Interplay of Donor-acceptor Interactions in Stabilizing Boron Nitride Compounds : Insights from Theory

Isolated BN is a challenging system as the lowest singlet and triplet states both have multireference character and are nearly isoenergetic; the triplet state has been determined experimentally to be more stable by 0.71± 0.09 kcal/mol. The M05-2X/cc-pVTZ singlettriplet gap is overestimated at 21.7 kcal/mol (with the triplet state as more stable) but this is in keeping with most DFT methods and also many ab initio approaches. However, the present work is focused on electronic and structural characterization of the singlet complexes rather than relative singlet-triplet energetics of the isolated species. For example, our computed M05-2X/cc-pVTZ bond lengths in the triplet and singlet states (1.315 Å and 1.261 Å, respectively) agree well with high-level CCSD(T)/aug-cc-pVQZ results of 1.329 Å and 1.270 Å. Xu et al. have previously studied the singlet and triplet potential energy surfaces (PESs) of linear and cyclic B2N2 isomers by means of the coupled cluster CCSD method with the ∗To whom correspondence should be addressed


Introduction
Boron nitride materials (BN) n are isoelectronic with various carbon allotropes (e.g., diamond, graphene, nanotubes), 1-3 however, they possess vastly different properties due to the presence of polarized B-N linkages. Two specific properties, wide electronic band gaps (5.9 eV in hexagonal BN) and chemical inertness, 4 make boron nitride of significant interest for the electronics industry, with the construction of devices based on BN/graphene heterostructures being a promising recent development. 5,6 One hindrance to the widespread examination and application of BN materials is the harsh conditions required for their syntheses, i.e., heating above 900 1C and/or the use of plasma conditions. [1][2][3] With these challenges in mind, we have embarked on a program wherein complexes of the general form [LBÁBN] n (n Z 1; LB = Lewis base) might be formed with suitable carbon-based donors. Upon heating in solution, the target [LBÁBN] n complexes could afford bulk boron nitride and free Lewis base. To provide a solid fundamental basis for future experimental explorations, we present quantum mechanical computations on the Lewis base-stabilized linear and cyclic boron nitride species (BN) n (n = 1-3) including the donor-acceptor adducts LBÁ(BN) n ÁLA (n = 1-3, LA = Lewis acid). Recent examples of stabilizing main group element units (e.g., Si 2 ) with the aid of strong carbon-based donors are numerous in the literature. [7][8][9][10][11][12][13][14][15] Moreover, donor-acceptor stabilization has been used to great success to isolate heavier group 13-15 element species, [16][17][18][19][20][21] while related computational studies have been reported. 22,23 More specifically, DFT predicted a significant thermodynamical stabilization of group 13-15 cubane systems (e.g., B 4 N 4 ) upon addition of NH 3 and BH 3 as donor and acceptor molecules, respectively. 22 In this work we present our analyses of the bonding within Lewis base-substituted boron nitride compounds in the presence and/or absence of Lewis acid. Specifically we examined the binding of the carbon-based donors, ImMe 2 (ImMe 2 = [(HCNMe) 2 C:]), ImMe 2 CH 2 and Me 3 PCH 2 to (BN) n units, given our use of their sterically hindered analogues to bind/stabilize inorganic methylene and ethylene units (EH 2 and H 2 EE 0 H 2 ; E and E 0 = Si, Ge and/or Sn). 14,[24][25][26][27][28][29][30][31] We also provide computations on LBÁ(BN) n ÁBH 3 and LBÁ(BN) n ÁW(CO) 5 adducts (n = 1-3) featuring coordinated (BN) n units and show that this overall donor-acceptor approach is a viable means of intercepting a complex of molecular boron nitride. Finally, based on detailed EDA-NOCV computations, we will comment on the strength and nature of both the carbene-boron and nitrogen-tungsten donor acceptor bonds in the ImMe 2 substituted BNÁW(CO) 5 and B 3 N 3 ÁW(CO) 5 adducts.

