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Taming the Antiferromagnetic Beast: Computational Design of Ultrashort Mn−Mn Bonds Stabilized by N‐Heterocyclic Carbenes

Abstract The development of complexes featuring low‐valent, multiply bonded metal centers is an exciting field with several potential applications. In this work, we describe the design principles and extensive computational investigation of new organometallic platforms featuring the elusive manganese‐manganese bond stabilized by experimentally realized N‐heterocyclic carbenes (NHCs). By using DFT computations benchmarked against multireference calculations, as well as MO‐ and VB‐based bonding analyses, we could disentangle the various electronic and structural effects contributing to the thermodynamic and kinetic stability, as well as the experimental feasibility, of the systems. In particular, we explored the nature of the metal‐carbene interaction and the role of the ancillary η 6 coordination to the generation of Mn2 systems featuring ultrashort metal‐metal bonds, closed‐shell singlet multiplicities, and positive adiabatic singlet‐triplet gaps. Our analysis identifies two distinct classes of viable synthetic targets, whose electrostructural properties are thoroughly investigated.


Introduction
The pioneering work on rhenium clusters by Cotton in the 1960s, with the attribution of the first double, [1] triple, [2] and quadruple [3] bonds between transition metal atoms, has opened the intriguing field of multiple metal-metal bonding. [4] Since then, this topic has expanded significantly, [5] with a myriad of novel compounds featuring homonuclear or heteronuclear metal-metal bonds, [6] and some whose bond orders between the metal atoms are even greater than four. [7] The motivation for studying these systems arises from fundamentals [8] to a desire of elucidating novel molecular motifs with peculiar electronic structures and bonding properties, which culminates in potential chemical applications. As a consequence, compounds featuring metal-metal bonds are now widely used in organometallic catalysis, [9] small molecule activation, [10] photochemistry, [11] and in the development of metal-organic frameworks [12] and extended metal atom chains. [13] Metal-metal bonds also play a crucial role in biological processes, not only stabilizing low-valence states and initiating oxidative addition reactions in metalloenzymes, [14] but also allowing the transfer of phosphate groups in for example DNA polymerases. [15] In striking difference with other homonuclear diatomic molecules featuring first-row transition metals, the naked Mn 2 species is a weakly bonded van der Waals dimer featuring antiferromagnetic coupling and a very long metal-metal distance of 3.7-3.9 Å. [16] Up to now, only a few systems featuring MnÀ Mn bonds in the range of 2.2-2.7 Å are known. [17] Recently, Alonso-Lanza and co-workers [18] predicted that an ultrashort MnÀ Mn bond of about 1.8 Å can be achieved in the 16-electron Mn 2 Bz 2 complex (Bz=C 6 H 6 , Scheme 1). However, the benzene ligand is not sufficiently bulky to stabilize the metal centers in Mn 2 Bz 2 and prevent them from further decomposition due to undesired reactions. In order to circumvent this problem and to design experimentally stable organometallic platforms featuring reactive metal-metal bonds, it is necessary to use appropriate ligands which are capable of shielding the metal centers.
