Side-On Bonded Beryllium Dinitrogen Complexes

Experimental Studies

The beryllium dinitrogen complexes were prepared by the reactions of pulsed laser evaporated beryllium atoms and dinitrogen in solid neon at 4 K. The product species were detected using infrared absorption spectroscopy.³¹ The experiments were performed using relatively low laser energy to avoid the formation of multinuclear species. The previously reported dinuclear species are barely observed.¹¹ Figure 2 shows the spectra in the N–N stretching frequency region from the experiment using a 0.5 % N₂/Ne sample (on the basis of volume). The spectra in the Be–N stretching region are shown in Figure S1 (see the Supporting Information). Several new product absorptions are observed, and can be classified into four groups based on their annealing and photochemical behaviors (labeled as A–D in Figure 2). Only one band is observed for species A, which is observed on sample deposition and is destroyed upon irradiation with 617 nm light. The species B involves three absorptions with comparable intensities (Table 1), which appear on sample deposition, remain unchanged upon irradiation with 617 nm light. The group C absorptions appear on sample deposition and are completely destroyed under irradiation with 617 nm light, during which the group D absorptions markedly increase. All these absorptions remain almost unchanged or slightly decrease upon sample annealing when the matrix is annealed first and then irradiated. All of them remain unchanged under irradiation from the source of the IR spectrometer, but are completely destroyed under yellow (580–595 nm), blue (435–480 nm), and UV (λ>250 nm) light. Experiments with isotopically substituted N₂ samples allow the unambiguous identification of these absorptions through isotopic shifts and splittings (see Figures S2–S5). An experiment using pure dinitrogen as a matrix was also performed (see Figure S6). Only the absorptions of C and D are observed in solid nitrogen, suggesting that both species are saturate-coordinated complexes. The species C is converted into D under irradiation with 617 nm light as observed in solid neon.

The species A, with absorption at 1820.4 cm⁻¹ in Ne, can be identified as the Be(NN)₂ complex with two end-on bound N₂ ligands on the basis of spectra in the experiments with 0.25 % N₂ + 0.25 % ¹⁵N₂ and 0.25 % N₂ + 0.5 % ¹⁴N¹⁵N + 0.25 % ¹⁵N₂ mixed samples (see Figure S2). The band position is only 3.0 cm⁻¹ red-shifted from the argon matrix value.¹¹ The species B is assigned to the NNBe(η²-N₂) isomer involving one end-on and one side-on bonded N₂ ligands. The 1948.9 cm⁻¹ band is the N–N stretching mode of the end-on bonded N₂ ligand, while the 1624.1 cm⁻¹ band is the N–N stretching mode of the side-on bound ligand with two equivalent N atoms. The 1030.2 cm⁻¹ band originates from the Be–N stretching vibration. The group C absorptions are assigned to different vibrational modes of the (NN)₂Be(η²-N₂) complex (Table 1). The 2173.5 and 1985.8 cm⁻¹ bands are symmetric and antisymmetric, respectively, N–N stretching modes of the two equivalent end-on bound N₂ ligands. The 1694.9 cm⁻¹ band is the N–N stretching vibration of the side-on bonded N₂ ligand. The 819.0 cm⁻¹ band is attributed to the Be-N₂ stretching mode, while the 622.8 cm⁻¹ band is due to the antisymmetric NN-Be-NN stretching mode. These modes are observed at 2183.6, 2007.1, 1683.0, 820.5, and 622.3 cm⁻¹ in solid nitrogen. The species D is assigned to the Be(NN)₃ complex. Only one band at 1890.3 cm⁻¹ is observed in the N–N stretching frequency region in Ne, and it is due to the doubly degenerate N–N stretching mode. The isotopic splitting patterns in the experiments with 0.25 % N₂ + 0.25 % ¹⁵N₂ and 0.25 % N₂ + 0.5 % ¹⁴N¹⁵N + 0.25 % ¹⁵N₂ samples (see Figure S2) confirm that three equivalent N₂ ligands are involved in this mode. The 836.5 and 825.0 cm⁻¹ bands are attributed to the B–N stretching mode in two trapping sites. These two modes are observed at 1890.0 and 843.6/817.5 cm⁻¹ in solid nitrogen.