Computational methods
Geometry optimizations were performed using density functional theory (DFT) with the M05-2X 32 functional. The computations employed the following basis sets: cc-pVTZ 33,34 for all period 1, 2 and 3 atoms and cc-pVTZ-PP, 35,36 combined with the corresponding small core (60 electrons) effective core potential (ECP) for tungsten (W). The basis set and ECP for tungsten were obtained from the basis set exchange. 37,38 For convenience, these computations are simply labeled as M05-2X/cc-pVTZ throughout the text. Triplet states for BN, linear BNBN, and cyclic B 2 N 2 were computed using an UHF reference. For geometry optimizations, ''Tight'' convergence criteria were applied: maximum force = 1.5 Â 10 À5 a.u., RMS force = 1.0 Â 10 À5 a.u., maximum displacement = 6.0 Â 10 À5 , and RMS displacement = 4.0 Â 10 À5 . The grid used for numerical integration in DFT was set to ''Ultrafine'' with a pruned grid of 99 radial shells and 590 angular points per shell. Harmonic vibrational frequencies were computed analytically at the same level of theory in order to characterize the stationary points as minima, representing equilibrium structures on the potential energy surfaces.
Energy decomposition analyses (EDA) were performed for all the mono-substituted complexes using the GGA BP86 density functional 39,40 and the TZ2P basis set; 41 relativistic effects were considered for the tungsten atom using the ZORA approximation. As originally developed by Morokuma, 42 Ziegler and Rauk, 43 EDA analysis can provide valuable insight into the nature and strength of a bond. It decomposes the bond dissociation energy (D e ) between two fragments (A and B) into the interaction energy (DE int ) and the preparation energy (DE prep ): The preparation energy, which pertains to the amount of energy required to distort and/or electronically excite the two fragments to their states in the complex, is defined as: E A/B and E 0 A/B are the energies of the fragments for their geometries in the complex and as free ligands, respectively. To obtain these energies, all of the boron nitride, Lewis basic (LB) and Lewis acidic (LA) molecules as well as their complexes were re-optimized at the BP86/TZ2P level of theory. When the optimized geometries for the M05-2X/cc-pVTZ and BP86/TZ2P methods were compared, no significant differences were observed, see discussion in (ESI †).
The interaction energy (DE int ) can be decomposed into three terms: (1) the Pauli exchange repulsion term (DE Pauli ), (2) the electrostatic interaction energy (DE elstat ) between charge densities of the fragments, and (3) the orbital interaction energy (DE orb ) which results from orbital mixing of the A and B fragments: The first term (DE Pauli ) is always positive while in most cases DE elstat and DE orb are negative. For more information regarding this method and its application in studying chemical bonds including donor-acceptor complexes the reader is referred to the literature. [44][45][46][47][48] The natural orbitals for chemical valence (NOCV) approach can be utilized to obtain both a qualitative and quantitative picture of the chemical bond (eqn (4)). 49 In this approach, the deformation density Dr(r) is decomposed into pairwise c k and c Àk complementary eigenfunctions (NOCVs) with eigenvalues of n k and n Àk that have the same magnitude but opposite sign: Positive and negative values describe, respectively, density accumulation and density depletion; the bond forms through flowing electron density from the negative part of the molecule (shown later in red color) to the positive part (shown in blue).
For quantitative results, one can represent the orbital interaction energy in terms of the NOCV eigenvectors: where F TS Àk,Àk and F TS k,k are diagonal transition state Kohn-Sham matrix elements over the corresponding NOCVs. Therefore, eqn (4) and (5) provide the qualitative and quantitative pictures of a chemical bond even for asymmetric complexes. For further details on this approach please see the original paper. 49 The nature of the bonding in the Lewis base (LB) substituted adducts was also assessed using both natural bonding orbital (NBO) 50 and atoms-in-molecules (AIM) 51 analyses. NBO population analyses were done at the M05-2X/cc-pVTZ level of theory by using the NBO suite available in Gaussian 09. 52 AIM analyses were carried out at the same level of theory using the AIMALL software package. 53 Nucleus independent chemical shift (NICS) 54 computations were also performed using the gauge-independent atomic orbital (GIAO) method at the center of and 1 Å above the ring at the M05-2X/cc-pVTZ level of theory. All the electronic structure calculations were performed using Gaussian 09 52 and ADF 2013 55 packages.
