The Triply Bonded Al≡Sb Molecules: A Theoretical Prediction The Triply Bonded Al ☰ Sb Molecules: A Theoretical Prediction

The effect of substitution on the potential energy surfaces of RAl ☰ SbR (R = F, OH, H, CH 3 , SiH 3 , SiMe(Si t Bu 3 ) 2 , Si i PrDis 2 , Tbt, and Ar*) is investigated using density functional theo- ries (M06-2X/Def2-TZVP, B3PW91/Def2-TZVP, and B3LYP/LANL2DZ + dp). The theoretical results demonstrated that all the triply bonded RAl ☰ SbR compounds with small substituents are unstable and can spontaneously rearrange to other doubly bonded iso- mers. That is, the smaller groups, such as R = F, OH, H, CH 3 and SiH 3 , neither kinetically nor thermodynamically stabilize the triply bonded RAl ☰ SbR compounds. However, the triply bonded R ’ Al ☰ SbR´ molecules that feature bulkier substituents (R´ = SiMe(Si t Bu3)2, Si i PrDis2, Tbt, and Ar*) are found to possess the global minimum on the singlet potential energy surface and are both kinetically and thermodynamically stable. In particular, the bonding characters of the R ’ Al ☰ SbR´ species agree well with the valence-electron bonding model (model) as well as several theoretical analyses (the natural bond orbital, the natural resonance theory, and the charge decomposition analysis). That is to say, R ’ Al ☰ SbR´ molecules that feature groups are regarded as R 0 d Al Sb d R 0 . Their theoretical evidence shows that both the electronic and the steric effects of bulkier substituent groups play a decisive role in making triply bonded R 0 Al ☰ SbR 0 species synthetically accessible and isolable in a stable form.


Introduction
The chemical synthesis and structural characterization of molecules that feature triple bonds [2] between heavier group 14 elements (E14 = Si, Ge, Sn and Pb) are of interest because of their interesting structural chemistry and their potential applications in organic and inorganic synthesis [1][2][3][4][5][6][7][8][9][10]. Although understanding of these RE14☰E14R molecules that feature heavier group 14 atoms has increased during the last two decades, the understanding of the RE13☰E15R compounds, which are isoelectronic to acetylene from a valence electron viewpoint, is still limited. The reason for this limited knowledge of acetylene analogues, RE13☰E15R, could be due to the fact that there has been limited preparation and the isolation of these species in a stable form [11,12]. Theoretical methods allow a theoretical design of the RE13☰E15R molecules to be made that increases understanding of their potential properties.
The III-V semiconductors that contain antimony have several important applications in optoelectronic devices that operate in the infrared region and in high-speed devices, which has prompted widespread studies of promising precursor systems for these materials [13]. In particular, the chemical synthesis and structural characterization of AlSb single-source precursors of the type R3Al-SbR´3 has attracted much attention, owing to their importance in CVD procedures [14], which is a developing industry for the production of thin films of the corresponding semiconducting materials [15]. As far as the authors are aware, only a handful of group 13 antimonides that contain AldSb σ-bonds have been discovered [16], No triply bonded RAl☰SbR species, which is isoelectronic to HC☰CH, has been reported both experimentally and theoretically.

General considerations
The valence-bond bonding model is a well-known satisfactory method, which is an approximate theory to explain the electron pair or chemical bond by quantum mechanics, for predicting molecular geometries [20]. Two valence-bond bonding models ( Figure 1) are thus used to interpret the bonding properties of triply bonded RAl☰SbR species. In model [1], the RAl☰SbR molecule is partitioned into two units: a singlet RdAl and a singlet RdSb. In model [2], the RAl☰SbR compound is divided into two moieties: a triplet RdAl and a triplet RdSb.  As a result, the choice of the bonding model that is used to explain the bonding characters of RAl☰SbR depends on the promotion energies (ΔE ST = E triplet À E singlet ) of the RdAl and RdSb fragments. According to current theoretical calculations (see below), it is known that RdAl occupies the singlet ground state, but RdSb occupies the triplet ground state. In consequence, if the value of ΔE ST for RdAl is much larger than that for RdSb, the latter easily jumps to the singlet excited state. Hence, model [1] can be used to explain the bonding nature of the RAl☰SbR molecule. In contrast, if the value of ΔE ST for RdAl is smaller than that for RdSb, the former is readily promoted to the excited triplet state. Therefore, model [2] is used to interpret the bond constitutions of the RAl☰SbR compound.
