Super Strong Be–Be Bonds: Theoretical Insight into the Electronic

Article Cite This: J. Phys. Chem. A 2018, 122, 2258−2265

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Super Strong Be−Be Bonds: Theoretical Insight into the Electronic Structure of Be−Be Complexes with Radical Ligands Published as part of The Journal of Physical Chemistry virtual special issue “Manuel Yáñez and Otilia Mó Festschrift”. Oriana Brea*,† and Inés Corral*

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Departamento de Química, Facultad de Ciencias, Módulo 13, and Institute of Advanced Chemical Sciences (IadChem), Universidad Autónoma de Madrid, Campus de Excelencia UAM-CSIC, Cantoblanco, 28049 Madrid, Spain S Supporting Information *

ABSTRACT: The electronic structure of complexes formed by the interaction of Be2 with radical ligands (L:Be−Be:L) has been studied by means of the high-level theoretical protocol CCSD(T)/cc-pVTZ. At this level of theory, no matter the nature of the ligand, the Be−Be bond becomes up to 300 times stronger compared to isolated Be2, indicating that these kinds of complexes are thermodynamically stable and, thus, that they could be experimentally detected. Moreover, among all of the ligands considered, the strength of the Be−Be bond for L = [CN]• was calculated to be 330 kJ·mol−1, slightly greater than the strongest up to date L = F• complex, thus setting a new mark for the strongest Be−Be bond reported so far in the literature. Wave function analysis methods explain this strong interaction as a result of the oxidation of the Be2 moiety to Be22+ due to charge transfer toward the L ligands. In this study, we have also considered F:Mg−Mg:F complexes, which show very similar properties as the ones described for the analogous F:Be− Be:F.

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INTRODUCTION The lack of experimental and theoretical information about the beryllium molecule and its derivatives is attributed to two reasons: (1) the high toxicity of the metal and (2) the entangled electronic structure of this system.1−8 Just one of the many proofs illustrating the complexity of the beryllium molecule is all of the early attempts to synthesize it, which yielded beryllium oxide.9,10 The experimental challenges connected to Be2 synthesis and thus its characterization have been associated with the high melting and boiling points of the molecule because at these temperatures Be vapor is almost monatomic, and on top of that, beryllium is very easily oxidized. Despite all of these technical challenges, in 1984, Bondybey and collaborators obtained beryllium molecules by laser ablation of metallic Be.11 The beryllium dimer was characterized as a weakly bonded molecule with a bond dissociation energy (BDE) of 10 kJ·mol−1 and a bond distance amounting to 2.45 Å.11,12 The theoretical description of this molecule is also complicated. For instance, Molecular Orbital Theory predicts a bond order of zero for the beryllium dimer.13−15 In agreement, early valence bond calculations described the Be2 molecule as a repulsive system.16 The extraordinary development experienced by electronic structure methods over the last decades has allowed an accurate description of this system. Full © 2018 American Chemical Society

Configuration Interaction (FCI) method, for example, calculates a single minimum at 2.47 Å, in line with the experimental data (see Figure 1 and refs 17−19). The computational cost of the FCI method is, however, prohibitive

Figure 1. Potential energy curves for the ground state of Be2, calculated at different levels of theory with the cc-pVTZ basis set. Received: November 29, 2017 Revised: January 23, 2018 Published: January 26, 2018 2258

DOI: 10.1021/acs.jpca.7b11758 J. Phys. Chem. A 2018, 122, 2258−2265

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fluorine22 beryllium complexes previously studied by other authors (see Figure 2).