Theoretical Studies

We calculated the structures and properties of isomeric forms of Be(NN)_n, where n=2 or 3, using ab initio methods at the CCSD(T)-Full/cc-pVTZ level and using density-functional theory (DFT) at the M06-2X-D3/cc-pVTZ level (see Figure S7 for DFT results). Details of the methods are given in the Supporting Information. Figure 3 shows the optimized geometries and the calculated bond lengths and angles of the equilibrium structures in the electronic singlet and triplet states. The calculations suggest that the most stable form of Be(NN)₂ is the NNBe(η²-N₂) isomer 1 with C_2v symmetry in the singlet (¹A₁) electronic state. The double end-on isomer 2 has a triplet (³B₁) electronic state and a bent C_2v geometry with a bending angle of 108.8°. The structure 2 is only 1.6 kcal mol⁻¹ higher in energy than 1. The energy difference is slightly larger (2.1 kcal mol⁻¹) when a larger basis set at the CCSD(T)-Full/aug-cc-pVQZ level is employed. Energetically, the next low-lying isomer, 3, in the triplet (³A′′) electronic state with C_s symmetry is 7.9 kcal mol⁻¹ above 1 (Figure 3). The linear Be(NN)₂ species 4 in the electronic singlet (¹Σ_g) state is 9.7 kcal mol⁻¹ higher lying than 1. Two energetically close isomers, 5 and 6, in the electronic singlet state are predicted as the most stable forms of Be(NN)₃. The (NN)₂Be(η²-N₂) isomer 5 with C_2v symmetry is only 1.7 kcal mol⁻¹ (0.9 kcal mol⁻¹ at CCSD(T)-Full/aug-cc-pVQZ) lower in energy than the D_3h symmetric structure 6 of Be(NN)₃. The triplet isomers (NN)₂Be(η²-N₂) 7 and Be(NN)₃ 8 are 24.4 and 25.1 kcal mol⁻¹, respectively, higher in energy than 5 at the CCSD(T)-Full/cc-pVTZ//CCSD/cc-pVTZ level.

The calculations at the CCSD(T)-Full/aug-cc-pVQZ level thus predict that the cyclic species with side-on bonded η²-N₂ ligands, 1 and 5, are the energetically lowest lying isomers of Be(NN)₂ and Be(NN)₃, respectively, with the end-on bonded forms 2 and 6 being slightly higher in energy. We assigned the spectroscopically identified species A—D to the four energetically lowest lying isomers as 1(B), 2(A), 5(C), and 6(D). Table 1 shows the calculated vibrational frequencies of 1, 2, 5, and 6 in the experimentally recorded range. The full set of calculated frequencies is given in Tables S2 and S3. The calculated harmonic frequencies are scaled with the factor 0.9848, which is obtained from the ratio of experimental stretching frequency of 2330 cm⁻¹ for N₂³² and the calculated value of 2366 cm⁻¹. The agreement between the calculated harmonic frequencies and the anharmonic experimental values is quite good. This agreement is particularly good for the N–N stretching mode of the side-on bonded N₂ ligands in 1(B) and 5(C), where the theoretical and the observed frequencies nicely match. Further support for the assignment of the vibrational spectra of A–D to the four energetically lowest lying isomers 1, 2, 5, and 6 comes from the ¹⁴N/¹⁵N isotope shifts Δ, which span a range between −3 and −75 cm⁻¹. The nearly perfect agreement between the calculated and experimental isotope shifts leaves no doubt that the assignments 1(B), 2(A), 5(C), and 6(D) are correct.