The isolated (BN) 2 and (BN) 3 species, as well as higher oligomers, have been the subjects of numerous computational investigations; 69-74 monomeric BN has also been studied extensively. [75][76][77] The isolated systems are not the focus of the present study, however, results for the isolated species are reported for the corresponding isomers considered in the complexes for completeness. The isolated (BN) n (n = 1-3) molecules are discussed in the ESI. † In each case, the carbon-based donors were bound to electron deficient boron sites, in line with prior adduct formation with amino-boranes (R 2 N-BH 2 ). [78][79][80][81] The NHC-bound adducts of the BN chains, ImMe 2 ÁBN and ImMe 2 ÁBNBN, each adopt linear C ImMe2 -(BN) n configurations; geometry optimizations initiated with non-linear configurations return to linearity. On the other hand, appreciably bent C-B-N and intrachain N-B-N angles are found within the related ImMe 2 CH 2 and Me 3 PCH 2 -capped boron nitride adducts. For example, the C-B-N angles of the ImMe 2 CH 2 substituted BN and BNBN adducts are 162.571 and 152.261, respectively, and the C-B-N bond angles are 156.501 and 156.321 for the corresponding Me 3 PCH 2 substituted analogues. In general, within the monoadducts, the B 2 N 2 and B 3 N 3 rings adopt planar geometries; the B 3 N 3 rings in ImMe 2 and ImMe 2 CH 2 are slightly puckered. The B-N bond lengths involving the donor-bound boron atoms in these B 2 N 2 and B 3 N 3 rings are each ca. 0.12 Å longer than the remaining B-N bonds involving donor-free, two coordinate boron centers. This bond lengthening implies an increase in B-N p-interactions and/or enhanced ionic contribution to the B-N s-bonds. Within the ImMe 2 monoadduct series, the formally dative C-B linkages range from 1.510 Å in the terminal adduct ImMe 2 ÁBNBN to elongated values of 1.560 and 1.612 Å in the heterocyclic B 2 N 2 and B 3 N 3 adducts. For comparison, the C-B bond length in the coordinatively saturated amino-borane adduct IPrÁBH 2 -NHDipp (IPr = [(HCNDipp) 2 C:]; Dipp = 2,6-i Pr 2 C 6 H 3 ) was determined to be 1.627(4) Å, 81 while in the diboryne adduct IPrÁBRBÁIPr this bond length is 1.491(4) Å (avg.). 7 In general the computed C-B bonds in the ImMe 2 adducts were shorter by ca. 0.02 to 0.05 Å compared to the corresponding ImMe 2 CH 2 and Me 3 PCH 2 complexes; of note, it has been found that N-heterocyclic carbenes are stronger s-donors than their N-heterocyclic olefin counterparts (such as IPrCH 2 ). 62 The coordination of the Me 3 PCH 2 units to boron leads to a large increase in the ylidic P-C bond length from 1.672 Å in the free ligand to bond length values as long as 1.829 Å in Me 3 PCH 2 ÁBNBN. This observation could be traced to a reduction of H 2 C -P-C(s*) hyperconjugative interactions 31,82 in Me 3 PCH 2 as the terminal CH 2 unit participates in coordination to boron. The same phenomenon can be observed in the case of the ImMe 2 CH 2 adducts: the terminal C-C bond length increases from 1.353 Å in the free ligand to 1.494 Å in the BNBN substituted adduct ImMe 2 CH 2 ÁBNBN. For the isolated ImMe 2 CH 2 and Me 3 PCH 2 ligands, the P-C and C-C bonds have Wiberg bond indices (WBIs) of 1.328 and 1.613, respectively, based on NBO analyses, see section 3.3. These are reduced to 0.906-1.046 and 1.026-1.284, respectively, upon binding of the (BN) x units reflecting the loss of double bond character, and, hence, the corresponding bond elongation.