to be applied to beryllium derivatives, and less computationally expensive methodologies might not perform correctly (see Figure 1). The methods so far employed in the description of the Be−Be, and whose quality has been assessed in this and previous works,7,20 can be classified into three main groups according to the characterization that they provide for the bond (see Figure 1). 1. Repulsive Be−Be bond: Hartree−Fock (HF) and f ullvalence Complete Active Space Self-Consistent Field [CASSCF(4,8)] find a repulsive interaction between Be atoms. 2. van Der Waals Be−Be bond: Coupled Cluster Singles and Doubles (CCSD) describes the Be molecule as a van Der Waals complex, with a Be−Be bond distance of around 4.5 Å. 3. Covalent bond: Other high-level methodologies predict for this system a shorter Be−Be bond (∼2.4−2.6 Å). These methods can be subdivided into two subgroups considering the nature of electron correlation that they incorporate: a. Single-determinantal methods: B3LYP and MP2 dissociation curves, respectively, over- and underestimate the strength of the Be−Be bond. Only Coupled Cluster Singles Doubles with Perturbative Triples [CCSD(T)] is able to correctly reproduce the FCI dissociation curve. b. Multideterminantal methods: Second-order perturbation theory based on the f ull-valence CASSCF reference wave functions [CASPT2/CASSCF(4,8)] improves the CASSCF result. However, this method still does not reproduce the FCI potentials, unless the active space is increased to (4,16). The discrepancy among theoretical methods has awakened a controversial debate around the real nature of the bond in a Be−Be molecule. Is Be2 a van der Waals complex? Is the Be− Be bond too weak to be considered a covalent bond? These are straightforward questions that can be drawn from the above results. Only recently, the bond in the Be dimer has been characterized as an interaction based on nondynamical electron correlation considering the two quasi-degenerate orbitals with a rather low occupancy present in the molecule.21 Thus, the chosen theoretical method to study Be2 (and its derivatives) should, in principle, on the one hand provide an accurate description of dynamical electron correlation but also must consider nondynamical electron correlation which is crucial to accurately account for the nature of this bond. The challenging accurate representation of the Be2 molecule has also been connected to the weakness of the Be−Be bond, amounting to 10 kJ·mol−1. To reinforce this bond, the complexation of Be2 with electron donor ligands (L:Be− Be:L), profiting the high electron deficiency of the Be atoms, has been suggested as a promising strategy; see, for instance, ref 22. In this line, the contributions from Professors Mó and Yáñez and collaborators have been of remarkable importance. They have proposed the formation of super strong Be−Be bonds upon electron attachment23 and have enriched Be chemistry through the discovery of beryllium bonds24−35 and Be-based anion sponges.36,37 The present contribution focuses on the description of novel Be derivatives, analogous to the CO,38 N-heterocyclic carbenes (NHCR, where R stands for the cycle substituent),39 and

Figure 2. Comparison of the BDEs for the complexes between Be2 and electron donor ligands (L). BDEs and geometries (from left to right) were taken from refs 38 (CO), 39 (NHCR), and 22 (F). The dotted line represents the BDE for the isolated Be2 molecule.

The tetra-CO substituted Be2 complex, (CO)2:Be−Be: (CO)2, was first described by Sunil in 199238 as a classical complex with the CO interacting with the metal atoms through a σ-type bonding involving the lone pairs (LPs) of the CO and hybrid s, p orbitals of Be, followed by a π-backdonation between the 2pBe and the π*CO orbitals at the MP4(SDQ)/631G*(5d)//HF/6-31G*(5d) level. According to this study, Be−Be interaction is characterized as a double bond, with σ and π components. The Be−Be bond distance was calculated to be 1.938 Å (0.5 Å shorter than in the isolated molecule), with the BDE amounting to 209 kJ·mol−1 (∼200 kJ·mol−1 stronger than that in the free molecule). The double character of the Be−Be bond proposed by Sunil was later questioned, based on theoretical grounds, after considering bond indices and rotational energies for these and other complexes (CO)n:Be− Be:(CO)n (with n = 1 and 2)40,41 and IR experiments.42 Alternatively, these works suggested rather a single Be−Be bond or a three-center C−Be−Be bond. The works by Frenking and collaborators on NHCR39 and F • 22 beryllium complexes are more recent. Different NHCR:Be−Be:NHCR complexes were characterized by means of density functional theory (DFT), with the bond analysis performed considering electron decomposition analysis (EDA) and bond indices. The nature of the NHCR:Be and Be−Be interactions was found to be similar to that of beryllium CO complexes: there is a σ-donation and π-backdonation between NHCR and Be, with the Be−Be bond presenting a multicenter character. Be−Be bond distances and BDEs in NHCR:Be− Be:NHCR were found to depend on the R substituent, with values around 1.95 Å and up to 271 kJ·mol−1, respectively. The strongest Be−Be bond has been reported for the F:Be− Be:F complex and amounts to 322 kJ·mol−1 at the CCSD(T)/ cc-pVTZ level of theory. However, the Be−Be bond distance was found to be longer than that in the systems containing carbene ligands (2.07 Å vs 1.95 Å).39 Surprisingly, there is no clear correlation between bond strength and bond length, which has been ascribed to the electronically excited character of the singlet state of the NHCR:Be−Be:NHCR complexes, the ground state being characterized by a triplet multiplicity. 2259

