Super Strong BeâBe Bonds: Theoretical Insight into the Electronic

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Super Strong Be-Be Bonds: A Theoretical Insight into the Electronic Structure of Be-Be Complexes with Radical Ligands Oriana Brea, and Ines Corral J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b11758 • Publication Date (Web): 26 Jan 2018 Downloaded from http://pubs.acs.org on January 30, 2018

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The Journal of Physical Chemistry

Super Strong Be-Be Bonds: A Theoretical Insight into the Electronic Structure of Be-Be Complexes with Radical Ligands Oriana Brea†* and Inés Corral*. Departamento de Química, Facultad de Ciencias. Módulo 13, and Institute of Advanced Chemical Sciences (IadChem). Universidad Autónoma de Madrid. Campus de Excelencia UAMCSIC, Cantoblanco, 28049-Madrid. Spain. †

Present Address: Stockholm University. Department of Organic Chemistry, Arrhenius Laboratory, SE-106 91, Stockholm, Sweden. *Corresponding author: [email protected], [email protected]

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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)/ccpVTZ. 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 this kind of complexes are thermodynamically stable and, thus, that they could be experimentally detected. Moreover, among all 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 a charge transfer towards 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:BeBe:F.


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INTRODUCTION The lack of experimental and theoretical information about the beryllium molecule and its derivatives obeys 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 are all 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, since at these temperatures Be vapor is almost monoatomic; and on top of that, beryllium is very easily oxidized. Despite all these technical challenges, in 1984, Bondybey and collaborators obtained Beryllium molecule 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 2.45Å.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 the accurate description of this system. Full Configuration Interaction (FCI) method, for example, calculates a single minimum at 2.47Å, in line with the experimental data (see Figure 2 and ref 1719

). The computational cost of the FCI method is, however, prohibitive 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 they provide for the bond (see Figure 1).


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1. Repulsive Be-Be bond: Hartree Fock (HF) and full-valence 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) describe the Be molecule as a Van Der Waals complex, with a Be-Be bond distance around of 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 sub-divided into 2 subgroups considering the nature of electron correlation 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. Multi-determinantal methods: Second-order perturbation theory based on the full-valence CASSCF reference wave functions [CASPT2/CASSCF(4,8)] improve CASSCF results. However, this method still does not reproduce the FCI potentials, unless the active space is increased to (4,16).


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Figure 1. Potential energy curves for the ground state of Be2, calculated at different levels of theory with the cc-pVTZ basis set. The discrepancy among theoretical methods has awakened a controversial debate around the real nature of the bond in Be-Be molecule. Is Be2 a Van der Waals complex? Is the Be-Be bond too weak to be considered a covalent bond? 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 non-dynamical electron correlation, as a result of two the 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 the non-dynamical electron correlation nature of this bond. The challenging accurate representation of the Be2 molecule has also been connected to the weakness of the Be-Be bond, 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 Prof. Mó, and Yáñez, and collaborators have been of remarkable importance. They have proposed the formation of super strong Be-Be bonds upon electron attachment,23 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 CO38, N-heterocyclic carbenes (NHCR, where R stands for the cycle substituent)39 and fluorine22 beryllium complexes previously studied by other authors (See Figure 2).


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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 Ref

38

(4CO),

39

(NHCR) and

22

(F). The dotted line represents the BDE for the isolated Be2 molecule.

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 (LP) of the CO and hybrid s-, p- orbitals of Be, followed by a πbackdonation between the 2pBe and the π*CO orbitals at MP4(SDQ)/6-31G*(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 the isolated molecule) with the BDE amounting to 209 kJ·mol-1 (~200 kJ·mol-1 stronger than 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


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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 multi-center 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 CCSD(T)/cc-pVTZ level of theory. However, the Be-Be bond distance was found to be longer than 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 complex, the ground state being characterized by a triplet multiplicity. 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]·,[CH2]·, [NH2]·, [OH]· and F·). What is the nature of the Be2 bond in this type of complexes? Can these systems be accurately described by means of single-reference methodologies? Why does the Be-Be bond become up to thirty times stronger in this type of systems compared to the isolated molecule? Are some of the question 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 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). The 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 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


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on a single atom and can be classified either as core or lone pairs. 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 of 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 the bonding analysis. This method does not perform a 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 a second order perturbation analysis. To this purpose, we have used the NBO-6.0 program.53

RESULTS AND DISCUSSIONS 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 the L:Be-Be:L complexes considered in this study are characterized by a mono-reference wave function, according to the T1 diagnostic (See Table S1).54 This result can be readily explained considering the valence electronic configurations of Be2 and its ionic forms: Be2 = (σBeBe)2(σ*BeBe)2, Be2+ = (σBeBe)2(σ*BeBe)1, and Be22+ = (σBeBe)2(σ*BeBe)0. The multi-reference character of the neutral molecule arises from the double occupation of the σ anti-bonding orbital, which facilitates excitations towards the lowlying pBe orbitals. The pBe orbitals lie, however, higher in energy in the cations, and indeed it has


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been found that while single-reference methodologies fail in the description of Be2, these methods are able to correctly reproduce the 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 the complexes 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 towards 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 closedshell and, thus, single-reference, explaining the values below 0.2 found for the T1 diagnostic.

Table 1. NBO charge for the Be atoms (qBe) and the L ligands (qL). The electronic configuration for the Be atoms within the L:Be-Be:L complexes is also shown. 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). L

qBe (au)

qL (au)

Be Electronic configuration

F·

0.86

-0.86

[He]2s0.93 2p0.20

CN·

0.85

-0.85

[He]2s0.99 2p0.14

CH3O·

0.81

-0.81

[He]2s0.96 2p0.22

CH3·

0.80

-0.80

[He]2s1.04 2p0.15

OH·

0.82

-0.82

[He]2s0.96 2p0.21

NH2·

0.80

-0.80

[He]2s0.99 2p0.19


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Geometric and Bonding Properties of the L:Be-Be:L complexes For all the complexes, four different isomers were initially considered: linear (scheme 1(a)), trans (scheme 1(b)), cis (scheme 1(c)) and scissor-like (scheme 1(d)) structures. In all 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.

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 and dicationic forms of Be2. The Be2 complexation with the radical ligands considered in this study leads to Be-Be bond distances 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.


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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 CCSD(T)/cc-pVTZ level of theory. For the neutral Be dimer, the CASPT2//CASSCF(4,16)/ccpVTZ protocol was used instead. 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 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 non-interacting 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+. Whilst the molecular graph of Be2 free neutral molecule shows a Be-Be BCP carrying a small value of ρ (0.030 au), those of Be22+ dication and Be2 moieties in the complexes are characterized by the


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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 to 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 functions (DFT, CASSCF, HF), and basis sets (ccpVXTZ with X=D, T and Q), in the range of Be-Be bond distances comprised between 1.5 and 5.0 Å. In all the 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.


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Figure 4. Comparison of wave function analysis for Be2, Be22+ and CN:Be-Be:NC complex. 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 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 B3LYP/cc-pVTZ level of theory.

For all the systems (Be2, Be22+ and L:Be-Be:L) considered, QTAIM registers the concentration of electron density along the Be-Be bonding region [∇2ρ(r)

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