Bonding in M(NHBMe)2 and M[Mn(CO)5]2 complexes (M=Zn, Cd, Hg; NHBMe=(HCNMe)2B): divalent group 12 metals with zero oxidation state

Quantum chemical studies using density functional theory were carried out on M(NHBMe)2 and M[Mn(CO)5]2 (M=Zn, Cd, Hg) complexes. The calculations suggest that M(NHBMe)2 and M[Mn(CO)5]2 have D2d and D4d symmetry, respectively, with a 1A1 electronic ground state. The bond dissociation energies of the ligands have the order of Zn > Cd > Hg. A thorough bonding analysis using charge and energy decomposition methods suggests that the title complexes are best represented as NHBMe⇆M0⇄NHBMe and Mn(CO)5⇆M0⇄Mn(CO)5 where the metal atom M in the electronic ground state with an ns2 electron configuration is bonded to the (NHBMe)2 and [Mn(CO)5]2 ligands through donor–acceptor interaction. These experimentally known complexes are the first examples of mononuclear complexes with divalent group 12 metals with zero oxidation state that are stable at ambient condition. These complexes represent the rare situation where the ligands act as a strong acceptor and the metal center acts as strong donor. The relativistic effect of Hg leads to a weaker electron donating strength of the 6s orbital, which explains the trend of the bond dissociation energy.

We report in this work a theoretical analysis on M(NHB Me ) 2 and M[Mn(CO) 5 ] 2 (M=Zn, Cd, Hg) using state-of-the-art charge and energy decomposition methods, which shows that the title complexes are best described with dative bonds NHB Me ⇆M 0 ⇄NHB Me and Mn(CO) 5 ⇆M 0 ⇄Mn(CO) 5 , where M is in the electronic ground state with an ns 2 electron configuration binding to with (NHB Me ) 2 and [Mn(CO) 5 ] 2 ligands via donor-acceptor interaction. It is suggested that the adducts are the first examples of mononuclear complexes of divalent group 12 metals with zero oxidation state that are stable at ambient condition.
In the EDA method, the interaction energy (ΔΕ int ) between two prepared fragments is divided into three energy terms, viz. the electrostatic interaction energy (ΔE elstat ), which represents the quasiclassical electrostatic interaction between the unperturbed charge distributions of the prepared atoms, the Pauli repulsion (ΔE Pauli ), which is the energy change associated with the transformation from the superposition of the unperturbed electron densities of the isolated fragments to the wavefunction that properly obeys the Pauli principle through explicit antisymmetrization and renormalization of the product wavefunction, and the orbital interaction energy (ΔE orb ), which is originated from the mixing of orbitals, charge transfer and polarization between the isolated fragments. Use of D3(BJ) gives additional dispersion interaction energy (ΔE disp ) between two interacting fragments. Therefore, the interaction energy (ΔΕ int ) between two fragments can be defined as: The orbital term may be further divided into contributions from each irreducible representation of the point group of the interacting system as follows: The EDA-NOCV combination allows the partition of ΔE orb into pairwise contributions of the orbital interactions, which gives important information about bonding. The charge deformation Δρ k (r) which is originated from the mixing of the orbital pairs ψ k (r) and ψ -k (r) of the interacting fragments gives the size and the shape of the charge flow because of the orbital interactions (Eq. 3), and the corresponding ΔE orb reflects the amount of orbital interaction energy coming from such interaction (Eq. 4).

Results and discussion
We calculated the model compounds M(NHB Me ) 2 (M=Zn, Cd, Hg) in place of M(NHB Dipp ) 2 where the larger Dipp group linked to N centers is replaced by the Me group. The minimum energy geometries of the resulting complexes have a D 2d symmetry and 1 A 1 electronic state ( Fig. 1). The M-B bond lengths in M(NHB Me ) 2 match excellently with those of the experimental ones in M(NHB Dipp ) 2 . The B-M-B moiety in M(NHB Me ) 2 is perfectly linear, while due to the unsymmetrical structure of M(NHB Dipp ) 2 , the B-M-B angle in the experimental geometries ranges from 177.4° (Cd) to 179.1° (Hg). The only larger difference between the geometries of the model compounds and the experimental structures concerns the torsional angle t(N1B1B2N2) which is 90° in the model systems while it ranges from 41.8 (Cd) to 46.3 (Hg) in M(NHB Dipp ) 2 . This is most likely caused by the different steric interactions of the larger Dipp group compared with Me group. But the excellent matching in bond distances and B-M-B angles between the calculated and experimental values indicates that the model systems can be safely used to reflect the bonding situation in the experimental complexes.