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RESULTS AND DISCUSSION Character of L:Be−Be:L Complexes’ Wave Function. As already stated in the Introduction, the Be2 molecule has been defined as a highly electronically correlated system. By contrast, all of the L:Be−Be:L complexes considered in this study are characterized by a monoreference wave function, according to the T1 diagnostic (see Table S1).54 This result can be readily explained considering the valence electronic configurations of Be 2 and its ionic forms: Be 2 = (σBeBe)2(σ*BeBe)2, Be2+ = (σBeBe)2(σ*BeBe)1, and Be22+ = (σBeBe)2(σ*BeBe)0. The multireference character of the neutral molecule arises from the double occupation of the σ antibonding orbital, which facilitates excitations toward the low-lying pBe orbitals. The pBe orbitals lie, however, higher in energy in the cations, and indeed, it has been found that, while single-reference methodologies fail in the description of Be2, these methods are able to correctly reproduce the electronic properties of the cations.55−57 Please note that the dication is electronically equivalent to the Li2 molecule, which is also a single-reference system. Table 1 compiles the NBO charges for the Be atoms in the different L:Be−Be:L complexes. For all of the complexes

This study aims at exploring the energetic and bonding properties of complexes of the type L:Be−Be:L, where L corresponds to radical ligands (L = [CN]•, [CH3]•, [CH3O]•, [NH2]•, [OH]•, and F•). What is the nature of the Be2 bond in this type of complex? Can these systems be accurately described by means of single-reference methodologies? Why does the Be−Be bond become up to 30 times stronger in this type of system compared to that in the isolated molecule? These are some of the questions that we would like to address in this contribution.

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COMPUTATIONAL DETAILS The geometries, harmonic frequencies, and energetic properties necessary for the description of the L:Be−Be:L complexes were explored considering the CCSD(T)43 method combined with the cc-pVTZ44 basis set. All of the calculations were performed with the MOLPRO-2015 computational package45 (see the Results and Discussion section for the specific levels of theory used at each stage of the research). Analysis of the Be−Be and Be:L bonds was carried out considering three complementary methodologies: Quantum Theory of Atoms in Molecules (AIM),46 Electron Localization Function (ELF),47 and Natural Bond Orbital (NBO).48 The first two methods, based on the topological analysis of the electron density, were applied on highly electronically correlated wave functions obtained from B3LYP/cc-pVTZ single-point calculations. The QTAIM approach locates critical points of ρ(r) to build molecular graphs of the complexes under study. The critical points of ρ(r) can be classified into nuclear critical points (NCPs), which are maxima of ρ(r); bond critical points (BCPs), which are first-order saddle points of ρ(r) connecting two atoms; and ring critical points (RCPs), which are second-order saddle points of ρ(r), defining a ring. Finally, in a molecular graph, the atoms are connected through bond paths, which are the lines of maximum density that connect two NCPs bonded by a BCP. This representation provides a more realistic picture of how atoms bond to each other, beyond the structural information. QTAIM calculations were carried out with the AIMAll program package.49 The ELF theory allows locating regions of the physical space where there is a probability maximum (basins) to find a pair of electrons. By considering the atoms hosting each basin, this method is able to recover the Lewis-type description of a molecule. Disynaptic (or polysynaptic) basins are basins centered over two (or more) atoms. Monosynaptic basins, in turn, are centered on a single atom and can be classified either as core or LPs. The ELF calculations included in this work were performed with the TopMod program.50−52 The strength and characteristics of chemical bonds are directly related to the properties of BCPs and basins within the AIM and the ELF frameworks, respectively. For example, qualitative information on the strength of a bond can be inferred from the value of ρ(r) at the BCP or the population of the basin.46 Finally, the NBO method was also applied for bonding analysis. This method does not perform topological analysis of the electron density but rather partitions the one-particle density matrix into atomic-local blocks. This partition permits determining the atomic charges, the Lewis structure of the system, and the charge transfer between occupied and virtual orbitals through second-order perturbation analysis. To this purpose, we have used the NBO-6.0 program.53

Table 1. NBO Charge for the Be Atoms (qBe) and the L Ligands (qL) along with the Electronic Configuration for the Be Atoms within the L:Be−Be:L Complexesa L

qBe (au)

qL (au)