The M05-2X/cc-pVTZ optimized geometries of the di-and tri-substituted adducts (LBÁ(BN) n , n = 2 and 3) are depicted in Fig. 3. In general, addition of a second equivalent of Lewis base to the B 2 N 2 and B 3 N 3 units leads to elongation of the average C-B bond length. The C-B bonds increase in length by ca. 0.06-0.09 Å for the B 2 N 2 rings, while a more modest increase of ca. 0.01 to 0.04 Å was noted upon binding two donors to a B 3 N 3 unit. Despite the planar nature of the B 2 N 2 rings, the intraring B-N distances within the bis-adducts (ImMe 2 ) 2 ÁB 2 N 2 , (ImMe 2 CH 2 ) 2 ÁB 2 N 2 ,  Each of the coordinative C-B distances are slightly longer in (ImMe 2 ) 3 ÁB 3 N 3 (1.645 to 1.655 Å) in relation to the values found in the bisadduct (ImMe 2 ) 2 ÁB 3 N 3 (1.622 Å). The ylide-bound tris adducts (Me 3 PCH 2 ) 3 ÁB 3 N 3 and (ImMe 2 CH 2 ) 3 ÁB 3 N 3 feature very long C-B bonds of 1.717-1.732 and 1.687-1.702 Å, respectively, suggesting that these species would have reduced stability.
Very recently, Tai and Nguyen have studied the stability of (ImMe 2 ÁB) n (n = 1-6) adducts using quantum mechanical computations with the B3LYP method. 88 They attributed the stability of these systems to the degree of p conjugation and aromatic character within the core B n (n = 3-6) rings. In order to probe the aromaticity in the (BN) x rings, NICS analyses of the free (singlet) B 2 N 2 and B 3 N 3 molecules as well as their adducts were performed using the GIAO method at the M05-2X/cc-pVTZ level of theory. The NICS results were compared to the corresponding values determined at the same level of theory for well known aromatic benzene and anti-aromatic cyclobutadiene molecules (Table S1, ESI †) to examine changes in aromaticity upon binding of Lewis bases. NICS data are sensitive to the position at which they are evaluated and to interference from other parts of the molecule, especially for non-planar compounds. 23 The changes in aromaticity/anti-aromaticity are discussed in terms of NICS (1.00) zz values, see Table S1, ESI † for complete NICS data.

Energies of the Lewis base (LB) bound LBÁ(BN) n (n = 1-3) adducts
The total stabilization energies and Gibbs free energies of the (BN) n (n = 1-3) molecules upon complexation with the three Lewis bases were computed using the M05-2X/cc-pVTZ level of theory and the results are summarized in Table 1. The sequential stabilization energies, DE seq. , (DE + ZPE) seq. , and DG seq: , which take into account the impact of adding one additional Lewis base to the existing (LB) x ÁB 2 N 2 and (LB) x ÁB 3 N 3 (x = 0-2) complexes were also evaluated. Notably, in two separate articles, Jones, Frenking and co-workers have studied the ImMe 2 -and phosphine-bound Group 13 element complexes along with their possible applications for hydrogen storage. 89,90 More specifically, they found that the Gibbs free energies of À29.8 and À45.8 kcal mol À1 for the Me 3 P and ImMe 2 bound BH 3 adducts, respectively, at the RI-BP86/def2-TZVPP level of theory; which is very close to the À46.9 kcal mol À1 computed for the latter complex, ImMe 2 ÁBH 3 , at the M06-2X/cc-pVDZ level of theory. 91 In another recent study, Sarmah et al. examined complexes of normal and abnormal N-heterocyclic carbenes with Group 13 element based Lewis acids (EX 3 ; E = B, Al, Ga; X = H, F, Cl, OH, NH 2 , CH 3 , CF 3 ) and performed corresponding NBO and AIM analyses of the adducts. 92 They computed a complexation energy of À49.2 kcal mol À1 at the B3LYP/6-31 + G* level of theory for the ImMe 2 ÁBH 3 adduct which is close to the values found previously by Frenking, Jones and co-workers 89,90 as well as Brown and coworkers. 