Two points are worthy of note. The first is that since aluminum and antimony respectively belong to group 13 and group 15 and both elements have different atomic radii (covalent radii: 118 pm and 140 for Al and Sb, respectively) [20], the overlapping populations between Al and Sb should not be strong. The second is that the lone pairs of both aluminum and antimony feature the valence s character. This, in turn, makes the overlap integrals between the lone pair orbital and the pure p orbital small. These two factors mean that the triple bond between aluminum and antimony is weak, unlike the traditional triple bond in acetylene.
Bearing the above bonding analyses in mind, theoretical evidences are given in the following sections.

Small ligands on substituted RAl☰SbR
Five small substituents (R = F, OH, H, CH 3 and SiH 3 ) are chosen, which include electronegative and electropositive groups, to determine their stability and bonding properties on the triply bonded RAl☰SbR molecules using the three types of DFT calculations (i.e., M06-2X/Def2-TZVP, B3PW91/Def2-TZVP and B3LYP/LANL2DZ + dp). Figure 2 shows the potential energy surfaces of the intra-molecular 1,2-migration reactions for five triply bonded RAl☰SbR compounds that feature small substituents. That is to say, the triply bonded RAl☰SbR species can undergo a 1,2-shift to give either R2Al〓Sb: or: Al〓SbR2 doubly bonded isomers.
As seen in Figure 2, the three DFT computational results demonstrate that the triply bonded RAl☰SbR species that feature small substituents are all both kinetically and thermodynamically unstable on the intra-molecular 1,2-migration reaction potential energy surfaces. In other words, once the triply bonded RAl☰SbR with small substituents is formed, it can easily proceed along the 1,2-migration to give the thermodynamically stable doubly bonded isomer, either R2Al〓Sb: or: Al〓SbR2. The theoretical findings give strong evidence that the triply bonded RAl☰SbR molecules that feature the small ligands are highly unlikely to be detected experimentally.
Although current theoretical observations show that the formation of RAl☰SbR involving small ligands is not likely, some of their physical properties, which are shown in Table 1, must be theoretically determined in order to design much more stable aluminum☰antimony acetylene analogues.   6 The Wiberg bond index (WBI) for the Al☰Sb bond: see Ref. [22].  Table 1 show that most of the singlet-triplet energy splitting (ΔE ST ) of R-Al is larger than that of the corresponding RdSb. This strongly implies that the bonding characters of the triply bonded RAl☰SbR species that feature small substituents are better described by model [1], as shown in Figure 1. In other words, the triple bond consists of one donor-acceptor σ bond and two donor-acceptor π bonds, which are schematically represented as RdAl SbdR. As previously mentioned, since the lone pair orbitals of both the R-Al and the R-Sb fragments feature the valence s character, their overlapping populations between the lone orbital and the valence p orbital should be smaller. Indeed, the supporting evidence from Table 1 shows that all bond orders for the RAl☰SbR species are estimated to be less than 2.0 (WBI = 1.474-1.799), which is less than the bond order for the C☰C triple bond in acetylene (WBI = 2.99).
In brief, the three DFT calculations shown in this work show that irrespective of their electronegativity, the triply bonded RAl☰SbR molecules that feature small ligands are highly unlikely to exist, even in the low-temperature matrices. In particular, the bond orders of these Al☰Sb triple bonds are theoretically predicted to be a weak double bond, rather than a triple bond.

