F2BMF (M = B and Al) Molecules: A Matrix Infrared Spectra and Theoretical Calculations Investigation

Reactions of laser-ablated B and Al atoms with BF3 have been explored in the 4 K excess neon through the matrix isolation infrared spectrum, isotopic substitutions and quantum chemical calculations. The inserted complexes F2BMF (M = B, Al) were identified by anti-symmetric and symmetric stretching modes of F-B-F, and the F-11B-F stretch modes are at 1336.9 and 1202.4 cm−1 for F211B11BF and at 1281.5 and 1180.8 cm−1 for F211BAlF. The CASSCF analysis, EDA-NOCV calculation and the theory of atoms-in-molecules (AIM) are applied to investigate the bonding characters of F2BBF and F2BAlF molecules. The bonding difference between boron and aluminum complexes reveals interesting chemistries, and the FB species stabilization by a main group atom was first observed in this article.


Introduction
B 2 species, comprising electron-precise B-B bonds, have witnessed swift developments in the past twenty years, in which B 2 X n (X = F, Cl, Br, n = 2,4) molecules are important precursors for synthesizing boron-containing compounds, which garnered much attention from scientists [1]. As for B 2 F 4 , Trefonas and Lipscomb showed that B 2 F 4 has a planar structure in the solid phase by X-ray diffraction [2], while several earlier Raman and infrared spectroscopic studies suggested a staggered structure [3][4][5]. In 1977, Danielson, Patton, and Hedberg confirmed that the gaseous B 2 F 4 molecule has a D 2h symmetry by electron diffraction [6]. Fan and Li also found that the ground state of B 2 F 4 has an eclipsed conformation (in D 2h symmetry) [6]. Later, Danielson, Patton, and Hedberg demonstrated that the experimental difficulties in determining the structure of B 2 F 4 were probably due to its very low internal rotation barrier around the B-B bond (0.42 kcal·mol) [7]. For F 2 B 2 , the linear singlet structure FBBF (D ∞h , 3 Σ − ) is a second-order stationary point at MBPT (2), and it could convert into a bent structure (C 2h , 1 A g ), which is 5.0 kcal/mol higher in energy than a linear structure at MBPT(2) [8]. The double-bond character for the bent structure is suggested by the NBO analysis (WBI-[BB] = 1.432 Å), involving two highest occupied a g and b u MO's, which can be visualized as a donor-acceptor complex formed by the delocalization of σ lone pairs into empty p π orbitals lying in the molecular plane. The association of two ground-state BF molecules into the C 2h bent structure has a very low barrier (<1.0 kcal/mol) via a loose C 2h symmetric transition state (R BB = 2.434 Å) [8].
Recently, our assignment of the experimentally observed B-F stretching frequencies at 1327 cm −1 to the trans-bent isomer FBBF is therefore very tentative due to similarity in the calculated anti-symmetric B-F stretching frequencies of the linear and bent isomers [9].
Although B 2 F 4 and B 2 F 2 have already been known well, there seems to be no relevant report on the B 2 F 3 molecule. As we know, B 2 F 3 should possesse FB 2 and FB fragments, having significant differences from B 2 F 4 and B 2 F 2 molecules, but its structure and properties have not yet been understood. Boron is the main group element in the periodic table, and bonding between boron and main group elements has also been an attractive subject [10][11][12][13][14]. For example, by laser vaporization of a mixed B/Bi target, the Bi ≡ B and Bi = B multiple bonds in BiB 2 O 2 − and Bi 2 B − are observed and are characterized by photoelectron spectroscopy and ab initio calculations [15]. Several years ago, we reported some boryl complexes F 2 BMF (M = C, Si, Ge, Sn, Pb) [14], and DFT and CCSD(T) calculations demonstrate that triplet F 2 BCF is the most stable isomer with two singly occupied molecular orbitals, while singlet F 2 BMF (M = Si, Ge, Sn and Pb) molecules possess a near right angle B-M-F moiety with lone pair electrons on the M atom. In this paper, the laser-ablated B and Al were demonstrated to react with BF 3 to produce the fluoroboryl complexes F 2 BBF and F 2 BAlF, which have been identified by boron isotopic substitution and theoretical frequency calculations. The bonding formation for B-B as well as B-Al in fluoroboryl complexes of F 2 BMF was investigated by EDA-NOCV and CASSCF calculations. The active molecular orbital and NBO analysis, and the bonding difference, were analyzed in detail.