91 The complexation (stabilization) energy associated with the formation of our mono-substituted (BN) n (n = 1-3) adducts was computed to be greater than À100 kcal mol À1 for all species except the B 3 N 3 adducts, where zero-point corrected energies (DE + ZPE) are in the range of À57.4 to À69.7 kcal mol À1 . The ZPE correction to the electronic energies changes the value of DE by B4-10 kcal mol À1 . The Gibbs free energy differences are also lower than the ZPE corrected values by B10-40 kcal mol À1 . For the sake of brevity and consistency, the Gibbs free energy differences will be discussed throughout the text. We will comment on the nature of the formed  (Fig. S3, ESI †). For B 3 N 3 , the ImMe 2 and ImMe 2 CH 2 bound adducts exhibit a modest decrease in the HOMO-LUMO gap upon binding the first ligand (for Me 3 PCH 2 there is a small increase of E0.3 eV) and then for all ligands, there is a larger (E1 eV) decrease upon binding the second and third ligands. The free energies associated with the sequential addition of Lewis base equivalents to molecular B 2 N 2 and B 3 N 3 molecules DG seq: follow the general trend that it becomes increasingly less favorable to bind multiple donors to these rings (Fig. 4).
This effect can be explained by a decrease in Lewis acidity of the (BN) n rings as electron density is being donated from the carbonbased ligands; this phenomenon can be easily observed from the gradual destabilization of the LUMO energy levels of the B 2 N 2 and B 3 N 3 rings after addition of the Lewis bases (Fig. S3, ESI †). Overall, the binding of subsequent equivalents of Lewis base to the BN rings is exergonic, however, a slightly disfavoured binding event was computed for the formation of the tris adduct (ImMe 2 CH 2 ) 3 Á B 3 N 3 (+3.4 kcal mol À1 ), placing this species on the cusp of stability.

Bonding properties through NBO and AIM analyses
NBO and AIM computations were performed on all (BN) n species including their free and as well as their ligand bound forms at the M05-2X/cc-pVTZ level of theory (see Table 2; for the NBO and AIM analyses of the di-and tri-substituted compounds see Tables S2-S9 and Fig. S2, ESI, † respectively). The computed NBO atomic charges of the boron atoms show a significant decrease (0.5 to 0.6 e À ) upon attachment of the Lewis bases. However, the change in charge of the bonding carbon atom upon complexation is much more modest ca. 0.1 to 0.2 (Table 2 and Table S2, ESI †). The charge transfer to the boron center is highest for the ImMe 2 and lowest for the Me 3 PCH 2 substituted BN and BNBN adducts. For both B 2 N 2 Table 1 Computed total a and sequential b stabilization energies (in kcal mol À1 ), with ZPE (DE + ZPE) and without ZPE (DE), and free energies (DG1) at the M05-2X/cc-pVTZ level of theory    Table 1 for the values. and B 3 N 3 adducts, the highest charge transfer to the boron atom belongs to the ImMe 2 and Me 3 PCH 2 ligands, respectively, but the lowest to the ImMe 2 CH 2 ligand (Table 2). Interestingly, the NBO analysis does not show a significant charge difference for the nitrogen atom attached to the boron center in the LBÁBN adducts compared to the isolated species (Tables S2 and S3  Analysis of the energy density (H(r)) at the C-B and B-N bond critical points shows that all of these bonds are predominantly covalent in character (i.e., negative values for H (C-B) and H (B-N) ). This data agrees well with the EDA-NOCV results which will be discussed later and points to the existence of covalent bonding between the carbon donors and boron acceptors, which is accompanied by p-backbonding in these systems as previously noted in LBÁBX 3 (X = H, F, Cl) adducts. 