Beryllium Dimer Reactions with Acetonitrile: Formation of Strong Be−Be Bonds

Laser ablated Be atoms have been reacted with acetonitrile molecules in 4 K solid neon matrix. The diberyllium products BeBeNCCH3 and CNBeBeCH3 have been identified by D and 13C isotopic substitutions and quantum chemical calculations. The stabilization of the diberyllium species is rationalized from the formation of the real Be−Be single bonds with bond distances as 2.077 and 2.058 Å and binding energies as −27.1 and −77.2 kcal/mol calculated at CCSD (T)/aug-cc-pVTZ level of theory for BeBeNCCH3 and CNBeBeCH3, respectively. EDA-NOCV analysis described the interaction between Be2 and NC···CH3 fragments as Lewis “acid−base” interactions. In the complexes, the Be2 moiety carries positive charges which transfer from antibonding orbital of Be2 to the bonding fragments significantly strengthen the Be−Be bonds that are corroborated by AIM, LOL and NBO analyses. In addition, mono beryllium products BeNCCH3, CNBeCH3, HBeCH2CN and HBeNCCH2 have also been observed in our experiments.


Introduction
The chemistry of beryllium is predicted to be the richest among the alkaline earth metals due to its small size and the highest electronegativity and ionization energy among s-block elements [1,2], which is, however, largely unexplored due to the high toxicity of the compounds containing this element [3,4].Over the past few decades, the very weak beryllium-beryllium interaction has been the most studied for s-block metal-metal interactions [5][6][7].Isolated beryllium dimer was characterized as a typical weakly bound molecule with a bonding interaction of 11.2 kJ mol −1 (calc.)and a large bond distance of 2.45 Å as a result of the both doubly occupied bonding 2σ g + orbital and antibonding 2σ u + orbital [8][9][10].
Up to now, diberyllium complexes have aroused a great deal of enthusiasm among researchers, and many theoretical strategies have been proposed to enhance the strength of Be−Be bond [5,[11][12][13][14][15]. Removing/adding an electron from/to this dimer by interaction with some other molecules is a general formula to stabilize the system.The complexation of Be 2 with electron-withdrawing ligands such as F [16] or CN [17], or electron-deficient conjugated fragments such as cyclopentdienyl [18,19], pentadienyl [20] and phospholyl [21] is able to obtain a classical Be−Be σ single bond by pulling one or both electrons from antibonding orbital of Be 2 to ligands.Despite the intrinsic electron-deficient nature of beryllium, reports indicate that the Be 2 moiety in these molecules is essentially a dication Be 2 2+ , [17] which exhibits the formation of a strong bond in the presence of a counterion.Strong Be-Be bonds are also formed via electron transferring from Be atoms to C n H n (n = 3, 5, 7), π-radicals [22] and SO ligands.[23] Furthermore, a neutral odd-electron Be−Be bond is firstly identified in the tri-AMD-ligands-chelated D 3h -Be 2 (AMD) 3 complex by one AMD ligand attracting one electron from Be antibonding σ* orbital [24].A strong 2-center-1-electron Be−Be bond is also formed by attaching one electron to 1,2-diBeX-benzene (X = H, F, Cl, CN) derivatives [25].Be-Be double-π bonds are first achieved in the predicted octahedral cluster of Be 2 (µ 2 -X) 4 (X = Li, Cu, BeF) by a novel concerted electron-donation from four s 1 -type electron-donating ligands [15].The Be-Be triple bonds are formed in theoretically predicted Li 6 Be 2 [26] species, which are stabilized by six s 1 -type donor ligands and in Be 2 X 4 Y 2 (X = Li, Na; Y = Na, K) [27] clusters where six alkali metals are electrondonating ligands.Another way to form a Be−Be covalent bond is by adding radical ligands to an excited Be 2 moiety.The neutral Be 2 moiety in an excited state adding ligands such as (HCNMe) 2 B [28] and N-heterocyclic carbenes (NHCs) [29] can form a single or double bond, respectively.
Acetonitrile is known as an effective electron donor based on the previous research of reactions with metal atoms [30][31][32][33][34][35][36][37], and it could be a good candidate for stabilizing the Be 2 dimer.In this paper, we investigated the reactions of beryllium atoms with acetonitrile by means of matrix-isolation infrared spectroscopy and theoretical calculations, in order to further supplement the reactions of alkali metal with acetonitrile, and search for stable diberyllium complexes that might be formed.Six different products were spectroscopically identified in solid neon including two complexes possessing Be−Be single bonds, and three related reaction paths were presented.