We analyzed the nature of the beryllium–dinitrogen interactions with charge- and energy-partitioning methods. Figure 3 shows also the atomic partial charges in the calculated species. As expected, the beryllium atom carries a large positive charge while the dinitrogen ligands are negatively charged. The positive charge at Be in the side-on species is always somewhat larger than in the other isomers. The question arises if the species with a side-on bonded η²-N₂ ligand are better described in terms of donor–acceptor interactions following the DCD model,¹ or as metalladiazirines, which are cyclic compounds with genuine Be–N electron sharing bonds. Both models are schematically shown in Figure 1. The dichotomy of the two bonding models is well known in transition-metal chemistry, where, for example, π complexes of alkenes and alkynes are distinguished from metallacyclopropanes and metallacyclopropenes.³³ Diazirines (R₂CN₂) are experimentally studied compounds and the structures of the parent systems with R=H, F, and CH₃, are available from the gas phase measurements.³⁴ The question as to whether 1 and 5 should be considered metalladiazirines or π-bonded η²-N₂ complexes can be addressed with energy decomposition analysis (EDA) in combination with natural orbital for chemical valence (NOCV) theory using N₂ and Be(NN)_n (n=1,2) in the electronic triplet and singlet states as interacting species. A particular strength of the EDA-NOCV method lies in its ability to determine the most suitable fragments for the formation of a chemical bond, which is given by the smallest change in the associated orbital interaction, ΔE_orb. This ability has been demonstrated for a variety of chemical bonds.³⁵

Table 2 shows the numerical results of the EDA-NOCV results of 1 and 5. The calculations for both molecules give much smaller ΔE_orb values when singlet fragments are employed instead of triplet fragments. These values mean that the fragments in the electronic singlet states undergo much less change in the electronic structure and thus, are better prepared for bond formation than the triplet fragments. The EDA-NOCV results suggest that both 1 and 5 should be classified as π-bonded η²-N₂ complexes rather than metalladiazirines. Figure 4 shows the deformation densities, Δρ_(1)-(2), of 1 and 5 that are associated with ΔE_orb(1) and ΔE_orb(2), and the interacting donor and acceptor fragment orbitals. It becomes obvious that the strongest interaction, ΔE_orb(1), comes from (NN)_nBe→η²-N₂ π back-donation while the much weaker second strongest orbital term, ΔE_orb(2), is due to (NN)_nBe←η²-N₂ σ donation. The dominant orbital interactions in 1 and 5 are archetypical examples of HOMO/LUMO donation and back-donation following the frontier orbital theory of Fukui,³⁶ where the vacant in-plane π_∥* orbital of N₂ serves as an acceptor MO in the stronger orbital interaction, ΔE_orb(1), and the occupied in-plane π_∥ orbital of N₂ is the donor part in the weaker orbital interaction ΔE_orb(2).

The results of the EDA-NOCV calculations of 1 and 5 are nicely complemented by the QTAIM analysis of the electronic structures. Figure 5 shows the Laplacian distribution of the two complexes in the plane of the cyclic moiety. There is an area of local charge concentration (∇²ρ(r_c)<0; red dashed lines) at the beryllium atoms pointing in the direction toward the nitrogen atoms of the η²-N₂ ligands. This unusual scenario supports the classification of 1 and 5 as π-bonded η²-N₂ complexes where the dominant orbital contribution is due to (NN)_nBe→η²-N₂ π back-donation.