Since the first synthesis of a persistent N-heterocyclic carbene (NHC) by Arduengo et al., [19] there is an increasing interest in the coordination chemistry of these compounds. The diversity of structures and electronic properties of NHCs and their complexes encouraged intense research in distinct topics, [20] from fundamentals to for example catalysis, [21] medicinal, [22] and photochemical [23] applications. Indeed, NHCs have been instrumental in enhancing the photophysical properties of organometallic compounds of first-row, Earth-abundant transition metal elements, [24] particularly those of iron [25] and cobalt, [26] making them promising materials for light-harvesting and photocatalysis. Another remarkable property of NHCs is their ability to stabilize unusual and reactive main group [27] and transition metal species. Consequently, completely new structures have been isolated and characterized, such as the boron dimer featuring double and triple bonds, [28] molecular silicon oxides, [29] doubly bonded Si 2 , [30] Ge 2 , [31] Sn 2 , [32] Al 2 , [33] and Ga 2 , [34] phosphorus clusters, [35] low-valent Be, [36] B, [37] C, [38] and Al [39] species, coinage metal atoms, [40] and many others. Moreover, NHCs have also been systematically incorporated in periodic systems [41] and extended networks, [42] and their ability to stabilize main group dimers into these structures is currently under investigation. [43] In parallel with the extraordinary development of the coordination chemistry of NHCs with main group and mononuclear transition metal species, these ligands have also been used to prepare stable derivatives of low-valent metal compounds featuring metal-metal bonds. Indeed, complexes of dinuclear Fe 0 stabilized by IMes and IDipp were synthesized, with Fe-Fe distances of 2.621 and 2.583 Å. [44] Stable low-valent, dinuclear metal-metal systems were also obtained by coordination with cyclic (alkyl)(amino) carbenes (CAAC), [45] particularly for homonuclear Au [46] and Co [47] motifs. In both cases, the metalÀ metal bond distances are in the range of 2.5-2.7 Å, and the systems have closed-shell singlet ground states. For Co 2 (CAAC) 2 , an ancillary η 6 coordination of the Dipp substituents at the nitrogen CAAC to the cobalt atoms is also present (Scheme 1), allowing the metal centers to achieve an 18electron configuration.
Inspired by the vast body of literature illustrating the ability of NHCs to stabilize elusive main group and transition metal species, in this work we perform a thorough computational exploration of the use of these ligands for stabilizing the manganese dimer (Scheme 1). In our approach, we investigate distinct Mn 2 L 2 species following the design principles depicted in Scheme 1, and make use of DFT calculations benchmarked against a multireference approach to investigate their main electrostructural features, aiming at selecting potential targets for future experimental realization.

Computational Details
We start our investigation by analyzing the Mn 2 Bz 2 system. This molecule was chosen for a preliminary benchmark study (see the Supporting Information for details) in order to derive an appropriate functional for the DFT calculations of the NHC-stabilized compounds, and also as a model system to investigate the role of the η 6 coordination on the stability of the Mn 2 dimer. By comparing the DFT results with high-level calculations based on the complete active space self-consistent field (CASSCF) method, [55] with active spaces of up to 14 electrons and 14 orbitals, and additional Nelectron valence state second-order perturbation theory (NEVPT2) [56] calculations, we adopted the PBE [57] -D3 [58] (BJ) [59] /def2-SVP;def2-TZVP (Mn) [60] level of theory as it provided the best results in comparison with the multireference calculations (from now on this basis set will be referred as bs1). Additionally, for a better comparison with the results obtained by Alonso-Lanza and others, [18] we also performed spin-polarized DFT calculations with plane-wave basis sets. These results are discussed in the Supporting Information.
In all cases, geometry optimizations and hessian calculations were obtained at the mentioned DFT level considering closed-shell singlet wave functions. All optimized geometries were characterized as minimum energy structures as all vibrational frequencies have positive eigenvalues. Additional calculations were performed considering triplet multiplicities in order to obtain the vertical and adiabatic singlet-triplet gaps (Δ ST ). Unless otherwise stated, the Δ ST values refer to the vertical ones. The following notation is used: In order to gain insights into the bonding situation of the systems, we performed calculations based on the intrinsic bond orbital (IBO), [61] natural bond orbital (NBO), [62] natural resonance theory (NRT), [63] and generalized valence bond at the perfect-pairing approximation (GVB-PP) [64] methods, the latter with the 6-31G* basis set. These distinct approaches gave qualitatively similar descriptions. We will mainly focus on the results obtained by analysis of the canonical Kohn-Sham molecular orbitals (MOs) and the GVB-PP mono-occupied orbitals, while further calculations obtained with the other approaches are found in the Supporting Information. Mayer bond orders (MBOs) [65] were also estimated for all systems.