93,94 The computed value of the electron density (r) for the C-B bonds also shows that its strength decreases in the order of ImMe 2 4 Me 3 PCH 2 4 ImMe 2 CH 2 in the case of the BN, BNBN, and the B 2 N 2 adducts. For the mono-substituted B 3 N 3 adducts, the trend in r is ImMe 2 CH 2 4 ImMe 2 E Me 3 PCH 2 (Table 2) although the differences in r are very small (o0.003 e À ). The r values for the B-N bonds in each of the adducts increase from 0.185 e À to 0.300 e À on going from the B 3 N 3 adducts to the BN Table 2 Selected NBO atomic charges of the carbene carbon and boron atoms (q C and q B ) along with the total charge of the acceptor molecules (q LA ), Wiberg bond indices (WBI) of the C-B and B-N bonds, and the electron density (r) and energy density at the bond critical points (H (C-B) and H (B-N) ) for all the mono-substituted species at the M05-2X/cc-pVTZ level of theory. B-N values refer to bonds adjacent to the carbene carbon atom. Values in parentheses correspond to two different B-N bonds connected to the carbene carbon atom  adducts, in line with the corresponding increase in WBI values for these species. From the optimized geometries, we found that the C-B bond length increases upon substituting more Lewis bases. AIM data are in agreement with the geometries as, for example, the r value for this bond decreases from 0.154 e À in the ImMe 2 ÁB 3 N 3 complex to 0.136-0.139 e À in (ImMe 2 ) 3 ÁB 3 N 3 while the C-B bond length increases from 1.612 Å to B1.650 Å (Fig. S2, ESI, † and Fig. 2 and 3). This trend mirrors the variation in stabilization energies, and indicate that the interaction between the Lewis base and the boron atoms becomes weaker in the presence of added equivalents of donor. The r values of the C-B bonds for (ImMe 2 CH 2 ) n ÁB 3 N 3 and (Me 3 PCH 2 ) n ÁB 3 N 3 also decrease by going from mono-to tri-substituted adducts: from 0.157 e À to 0.120 e À and from 0.154 e À to 0.127 e À , respectively (Fig. S2, ESI †); a trend reflected in the corresponding C-B bond length.

Energy decomposition analysis (EDA-NOCV)
To understand the nature of the bonding between different Lewis bases and the cyclic and acyclic boron nitride oligomers (LBÁ(BN) n , n = 1-3), EDA-NOCV computations were performed using the GGA BP86 functional and the TZ2P basis set (Table 3). For brevity, we only focus on the most stabilized and least stabilized boron nitride species, i.e., LBÁBN and LBÁB 3 N 3 , respectively. The order of bond dissociation energies (D e ) for the different Lewis bases follows the series ImMe 2 4 Me 3 PCH 2 4 ImMe 2 CH 2 . More specifically, the C-B bonds in the ImMe 2 substituted adducts are 4.3-21.7 kcal mol À1 stronger than their Me 3 PCH 2 and ImMe 2 CH 2 analogues. For a given boron nitride adduct, there is a clear correlation between C-B bond length on one hand and bond dissociation energy and Pauli repulsion values on the other hand ( Table 3). The percentage contribution of the electrostatic attraction (DE elstat ) and orbital interaction (DE orb ) terms to the total attractive energies are also provided in Table 3. Overall, the orbital interaction makes a significant contribution to the total attractive energy (more than 50%) in all complexes except ImMe 2 ÁB 3 N 3 where it is 49.1%. This high contribution indicates that C-B bonds retain substantial covalent character which is in agreement with our NBO/AIM results discussed above. The percentage contributions of the s and p orbitals to the total orbital interaction are shown in Table 3 while the relevant deformation densities (Dr) are depicted in Fig. 5. Notably, the ImMe 2 CH 2 ÁB 3 N 3 adduct shows the lowest p-contribution to the C-B orbital interaction (3.2%) amongst the compounds investigated, while in contrast, the ImMe 2 ÁBN and ImMe 2 CH 2 ÁBN adducts show the highest degree of p-character with 22.6% and 19.2% contributions, respectively. Thus from both Table 3 and Fig. 5 it is evident that p-backbonding between the boron nitride oligomers and the carbon-based ligands can be quite significant in some cases. The preparation energy (DE prep ), the difference between the fragment energies in their complexed and free geometries, is the lowest for the ImMe 2 ÁBN while it is the highest for the ImMe 2 CH 2 ÁB 3 N 3 adduct (Table 3).