Results and Discussion
The infrared spectra for acetonitrile (0.5% in solid neon) on pre-deposition and the reaction products on co-deposition, annealing and stepwise photolysis in the selected regions are shown in Figure 1.The isotopic substitution experiments with CD 3 CN and 13 CH 3 13 CN samples were performed and the infrared spectra are given in Figure 2. The absorptions of acetonitrile are extremely strong, so the changes of acetonitrile absorptions during the reaction are negligible compared with the products' absorptions.In addition to the absorptions assigned to the precursor and common species that were also observed in other experiments with CH 3 CN as reagent, several new product absorptions appeared, which can be classified into six groups based on their intensity changes.Table 1 shows the observed and computed vibrational frequencies of the products along with the assignment of the modes.The full sets of B3LYP calculated harmonic and anharmonic frequencies are all collected in Tables S1−S6.The laser intensity is relatively high in our experiments that are able to directly produce beryllium dimer.The infrared intensities of diberyllium products are much weaker with low laser power, while the intensities of mono beryllium products almost remain unchanged in Figure 1a.Several new absorptions located in N−C and C−N stretching region are almost diminished with low laser intensity.We tentatively assigned these weak absorptions to Be x (CH 3 CN), which were generated from the reactions of Be clusters and acetonitrile with high laser power.
The relatively weak absorptions in the original deposition spectra marked "1" were completely destroyed under visible irradiation.New product absorptions denoted with "2" also appeared upon sample deposition, which decreased after annealing to 8 K and totally disappeared on the first visible (λ = 520 nm) irradiation.On the opposite, the intensities of the bands marked with "3" and "4" tripled and doubled upon full arc irradiation (λ > 220 nm) compared with the co-deposition spectra.In addition, the relatively weak absorptions marked "5" and "6" only appeared after full arc irradiation.

End-On Products: BeBeNCCH 3 and BeNCCH 3
The absorption of C−N stretching mode for BeBeNCCH 3 complex was observed at 1927.8 cm −1 on co-deposition, and its corresponding 13 C counterpart was located at 1889.4 cm −1 , but unfortunately the corresponding D isotopic absorption was covered by the precursor bands.The observed absorptions matched well with the computed IR frequencies with strongest intensities at 1986.0 and 1942.7 cm −1 for 12 C and 13 C, respectively.The band at 994.1 cm −1 is attributed to the CH 3 bending mode, with D and 13 C counterparts observed  S1.Be−H str.
a All frequencies are in cm −1 and the calculated IR intensities are in the parentheses (km mol −1 ).The computed frequencies are given at the B3LYP−D3/aug−cc−pVTZ level of theory.b Absorptions covered by precursor bands.The assignment of the mono beryllium end-on complex BeNCCH 3 was confirmed by the experimental observation of three bands at 1915.4,1082.3 and 831.4 cm −1 .The strong 1915.4cm −1 band showed a large 13 C shift to 1875.4 cm −1 , exhibiting a 12 C/ 13 C isotopic frequency ratio of 1.0213, while its corresponding D counterpart was at 1911.2 cm −1 .We assigned this band to the C−N stretching mode of BeNCCH 3 based on the isotopic shifts and good consistence with the calculated value of 1953.5 cm −1 .The bands at 1082.3, 1020.8 and 1068.7 cm −1 for 12 C, D and 13 C isotopes are in good agreement with the calculated results of N−Be stretching mode at 1106.0 ( 12 C), 1043.4 (D) and 1091.5 cm −1 ( 13 C), respectively.The absorption observed at 831.4 cm −1 with a 13 C isotopic substitution at 811.6 cm −1 lays in the region expected for a C−C stretching vibration, [37] and the large 12 C/ 13 C ratio of 1.0244 was obtained to verify our assignment.The corresponding D isotopic absorption was covered by the precursor bands.All calculated frequencies of BeNCCH 3 are listed in Table S2.a All frequencies are in cm −1 and the calculated IR intensities are in the parentheses (km mol −1 ).The computed frequencies are given at the B3LYP−D3/aug−cc−pVTZ level of theory.b Absorptions covered by precursor bands.