Finally, we calculated the dissociation enthalpies at 298.15 K ( DH 0 298:15 ) and the thermochemistry of the ligand exchange reaction from Mn 2 Bz 2 to Mn 2 L 2 aiming at investigating the stabilization gain provided by the distinct carbene moieties. The kinetic stability of η 6 -coordinated Mn 2 L 2 systems was also investigated. The enthalpy of ligand exchange, ΔH ex , is calculated as: where H includes the zero-point energy and all thermal contributions to enthalpy, and L varies from L = I, IH to L = XVIII, B 2 NHC (Scheme 2). For this discussion, we also included truncated, uncoupled model systems of the type Mn 2 (Bz) 2 (IH) 2 (mod-A and mod-B). The stability of these species is analyzed by calculating the binding enthalpy, ΔH b defined as: All DFT calculations with Gaussian basis sets were performed in Gaussian 16, [66] while those with plane waves were done in VASP. [67] The multireference calculations were performed using ORCA 4.2. [68] The MBOs were obtained with Multiwfn 3.7. [69] NBO and NRT calculations were done with the NBO 7.0 program, [70] while the GVB-PP computations were performed with VB2000. [71] Results and Discussion

Computational description of Mn 2 Bz 2 and the η 6 coordination
In this section, we discuss the electronic structure of Mn 2 Bz 2 , as it provides a basis for understanding the η 6 interaction between manganese and the phenyl group in the carbene-stabilized Mn 2 systems. At the CASSCF (14,14)/bs1 level of theory, the Mn 2 Bz 2 species converges to a structure of D 6h symmetry, with an MnÀ Mn bond of 1.74 Å ( Table S1 in the Supporting Information). This metal-metal bond is slightly shortened in comparison to the one reported by Alonso-Lanza and co-workers [18] using DFT with plane-wave basis set. The weight of the closed-shell configuration is 0.62, with no particular excited configuration contributing more than 0.025 to the overall CASSCF wave function. The biradical character index y 0 of Mn 2 Bz 2 , calculated following the Yamaguchi formula [72] as shown in Equations (S1)-(S4), is 0.03 at this level of theory. Indeed, the exploratory DFT calculations using either the spin-polarized formalism with plane waves (Table S2) or the broken-symmetry approach also converged to a closed-shell singlet with no spin density at the metal atoms. At the NEVPT2/CASSCF(10,10)/bs1 level, the vertical Δ ST gap is 35.9 kcal mol À 1 , with dynamic correlation stabilizing the triplet by 13.5 kcal mol À 1 . Taken together, these results give strong evidence that the singlet state has no biradical character, and that the system can be appropriately described by single-reference methods. As for the DFT calculations with a singlet closed-shell wave function and Gaussian basis sets, our results indicate that hybrid functionals significantly underestimate both the MnÀ Mn bond distance and Δ ST in comparison to those obtained with multireference approaches, as shown in Table S3. The best agreement with the CASSCF/NEVPT2 results comes from calculations in the PBEÀ D3(BJ)/bs1 level, where the MnÀ Mn bond length is 1.73 Å, and Δ ST is 30.6 kcal mol À 1 . At this level of theory, the optimized structure also has D 6h symmetry, with the Mn 2 moiety pointing to the center of the benzene rings. The angle between the centroid of the benzene ring and the two Mn atoms, herein labeled as θ(BzÀ MnÀ Mn), is, therefore, 180°( Figure 1a). Interestingly, an isoenergetic, staggered isomer with a slightly distorted D 6d symmetry is also found ( Figure S2), suggesting that the benzene ligands in Mn 2 Bz 2 have some degree of fluxionality, and that the system could be described as a nanowheel-type compound.