F• CN• CH3O• CH3• OH• NH2•

0.86 0.85 0.81 0.80 0.82 0.80

−0.86 −0.85 −0.81 −0.80 −0.82 −0.80

Be electronic configuration [He]2s0.93 [He]2s0.99 [He]2s0.96 [He]2s1.04 [He]2s0.96 [He]2s0.99

2p0.20 2p0.14 2p0.22 2p0.15 2p0.21 2p0.19

a

Electronic configuration of the Be atoms in Be2: [He]2s1.74 2p0.24 [CASSCF(4,16)/cc-pVTZ]; electronic configuration of the Be atoms in Be22+: [He]2s0.87 2p0.13 (B3LYP/cc-pVTZ).

examined, the Be2 moiety was found to present a dicationic character. Consistently, the electronic configuration of the Be atoms in the complexes is equivalent to that of Be+ ([He]2s1; see Table 1). In fact, we observe the migration of the two electrons from the σ*BeBe orbital toward the L ligands, in such a way that each L ligand recovers a closed-shell character (L−). In L:Be−Be:L complexes, where L is a radical species, each fragment is closed-shell and, thus, single-reference, explaining the values below 0.2 found for the T1 diagnostic. Geometric and Bonding Properties of the L:Be−Be:L Complexes. For all of the complexes, four different isomers were initially considered: linear (Scheme 1a), trans (Scheme 1b), cis (Scheme 1c), and scissor-like (Scheme 1d) structures. In all of the cases, the most stable geometrical arrangement corresponds to the linear configuration. In fact, any attempt to minimize the remaining isomers either converged to the linear structure or failed to optimize. The stability of the linear isomers is related to the optimal overlap between the σBeBe and the pL orbitals. For the particular case of L = [CN]•, two possible linear isomers were studied: one where Be binds through the N atom and another one where it binds to the C atom. The complex where the metals interact with the N atoms was found to be 39 kJ·mol−1 more stable than the one bonded through the carbon atom. 2260

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The Journal of Physical Chemistry A Scheme 1. L:Be−Be:L Isomers Considered in the Study

Figure 3 shows the structure and most important bond distances for the optimized complexes, as well as for the neutral

Figure 3. Geometries of the global minima of Be2, Be22+, and L:Be− Be:L complexes. Most relevant bond lengths are shown in Å. All calculations, except for Be2, were performed at the CCSD(T)/ccpVTZ level of theory. For the neutral Be dimer, the CASPT2// CASSCF(4,16)/cc-pVTZ protocol was used instead.

Figure 4. Comparison of wave function analysis for Be2, Be22+, and CN:Be−Be:NC complexes. Molecular graphs and contour maps of the Laplacian of ρ [∇2ρ(r)] (first row). Green and pink dots stand for BCPs and NNAs, respectively. The blue and red lines respectively correspond to values of ∇2ρ(r) > 0 and ∇2ρ(r) < 0. ELF isosurface plots with monosynaptic basins (red) and disynaptic basins (green), (second row). NBO localized MO involving the Be atoms (last row). All calculations were performed at the B3LYP/cc-pVTZ level of theory.

and dicationic forms of Be2. The Be2 complexation with the radical ligands considered in this study leads to Be−Be bond distances of around 2.1 Å, which are very close to the bond distance calculated for the (Be−Be)2+ species and 0.4 Å shorter than the neutral isolated molecule. Wave function analysis methods characterize the bonding of the Be2 moiety in L:Be−Be:L closer to that of Be22+ than to the neutral molecule, suggesting that the Be−Be bond in the L:Be− Be:L complexes could be described as a classic 2c,2e− bond. ELF and NBO approaches describe neutral Be2 as two noninteracting atoms, as confirmed by the absence of a Be− Be disynaptic basin [V(Be,Be)] (see Table 2) or a NBO bonding orbital [BD(Be,Be)] (see Figure 4). This is at contrast with isolated Be22+ and Be2 fragments in L:Be−Be:L, for which the same theories locate V(Be,Be) basins and BD(Be,Be) bonding orbitals with populations close to 2e−. QTAIM also

predicts similar bonding patterns for the Be−Be fragment in L:Be−Be:L and Be22+. While the molecular graph of the Be2 free neutral molecule shows a Be−Be BCP carrying a small value of ρ (0.030 au), those of the Be22+ dication and Be2 moieties in the complexes are characterized by the presence of non-nuclear attractors (NNAs). NNAs correspond to local maxima of ρ(r) not coinciding with nuclei positions.58−61 The existence of NNAs has been associated with specific internuclear distance ranges between the atoms participating in the bond.62−64 For the particular case of Be−Be bonds, NNAs were found for internuclear distances between 1.4 and 2.1 Å, which coincides with the Be−Be equilibrium bond distance in the dication and in the complexes but not to that of the neutral molecule. The existence of NNAs for the particular case of F:Be−Be:F was investigated considering different wave