Insertion Products: CNBeBeCH 3 and CNBeCH 3
The strong band at 2111.0 cm −1 is due to the N−C stretching vibration for the diberyllium insertion product CNBeBeCH 3 , and the D and 13 C isotopic substitutions were observed at 2111.9 and 2068.1 cm −1 , respectively, conforming to the N−C stretching mode shifts.The low-intensity band of CH 3 wagging mode is located at 1226.1 cm −1 , the predicted value of which is at 1249.1 cm −1 .The most decisive band for the diberyllium insertion product was observed at 1105.6 cm −1 , which matched well with the calculated absorption for Be−Be stretching mode at 1109.8 cm −1 .Unfortunately, the isotopic counterparts for these two absorptions were too weak to be observed in our experiments.The C−Be stretching mode was observed at 1013.4 and 913.4 cm −1 in D and 13 C spectra, but this mode was covered by the extremely strong precursor absorption in 12 C experiments.
The most intense absorption at 2100.2 cm −1 in the spectrum after full arc irradiation showed essentially no shift upon D substitution, but largely shifted to 2064.3 cm −1 on 13 C.The B3LYP isotope ratio for 13 C substitution of 1.0187 was in accordance with the experimental ratio of 1.0174.We therefore assigned the uniquely strong 2100.2cm −1 band to the N−C stretching vibration of the mono beryllium insertion complex.The strong CH 3 wagging absorption observed at 1237.8 cm −1 showed its D and 13 C isotopic absorptions at 1205.0 and 1223.8 cm −1 , and these bands are in excellent consistence with calculated values of 1269.2, 1217.9 and 1255.5 cm −1 , respectively.A medium absorption was observed at 1162.9 cm −1 along with its 13 C counterpart at 1160.5 cm −1 , and it is indicative of the antisymmetric CBeN stretching vibration.The observed bands are in the good agreement with the calculated frequencies of 1186.4 and 1183.2 cm −1 for 12 C and 13 C isotopes.Though the band at 668.3 cm −1 is common in the matrix spectra of CH 3 CN + M reactions, it only doubled under full arc irradiation in the case of beryllium, and tracked with other bands labeled "4".Unfortunately, its D and 13 C counterparts were not detected because of our detector noise.We tentatively assigned this band to the CBeN bending mode of CNBeCH 3 .The B3LYP functional predicted this band at 695.6 cm −1 , which is only 27.3 cm −1 higher than observed.The other infrared absorptions of CNBeCH 3 are very weak, which are not observed in the experiment (Table S4).

HBeCH 2 CN and HBeNCCH 2
The band at 2141.4 cm −1 only appeared after full arc irradiation showing almost no 13 C shift at 2141.8 cm −1 .The Be−D stretching mode of HBeCH 2 CN was calculated at 1654.6 cm −1 , and was observed at 1608.3 cm −1 among the strong absorptions of water impurity existing in all our experiments.We assigned these bands to the Be−H stretching mode of HBeCH 2 CN.In the low frequency region, a weak absorption at 685.9 cm −1 tracked with 2141.1 cm −1 band, and it showed a large D shift to 579.9 cm −1 and very small 13 C shift to 680.6 cm −1 .The band position and large D shift of 106.0 cm −1 suggested a Be−H bending vibration.The observed bands are in excellent agreement with the calculated frequencies of 710.2, 596.8 and 703.2 cm −1 , respectively.The observation of the Be−H bending mode overwhelmingly confirmed our assignment of HBeCH 2 CN.
The band at 2147.7 cm −1 exhibited its D and 13 C counterparts at 2114.6 and 2075.7 cm −1 .The B3LYP computed 12 C/ 13 C isotopic frequency ratios for C−N stretching mode of HBeNCCH 2 was 1.0352, very slightly lower than the observed value of 1.0347.For D counterpart, the calculation result showed that the C−N stretching mode is coupled with CD 2 symmetric stretching vibration, which is the reason of the large D shift observed in the experiment.The coincident coupled frequency in D substitution is decisive for the confirmation of product HBeNCCH 2 .The Be−H stretching mode was observed at 1661.8 and 2169.0 cm −1 for D and 13 C, and the predicted values were at 1688.5 and 2197.2 cm −1 , respectively.The calculated intensities of the other infrared bands are all weak in Table S6.