The equilibrium geometries of M[Mn(CO) 5 ] 2 (M=Zn, Cd, Hg) have D 4d symmetry at the BP86-D3(BJ)/def2-TZVPP level which is in contrast to the X-ray structure of Hg[Mn(CO) 5 ] 2 which has approximately a D 4h symmetry. The calculated D 4h symmetric structure has a small imaginary frequency which corresponds to the internal rotation of two Mn(CO) 5 units with respect to each other (see Table S1). Very soft modes of rotation and small relative energies indicate very flat potential energy surface with respect to internal rotation, and the complexes are very floppy. Therefore, the D 4h symmetry in Hg[Mn(CO) 5 ] 2 is more likely because of solid state effect in the crystal structure. Figure 1 also shows the computed bond dissociation energy (BDE) for the most favorable dissociation pathway, ML 2 → M + 2L, while the complete set of BDE values for three possible dissociations via homolytic bond cleavage (ML 2 → M + 2L), heterolytic bond cleavage (ML 2 → M 2+ + 2L − ) and a mixture of them (ML 2 → M + + L + L − ) is given in Table S2, where L is NHB Me or Mn(CO) 5 . The BDE value at 298 K ranges from 69.4 kcal/mol to 81.6 kcal/mol for M(NHB Me ) 2 and from 31.7 kcal/mol to 51.9 kcal/mol for M[Mn(CO) 5 ] 2 showing the order Zn > Cd > Hg. The same order was earlier found for  [62]. The calculations suggest that NHB Me is a much stronger ligand than Mn(CO) 5 . Note that the stability order contradicts the usual trend for transition metals which usually shows the heaviest (sixth row) element having the maximum BDE value [63]. The reason can be understood from the EDA-NOCV results (vide infra).
We employed the QTAIM method to analyze the electronic structure of the complexes. Figure 2 shows the contour plots of the Laplacian of electron density (∇ 2 ρ(r)) at the Zn-B-N and Zn-Mn-C planes of Zn(NHB Me ) 2 and Zn[Mn(CO) 5 ] 2 complexes, respectively. The Laplacian distributions of the complete set of the systems are displayed in Figure S1. For a given type of systems, the distribution of  Figure 2 gives also the partial charges of the central atoms q(M) in the two sets of complexes. The group-12 metals carry a positive charge, which has the order Zn < Cd < Hg. The partial charges suggest that the [Mn(CO) 5 ] 2 ligands are stronger donor than (NHB Me ) 2 .
More details about the nature of chemical bonding between M and NHB Me or Mn(CO) 5 groups can be gained from the results of EDA-NOCV method. To get a reliable bonding situation in the complexes in the EDA-NOCV method, the selection of proper charge and electronic state of the interacting fragments is very crucial. One of the strengths of this method is that if there are more than one partitioning scheme available, one can choose the most suitable scheme to describe the bonding by using the size of ΔE orb as a probe. For a given interaction, those fragments, which give the lowest ΔE orb value, are the best one to describe the bonding situation as it indicates that the chosen fragments are most nearly prepared as those in the complex [69][70][71][72][73][74] Tables S3-S8. A comparison of the relative size of ΔE orb value indicates in all cases that the best description is provided using M in the ground state with (ns) 2 (np) 0 valence electronic configuration and (L) 2 in singlet spin state interacting through donor-acceptor type of bonding. Therefore, the complexes should be represented as NHB Me ⇆M 0 ⇄NHB Me and Mn(CO) 5 ⇆M 0 ⇄Mn(CO) 5 , where M is in the zero oxidation state.