Results and Discussion
The assignment of absorptions was based on the behavior of the products' absorptions upon stepwise annealing and photolysis behavior and will be discussed below. The typical infrared spectra in the selected regions and the absorption bands are shown in Figures 1-3  and Table 1, respectively. In addition, the calculated frequencies based on DFT are listed in the same tables for comparison. (a) co-deposition of 11 B + 1.0% 11 BF 3 for 60 min; (b) after annealing to 8 K; (c) after λ > 300 nm irradiation for 6 min; (d) after annealing to 12 K; (e) co-deposition of 10 B + 0.5% 10 BF 3 for 60 min; (f) after annealing to 8 K; (g) after λ > 300 nm irradiation for 6 min; (h) after annealing to 12 K.

F 2 BBF
In the reaction of laser-ablated 11 B with 11 BF 3 in excess neon, as shown in the Figure 1, the new product absorptions upon co-deposition appeared at 1336.9 and 1202.4 cm −1 . These two bands decreased slightly after annealing to 8 K and 12 K. These two bands shifted to 1370.6 and 1241.6 cm −1 in the reaction of 10 BF 3 with the 10 B target, which showed the similar behavior to that of the counterparts produced with 11 B + 11 BF 3 .
The 1336.9 cm −1 appeared at the BF 2 stretching region and shifted to 1370.6 cm −1 with 10 BF 3 + 10 B, giving the 1.0252 10 B/ 11 B isotopic frequency ratio, which are in good agreement with the isotopic frequency ratio of 1.0280 in the B 2 F 4 molecule [3]. The 1202.4 cm −1 shifted to 1241.6 cm −1 , giving the 10 B/ 11 B isotopic frequency ratio of 1.0326 that was close to the calculated ratio of 1.0350 and fit in the previously reported values of the F-B-F vibration mode [16]. Unfortunately, the BBF stretching mode was covered by precursor bands in our experiments. These bands are appropriate for the F 2 B-BF molecule based on the isotopic shifts and photochemical behavior.
In the reaction of 11 BF 3 with 10 B target (Figure 2a-d), two new bands appeared at 1338.7 and 1200.8 cm −1 in the BF 2 stretching region, which decreased slightly after annealing to 8 K and λ > 300 nm photolysis, and decreased obviously after λ > 220 nm irradiation. In addition, the other new group bands appeared at 1369.4 and 1223.8 cm −1 after λ > 220 nm irradiation. In the reaction of 10 BF 3 with 11 B (Figure 2e-h), 1369.4 and 1223.8 cm −1 bands appeared on deposition, which decreased largely upon λ > 220 nm irradiation. Meanwhile, new group bands were located at 1338.7 and 1200.8 cm −1 after λ > 220 nm photolysis. Obviously, we obtained the same two isomers in 10 BF 3 + 11 B and 11 BF 3 + 10 B experiments.
It is very interesting to observe that in the reaction of 11 BF 3 with 10 B (Figure 2a-d), F 2 11 B 10 BF was produced at first, but decreased with the emergence of F 2 10 B 11 BF on >220 nm irradiation. Similarly, in Figure 2e-h, F 2 10 B 11 BF was observed firstly and then F 2 11 B 10 BF appeared accompanied with no obvious change of F 2 10 B 11 BF on the >220 nm irradiation. Apparently, α-F transfer happened between the two species due to the photo irradiation. This assignment is supported by our DFT frequency calculations ( Table 1). The F 2 BBF molecule is predicted to have C s symmetry with 2 A ground state ( Figure 4). The antisymmetric and symmetric B-F stretching modes of the

F 2 BAlF
As shown in Figure 3 and Table 1, the new product absorptions located at 1281.5, 1180.8 and 819.6 cm −1 in the reaction of 11 BF 3 with laser-ablated Al atoms, increased on annealing to 8 K, but decreased sharply on the λ = 450 nm irradiation and increased again on annealing to 12 K. These bands shifted to 1324.6, 1217.1 and 819.6 cm −1 in the reaction of 10 BF 3 with Al atoms, which showed a similar response to kinds of photolysis and annealing.
The absorption bands at 1281.5 and 1180.8 cm −1 shifted to 1324.6 and 1217.1 cm −1 , giving 1.0336 and 1.0307 of 10 B/ 11 B isotopic frequency ratio, which match very well with the F-B-F radical vibration mode [16]. The absorption bands at 819.6 cm −1 showed no 10 B/ 11 B isotopic frequency ratio shift, indicating that only Al and F are involved in this mode. It is most likely that this absorption arises from terminal Al-F stretching vibrations. All these indicate that this group band is attributable to the F 2 BAlF molecular.
The B3LYP calculations predict the F 2 BAlF molecule to have C S symmetry with 2 A ground state. The calculated BF 2 anti-symmetric and symmetric mode using B3LYP is 1312.0 and 1172.2 cm −1 , being overestimated by about 2.3% and underestimated by about 0.7%, respectively. The calculated Al-F stretching vibration is overestimated by about 1.6%, which fits the observed values very well.