Molecular Structures and Bonding
The optimized structures of diberyllium and mono beryllium end-on and insertion complexes are shown in Figure 3, with the end-on products in C s symmetry and the insertion complexes possessing C 3v symmetry.The point groups of beryllium products happen to be reverse with the C 3v point groups of N-coordination transition-metal complexes and C s structures of transition-metal insertion complexes (except for Mn products) [30][31][32][33][34][35][36][37].According to the NBO analysis in Table S8, the electropositive beryllium forms sp hybrid orbitals, which make σ bonds with sp hybrid orbitals on the C atoms in the insertion complexes.The higher s contributions from Be in the C−Be bond lead to the linear structures, different from the higher d characters in the carbon−metal bond leading to the bent transition-metal structures.The unpaired spin destinies of triplet state BeNCCH 3 complex are most located on Be and C atoms (1.105 and 0.555, shown in Figure S1), which cause a bent structure with CCN bond angles of 134.6 • .
Unlike the tiny differences in the structures, the diberyllium products are much more exothermic compared with mono beryllium complexes, which may be caused by the formation of the Be−Be real single bonds.The binding energies of the Be-Be bonds in BeBeNCCH 3 and CNBeBeCH 3 are calculated to be −27.1 and −77.2 kcal/mol at CCSD(T)/ aug-cc-pVTZ level of theory, respectively.The Be-Be bond in CNBeBeCH 3 is also quantified by the EDA, as shown in Figure 4 and Table S9.The total interaction energy ∆E int is −73.72 kcal•mol −1 between the NCBe and BeCH 3 fragments, which consist of −65.54 kcal•mol −1 of electrostatic energy ∆E elstat , −41.61 kcal•mol −1 of orbital interaction energy ∆E orb , and 33.43 kcal• mol −1 of Pauli repulsion energy ∆E Pauli .For BeBeNCCH 3 , the Be-Be bond distance is calculated to be 2.077 Å, significantly shorter than that in the free Be 2 dimer of 2.509 Å.The Be−Be distance is further shortened in CNBeBeCH 3 with 2.058 Å.The Be-Be distances match the single bond value of 2.05 Å in reported calculations of comparable compounds, and the bond lengths are also closer to that of Be 2 2+ than to the neutral Be 2 molecule [17].Furthermore, the CN and CH 3 moieties are both doubly occupied rather than singly occupied in HOMO-2 and HOMO-3 (Figure S2), which also indicates charge transfer from Be 2 to the bonding fragments.As expected, the beryllium atoms in our diberyllium products carry positive charge and the NC and CH 3 moieties are negatively charged.According to the NPA charges showed in Figure 3, the Be 2 moiety carries positive charges of 0.38 and 1.32 for BeBeNCCH 3 and CNBeBeCH 3 , respectively.More positive charges on the Be 2 moiety lead to shorter Be−Be bond distances.Unlike the tiny differences in the structures, the diberyllium products are much more exothermic compared with mono beryllium complexes, which may be caused by the formation of the Be−Be real single bonds.The binding energies of the Be-Be bonds in BeBeNCCH3 and CNBeBeCH3 are calculated to be −27.1 and −77.2 kcal/mol at CCSD(T)/aug-cc-pVTZ level of theory, respectively.The Be-Be bond in CNBeBeCH3 is also quantified by the EDA, as shown in Figure 4 and Table S9.The total interaction energy ΔEint is −73.72 kcal•mol −1 between the NCBe and BeCH3 fragments, which consist of −65.54 kcal•mol −1 of electrostatic energy ΔEelstat, −41.61 kcal•mol −1 of orbital interaction energy ΔEorb, and 33.43 kcal• mol −1 of Pauli repulsion energy ΔEPauli.For BeBeNCCH3, the Be-Be bond distance is calculated to be 2.077 Å, significantly shorter than that in the free Be2 dimer of 2.509 Å.The Be−Be distance is further shortened in CNBeBeCH3 with 2.058 Å.The Be-Be distances match the single bond value of 2.05 Å in reported calculations of comparable compounds, and the bond lengths are also closer to that of Be2 2+ than to the neutral Be2 molecule [17].Furthermore, the CN and CH3 moieties are both doubly occupied rather than singly occupied in HOMO-2 and HOMO-3 (Figure S2), which also indicates charge transfer from Be2 to the bonding fragments.As expected, the beryllium atoms in our diberyllium products carry positive charge and the NC and CH3 moieties are negatively charged.According to the NPA charges showed in Figure 3, the Be2 moiety carries positive charges of 0.38 and 1.32 for BeBeNCCH3 and CNBeBeCH3, respectively.More positive charges on the Be2 moiety lead to shorter Be−Be bond distances.The energy decomposition analysis (EDA) in combination with the natural orbital for chemical valence (NOCV) theory has been carried out to further confirm the types of bonding in Table 2.There are two possibilities of interaction types in CNBeBeCH3: ionic or neutral interacting fragments.The most suitable fragments to describe the bonding situations yield the smallest amount of the orbital interaction energy (ΔEorb), because the least alteration of the electronic charge distribution is required to generate the electronic structure of the molecule.The significantly smaller ΔEorb value of ionic fragments (by 183.7 kcal/mol) convincingly shows that CNBeBeCH3 complex can be envisaged as the result of the interaction of Be2 2+ and (NC•••CH3) 2− through a donor-acceptor type of bonding rather than the electron-shared bonding between the neutral ones.The substantial electrostatic energy ΔEelstat (−640.7 kcal/mol) between the ionic interacting fragments contributes much more (75.9%) to the total attraction than the covalent contribution ΔEorb (24.0%).The polarization interaction caused by strong electrostatic interaction is also not neglectable.The corresponding deformation densities Δρ due to the electron transfer between the ionic interacting fragments are visualized in Figure 4.The direction of the The energy decomposition analysis (EDA) in combination with the natural orbital for chemical valence (NOCV) theory has been carried out to further confirm the types of bonding in Table 2.There are two possibilities of interaction types in CNBeBeCH 3 : ionic or neutral interacting fragments.The most suitable fragments to describe the bonding situations yield the smallest amount of the orbital interaction energy (∆E orb ), because the least alteration of the electronic charge distribution is required to generate the electronic structure of the molecule.The significantly smaller ∆E orb value of ionic fragments (by 183.7 kcal/mol) convincingly shows that CNBeBeCH 3 complex can be envisaged as the result of the interaction of Be 2 2+ and (NC•••CH 3 ) 2− through a donor-acceptor type of bonding rather than the electron-shared bonding between the neutral ones.The substantial electrostatic energy ∆E elstat (−640.7 kcal/mol) between the ionic interacting fragments contributes much more (75.9%) to the total attraction than the covalent contribution ∆E orb (24.0%).The polarization interaction caused by strong electrostatic interaction is also not neglectable.The corresponding deformation densities ∆ρ due to the electron transfer between the ionic interacting fragments are visualized in Figure 4.The direction of the charge flow is from the red region to the blue one.The colors also corroborate well with the NPA charges in Figure 3.It is obvious that the orbital interactions in CNBeBeCH 3 are mainly σ donations of the Lewis base (NC•••CH 3 ) 2− to the vacant σ u + orbitals of the Lewis acid Be 2 2+ .We also studied the topological analysis of electron density in these complexes to obtain a better understanding of the bonding situation.Figure 5 and Figure S3 display the contour plots of Laplacian of electron density (∇ 2 ρ(r)) at the molecular plane.The red dotted lines correspond to the areas of charge concentration (∇ 2 ρ < 0), while the blue solid lines indicate the areas of charge depletion (∇ 2 ρ > 0).The bond critical points identified between two beryllium atoms with negative Laplacian values (∇ 2 ρ cp = −0.1176 in BeBeNCCH 3 , −0.1079 in CNBeBeCH 3 ) support the formation of a real Be−Be bond, which exhibits covalent character.The negative values of the electronic energy density, E(r), as −0.3154 and −0.3997 in Table S10, also stand for the interactions with significant covalent character.All Be−N interactions present a positive bond critical point (BCP) value for the Laplacian ∇ 2 ρ(r) (∇ 2 ρ cp = 0.6479 in BeBeNCCH 3 , 0.7387 in BeNCCH 3 , 0.6078 in CNBeBeCH 3 , and 0.6073 in CNBeCH 3 ), denoting their ionic character.The negative electron energy densities at BCP (E(r)= −0.2494 in BeBeNCCH 3 , −0.3440 in BeNCCH 3 , −0.3663 in CNBeCH 3 and −0.3788 in CNBeBeCH 3 ) indicate the covalent character.Thus, the Be−N bonds are covalent polar bonds with a certain degree of both covalent and ionic contributions [38].The localized orbital locator (LOL) map is also introduced to characterize bond effects in Figure 5 and Figure S4.The LOL values of more than 0.9e (red regions) in Be−Be region of our products are significant larger compared with isolated Be 2 dimer.The strong electron localization indicates the aforementioned Be−Be covalent bonds.The strength of the Be−Be bonds in our products is also clear from the HOMO molecular orbitals involving the Be 2 moiety in Figure 5. Coherently, NBO describes the Be−Be bonds as σ bonds with a population of around two electrons (Table S8).The Wiberg bond index (WBI) for the Be-Be bonds is calculated to be 0.791 in BeBeNCCH 3 and 0.966 in CNBeBeCH 3 .It is worth noting that the strength of the Be−Be bond in CNBeBeCH 3 is just slightly weaker than the C-Be and N-Be bonds, the bond orders of which are 0.976 and 0.977, respectively.
CNBeCH3 and −0.3788 in CNBeBeCH3) indicate the covalent character.Thus, the Be−N bonds are covalent polar bonds with a certain degree of both covalent and ionic contributions [38].The localized orbital locator (LOL) map is also introduced to characterize bond effects in Figures 5 and S4.The LOL values of more than 0.9e (red regions) in Be−Be region of our products are significant larger compared with isolated Be2 dimer.The strong electron localization indicates the aforementioned Be−Be covalent bonds.The strength of the Be−Be bonds in our products is also clear from the HOMO molecular orbitals involving the Be2 moiety in Figure 5. Coherently, NBO describes the Be−Be bonds as σ bonds with a population of around two electrons (Table S8).The Wiberg bond index (WBI) for the Be-Be bonds is calculated to be 0.791 in BeBeNCCH3 and 0.966 in CNBe-BeCH3.It is worth noting that the strength of the Be−Be bond in CNBeBeCH3 is just slightly weaker than the C-Be and N-Be bonds, the bond orders of which are 0.976 and 0.977, respectively.

