energetics data in the study.The neutral B6Al2clusters also replenish the energy of the top low-lying isomeric structures at the M06-2X/6-311+G（2df）and CCSD（T）/6-311+G（2df）//M06-2X/6-311+G（2df）levels.

Chemical bonding was elucidated via the CMO analysis and AdNDP［36］.The AdNDP results are known to be insensitive to the basis set used，and such analysis was done herein using the 6-31G basis set.Orbital compositions were analyzed using the Multiwfn program［45］.The NBO analysis［37］was done using the NBO 6.0 program，which gives the Wiberg bond indices（WBIs）and natural atomic charges.Visualization of the CMOs and AdNDP results was accomplished using GaussView 5.0［46］.and Molekel 5.4.0.8［47］，respectively.All the electronic structure calculations were carried out using the Gaussian 09 package［48］.

2 Results

2.1 Structures and energetics

Based on the CK searches and comparative energetics data at the PBE0 and CCSD（T）levels of theory，binary B6Al2-/0/+clusters have a number of structures of particular interest，which are labeled as 1-7 in Figs S1-S3 at the PBE0 level.The optimized Cartesian coordinates for selected cluster structures are presented in Table S1 in the Supporting Information.Among these，clusters 1-4 are the key structures（Figs 1-3）.The B6Al2（1，D2h，1Ag）cluster is the lowest in energy at single-point CCSD（T）//PBE0 level，being only marginally lower than its nearest competitor，B6Al2（2，Cs，1A′），by 0.23 kcal·mol-1.Their energy order reverses at PBE0，which is secondary because that at CCSD（T）//PBE0 overrides it.Moreover，their energy order at CCSD（T）//PBE0 can also override them at M06-2X and CCSD（T）//M06-2X.（as shown in Table S2）.We assign cluster 1 as the neutral GM structure and cluster 2 a crucial lowlying isomer.For the anion cluster，B6Al2-（3，Cs，2A′）is consistently the GM structure at these two levels，being at least 7.44 kcal·mol-1more stable than alternative structures at CCSD（T）//PBE0.Cluster B6Al2+（4，D2h，2B2u）is consistently the cationic GM at the two levels，with a margin of 8.64 kcal·mol-1at CCSD（T）//PBE0.

Among the key structures，neutral GM cluster 1 and cationic GM cluster 4 are inverse sandwiches，which turn out to be similar.Therefore，we shall primarily discuss structures 1/2/3 in the paper.The latter two consist of a hybrid bowl-shaped B6Al motif and an isolated Al capping atom.The motif may also be described as a heteroatomic molecular wheel.The capping Al atom in 2 is substantially off the B ring（by 1.92 Å）.

According to the atomic covalent radii［49］，the upper bound for single B-B，double B=B，and single Al-Al bonds should be 1.70，1.56，and 2.52 Å，respectively.Typical single B-B and double B=B bonds are calculated to be 1.66 and 1.51 Å［7-8］.A single B-Al bond is estimated to be 2.11 Å，despite its polar nature.These values offer a qualitative reference to understand the present clusters.The peripheral B-B bond distances are 1.55/1.64，1.56/1.63，1.56/1.58，and 1.57/1.60 Å for structures 1-4，respectively，which are more or less uneven.Nevertheless，they fall in between single and double bonds，especially for the shorter B-B links，which suggest both Lewis-type B-B σ bonds and delocalized bonding. Interestingly，clusters 3/4 seem to be more uniform in peripheral B-B distances as compared to 1/2.The radial B-B links are 1.69-1.74 Å in 22 and 1.70-1.72 Å in 3，which are moderately longer than single bond（1.66 Å）［7］.Again，the bond distances in 33 are more uniform than those in 2.