Reaction Product Comparison and Bonding Consideration
Two stable complexes, F 2 BBF and F 2 BAlF, were calculated by the B3LYP functional and parameters are illustrated in Figure 4. The reaction of laser-ablated B atoms with BF 3 to produce inserted complex F 2 BBF is exothermic by 54.0 kcal/mol at CCSD(T) level. The subsequent α-F transfer reaction to give FBBF 2 requires an energy barrier of 31.7 kcal/mol. In our experiments of 11 BF 3 with 10 B or 10 BF 3 with 11 B, only one inserted species was observed first and then α-F transfer occurs upon 220 nm photolysis. In the reaction of BF 3 with Al atom, the F 2 BAlF molecule is produced with an exothermic 15.5 kcal/mol −1 reaction at the CCSD(T) level. However, the FB-AlF 2 produced by a-F transfer from F 2 B-AlF is endothermic by 6.8 kcal/mol −1 , which could not be observed in our experiments ( Figure 5).  Table S1, for the F 2 BBF molecule, both boron atoms have a good hybridization with the s and p orbital, while little hybridization occurs between the s and p orbital for the B-Al σ bond in the F 2 BAlF molecule. The energy decomposition analysis (EDA) can be used in quantitative interpretation of chemical bonds' formation in terms of three major components (Table 2) [19]. For the F 2 BBF molecule, the EDA shows that the total interaction energy of −148.3 kcal/mol between the F 2 B and BF fragments consists of an attractive electrostatic energy of −53.0 kcal/mol, an orbital interaction energy of −193.9 kcal/mol and a large Pauli repulsion of 97.5 kcal/mol. This interaction energy is bigger than that of the H-H single bond (−112.9 kcal/mol), but smaller than the N-N triple bond's (−232.2 kcal/mol) [19]. Surprisingly, this interaction between B and B is bigger than that of the triple bond between B and heavier transition metal atom that we observed previously [20]. It is possible to breakdown the orbital term ∆E orb into pairwise orbital contributions of the interacting fragments by EDA-Natural Orbitals for the Chemical Valence (NOCV) method [21][22][23]. Figure 6c clearly depicted the natural orbitals for the chemical valence of F 2 BBF. The σ bond between B and B is mainly caused by the outflow of electrons (most 2s electron of B) from FB to B of BF 2 and then the (p-p) π bond is formed by the outflow of one 2p electrons of B of BF 2 to 2p vacant orbital of B of BF. The decomposition of the orbital interaction shows that 42.7% (−82.8 kcal/mol) come from the σ bond, while 53.6% (−104.0 kcal/mol) come from the π bonds, respectively. For the F 2 BAlF molecular, only one σ bond existed between B and Al and both B and Al atom contribute to this σ bond together (Figure 6d). From Figure 6b, we can observe that the occupation of the σ bond is 1.93 e. Moreover, the Al atom possesses a single electron (most from the s orbital) which did not participate in bonding. Although B and Al atoms are in the same group, their bonding situation is very different. In Table S1, for the F 2 BBF molecule, both two boron atoms have good hybridization with the s and p orbital. While for the B-Al σ bond, the bonding electron is either from the s orbital or from the p orbital of the Al atom in a different phase and little hybridization happening between the s and p orbital. Thus, the 3s electrons of aluminum barely participates in bonding with other atoms and no π bond formed in the F 2 BAlF molecule.
Although the FBAlF 2 molecule was not observed in the experiment by the α-F transfer, a similar bonding composition could be demonstrated to that of FBBF 2 ( Figure S1). The B-Al is also caused by the outflow of electrons (most 2s electron of B) from FB to Al, and then the (p-p) π bond is formed by the inflow of one 3p electrons of Al to the 2p vacant orbital of B. The total interaction energy of −122.0 kcal/mol between BF and AlF 2 is very strong, and 29.3% (−39.5 kcal/mol) come from the σ bond and 68.3% (−91.9 kcal/mol) from π bond; thus, compounds with σ-donor and π-acceptor bonding modes formed [20].
For further analyzing the bond character, the atoms in the molecule theory (AIM) analysis were performed ( Figure S2). The negative value of local energy density H(r) = −0.12656 and −0.02651 for B-B and B-Al was obtained, respectively. The bond critical point between the B and B atom locates in the negative value of the Laplacian value (∇ 2 ρ cp = −0.426); however, this value is slightly positive (∇ 2 ρ cp = 0.058) and close to zero between the B and Al atom. Figure S3