In order to investigate the bonding situation in Mn 2 Bz 2 , we show in Figure 1b the canonical Kohn-Sham molecular orbitals of the system. HOMO-3 is formed by the + , + combination, with a 1g symmetry, of the Mn d z 2 orbitals along the intermetallic vector, and composes the metal-metal sigma bond. In turn, HOMO-2 and HOMO-1 are degenerate sets of two orbitals, related to the MnÀ Mn π and δ bonds. These five orbitals, which are bonding with respect to the MnÀ Mn bond, are contrasted with the remaining degenerate, low-lying HOMOs, which present antibonding character in the intermetallic region. The formal bond order of 3, as suggested by bonding/antibonding orbital counting, is corroborated by distinct computational approaches. The calculated Mayer Bond Order of the MnÀ Mn bond is 2.45, while that calculated using the NRT approach is exactly 3.00. Inspection of the GVB-PP orbitals, depicted in Figure 1c, reveals three bonding pairs located at the metal À metal region, related to the formation of one sigma and two π bonds, with the remaining metal d orbitals participating explicitly in the metal-benzene bonding. A similar bonding profile is obtained by inspecting the intrinsic bond orbitals (IBOs), whose metal-metal and metal-benzene bonding pairs are shown in Figure S3.
In opposition to their antibonding profile with respect to the MnÀ Mn bond, the degenerate HOMOs present a strong bonding character in the MnÀ Bz region. The influence of these orbitals on the metal-ligand interaction is also evidenced by analyzing the structure of the system where the electrons occupying these orbitals are removed, thus leading to the [Mn 2 Bz 2 ] 4 + tetracation (Figure 1a). In this case, the molecular

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Full Paper doi.org/10.1002/chem.202101116 symmetry is reduced to C 2 , and θ(BzÀ MnÀ Mn) goes to 156°. The MnÀ Bz bond distance elongates by about 0.4 Å (or 25 %), reaching 1.84 Å in the tetracation. This leads to a severe stability loss in the multiply charged system. A reduction of almost 30 kcal mol À 1 in Δ ST is experienced by the system after removal of the e 2u electrons, thus highlighting the important role of the η 6 interaction in the stabilization of the manganese dimer in its closed-shell singlet state. Interestingly, the MnÀ Mn bond length is not disturbed in the [Mn 2 Bz 2 ] 4 + system, despite the formal bond order increase to a value of five. This can be attributed to the Coulomb repulsion of the positive charges, which prevents the equilibrium bond length between the two MnBz fragments to be shortened.
Finally, the LUMO of Mn 2 Bz 2 (Figure 1b) has an a 2u symmetry, and is composed of a + ,À combination of the two Mn d z 2 orbitals. It is, therefore, antibonding with respect to the MnÀ Mn bond. The HOMO-LUMO gap is 1.49 eV at the PBEÀ D3(BJ)/bs1 level of theory, more than twofold as that calculated for the tetracation (0.61 eV). Interestingly, interaction with this orbital will play a role in the bonding situation of the Mn 2 L 2 systems, as we discuss in the following sections. Table 1 characterizes the various Mn 2 complexes with the ligands depicted in Scheme 2. The optimized structures of selected complexes are given in Figure 2 (other structures can be found in Figure S4). Inspection of the structures clearly indicates that in all cases the Mn 2 moiety is shielded by the carbene ligands. To investigate the influence of the covalent connection between benzene and the carbene moiety, we also calculated two model systems of type Mn 2 (Bz) 2 (IH) 2 , where the carbene and the benzene ligands are not covalently connected. These two isomers, whose geometries are fully optimized minimum energy structures of the potential energy hypersurface of Mn 2 (Bz) 2 (IH) 2 , are shown in Figure 3, and are labeled herein as mod-A and mod-B. While the mod-A structure, where the NHC moieties are terminal ligands oriented parallel with respect to the MnÀ Mn bond, resembles the ones observed in most of the Mn 2 L 2 systems, in mod-B the NHCs are bridging ligands oriented perpendicularly across the MnÀ Mn bond. To our surprise, mod-B is more stable than mod-A. Consequently, Mn 2 systems composed of more flexible carbenes exhibit structural features which are more closely related to mod-B.