The Al-Al distances are 3.30，3.62（not shown），2.75（not shown），and 3.44 Å in 1/2/3/4，respectively，which indicate negligible Al-Al bonding（except structure 3）.The peripheral B-Al links are 2.04 and 2.09 Å in 2/3，respectively，in line with single bonds（despite being polar）.A capping Al site normally coordinates closely with four B atoms.The corresponding B-Al distances amount to 2.19，2.32/2.38，2.23/2.35，and 2.26 Å in 1-4，showing moderate bonding.In addition，the radial B6-Al8 distance in 3 is 2.22 Å with moderate bonding，whereas that in 2 has negligible bonding（2.69 Å）.Overall，the peripheral B6or B5Al rings in clusters 1-4 are prolate rather than circular.Clusters 1/3/4 are elongated in the horizontal direction，whereas 2 is elongated vertically.It is reiterated that 3/4 are more circular than 1/2.

2.2 Wiberg bond indices and natural atomic charges

Calculated WBI values from the NBO analysis offer quantitative bonding information for clusters 1-4，as shown in Figs 2 and 3（b）.In line with the structural data in Section 2.1，the following observations are made.First，the peripheral B-B links all have WBIs greater than 1.0.Specifically，these WBIs are 1.17/1.52，1.06/1.25，1.26/1.43，and 1.28/1.38 in 1-4，respectively，which are attributed to both Lewis-type σ single bonds and delocalized π/σ bonding（vide infra）［1-2］.Again，clusters 3/4 have relatively uniform WBIs.Second，peripheral B-Al links in 2/3 have WBIs of 0.72 versus 0.83，suggesting quite strong covalent bonding（in addition to ionicity）.Third，the radial B-B links in 2 have substantial WBI values of 0.62-0.71，due to delocalized π/σ bonding.Likewise，those in 3 have WBIs of 0.61-0.76.Fourth，the radial B-Al bond in bowlshaped B6Al disk has a WBI of 0.24 in 3，although that in 2 has a negligible WBI（0.07）.The latter is associated to structural elongation along the vertical direction.Nevertheless，a peripheral Al center seems to play a minor role in delocalized π/σ covalent bonding.Fifth，a capping Al site in 1-4 interacts with four nearest B atoms with WBIs of 0.28，0.22，0.21/0.43，and 0.25，which are moderately strong，except for the B1-Al7 and B3-Al7 links in 3.The capping Al site is asymmetrically coordinated to the upper portion of B6Al disk.Lastly，direct Al-Al bonding is discernible only in cluster 3（WBI：0.23）.

For the natural atomic charges，neutral GM cluster 11（inverse sandwich）has positively charged Al centers（+1.13|e|）.The four B atoms closely coordinated to Al are more negative（-0.44|e|），as compared to the remaining two B atoms（-0.25|e|）.Its corresponding cationic cluster 4 has a similar charge distribution，except that the peripheral B ring is less charged due to detachment of an electron.The bowlshaped neutral cluster 2 is approximately composed of a heteroatomic［B6Al］-anion and a capping［Al］+cation；the latter carries a positive charge of+0.86|e|.It can be faithfully described as a charge-transfer［B6Al］-［Al］+complex.Of course，there is additional charge redistribution in the bowl，resulting in a peripheral Al center with+1.02|e|.Such redistribution is relatively local within a B-Al-B chain.For bowl-shaped anion cluster 3，the extra electron goes to the B5Al ring and especially the Al8/B2/B4/B5 sites.Indeed，these four sites in 3 collectively gain a net charge of-0.92|e|.Approximately，cluster 3 is described as a charge-transfer［B6Al］2-［Al］+complex.The exact formula is［B6Al］1.81-［Al］0.81+according to the NBO data.

3 Discussion

3.1 Chemical bonding analysis：conflicting π/σ aromaticity

For an in-depth understanding of clusters 1-4，it is essential to elucidate their chemical bonding.As reasoned above，we will mainly discuss clusters 1 and 3.Cluster 1 is a closed-shell system with 24 valence electrons，whose occupied CMOs are shown in Fig.4.The 12 CMOs are divided into four subsets on the basis of their constituent atomic orbitals（AOs）.Subset（a）has six σ CMOs that are primarily derived from B 2s AOs，which follow the orbital construction principles with zero up to three nodal planes from bottom up，including two quasi-degenerate pairs in between.These CMOs can be recombined and transformed to six Lewis-type two-center two-electron（2c-2e）B-B σ bonds on the periphery.Subset（b）involves only one CMO，being composed of 66.8%Al 3s and 25.8%Al 3p AOs.This CMO is basically nonbonding and equivalent to two Al 3s1half lone-pairs.Subsets（a）and（b）consume 14 electrons，thus leaving 10 electrons for delocalized π/σ bonding.