Large ligands on substituted R'Al☰SbRT
hree bulky groups were then used to search for kinetically stable triple-bonded R'Al☰SbRḿ olecules: R´(〓SiMe(SitBu3)2, SiiPrDis2, Tbt, and Ar*) [19]. These are shown in Scheme 1. It is known that London dispersion (nonvalent interactions) plays a prominent role in both chemical and physical properties of inorganic molecules [23]. As a result, the dispersion-corrected M06-2X/Def2-TZVP method is used in the present study to investigate the behaviors of the triply bonded R'Al☰SbR´compounds bearing bulky substituents. Similarly to the cases for small ligands on substituted RAl☰SbR, the dispersion-corrected M06-2X/Def2-TZVP level of theory is used to determine the potential energy surfaces for the intra-molecular 1,2-migration  Table 2. The reaction enthalpies for both the 1,2-shift reactions (R'Al☰SbR´! R2'Al〓Sb and R'Al☰SbR´! R2'Sb〓Al) are apparently too high. They are estimated to be at least 80 kcal/mol. The reason that both doubly bonded R2'Al〓Sb and R2'Sb〓Al isomers occupy such high energy points is simply because two bulky groups can cause steric overcrowding. As a consequence, the theoretical findings strongly suggest that the triply bonded R'Al☰SbR´, which is attached by two bulkier substituents, is kinetically stabilized. Table 2 shows that the Al☰Sb triple bond distance is predicted to be 2.422-2.477 Å. Since no experimental results for the Al☰Sb triple bond length have been reported, these values are estimates. These theoretical calculations also show that the geometrical structures of R 0 Al☰SbR 0 molecules that feature bulky groups adopt a bent structure; i.e., ∠R 0 dAldSb ≈ 160.0 and ∠AldSbdR 0 ≈ 120.0 . As stated previously, the triply bonded R 0 Al☰SbR 0 species feature this bent geometry because of the relativistic effect [23].
In addition, the bonding energy (BE) that is shown in Table 2 shows that the central aluminum and antimony atoms in the substituted R 0 Al☰SbR 0 compounds are strongly bonded, since the BE values are in the range 71-97 kcal/mol for R 0 = SiMe(SitBu3)2, SiiPrDis2, Tbt, and Ar*. Table 2 also shows that the modulus ΔE ST (kcal/mol) for AldR 0 and SbdR 0 fragments are predicted to be 43-27 and 31-16. These theoretical values allow two interpretations. Firstly, even when attached by bulkier groups, it is theoretically verified that both the AldR 0 and the SbdR 0 units occupy the ground singlet state and the ground triplet state, respectively. Since the ΔE ST values for AldR 0 are so small (compared with those for AldR, as shown in Table 1), model [2] in Figure 1 is most suitable to interpret the triple bonding characters in the R 0 Al☰SbR 0 species that feature bulky substituents. As schematically shown in Figure 1, the nature of the Al☰Sb triple bond can be considered as one conventional σ bond, one conventional π bond and one donor-acceptor π bond. That is, R 0 dAl SbdR 0 . It is worthy of note that two factors affect the overlapping populations between the central Al and Sb elements. The first is that the lone pair orbital of the SbdR 0 moiety features the valence s character. This, in turn, renders the overlap population between the pure p orbital of Al and the lone pair orbital of Sb very small. The other is that the sizes of the valence p orbitals for Al and Sb are quite different, since they belong to different rows of the periodic table having different principal quantum numbers. As a result, the triple bond in R 0 Al☰SbR 0 molecules that feature The charge density on the Al element. 2 The charge density on the Sb element. 3 ΔE ST (kcal mol À1 ) = E(triplet state for R 0 dAl) À E(singlet state for R 0 dAl). 4 ΔE ST (kcal mol À1 ) = E(triplet state for R 0 dSb) À E(singlet state for R 0 dSb).
The key geometrical parameters, the singlet-triplet energy splitting (ΔE ST ), the natural charge densities (QAl and QSb), the binding energies (BE), the HOMO-LUMO energy gaps, reaction enthalpies, and the Wiberg bond index (WBI) for R 0 Al☰SbR 0 at the dispersion-corrected M06-2X/Def2-TZVP level of theory.
bulky substituents is predicted to be quite weak. Indeed, the theoretical evidences given in Table 2 shows that the bond order is a little bit higher than 2.0 (WBI ≈ 2.17, 2.18, 2.07 and 2.02 for R 0 = SiMe(SitBu3)2, SiiPrDis2, Tbt, and Ar*, respectively). The bond order for the conventional C☰C bond in acetylene is estimated to be 2.99.