Our ÀD e values for the carbene-boron bonds are significantly more negative than the reported ÀD e values for the H 3 BÁNH 3 (À31.9 kcal mol À1 ) and H 3 BÁNMe 3 (À36.2 kcal mol À1 ) bonds computed at the BP86/TZ2P level of theory. [93][94][95] Tonner and Frenking have shown that replacing ammonia with the ImMe 2 ligand to form the ImMe 2 ÁBH 3 adduct changes the ÀD e to À57.9 kcal mol À1 computed at the same level. 96 Also, the amount  of p-backbonding in H 3 BÁNH 3 , Me 3 NÁBH 3 , and ImMe 2 ÁBH 3 are 10.1%, 13.0%, and 9.4%, respectively. The values are comparable to each other for all these three systems and are close to the corresponding value for the ImMe 2 ÁB 3 N 3 complex (Table 3).

Stabilization through donor-acceptor interactions
The HOMOs of both the ImMe 2 ÁBN and ImMe 2 ÁBNBN adducts have p character localized on the (terminal) BN unit as well as on the ImMe 2 ring (Fig. 6). On the other hand, the HOMOÀ4 of both complexes shows a directional lone pair on the terminal nitrogen atom (with some mixing with a B-N s bond) ready to be captured by a Lewis acid (LA). Herein we consider the previously employed donor-acceptor approach for stabilizing highly reactive heavier Group 14 element dihydrides, 14 by using BH 3 and W(CO) 5 as Lewis acids (LA), and ImMe 2 as a Lewis base. The M05-2X optimized Lewis acid/base bound (BN) n complexes as well as their complexation Gibbs free energies are shown in Fig. 7 (for a comparison between their electronic energies and Gibbs free energies see Table S12, ESI †). The C-B bond lengths in the Lewis acid bound adducts ImMe 2 ÁBNÁLA and ImMe 2 ÁBNBNÁLA (LA = BH 3 and W(CO) 5 95 Overall, W(CO) 5 appears to be a stronger Lewis acid compared to BH 3 as the DG1 values for the former adduct series are more favorable (negative) by 9.3-15.5 kcal mol À1 (Fig. 7); a similar conclusion regarding the relative Lewis acidity of W(CO) 5 versus BH 3 has been made previously. 46 These results support our experimental results within the IPrÁGeH 2 ÁLA complexes (LA = BH 3 and W(CO) 5 ) where the W(CO) 5 adduct is more stable. 25 The impact of complexing ImMe 2 and BH 3 molecules concurrently to the B 2 N 2 and B 3 N 3 units was studied. More specifically, the Gibbs free energies for the addition of the ImMe 2 ligand to the ImMe 2 ÁB 2 N 2 Á(BH 3 ) 2 and (ImMe 2 ) 2 ÁB 3 N 3 Á(BH 3 ) 3 adducts to form the fully saturated (ImMe 2 ) 2 ÁB 2 N 2 Á(BH 3 ) 2 and (ImMe 2 ) 3 ÁB 3 N 3 Á(BH 3 ) 3 complexes were found to be À74.2 and À60.9 kcal mol À1 , respectively (Table S10, ESI †).   Table 4 Computed EDA-NOCV components (in kcal mol À1 ) for the C-B and N-W bonds of the ImMe 2 ÁBNÁW(CO) 5 and ImMe 2 ÁB 3 N 3 ÁW(CO) 5 adducts at the BP86/TZ2P level of theory. The analogous values for the C-B bonds without Lewis acid are also provided in parenthesis. See Fig. 8 for the corresponding fragments

EDA-NOCV for BN and B 3 N 3 LB/LA substituted adducts
To further study the impact of adding a Lewis acid on stabilizing BN and B 3 N 3 molecules, C-B and N-W bonds in the ImMe 2 ÁBNÁ W(CO) 5 and ImMe 2 ÁB 3 N 3 ÁW(CO) 5 adducts were examined using the EDA-NOCV approach (Fig. 8 and Table 4); their corresponding deformation densities are presented in Fig. 9.