Overview of the Mn 2 L 2 systems
Besides various geometrical parameters, Table 1 Table 1 underlines that the combination of the benzene and carbene moieties indeed leads to considerably more stable complexes than the parent system Mn 2 Bz 2 , as expected based on the 18electron rule. The positive ΔH ex values of ligands without benzene moieties (I-III) show that the η 6 coordination is more important for the stabilization than the carbene moieties. The MnÀ Mn bond lengths of these complexes (1)(2)(3), which are in the range of 1.73-1.75 Å, are shorter than those of the carbene complexes featuring η 6 coordination (1.87-2.08 Å), but still

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Full Paper doi.org/10.1002/chem.202101116 slightly longer than that of the parent Mn 2 Bz 2 compound. The ΔH ex values of ligands in which the aromatic rings are directly coupled to the nitrogen of the imidazol-2-ylidene carbene (ligands IV-VI) range between À 66 and À 77 kcal mol À 1 . If the flexibility is increased by the presence of CH 2 bridges (ligands VII-VIII), the ΔH ex values increase to À 88 and À 94 kcal mol À 1 , revealing that the stability of the complexes is narrowed if the carbene and the phenyl moieties cannot adopt their optimal positions. This is underlined by the binding enthalpy of À 99 kcal mol À 1 computed for the model system Mn 2 (Bz) 2 (IH) 2 mod-B in which both ligands can orient independently. Accordingly, all DH 0 298:15 values of the Mn 2 L 2 complexes featuring the η 6 coordination (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) are significantly larger than that of Mn 2 Bz 2 , highlighting once more the thermodynamic stability of these systems. Figure 3 indicates that in the optimal geometry (mod-B) the benzene moieties behave as terminal ligands with η 6 orientation, while the NHCs are interacting with Mn 2 as bridging ligands, forming a butterfly-shaped C 2 Mn 2 structure. In mod-B the carbene moieties stand perpendicular to the MnÀ Mn bond,

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Full Paper doi.org/10.1002/chem.202101116 while they are parallelly oriented in all of the Mn 2 L 2 systems where the aromatic ring is directly attached to the carbene backbone. This orientation is necessary so that the η 6 coordination can be formed in such molecules featuring rigid carbene ligands. As a consequence, the carbene moieties are also shifted from the middle of the Mn 2 bond to the Mn centers, and the systems adopt a structure similar to mod-A. The decrease in stabilization experienced by these systems in comparison to the optimal geometry of mod-B can be analyzed by comparing the energies of the model systems. The difference in ΔH b going from mod-B to mod-A is about 12 kcal mol À 1 , and results from the reorientation of carbene moieties and the deviation of the benzene moiety from the perfect η 6 coordination. The importance of both effects is underlined by analyzing the structures of the Mn 2 complexes (7 and 8) with ligands VII and VIII. In both cases, the higher flexibility is not solely used to enforce a perfect η 6 orientation. In contrast, the system adopts a compromise between the optimal orientations of the carbene and the benzene moieties. Interestingly, in the highly stable complexes (e. g., mod-B, 7, and 8) with (partly) perpendicularly oriented NHCs, the Mn 2 bond is considerably longer (> 2.07 Å) than in those complexes in which the carbenes adopt parallel orientations (< 1.9 Å).
For the various complexes featuring imidazol-2-ylidene carbenes, strongly stabilized systems are obtained if the flexibility of the ligand is high enough to allow a good compromise between the perfect positions of the carbenes and the aromatic rings. By comparing these complexes with the ones featuring other carbene backbones, it becomes obvious that the nature of the carbene also influences the stability of the systems. Inspection of the ΔH ex values reveals that the most stable complex among the ones featuring the ligands shown in Scheme 2 is the one bearing the DACMes ligand (11, L = XI, ΔH ex = À 101 kcal mol À 1 ). This can be attributed to the fact that the diamidocarbene ligands have the greatest π-accepting character among the ones studied herein, as also evidenced by the relatively short CÀ Mn bond of 11 and 13. Conversely, replacement of imidazol-2-ylidene by CAAC (10, L = X) does not lead to a significant change in ΔH ex , even with the latter presenting the largest Δ ST gap among the systems of Scheme 2. Compounds with sulfur (14, L = IV, ATC) or boron (18, L = XVIII, B 2 NHC) in the carbene backbone also behave very similar to those of the classic NHC ligands, indicating that similar bonding effects are present. As these species are more difficult to handle experimentally and we do not predict exceptionally high stabilities, they will not be further discussed.