Detailed numerical results of EDA-NOCV for the most favorable scheme are provided in Tables 1 and 2. Similar to the BDE values, the intrinsic interaction between M and (L) 2 is the strongest for M=Zn followed by Cd and Hg, and for Except for Zn(NHB Me ) 2 , the M-L interaction is somewhat more electrostatic than covalent. Dispersion interaction is only responsible for 3-6% of total attraction. There are differences in the origin of obtained order in ΔE int between M(NHB Me ) 2 and M[Mn(CO) 5 ] 2 complexes. In the former case, increased Pauli repulsion and weakened ΔE orb values in going from Zn to Cd to Hg are responsible for the observed trend, whereas in the latter one, both weakened ΔE orb and ΔE elstat are accountable for this.
The breakdown of the ΔE orb into pairwise orbital interaction provides the most important information regarding the bonding between M and ligands. We have tabulated seven distinct pairwise contributions of ΔE orb for M(NHB Me ) 2 ( Table 1) and nine such orbital terms for M[Mn(CO) 5 ] 2 ( Table 2). Corresponding deformation densities Δρ for Zn complex are provided in Fig. 3 which help to understand the involved orbitals in the interaction. The Δρ plots for Cd and Hg homologues are very similar to the Zn complex. The results show that the strongest orbital contribution, ∆E orb (1) , is originated from the in-phase L←M(s)→L σ backdonation which accounts for 64-72% of total ΔE orb value. Note that because of relativistic contraction of 6s orbital in Hg, L←Hg(s)→L σ backdonation is the weakest one. The next strongest interaction, ∆E orb (2) , comes from the out-of-phase L→M(p σ )←L σ donation which is responsible for 17-22% of total ΔE orb . These two interactions together make the 81-94% of covalent interaction.
There are two weak degenerate L→M(p π )←L π donations ∆E orb (3) and ∆E orb (4) , which only contribute 4-7% to ΔE orb . There is also some d orbital participation in the L←M(d)→L backdonation, albeit even weaker than the participation of the p π orbitals. In case of M(NHB Me ) 2 , the participation of only three d orbitals is found, whereas in M[Mn(CO) 5 ] 2 , all five d orbitals are involved in the bonding where the CO groups also participate in the orbital interactions. Nevertheless, the combined effect of d orbitals provides only 3-5% to the covalent interaction. Interestingly, the present cases represent a rather rare scenario where L = NHB Me , Mn(CO) 5 act as dominant acceptor and M=Zn, Cd, Hg act as donor centers. We have recently carried out EDA-NOCV calculations on [M{Fe(CO) 5 } 2 ] + (M=Cu, Ag, Au), the isoelectronic complexes of M[Mn(CO) 5 ] 2 (M=Zn, Cd, Hg), taking M + as one fragment and (Fe(CO) 5 ) 2 as another [65]. The intrinsic interaction between coinage metal cation and (Fe(CO) 5 ) 2 is much stronger than that in the latter complex where both enhanced orbital and electrostatic interaction in the cationic complexes are responsible for this. Notably, despite cationic charge, [Fe(CO) 5 ]←M + (d)→[Fe(CO) 5 ] backdonation is much stronger (responsible for 13-24% of ΔE orb ) than Mn(CO) 5 ←M(d)→Mn(CO) 5 backdonation.
The dominant orbital interaction ∆E orb(1) coming from the L←M(s)→L σ backdonation is in agreement with the calculated partial charges q(M) given by the AIM method (Fig. 2). But the order of the donor strength of the group-12 atoms Zn > Cd > Hg given by ∆E orb(1) is opposite to the order of  53.3 46.5 47.4 the partial charges. Also, the [Mn(CO) 5 ] 2 ligands are more weakly bonded to the group-12 atoms than the (NHB Me ) 2 groups, although the charge donation of the former is larger compared with the latter. This shows that the size of the charge migration is not always a measure of the associated stabilization energy. This is a warning against premature correlations between charge migration and energy changes.  Funding Open Access funding enabled and organized by Projekt DEAL.

Declarations
Conflict of interest There are no conflicts or competing interests. The isovalue is 0.0001 au. The direction of the charge flow of the deformation densities is red → blue Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.