Besides these, Dapprich and Frenking developed a useful method [24], which is called the introduced charge decomposition analysis (CDA), from which one may analyze donoracceptor interactions of a A-B molecule. From CDA, one may obtain three parts. The first part is the number of electrons donated from the R 0 dAl unit to the R 0 dSb monomer, which can be considered as (R 0 dAl) ! (R 0 dSb). The second part is the number of electrons back donated from the R 0 dSb component to the R 0 dAl moiety, which can be represented as (R 0 dAl) (R 0 dSb). The third part is the repulsive interactions between (R 0 dAl) and (R 0 dSb), which can be described as The CDA results about the (SiMe(SitBu 3 ) 2 )Al☰Sb(SiMe (SitBu 3 ) 2 ) molecule based on the dispersion-corrected M06-2X/Def2-TZVP method are given in Table 3. As seen in Table 3, for the (R 0 dSb) fragment, its largest contribution is No. 267 (HOMO) orbital, displaying that a R 0 dSb component donates electrons to a R 0 dGa unit mainly through the HOMO orbital. In consequence, the net amount of electron transfer is estimated to be À0.207, implying that the R 0 dSb part donates more electrons to the R 0 dAl moiety. This theoretical finding agrees well with the valence-electron bonding model shown in Figure 1 (i.e., model [2]). Namely, the bonding character of R 0 Al☰SbR 0 can be recognized as R 0 Al SbR 0 . Summation of contributions from all unoccupied and occupied orbitals. Table 3. The charge decomposition analysis (CDA) for R 0 Al☰SbR 0 (R 0 = SiMe(SitBu 3 ) 2 ) system based on M06-2X orbitals, where a is the number of electrons donating from R 0 dAl unit to R 0 dSb unit, B is the number of electrons donating from R 0 -Sb moiety to R 0 -Al moiety and W is the number of electrons involved in repulsive polarization.
The bonding characters of the Al☰Sb triple bond in R 0 Al☰SbR 0 molecules were examined using the natural bond orbital (NBO) [22] and the natural resonance theory (NRT) [25] analysis, whose results are given in Table 4, are used to determine the bonding properties. For instance, Table 4 shows that for (SiMe(SitBu3)2)Al☰Sb(SiMe(SitBu3)2), the NBO model shows that the Al-Sb σ bonding orbital contains about 23% natural Al orbitals and 77% natural Sb orbitals. Also, the Al☰Sb π bonding orbital contains averagely about 25% natural Al orbitals and 75% natural Sb orbitals (Figure 3). These values give strong evidence that the Al☰Sb π bond is polarized. Table 4 also shows that the Al☰Sb π bonding interaction: π ⊥ (Al☰Sb) = 0.529 (3s3p 1.98 )Al + 0.849(5s5p 12.43 )Sb and π k (Al☰Sb) = 0.475(3s3p 99.99 )Al + 0.880(5s5p 99.99 )Sb, which again implies that the predominant bonding interaction between the AldR and the SbdR moieties originates from 3p(Al) 5p(Sb) donation. In other words, the electron deficiency on Al and the π bond polarity are partially balanced by the donation of the Sb lone pair to the empty Al p orbital ( Figure 3).

Conclusion
This study uses DFT computations to theoretically design substituted RAl☰SbR molecules that feature the Al☰Sb triple bond, that are stable from the kinetic viewpoint. The theoretical observations show that only bulky substituents (R 0 ) can significantly stabilize the triply Figure 3. The natural Al☰Sb π bonding orbitals ((i) and (ii)) for (SiMe(SitBu 3 ) 2 )Al☰Sb(SiMe(SitBu 3 ) 2 ). Also, see Figure 1.
bonded R 0 Al☰SbR 0 compounds, and not small substituents. The theoretical findings also show that the bonding characters of the R 0 Al☰SbR 0 species that feature bulky groups can be represented as R 0 dAl SbdR 0 . That is to say, the R 0 Al☰SbR 0 species contains a conventional σ bond, a conventional π bond and a donor-acceptor π bond. However, due to the poor overlapping populations between the Al and Sb elements, which is due to the different atomic sizes of the two elements and the nature of overlapping bonding orbitals, the Al☰Sb triple bond is very weak. The theoretical results also give strong evidence that the geometrical structures of the R 0 Al☰SbR 0 species adopt a bent conformation with a nearly perpendicular angle at the antimony center.