Reaction Mechanism
The calculated reaction paths including energies of products and transition states at the CCSD(T)//B3LYP−D3/aug−cc−pVTZ level of theory are illustrated in Figure 6.The reactions of beryllium atoms with acetonitrile in excess neon can be divided into three separate paths.For all products both singlet and triplet states are considered; unless noted, the following discussion relates to the lower energy singlet state species.
The calculations indicate that beryllium dimer reacts with acetonitrile on co-deposition to form the initial structure, BeBeNCCH 3 .The diberyllium end-on complex is more stable in the singlet ( 1 A') electronic state by exothermic 13.6 kcal/mol.BeBeNCCH 3 is also possible to be formed by adding another beryllium atom to the mono beryllium end-on complex in our experiments.The next step is both beryllium atoms bonding to the N atom to form a triangle intermediate (not observed), and an energetic barrier of 15.2 kcal/mol needs to be overcome.It later transfers to another energetically much lower cyclic intermediate via one beryllium atom bonding to the C atom by exothermic 45.9 kcal/mol.The infrared absorptions of this cyclic intermediate are calculated and showed in Table S7.Unfortunately, its main absorptions (1609.8,1095.5 and 768.1 cm −1 ) are all close to the extremely strong bands of water or precursor, so we cannot make sure whether it existed in our experiment or not.The last energy barrier of insertion into the C−N bond is pretty high with 67.8 kcal/mol, and the most stable diberyllium product CNBeBeCH 3 is finally generated.
For HBeCH2NC, the C−C and C-N bond distances are calculated to be 1.449 and 1.153 Å, respectively.After Be−H moiety transferring from CH2 to the N-end, the C−C bond is sizably shortened to 1.314 Å while the C−N bond is weakened (WBI from 2.923 to 1.924).The Wiberg bond order gives values of 0.985 and 1.825 for the C−C bonds of HBeCH2CN and HBeNCCH2, indicating single and double bonds, respectively.