Experimental and Computational Methods
Laser-ablated B and Al atoms react with 11 BF 3 and 10 BF 3 in excess neon during condensation at 4 K using a closed-cycle helium refrigerator (Sumitomo Heavy Industries Model SRDK-408D2, Japan). A Nd:YAG laser fundamental (1064 nm, 10 Hz repetition rate with 10 ns pulse width) was focused onto the rotating B, or Al target, and typically 20-30 mJ/pulse was used. The laser-ablated enriched 10 B (Eagle Pitcher, America, 93.8% 10 B, 6.2% 11 B), enriched 11 B (Eagle Pitcher, 97.5% 11 B, 2.5% 10 B), and Al (Alfa Aesar, America, 99.999%) atoms were reacted with 11 BF 3 and 10 BF 3 purchased from Jinglin (Shanghai, China) Chemical Industry Limited Liability Company (Shanghai, China, chemical purity, ≥99.99%) in excess neon spread uniformly onto the CsI window. Infrared spectra were recorded at a resolution of 0.5 cm −1 between 4000 and 400 cm −1 using a HgCdTe range B detector. Selected samples were irradiated by a mercury lamp (175 W, without globe) with the aid of glass filters to permit the allowed wavelengths to pass.
All structures were optimized at the BPW91/def2-TZVPP and B3LYP/def2-TZVPP [24,25] basis set via the Gaussian 09 program [26] and CAS(9e, 11o)/def2-TZVP [27,28] and CCSD(T)/def2-TZVP(-f) [29][30][31] basis set via the ORCA 4.0.1 program [32,33]. The single point energy calculations were performed with the correlated molecular orbital theory coupled cluster CCSD(T) [29][30][31] theory. Transition states were optimized with the Rational Function Optimization (RFO) method and were verified to link the desired reactant and product through the intrinsic reaction coordinate (IRC) calculations. Atoms in molecules' (AIM) [34] analysis was performed to elicit detailed information on the bonding characters with the Multiwfn code [35]. The orbital composition and effective bond order and Wiberg bond order were calculated by a natural bond orbital (NBO) population analysis [26,36]. In addition, ab initio calculations based on the high-level multi-configurational wavefunction method were also performed to obtain the accurate electronic structure information of BF 2 -MF compounds by the ORCA 4.0.1 program [32,33]. CASSCF [27] calculations including three active electrons in eight active orbitals [CAS(3e, 8o)], and NEVPT2 [37][38][39] calculations including three active electrons in four active orbitals [CAS(3e, 4o)] were performed with the def2-TZVP [28] basis set for all atoms. The effect of the dynamic correlation was taken into account by NEVPT2 [37][38][39] on top of the wavefunctions at CASSCF level to obtain more accurate energies. The energy decomposition analysis with the natural orbitals of the chemical valence (EDA-NOCV) method [21][22][23] were carried out with the ADF 2017 program [40] package to study the chemical bonding between the B and Al atoms with the B atom.

Conclusions
The reaction of laser-ablated B and Al atoms with BF 3 has been studied by the matrix isolation infrared spectrum and theoretical calculations. The structure and properties of the B 2 F 3 molecule, which can be drawn as F 2 B-BF, have been investigated. The F-B-F stretching mode was located at 1336.9 and 1202.4 cm −1 . For comparison, the F 2 BAlF molecule was also investigated and the F-B-F stretching mode was at 1281.5 and 1180.8 cm −1 . The CASSCF analysis, EDA-NOCV calculation, the theory of atoms-in-molecules (AIM) and localized orbital locator (LOL) are applied to investigate the bonding characters of the B-B and B-Al bond in F 2 BBF and F 2 BAlF molecules. The B-B bond in F 2 BBF favors the one and half bond order, in which two boron atoms have a good hybridization between s and p orbital. Meanhile, due to little hybridization between s and p orbital, 3s electrons of aluminum barely participate in bonding with other atoms, thus one bond order is formed for the B-Al bond.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules28020554/s1, Figure S1: Plot of the deformation densities ∆ρ of the BF→AlF 2 σ donation and AlF 2 →BF π back-donation in FBAlF 2 with the associated interaction energy ∆E orb and charge eigenvalues |ν n |(in e).; Figure S2: Contour line diagrams of the Laplacian of the electronic density of F 2 BMF (M = B, Al).; Figure S3: Color-filled maps of localized orbital locator of F 2 BMF molecules (M = B, Al).; Table S1: Compositions of Natural Bond Orbitals from NBO Analysis of F 2 BMF molecules (M = B, Al).; Table S2: Effective Bond Order Computed at B3LYP/def2-TZVPP level of F 2 BMF molecules (M = B, Al).; Table S3: Calculated Fundamental Frequencies of F 2 BBF and F 2 AlBF isotopomers in the Ground 2 A State.

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Conflicts of Interest:
The authors have declared no conflict of interest.