Interestingly, complexes 11 and 13 have large ΔH ex values despite being the systems where the θ(BzÀ MnÀ Mn) angles deviate the most from the ones of the perfect BzÀ Mn orientation. It is therefore obvious that the flexibility of these ligands is not high enough (Figure 2), and could be increased if CH 2 groups are introduced in the substituents at the nitrogen. However, the replacement of the Mes groups in 11 by the Bn groups in 12 does not make the ΔH ex of the latter more negative, in spite of its higher flexibility. This happens because of a steric clash between the Bn groups that are not involved in the η 6 coordination, which destabilizes 12 despite its better MnÀ L interaction. This becomes obvious after analyzing the ΔH ex values of the model systems 11' and 12' (Figure S5), where these nonparticipating groups are replaced by hydrogen. This modification makes 12' the system where ΔH ex has the most negative value among all the ones studied herein (À 111 kcal mol À 1 ), being around 10 kcal mol À 1 larger than that of 11'. This result evidences once more the important role of the η 6 coordination for the stabilization of the MnÀ Mn bond, and that the complex interplay between the nature and flexibility of the carbene, the relative position of the interacting phenyl rings, and steric effects of nonparticipating substituents must be taken into account for designing complexes capable of stabilizing highly reactive species featuring metal-metal bonds.
We also investigated the kinetic stability of the Mn 2 L 2 complexes featuring the η 6 coordination. These calculations were conducted for the phenyl-substituted imidazolylidene (IPh) ligand, and the results are summarized in Figure 4 (see Figures S7 and S8 for selected relaxed scans). The free energy of dissociation of the MnÀ C bond of Mn 2 (IPh) 2 (A) to compound B is uphill by 31.2 kcal mol À 1 . In turn, ligand dissociation from B is also uphill by 43.2 kcal mol À 1 , with compound C lying 74.4 kcal mol À 1 above A. The dissociation of the second MnÀ C bond, which leads to compound D, has a kinetic barrier (TS1) of 40.1 kcal mol À 1 , with D lying 110.5 kcal mol À 1 above A. In this structure, the Mn 2 motif is only interacting with the phenyl moiety. Ligand dissociation from D to form isolated Mn 2 and 2 IPh species is nearly equiergic. The coupling of the two IPh ligands to form the alkene PhI=IPh is exergonic by merely 6.4 kcal mol À 1 . Therefore, our results strongly suggest that the η 6 -coordinated Mn 2 L 2 complexes are kinetically stable towards dissociation to isolated Mn 2 and carbene ligands, and that their formation from the isolated constituents should not be kinetically hindered.
Comparing the stability of the various complexes, the following questions arise. i) Why do the NHC moieties try to

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Full Paper doi.org/10.1002/chem.202101116 orient perpendicular to the Mn 2 bond in the systems featuring η 6 coordination, following mod-B, and ii) why does it lead to a lengthening of the Mn 2 bond? iii) How does the bonding situation change going from perpendicularly oriented carbenes positioned across the MnÀ Mn bond to parallelly oriented carbenes which are shifted towards the Mn centers? iv) Why does the C 2 Mn 2 ring is butterfly-shaped rather than planar? These issues are addressed in the following section.

Understanding the electrostructural properties of Mn 2 L 2
In order to investigate the origin of the main structural and electronic features of the Mn 2 L 2 systems, we focus on the description of the model systems mod-A and mod-B (Figure 3), as well as on the corresponding systems 1 and 1 b (see Figure 5), which features the IH ligand, but not the benzene rings. Selected structural properties and canonical Kohn-Sham molecular orbitals of mod-A and mod-B are shown in Figure 3. A comparison of the structures of 1 and 1 b can be visualized in Figure 5. The molecular orbitals of 1 are shown in Figure 6.