Reaction Mechanism
The calculated reaction paths including energies of products and transition states at the CCSD(T)//B3LYP−D3/aug−cc−pVTZ level of theory are illustrated in Figure 6.The reactions of beryllium atoms with acetonitrile in excess neon can be divided into three separate paths.For all products both singlet and triplet states are considered; unless noted, the following discussion relates to the lower energy singlet state species.The calculations indicate that beryllium dimer reacts with acetonitrile on co-deposition to form the initial structure, BeBeNCCH3.The diberyllium end-on complex is more stable in the singlet ( 1 A ) electronic state by exothermic 13.6 kcal/mol.Be-BeNCCH3 is also possible to be formed by adding another beryllium atom to the mono beryllium end-on complex in our experiments.The next step is both beryllium atoms bonding to the N atom to form a triangle intermediate (not observed), and an energetic barrier of 15.2 kcal/mol needs to be overcome.It later transfers to another energetically For the mono beryllium reactions, calculations suggest that the initial end-on complex BeNCCH 3 is more stable in the triplet state, and the laser power in our experiments is able to initiate this N-coordination process.The CNBeCH 3 complex is calculated to be the global minimum for the mono beryllium products as 61.8 kcal/mol exothermic.The insertion process occurs in a single step involving the breaking of C−C bond and the formation of a new C−Be bond, which only requires to cross an energy barrier of 25.4 kcal/mol.The insertion reaction is also the primary reaction according to the strongest infrared absorptions of the product "4" after full arc irradiation.The C−H bond insertion products of acetonitrile in cryogenic matrix experiment were first observed in our experiment.The C−H insertion reaction proceeded with a high energetic cost of 62.9 kcal/mol, which was apparently supplied by photon energy during full arc photolysis, and in line with the experimental observation of HBeCH 2 CN and HBeNCCH 2 only after full arc irradiation.The HBeCH 2 CN complex is found to be 35.6 kcal/mol more stable than the reactants.The next step involves a relatively low energy barrier of 8.8 kcal/mol to obtain the more stable product, HBeNCCH 2 , which is exothermic by 37.8 kcal/mol.