Subset（c） has three π CMOs.Their spatial shapes mimic the π sextet in benzene，which render π aromaticity to cluster 1 according to the（4n+2）Hückel rule.Subset（d）represents the delocalized σ framework.The lower HOMO-4（HOMO refers to the highest occupied molecular orbital）is completely bonding，which is composed of B 2p AOs that orient radially.The HOMO is similarly oriented and yet with one nodal plane.The HOMO-4/HOMO combination is the same as an antiaromatic 4π system in cyclobutadiene（C4H4），except that the former is σ in nature.Such a 4σ framework is intrinsically delocalized and cannot be transformed to Lewis-type σ bonds.Its 4σ electron-counting conforms to the 4n Hückel rule for antiaromaticity.Cluster 1 is σ antiaromatic.Overall，cluster 1 is an unusual bonding system with conflicting π/σ aromaticity，in line with its elongated D2hsymmetry（Fig.1（a））.The above bonding picture is perfectly borne out from the AdNDP analysis（Fig.5）.All occupation numbers（ONs）are close to ideal.Interestingly，two capping Al atoms have marked contributions to the π sextet，albeit not the 4σ framework.An alternative 6c-2e π AdNDP scheme lower the ON values from 2.00 down to 1.56|e|（Fig.S4）.For a technical note，the 4σ framework in B6Al2cluster can also be in a triplet σ2σ1σ1configuration，leading to two virtually circular inverse sandwiches；that is，the 21st and 25th isomers in Fig.S1［50］.Cationic cluster 4 has a 3σ framework，which is less σ antiaromatic with minor structural elongation（Fig.3（a））.

Fig.1 Optimized structures of（a）global-minimum（GM）B6Al2（1，D2h，1Ag），（b）low-lying isomeric B6Al2（2，Cs，1A′），and（c）GM B6Al2-（3，Cs，2A′）clusters at the PBE0/6-311+G（2df）level.Atoms are labeled numerically and the bond distances are shown in Å.The 2.22 Å distance in 3 refers to the B6-Al8 link.The B atoms are depicted in blue color andAl in orange

Fig.2 Calculated Wiberg bond indices（WBIs；in black color）and natural atomic charges（in|e|；red color）from the natural bond orbital（NBO）analyses.（a）B6Al2（1）；（b）B6Al2（2）；（c）B6Al2-（3）

Fig.3 Optimized GM structure of B6Al2+（4，D2h，2B2u）at the PBE0/6-311+G（2df）level.（a）Geometry and bond distances（in Å）；（b）WBIs（in black color）and natural atomic charges（in|e|；red color）.The B atoms are depicted in blue color and Al in orange

Fig.4 Pictures of occupied canonical molecular orbitals（CMOs）of B6Al2（1）cluster.The CMOs are sorted to four subsets according to their constituent atomic orbitals（AOs）.（a）Six CMOs for Lewis-type two-center two-electron（2c-2e）B-B σ single bonds along the peripheral B6ring.（b）One σ CMO composed of Al 3s AOs on two capping Al sites，which is equivalent to two half Al 3s lone-pairs with negligible net bonding.Also shown is the lowest unoccupied molecular orbital（LUMO）.（c）Three delocalized π CMOs（π sextet）.（d）Two delocalized σ CMOs

Fig.5 Chemical bonding pattern of B6Al2（1）on the basis of adaptive natural density partitioning（AdNDP）analysis.Occupation numbers（ONs）are shown.The Al-Al σ“bond”in（b）is formal only，being equivalent to two Al 3s1half lone-pairs