The isomer mod-A, which bears structural similarities with most of the Mn 2 L 2 systems, is characterized by the presence of terminal NHC and Bz ligands at both metal centers, with the NHCs parallelly oriented to the metal-metal bond. Due to the steric hindrance between the NÀ H hydrogen and the hydrogen attached to benzene, the two NHCs are positioned almost orthogonal to each other. Because of the parallel orientation of the NHCs, the benzene rings distort significantly from their optimal position due to sterics, and θ(BzÀ MnÀ Mn) reaches 146°f or mod-A. In contrast, if the NHCs are perpendicularly oriented across the MnÀ Mn bond, such as in mod-B, the benzene rings can accommodate in a more appropriate position, keeping θ(BzÀ MnÀ Mn) as close to 180°as possible and shortening the metal-benzene distance. As the η 6 coordination contributes the most for the stabilization of the systems studied herein, mod-B is approximately 12 kcal mol À 1 more stable than mod-A. Additionally, the surrounding benzene ligands decrease electron density in the intermetallic region with respect to that of the Mn 2 dimer in the absence of η 6 coordination. This effect also plays a major role, and explains the destabilizing nature of 1 b ( Figure 5). The preferred orientation of the NHCs is, therefore, dictated by the η 6 coordination, whose interaction is more effective if the carbenes occupy bridging positions, while at the same time enabling this orientation due to depletion of intermetallic electron density.
The preference of the η 6 coordination over the carbenemetal bond in driving the optimal geometries of the compounds studied herein is also visualized by inspection of the bonding situation of the distinct model systems. These can be assessed by analyzing their corresponding canonical molecular orbitals, as shown in Figure 3, and the ones of the isolated Mn 2 Bz 2 and (NHC) 2 fragments in the same geometries as those of the model compounds. The distortion from the

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Full Paper doi.org/10.1002/chem.202101116 θ(BzÀ MnÀ Mn) = 180°in both model systems removes the degeneracies observed in the orbitals of the optimized Mn 2 Bz 2 (see Figure 1 to visualize the optimal orbitals). The sigma donation of the carbenes to Mn 2 Bz 2 in mod-A is illustrated for example in HOMO-13. In turn, the HOMO of mod-A involves interaction of the HOMO of Mn 2 Bz 2 with the empty p orbitals of the NHCs. This evidences that π back donation is indeed at play in the metal-NHC interaction. In contrast, the HOMO of mod-B is formed by the interaction of the LUMO of Mn 2 Bz 2 and the vacant p orbitals of the NHCs. This occupied orbital is strongly antibonding with respect to the MnÀ Mn bond, as it is composed of the + ,À combination of the Mn d z 2 atomic orbitals. This picture is in accordance with the metal-metal bond lengthening of mod-B in comparison to those of mod-A and the optimized Mn 2 Bz 2 . Furthermore, inspection of the energies of 1 and 1 b ( Figure 5) clearly shows that the metal-NHC interaction when the ligands occupy bridging positions is less favored than the one featuring terminal NHCs, which is particularly true for the case where no η 6 interaction takes place. This also explains the smaller HOMO-LUMO gap and Δ ST of mod-B in comparison to those of mod-A. The greater thermodynamic stability of mod-B, therefore, can be attributed preferentially to the better orientation of the η 6 coordination, and not due to the position of the NHCs.