Table 2. Electron Density at the Be−Be and Be−L BCPs, Population of the ELF Be−Be and Be−L Disynaptic Basins, and NBO Second-Order Perturbation Energies Calculated for Be2L2 complexesa Be2/L

ρBe−Be BCPb (au)

ρBe−L BCP (au)

V(Be,Be) pop (au)

V(Be,L) pop (au)

LP(L) → σBe−Be (kJ·mol−1)

LP(L) → pBe (kJ·mol−1)c

Be2 Be22+ F• CN• CH3O• CH3• OH• NH2•

0.031 0.065 0.072 0.074 0.066 0.068 0.070 0.070

0.071 0.073 0.066 0.068 0.069 0.070

2.0 2.0 2.0 2.0 1.9 2.0 2.0

2.1 3.6 2.2 2.2 2.8 2.1

79.55 90.90 82.78 113.55 88.22 97.64

241.7 145.4 176.4 194.6 202.1 181.2

a

All calculations were performed at the B3LYP/cc-pVTZ level of theory, except for Be2 where the CASSCF(4,16)/cc-pVTZ protocol was used instead. bFor L:Be−Be:L and Be22+, this corresponds to ρ evaluated at Be-NNA BCPs. cThese values correspond to the sum of different charge transfer contributions toward the pBe orbitals along the bond and in perpendicular directions. See Table S2 for a detailed description of each contribution. 2261

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Figure 5. Representation of the localized MO participating in the NBO second-order perturbation energies for the interaction between CN• and Be2 in the CN:Be−Be:NC complex. The NBO orbitals were calculated at the B3LYP/cc-pVTZ level of theory.

Energetic Properties. The thermodynamic cycle in Scheme 2 overviews the different possible dissociation

functions (DFT, CASSCF, HF) and basis sets (cc-pVXTZ with X = D, T, and Q) in the range of Be−Be bond distances comprised between 1.5 and 5.0 Å. In all cases, an internuclear Be−Be local electron density maximum was found approximately within the range of internuclear distances for which NNAs were identified for the Be2 molecule. Our analysis was completed with other complexes already examined in the literature, such as CO38 and NHCH,39 for which Be−Be NNAs were also localized in the same range of Be−Be distances. For all systems (Be2, Be22+, and L:Be−Be:L) considered, QTAIM registers the concentration of electron density along the Be−Be bonding region [∇2ρ(r) < 0], showing covalent character independently on the bond strength (see Figure 4 and Tables 2 and S2). The origin of the dicationic character of Be2 within L:Be− Be:L is the interactions of the Be2 moiety with the L. Thus, understanding the nature of the Be−L bonds is crucial to build a complete picture of the bonding of theses complexes. [Be-L]• fragments were optimized at the CCSD(T)/cc-pVTZ level of theory; see Table S3 for the compilation of Be−L bond distances. The Be−L bond distances in the [Be−L]• fragments were found to be very similar or slightly reinforced (0.01 Å) compared to those within the L:Be−Be:L complexes, indicating a very strong Be−L interaction, not importantly affected by the bonding between the two BeL fragments (see Table S3 and Figure 3). Furthermore, the three wave function and bond analysis methods considered, ELF, AIM, and NBO, support the ionic character of the Be:L bond within the complexes: • ELF locates Be−L disynaptic basins with populations larger than 2e−. These basins are not however symmetrically arranged along the bonding region but are closer to the more electronegative L ligands (see Figure 4 and Table 2). For L = [CN]• and [OH]•, ELF locates a population larger than 2e− for the V(Be,L) basins, which are ascribed to contributions from V(L) monosynaptic basins. • QTAIM locates Be−L BCPs with ρ values over 0.1 au and a positive Laplacian (see Figure 4 and Table 2). • NBO theory does not calculate bonding orbitals between Be and the L, but the second-order perturbation analysis shows strong interactions from the LP(L) orbitals of the ligand toward the BD*(Be,Be) and pBe orbitals, with values up to 200 kJ·mol−1 (see Figure 5 and Table 2). In summary, both the structural and wave function analyses support that the shorter Be−Be bond distance in L:Be−Be:L compared to the neutral isolated Be2 molecule is a reflection of the oxidation of Be2, promoted by the formation of strong ionic interactions with the L ligands.