Experimental and Computational Methods
The experimental details in conjunction with matrix infrared spectroscopy investigation have been described previously [39][40][41][42].Briefly, the Nd:YAG laser fundamental (1064 nm, 10 Hz repetition rate with 10 ns pulse width) was focused onto a rotating beryllium metal target (Alfa Aesar, Haverhill, MA, USA), and the ablated beryllium atoms were co-deposited with the gas mixture of neon and acetonitrile (Sinopharm Chemical Reagent Co., Ltd., Shanghai, China) onto a substrate (CsI) maintained at 4 K using a closed-cycle helium refrigerator (Sumitomo Heavy Industries Model RDK 205D, Tokyo, Japan) for normally 60 min.Matrix samples then were annealed and subjected to LED lights or a high-pressure mercury arc lamp (Philips, 175 W, Beijing, China) with the globe removed, and the products were confirmed by IR spectra recorded on a Bruker 80 V spectrometer in the range from 400 to 4000 cm −1 at 0.5 cm −1 resolution.The experiments were repeated using CD 3 CN (Sigma-Aldrich, St. Louis, MO, USA) and 13 CH 3 13 CN (Cambridge Isotope Laboratories, Cambridge, Britain) samples to further confirm our assignment of the products.
Quantum chemical calculations were carried out using the Gaussian 09 software package [43].The geometry optimization and frequency calculations were performed using the hybrid B3LYP [44,45] functional including Grimme's D3-dispersion correction [46] with aug-cc-pVTZ [47,48] basis set employed for all atoms.The second-order vibrational perturbation theory (VPT2) was used to calculate the anharmonic values of the spectral parameters [49,50].Geometries of products were reoptimized using the more strenuous CCSD method [51] and the single-point energy calculations were separately performed at the CCSD(T) [52][53][54]/aug-cc-pVTZ level with B3LYP-D3-optimized geometries.Bonding analyses were carried out considering Quantum Theory of Atoms in Molecules (AIM) [38], localized orbital locator (LOL) map [55] and Natural Bond Orbital (NBO) [56].The AIM and LOL analyses were performed using Multiwfn code [57] and the NBO analysis was computed using the NBO 3.1 program.The Multiwfn and VMD [58] programs were applied for plots of HOMO molecular orbitals.The energy decomposition analysis (EDA) [59,60] combined with the natural orbital for chemical valence (NOCV) theory [61,62] was performed using the ADF 2020.101 program packages to analyze the interaction nature of the bonding fragments [63,64].Uncontracted triple-ζ Slatertype orbital (STO) basis sets plus two sets of polarization functions (TZ2P) [65] were used for all elements.The scalar relativistic effects were included via the zeroth-order regular approximation (ZORA) Hamiltonian [66].