When the carbene ligands are perpendicularly oriented across the MnÀ Mn bond, a butterfly-shaped C 2 Mn 2 moiety is formed. This bonding motif can be rationalized in terms of the carbene interaction with the π orbitals of Mn 2 . In this sense, the planar structure is avoided so that the carbenes do not interact with the same metal-metal π orbital. If the carbenes are completely orthogonal, they would interact with distinct metalmetal π systems. However, bringing the carbenes to this orientation is not favored due to steric repulsion of the nitrogen substituents, which also contributes to the high energy of 1 b in comparison to 1 ( Figure 5). The C 2 Mn 2 butterfly structure, therefore, is obtained as the result of an interplay between electronic effects driven by the carbenes and steric effects driven by the substituent groups at the nitrogen.
One last question remains to be addressed. In our Mn 2 L 2 systems, the ones where no η 6 coordination is formed are those featuring the smallest metal-metal bond lengths. This is discussed by the analysis of the canonical molecular orbitals of 1, which are shown in Figure 6. HOMO-6, HOMO-5, and HOMO-4 are related to the σ and π bonds of Mn 2 , while HOMO-3 and HOMO-2 compose the δ bonds, with HOMO-3 also including contribution from the Mn 4 s orbitals. HOMO-1 is a nonbonding orbital, whose lobes are pointing to the vacant sites of the trans-bent structure. Finally, HOMO is π antibonding with respect to the Mn 2 dimer, and π bonding with respect to the carbene moieties, suggesting the presence of metal-to-ligand π-backbonding interactions. In contrast to the Mn 2 L 2 systems featuring η 6 coordination, a formal bond order of 4 is therefore expected to Mn 2 in 1-3, which is supported by the Mayer bond order values (3.65 to 3.86) and also by NRT and GVB-PP calculations (see Section S2.2). This higher bond order explains why the MnÀ Mn bond in 1-3 is shorter than those of the other Mn 2 L 2 systems. However, the absence of η 6 coordination severely affects the stability of the systems, as evidenced by their negative Δ ST values (Table 1) and the narrow HOMO-LUMO gap of 1, which is merely 0.31 eV.
Given the remarkable similarity between the structures obtained herein and those synthesized for complexes featuring Co 2 and Fe 2 ( Figure S6), it becomes relevant to investigate if our findings can be extrapolated to other transition metal complexes featuring NHC-stabilized metal-metal bonds. Such calculations are currently underway, and the results will be presented in due course.

Conclusion
In summary, we have reported herein the first examples of 18electron organometallic platforms featuring low-valent, ultrashort manganese-manganese bonds stabilized by experimentally realized N-heterocyclic carbene ligands. Our thorough computational exploration indicates the synthetic feasibility of these systems and identifies their main electrostructural features. In particular, our analysis reveals which factors contribute the most to generating stable, closed-shell singlet structures with positive adiabatic singlet-triplet gaps, and how they affect the metal-metal bond. The ancillary η 6 coordination from the phenyl substituent of the carbene backbone is a fundamental requirement for the formation of kinetically and thermodynamically stable Mn 2 L 2 complexes. If this interaction is present, two classes of potential synthetic targets emerge, depending on the ligand flexibility. For rigid carbenes, structures where these ligands occupy terminal positions are obtained, with MnÀ Mn bond lengths ranging from 1.8-2.0 Å. On the other hand, systems featuring bridging carbenes are formed if more flexible substituents are involved. The latter structures are thermodynamically favored, even with the drawback of increasing the metal-metal bond length to values in the range of 2.0-2.2 Å. By disentangling electronic and steric effects, we could identify that the preference of systems featuring bridging carbenes over those where these ligands occupy terminal positions is due to a better orientation of the η 6 coordination, which also contributes to the bridging coordination by depleting intermetallic electron density. From our analysis, we suggest that IDipp (L = VI), IBn (L = VII), BIBn (L = VIII), CAAC (L = X), and DACMes (L = XI) are the best candidates as ligands for the experimental realization of Mn 2 L 2 systems. These results clearly show that new and exciting avenues in Lewis base chemistry with metal-metal bonding are yet to be explored.
Research Fellowship. R.R.O. acknowledges the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer which has contributed to the research results reported within this paper (http://sdumont.lncc.br). Open access funding enabled and organized by Projekt DEAL.