Anionic cluster 3 is chemically dictated by a hybrid bowl-shaped B6Al unit，upon which a capping Al atom is situated.It can be formulated as a chargetransfer［B6Al］2-［Al］+complex.The cluster has 25 valence electrons.Its CMOs are presented in Fig.6.Basically，the bonding pattern is similar to that of neutral cluster 1.Cluster 3 also has six Lewis-type 2c-2e σ bonds on the periphery：four B-B σ bonds versus two Al-B σ bonds（Fig.6（a））.It features a π sextet as well（Fig.6（c））.The extra electrons participate in the delocalized σ framework；that is，the singly occupied molecular orbital（SOMO；Fig.6（d））.As a consequence，the 5σ framework is closer to the（4n+2）electron counting，although it does not precisely conform to the Hückel rule.The 5σ framework make cluster 3 more circular relative to elongated cluster 1.Lastly，HOMO-2 is dominated by 61.8%Al 3s/3p AOs from the capping Al atom（32.4%Al 3s；29.4%Al 3p），which can，at the zeroth order，be viewed as an Al lone-pair of mixed 3s/3p nature.Again，the bonding picture is borne out from AdNDP analysis（Fig.7）.Note that the 7c-2e π bonds（Fig.7（c）） have relatively low ONs，suggesting that the capping Al site makes certain contribution.The capping Al atom seems to have negligible contribution to delocalized σ framework.Not surprisingly，the Al 3s2lone-pair is imperfect（Fig.7（b）），hinting at complicated interactions between this Al site and the bowl（such as Al-Al bonding）.Nevertheless，the ON of 1.80|e|is acceptable.Chemical bonding in cluster 2 is the same as that in 3，except for one less electron in σ framework.Cluster 2 also has conflicting 6π/4σ aromaticity（Figs S5 and S6）.

Fig.6 Pictures of occupied CMOs of B6Al2-（3）cluster.（a）Six CMOs for peripheral Lewis-type σ bonding：four 2c-2e B-B σ bonds versus two 2c-2e B-Al σ bonds.（b）One CMO primarily responsible for an Al 3s lone pair on the capping Al site.（c）Three delocalized π CMOs.（d）Three delocalized σ CMOs，in which SOMO stands for singly occupied molecular orbital

Fig.7 AdNDP bonding pattern of B6Al2-（3）cluster.The ONs are shown.One extra electron is added in the analysis，owing to the open-shell nature

3.2 Structural competition between inverse sandwiches and molecular wheels

Two kinds of structural motifs are present in the lowest-energy B6Al2-/0/+clusters：inverse sandwiches（1/4） versus bowl-like molecular wheels（2/3）.These two motifs are energetically competitive for neutral B6Al2cluster，for which GM 1 and isomeric 2 are within 0.23 kcal·mol-1at single-point CCSD（T）//PBE0 level.Inverse sandwich GM cluster 1 is slightly favored for neutral.Cationic cluster 4 also has an inverse sandwich GM structure.In contrast，anionic cluster 3 favors a molecular wheel geometry.Thus，there is a structural transition from inverse sandwich to molecular wheel along this series of clusters.

As discussed in Sections 2.1 and 3.1，structures 1-4 are more or less elongated（albeit along different directions）.Structures 1/3/4 are elongated horizontally and structure 2 in the vertical direction.Neutral B6Al2cluster also has a horizontally elongated isomer 6（Fig.S1）.Among the isomeric structures，one can find the corresponding molecular wheel isomer 7 for cation，as well as an inverse sandwich isomer 5 for anion.Three inverse sandwiches 4/1/5 and three molecular wheels 7/6/3 show an intriguing evolution trend from cation，neutral，to anion，as illustrated in Fig.8.All energies are calculated at singlepoint CCSD（T）//PBE0 level.It is clearly observed that cationic B6Al2+cluster 4 comfortably assume an inverse sandwich geometry，by a margin of 1.06 eV relative to molecular wheel 7.The edge shrinks by almost 77%down to 0.24 eV for neutral B6Al2cluster，although inverse sandwich GM 1 remains favorable with respect to molecular wheel isomer 6.For anionic B6Al2-cluster，the potential landscape overturns and molecular wheel GM 3 becomes 0.32 eV more stable than inverse sandwich isomer 5.The molecular wheel structures gradually and monotonically gain an advantage，by as much as 1.38 eV from cation to anion.