We also analyzed the side-on and end-on bonded dinitrogen complexes with the EDA-NOCV method to elucidate the peculiar stability of the former bonding mode. The calculations were restricted to 5 and 6 because they are both in the electronic singlet state. We choose the neutral fragments of Be in the singlet state with the electronic reference configuration (2s⁰2p²), and the three dinitrogen ligands in the singlet state as interacting moieties, which refer to the symmetry-allowed dissociation products. The alignment of the occupied 2p AO of beryllium was chosen following the occupied MOs of 5 and 6. The numerical results are shown in Table 3. The intrinsic interaction energy between the beryllium atom and the dinitrogen ligands (ΔE_int) in the side-on bonded (NN)₂Be(η²-N₂) complex 5 is larger (−211.8 kcal mol⁻¹) than in the end-on bonded isomer 6 (−199.8 kcal mol⁻¹). The inspection of the energy terms indicates that this difference comes mainly from the attractive contributions of the Coulomb term ΔE_elstat and particularly from the covalent (orbital) interactions (ΔE_orb). The breakdown of the latter term into pairwise orbital interactions reveals that the dominant orbital stabilization, ΔE_orb(1), is due to the back-donation of the 2p electron pair of beryllium into the π* MO of the N₂ ligands. The ΔE_orb(1) term in 5 is much larger (−198.4 kcal mol⁻¹) than in the end-on bonded isomer 6 (−139.1 kcal mol⁻¹). The associated deformation densities Δρ₍₁₎ shown in Figure 6 reveal that the π back-donation Be(2s⁰2p²)→η²-N₂ into the in-plane π_∥* orbital of the side-on bonded ligand is much larger than the back-donation into the end-on bonded N₂ ligands. This difference comes from the larger overlap of the in-plane π_∥* orbital of the side-on bonded N₂ with the 2p AO of Be. The result has bearings for future studies of dinitrogen complexes. Complexes with side-on bonded N₂ ligands may be favored over end-on bonded isomers when the π back-donation from the metal to the ligands is particularly strong. Isomers of Be(NN)_n with more than one side-on bonded (η²-N₂) ligands are not minima on the potential energy surface because there is only one electron pair of the metal available for π back-donation.

The EDA-NOCV results in Table 3 suggest that the beryllium-dinitrogen bonds in 5 and 6 have a stronger covalent than electrostatic character. The orbital term ΔE_orb accounts for almost 80 % of the total attraction between the neutral units, but this includes the polarization within the fragments during bond formation. The dominance of covalent bonding remains when the final bonding situation is analyzed. Tables S4 and S5 show the EDA-NOCV results for 5 and 6 using neutral and charged fragments as interacting moieties. The smallest ΔE_orb values are found when the singly charged species Be⁺ and (N₂)₃⁻ are used for the calculations, which is a measure for the best description of the bonds finally formed.³⁵ The covalent (orbital) part of the attractive interactions still constitutes greater than 50 % of the total attraction.

The large ΔE_int values in Table 3 of 5 and 6 come from the interactions of the beryllium atom in the excited electron configuration (2s⁰2p²) with the ligands. We calculated the thermodynamic stabilities of the observed species 1, 2, 5, and 6 for loss of the N₂ ligands. The results are shown in Table 4. The most stable three-coordinated complex 5 is thermodynamically stable, even at room temperature, for loss of one N₂ yielding 1 by ΔG²⁹⁸=9.0 kcal mol⁻¹. The dissociation of all three N₂ ligands from 5 and 6, yielding a Be atom in the electronic ground-state configuration is barely endergonic at 4 K by 4.4 kcal mol⁻¹ and 2.5 kcal mol⁻¹, respectively, but the reactions are exergonic at room temperature. The two-coordinated complexes 1 and 2 even have negative bond dissociation energies and are thermodynamically unstable toward loss of the N₂ ligands. The calculations suggest that 1 and 2 are only kinetically stable, consistent with the experimental observation that 1 and 2 are only formed on sample deposition during which some laser-evaporated excited atoms are involved.

The preference of formation of side-on bonded dinitrogen complexes for the main-group metal beryllium is quite unusual, as the end-on coordination is the energetically preferred binding mode. All the experimentally known main-group element complexes are end-on bonded except the LiN₂ complex, which was suggested to have a side-on bonded structure as the bonding between Li and N₂ is almost purely ionic.²⁰ The end-on mode is also energetically favored over the side-on mode for mononuclear transition-metal complexes, and the side-on isomers could only be generated photochemically.³⁷