Scheme 2. Thermodynamic Cycle Summarizing the Different Pathways to Dissociate L:Be−Be:L Complexes

mechanisms for the L:Be−Be:L complexes. This process could occur in a single step through the simultaneous breaking of Be−Be and the two Be:L bonds (ΔE5), upon providing, as expected, a huge amount of energy (up to 1400 kJ·mol−1). The dissociation of the L:Be−Be:L complexes could be also envisaged as a two-step mechanism. The first step would involve the rupture of a Be:L bond (ΔE1) or the Be−Be bond (ΔE3). The greater bond strength of the Be:L compared to Be−Be becomes apparent by comparing ΔE1 and ΔE3, the first being twice as large as the second (see Table 3). This also Table 3. Bond Dissociation Energies Including Zero-Point Energies (ZPEs) for L:Be−Be:L and F:Mg−Mg:F Complexes As Defined in Scheme 2a L:Be−Be:L

ΔE1

ΔE2

ΔE3

ΔE4

ΔE5

F• CN• CH3O• CH3• OH• NH2• F:Mg−Mg:F

736 573 535 375 614 500 575

662 500 464 303 539 426 463

313 320 306 298 310 308 197

1085 752 693 380 843 618 841

1398 1072 998 678 1153 926 1038

a

All dissociation energies were calculated at the CCSD(T)/cc-pVTZ level of theory and are reported in kJ·mol−1. The values highlighted in bold correspond to processes involving species with multireference wave functions according to the T1 diagnostic.

suggests that the dissociation mechanism with the rupture of the Be−L bond preceding Be−Be breaking is disfavored with respect to starting with the dissociation of the metal−metal bond. The rupture of the Be−Be bond (ΔE3) has an energetic cost of about 320 kJ·mol−1, the ligand having very little influence. The strongest Be−Be bond was calculated for L = [CN]•, 320 kJ·mol−1 (330 kJ·mol−1 not considering ZPE), around 308 kJ·mol−1 stronger than that for the isolated neutral 2262

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Figure 6. (a) Molecular graph superimposed on the Laplacian of the ρ contour map [∇2ρ(r)] for F:Mg-Mg:F complex. The values of ρ and ∇2ρ(r) (in bold) are shown. (b) ELF isosurface plot. (c) Localized MO involving the Mg atoms considering the NBO approach. Both the disynaptic V(Mg,Mg) basin and the NBO BD(Mg,Mg) orbital have population of 2e−. Same conventions as in Figure 4.