Fig.8 An energetic relationship between two isomeric structures in three charge states.The energies are shown at the CCSD（T）/6-311+G（2df）//PBE0/6-311+G（2df）level.The differences of structures 1/6 in their ionization potentials（IPs）and electron affinities（EAs），denoted as ΔIP and ΔEA，respectively，govern this evolution.Structures 5/6/7 can be found in Figs S1-S3

To elucidate the above structural and energetic evolutions，it is instructive to assess the adiabatic ionization potentials（IPs）and adiabatic electron affinities（EAs）of neutral structures 1/6.At single-point CCSD（T）//PBE0，cluster 1 has an IP of 7.17 eV and an EA of 2.35 eV.In contrast，cluster 6 has an IP of 7.99 eV and an EA of 2.91 eV，which are larger than those of cluster 1.Their difference in IP（denoted as ΔIP）amounts to 0.82 eV，which induces enhanced destabilization to molecular wheel structure 7 upon ionization.In other words，inverse sandwich structure 4 gains a relative advantage in the cationic charge state.

Similarly，the difference in EA（denoted as ΔEA）between clusters 1 and 6 is as large as 0.56 eV，which leads to extra stabilization to molecular wheel anion cluster 3.The extra effect of 0.56 eV is more than enough to offset the edge of 0.24 eV for inverse sandwich cluster 1 in the neutral state，thus overturning the potential landscape from neutral to anion.The sizable ΔEA is associated to the SOMOs of 3/5（Fig.9）.The SOMO of 5 is basically nonbond-ing and composed of Al 3s/3p AOs.The SOMO of 3 is a portion of the delocalized σ framework，as discussed in Section 3.1，which has substantial bonding effect along the B ring and between the capping Al sites and the B ring.Energetically，the latter SOMO is more stable，which underlies the anion molecular wheel GM cluster and holds the key to structural transformation.

Fig.9 Comparison of the SOMOs of（a）B6Al2-（5，D2h，2B3u）and（b）GM B6Al2-（3，Cs，2A′）

Lastly，we shall make a general comment on the structural elongation of GM or low-lying clusters 1-4，as well as their complementary structures 5-7（Fig.8）.These species have from 23 to 25 valence electrons.They assume distinct types of geometries：inverse sandwiches（1/4/5）versus molecular wheels（2/3/6/7）.In terms of bonding，the seven structures have the same six Lewis-type 2c-2e σ bonds on periphery and delocalized π sextet，which consume 18 electrons.For the Al lone-pair or nonbonding electrons，structure 5 has three and all other six structures each have two.The remaining 3 to 5 electrons constitute the delocalized σ framework.Cluster 1 has 4σ antiaromaticity.Similarly，2/6/5 have 4σ antiaromaticity.The structural consequence is that 1/6/5 are elongated horizontally，whereas 2 is elongated vertically.Specifically，clusters 1，6，5，and 2 have the B-B distances of 1.64/1.55， 1.62/1.56/1.53，1.61/1.55，and 1.56/1.63 Å，respectively.On the other hand，3/4/7 have a delocalized 5σ/3σ/3σ framework，respectively，which deviate from ideal 4σ antiaromaticity.Their structural distortion is anticipated to be smaller.Indeed，the elongation in 3，4，and 7 are minor，being 1.58/1.56，1.60/1.57，and 1.62/1.57/1.52 Å，respectively.In particular，cluster 3 has a relatively circular shape，because its 5σ electron counting is close to the（4n+2）Hückel rule.

3.3 Classification of three-types of Al sites in alloy B-Al clusters：the“isoelectronic Al-B substitution”is not completely isoelectronic

One of the motivations to study mixed B-Al clusters is to examine how the so-called“isoelectronic Al-B substitution”alters bare boron clusters［27-28］.However，it should be stressed that the concept is purely an assumption，rather than a scientific fact.As far as we are concerned，the current knowledge in literature of Al sites in binary B-Al clusters remains insufficient.The current B6Al2-/0/+clusters allow an understanding of the nature of three-types of Al sites，as illustrated in Fig.10 using clusters 1-3 as the selected examples.