Conclusions
Beryllium atom reactions with CH 3 CN give six new products.The diberyllium complexes BeBeNCCH 3 and CNBeBeCH 3 were found to be 30 kcal/mol more exothermic than the mono beryllium products because of the formation of the Be−Be single bonds.The calculated binding energies of the Be-Be bonds are −27.1 and −77.2 kcal/mol for BeBeNCCH 3 and CNBeBeCH 3 at CCSD(T)/aug−cc−pVTZ level of theory, respectively.In spite of the fact that Be is an electron-deficient element, the Be 2 moiety shows a distinct cationic character and the electron transfer from Be 2 antibonding orbitals to the bonding fragments strengthens the Be−Be bonds.AIM, LOL and NBO analyses confirm the existence of the covalent Be−Be bonds.EDA-NOCV analysis demonstrates clearly that the CNBeBeCH 3 complex can be seen as a result of the interaction between Be 2 2+ and (H 3 C•••NC) 2− anions.The bonding interactions between Be and N atoms are identified as covalent polar bonds because of the coexisting ionic and covalent characters from AIM analyses.Lower yields of HBeCH 2 CN and HBeNCCH 2 have also been observed after full arc irradiation, and the double C=C and C=N bonds are formed after Be−H moiety transferring from CH 2 to the N-end.Finally, we hope the present study can further extend knowledge of the reactions and bonding investigations of beryllium complexes, and attract further theoretical and experimental research about beryllium chemistry.

Supplementary Materials:
The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules29010177/s1, Figure S1: The Spin Density Plots of BeNCCH 3 at the B3LYP−D3/aug−cc−pVTZ Level of Theory.Figure S2: Selected frontier molecular orbitals of CNBeBeCH 3 calculated at B3LYP−D3/aug−cc−pVTZ level of theory.Figure S3: Contour line diagrams of the Laplacian of the electronic density of the mono beryllium products.Figure S4: 0 and 981.2 cm −1 , respectively.The computed infrared absorptions of BeBeNCCH 3 are shown in Table

Molecules 2024 , 15 Figure 3 .
Figure 3. Optimized structures of the reaction products at the B3LYP−D3 (bold) and CCSD (italic) levels.The aug−cc−pVTZ basis was set for all atoms.Black color: bond length in Å and bond angle in degree; red color: the atomic partial charges calculated by the NBO method.

Figure 3 .
Figure 3. Optimized structures of the reaction products at the B3LYP−D3 (bold) and CCSD (italic) levels.The aug−cc−pVTZ basis was set for all atoms.Black color: bond length in Å and bond angle in degree; red color: the atomic partial charges calculated by the NBO method.Molecules 2024, 29, x FOR PEER REVIEW 8 of 15

Figure 4 .
Figure 4. Plots of the deformation densities Δρ.ΔEorb are in kcal mol −1 .The direction of the charge flow is red → blue.

Figure 4 .
Figure 4. Plots of the deformation densities ∆ρ.∆E orb are in kcal mol −1 .The direction of the charge flow is red → blue.

Figure 5 .
Figure 5. Contour line diagrams of the Laplacian electronic density of the diberyllium products (first row).Blue dots stand for BCPs.The blue solid lines and red dotted lines correspond to values of ∇ 2 ρ(r) > 0 and ∇ 2 ρ(r) < 0, respectively; 2D Localized Orbital Locator (LOL) map of the diberyllium products (second row).The HOMO molecular orbitals involving the Be 2 moiety (last row).The length unit is Bohr for Laplacian and LOL map.For HBeCH 2 NC, the C−C and C-N bond distances are calculated to be 1.449 and 1.153 Å, respectively.After Be−H moiety transferring from CH 2 to the N-end, the C−C bond is sizably shortened to 1.314 Å while the C−N bond is weakened (WBI from 2.923 to 1.924).The Wiberg bond order gives values of 0.985 and 1.825 for the C−C bonds of HBeCH 2 CN and HBeNCCH 2 , indicating single and double bonds, respectively.

Figure 6 .
Figure 6.Calculated reaction paths in relation to the reactants [Be/Be2 + CH3CN].(a) diberyllium reaction paths; (b) mono beryllium reaction paths.Relative energies are given in kcal mol −1 .S and T denote singlet and triplet electronic states, respectively.

Figure 6 .
Figure 6.Calculated reaction paths in relation to the reactants [Be/Be 2 + CH 3 CN].(a) diberyllium reaction paths; (b) mono beryllium reaction paths.Relative energies are given in kcal mol −1 .S and T denote singlet and triplet electronic states, respectively.

Table 1 .
Experimentally observed (in Ne) and calculated vibrational frequencies of products from reactions of beryllium atoms with acetonitrile a .
a Energy values are given in kcal/mol.bThepercentage contribution to the total attractive interactions (∆E elstat + ∆E orb + ∆E disp ) is given in parentheses.cThepercentage contribution to the total orbital interactions is given in parentheses.