Comparing the interaction energies in the BN and the B 3 N 3 adducts reveals that the C-B bond becomes 36.5 kcal mol À1 stronger upon W(CO) 5 Lewis acid attachment in the former adduct, but surprisingly it becomes 1.8 kcal mol À1 weaker in the latter (Fig. 7). More specifically, addition of tungsten pentacarbonyl as a Lewis acid significantly decreases the Pauli repulsion portion of the C-B bond; from 211.6 kcal mol À1 in ImMe 2 ÁBN to 151.1 kcal mol À1 in ImMe 2 ÁBNÁW(CO) 5 but increases it from 203.9 kcal mol À1 in ImMe 2 ÁB 3 N 3 to 220.7 kcal mol À1 in ImMe 2 Á B 3 N 3 ÁW(CO) 5 (Fig. 7). Lewis acid attachment also decreases the contribution of electrostatic and orbital interactions by 13.9 and 9.9 kcal mol À1 for ImMe 2 ÁBN adduct but it increases them to 6.6 and 8.4 kcal mol À1 for the ImMe 2 ÁB 3 N 3 adduct. An inspection of the s and p orbital interaction components for the C-B bonds in the BN adduct proves that the decrease in DE orb upon bonding to the Lewis acid comes mainly from the decrease of p-backbonding rather than s-donation. Moreover, comparing the percent contribution of the DE orb component to the total interaction energy confirms the ionic nature of the N-W bonds (35.6% and 43.2% for the BN and B 3 N 3 adducts, respectively). It is also worthwhile mentioning that no stationary point was found for the BNÁW(CO) 5 or B 3 N 3 ÁW(CO) 5 adducts which points towards the instability of the N-W bond in these species in the absence of the Lewis base.
Given that the free energies of complexation associated with coordinating ImMe 2 ÁBN and ImMe 2 ÁBNBN units by BH 3 and W(CO) 5 are quite favorable, Lewis acid coordination can provide even more stability for these highly elusive boron nitride species, 83,97,98 and research towards preparing these compounds in the laboratory is ongoing.

Conclusions
A variety of acyclic and cyclic (BN) n (n = 1-3) adducts with different Lewis bases including an N-heterocyclic carbene, an N-heterocyclic olefin and a Wittig donor were examined using M05-2X/cc-pVTZ computations. Considering the Gibbs free energies, values greater than À50 kcal mol À1 were found for the complexation energies. From the NBO, AIM and EDA-NOCV approaches, the existence of a polar covalent bond between carbene and boron atom was confirmed in each adduct studied. On the other hand, computed NPA charges illustrated rather significant amounts of charge transfer from the carbene center towards the boron atom upon C-B bond formation. A donor-acceptor strategy, in analogy with our synthesis of heavier group 14 element dihydride adducts, 14 show that LBÁ (BN) n W(CO) 5 (n = 1-3) complexes could be experimentally achievable. Finally, both the C-B donor and N-W acceptor bonds were decomposed into their s and p bonding components in the ImMe 2 substituted BN and B 3 N 3 adducts with and without W(CO) 5 as a Lewis acid. Analysis of the EDA-NOCV results in these adducts showed that the carbene-boron bonds are stronger in the presence of W(CO) 5 as a Lewis acid mainly because of a dramatic decrease in Pauli repulsion rather than an increase in the electrostatic/orbital attraction.