molecule and 7 kJ·mol−1 stronger than that for the complex with L = F•, which corresponds to the strongest Be−Be bond reported so far in the literature.22 The Be−Be BDEs for the complexes dramatically contrast with the values estimated for the Be2 dication, which is a metastable species. The dissociation products (Be+ + Be+) lie 212 kJ·mol−1 below the Be22+ minimum; however, an energetic barrier of 106 kJ·mol−1 needs to be overcome to reach these products.57,65 The instability of the dissociation products in the complexes is attributed to the destabilizing interaction of the L. The barriers connected to the dissociation of the Be−L bonds lie in the range between 380 and 1100 kJ·mol−1, reflecting the strength of the Be−L interaction. ΔE1 was previously evaluated for a Be2 CO-disubstituted complex.42 HF calculations predict this process to be exothermic, concluding that the CO:Be−Be:CO system would exist as CO:Be−Be + CO. Our results, however, predict stable radical ligand complexes toward dissociation into L:Be− Be + L. All ΔE1 values reported in Table 3 are larger than 350 kJ·mol−1. For the sake of comparison, the thermodynamic cycle in Scheme 2 was revisited considering for ligands F• and [CN]•, this time, Gibbs free energies. The calculated ΔG values were found to be in line with the energies reported in Table 3, confirming as earlier proposed by Frenking and collaborators for L = F• in ref 22 that L:Be−Be:L complexes are thermodynamically stable toward dissociation into 2(L:Be) or (L:Be−Be + L) and thus that it should be possible to observe them experimentally, when L is a radical ligand. Mg Dimer (Mg2). Mg2 and Be2 molecules share the structure of the electronic valence shell, that is, both σMgMg and σ*MgMg are doubly occupied, and as a consequence, the Mg− Mg interaction is also weak (4.8 kJ·mol−166) and characterized by a long internuclear distance (3.89 Å).66 The complex between Mg2 and two fluorine atoms was also studied (see Table 3) in order to evaluate the effect of the radical ligand interaction on the Mg−Mg bond. The Mg−Mg bond within the F:Mg−Mg:F complexes shares structural and energetic similarities with the Be−Be bond in F:Be−Be:F: (1) Fluorine complexation decreases the Mg−Mg bond by 1 Å and increases the bond strength by about 198 kJ· mol−1, taking as a reference the isolated molecule; (2) the Mg− F bond in the F:Mg−Mg:F complex is sizably stronger (ca. 220 kJ·mol−1 greater) compared to Mg−Mg, suggesting a similar dissociation mechanism to the one described for F:Be−Be:F. The strength of the Mg:F interaction is a reflection of the oxidation of Mg atoms to Mg+, simultaneous to the gain of an electron by F•, which adopts anionic character. Strong similarities were also found between the pairs Mg:F/ Mg−Mg and Be:F/Be−Be as for the bonding properties, within the F:M−M:F (where M stands for Mg or Be). Mg:F

interaction presents a positive value for the Laplacian ∇2ρ(r) denoting its ionic character. Additionally, ELF locates a V(Mg,F) disynaptic basin (see Figure 6), and the NBO second-order analysis of the energies reveals significant charge transfer from the L to the metal, LP(F) → BD*(Mg,Mg) and LP(F) → pMg, amounting to 71 and 126 kJ·mol −1 , respectively. Regarding the Mg−Mg metallic bond, it is described as a 2c,2e− bond by ELF and NBO approaches, while QTAIM locates a NNA at the midpoint of the internuclear distance. Once more, the formation of NNA could be attributed to the redistribution of the electron density due to reinforcement of the Mg−Mg bond. Nevertheless, it must be noted that no NNAs have been reported at any bond distance for the isolated Mg2 molecule.62 Further insight into the nature and origin of NNAs will be the subject of future works in our group.

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CONCLUSIONS The present theoretical study shows that the complexes formed by the association of Be2 with radical ligands (L) present Be− Be bonds that are among the strongest reported in the literature, L = [CN]• leading to the strongest one. The strength of the Be−Be interaction can be explained as the result of the oxidation of the Be2 moiety via charge transfer toward the radical ligands that would deplete the doubly occupied antibonding orbital (σ*BeBe). Thus, these complexes could be rather described as the interaction between Be22+ and anionic ligands L−. According to our bonding analysis, the Be−Be bond in these complexes could be described as a classical 2c,2e− bond; however, the strong electronic density reorganization induced by charge depletion around the Be−Be internuclear region would lead to the formation of NNA between the two Be atoms, nonexistent in the isolated dimer. Similar bonding properties were characterized for the complexes resulting from the interaction of Mg2 molecules and radical fluorine ligands.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b11758. T1 diagnostic, geometrical parameters, and bonding analysis for the complexes studied (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (O.B.). *E-mail: [email protected] (I.C.). ORCID

Inés Corral: 0000-0002-9455-4906 2263

DOI: 10.1021/acs.jpca.7b11758 J. Phys. Chem. A 2018, 122, 2258−2265

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The Journal of Physical Chemistry A Present Address

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O.B.: Department of Organic Chemistry, Stockholm University, Arrhenius Laboratory, SE-106 91, Stockholm, Sweden. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the Project CTQ2015-63997C2 of the Ministerio de Economı ́a y Competitividad of Spain, FOTOCARBON-CM S2013/MIT-2841 of the Comunidad Autonóma de Madrid, and the COST Action CM1204. Computational time from the Centro de Computación Cientı ́fica (CCC) of Universidad Autónoma de Madrid is also gratefully acknowledged. I.C. gratefully acknowledges the “Ramón y Cajal” program of the Ministerio de Economı ́a y Competitividad of Spain.

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DOI: 10.1021/acs.jpca.7b11758 J. Phys. Chem. A 2018, 122, 2258−2265