Fig.10 A schematic illustration of three types of Al sites in B6Al20/-（1-3）clusters：I，Ⅱ，and Ⅲ.These are shown in different colors.See the text for further details

Among these Al sites，type I（Fig.10（b）and 10（c））can substitute the B atom in a truly isoelectronic manner.Here an Al site participates in a hybrid disk，although in a peripheral position rather than at the center.The latter is due to a smaller electronegativity of Al with respect to B.This type of Al site forms two Lewis σ bonds with two neighboring B atoms.It also participates in delocalized π/σ bonding.In short，such as Al site is no different from a typical B atom，contributing all three 3s/3p electrons in chemical bonding.The subtle difference is that the Al-B bonding is of mixed covalent/ionic nature.

For type Ⅱ sites（Fig.10（a）），two Al atoms form a bicapping dimer（although with no direct Al-Al bonding）.The Al2dimer collectively maintains two nonbonding Al 3s/3p electrons，albeit not a lonepair.In terms of chemical bonding，this type of Al site is valence two，rather than three.Such an Al-B substitution is clearly not isoelectronic.The Al2dimer can be chemically viewed as a carbon center，both behaving as valence four，which is a new version of electronic transmutation［51-52］.In this way，cluster B6Al2（1） is analogous to a B6C molecular wheel with hexacoordinate carbon，although the latter type of clusters do not favor a hypercoordinate carbon［53-55］.

A type Ⅲ site is capped on hybrid B6Al disk（Fig.10（b）and 10（c）），which maintains an approximate Al 3s/3p lone-pair.Its interaction with B6Al disk has predominant ionic character.In terms of bonding，this type of Al site is effectively valence one only.The corresponding Al-B substitution process is far from being isoelectronic.Overall，the Al-B substitution has diverse and distinct processes.An idea of“isoelectronic Al-B substitution”is oversimplified.Three types of Al site can be revealed，for which the Al atom behaves as valence three，two，and one，respectively.Only type I is an isoelectronic process.

A natural implication from Fig.10 is that the present B6Al2-/0/+clusters should not adopt the same structures as bare boron clusters（such as B8and B8-）［3］.The B8cluster has a beautiful D7hmolecular wheel GM structure with double 4π/6σ aromaticity in a triplet state，for which the reversed 4n Hückel rule applies for π framework.Clusters 1-4 each maintain an Al 3s lone-pair or two nonbonding electrons，which are equivalent to［B8］3+，［B8］2+，and［B8］+in chemical bonding.For a heptacoordinate molecular wheel，they would have only 7，8，or 9 electrons for delocalized π/σ frameworks，which are below the lower bound of 10 electrons（in a triplet state）.Moreover，a heptagonal B5Al2ring seems to be too large for a boron center（Figs S1-S3）.These two effects underlie the unconventional geometries for clusters 1-4.

4 Conclusions

We have investigated the structures，chemical bonding，and conflicting π/σ aromaticity of a series of binary B6Al2-/0/+clusters，using computer global searches and quantum chemical calculations.The cluster system has two distinct structural motifs.The neutral cluster features competing inverse sandwich and molecular wheel structures 1/2，of which the former is slightly favorable.Cationic cluster 4 strongly favors the inverse sandwich，whereas anion cluster 3 is a molecular wheel.Thus，structural transformation occurs from cation，neutral，to anion.The molecular wheel gradually gains an advantage upon sequential reduction.Chemical bonding in neutral clusters 1/2 is dominated by unique 4π/6σ conflicting aromaticity，resulting in elongated structures.Cationic 4 and anionic 3 clusters have delocalized 3σ/5σ frameworks，which deviate from ideal 4σ antiaromaticity and lead to more circular structures.The Al centers in the clusters fall into three distinct categories，which are chemically valence three/two/one，respectively.Only one out of three categories of Al sites follows the idea of isoelectronic Al-B substitution.We believe the present understanding should help design further examples of novel B-Al binary clusters.