Ultrashort Mn-Mn Bonds in Organometallic Complexes

TL;DR

This study uses density functional theory to reveal ultrashort Mn-Mn bonds in organometallic complexes, showing that benzene and similar molecules can cage Mn atoms to form Mn-Mn triple bonds with potential for synthesis.

Contribution

The paper demonstrates the existence of ultrashort Mn-Mn bonds in organometallic complexes and explores their stability and formation mechanisms through computational methods.

Findings

Mn-Mn bond length of 1.8 Å indicating a triple bond

Benzene cages facilitate ultrashort Mn-Mn bonds

Multiple spin states with energy barriers affect synthesis

Abstract

Manganese metallocenes larger than the experimentally produced sandwiched MnBz$_2$ compound are studied using several density functional theory methods. First, we show that the lowest energy structures have Mn clusters surrounded by benzene molecules, in so-called rice-ball structures. We then find a strikingly short bond length of 1.8 {\AA} between pairs of Mn atoms, accompanied by magnetism depletion. The ultrashort bond lengths are related to Bz molecules caging a pair of Mn atoms, leading to a Mn-Mn triple bond. This effect is also found when replacing benzenes by other molecules such as borazine or cyclopentadiene. The stability of the Mn-Mn bond for Mn$_2$Bz$_2$ is further investigated using dissociation energy curves. For each spin configuration, the energy versus distance plot shows different spin minima with barriers, which must be overcome to synthesize larger Mn-Bz complexes.

Figures

Full text

Introduction

A number of organometallic compounds have been synthesized and used in a wide range of applicationsCrabtree (2009); Omae (1998); Kollonitsch (1965); Coogan et al. (2012); Harrod and Laine (2012). The synthesis of ferroceneKealy and Pauson (1951); Miller et al. (1952); Dunitz et al. (1956); Werner (2012) stimulated a search for related metallocenes, such as cobaltoceneLiu et al. (2007), nickelocenePfab and Fischer (1953), rhodoceneCotton et al. (1953) and manganoceneWilkinson and Cotton (1954), in which a transition metal atom is located between two cyclopentadiene molecules. Similar compounds have been proposed combining transition-metal atoms with benzene molecules (TM-Bz compounds)Wedderburn et al. (2006). The basic unit of such compound is a transition metal atom over a single Bz ring, known as a half-sandwichPandey et al. (2001, 2000); Muhida et al. (2004). Such basic units can be combined to form larger compounds with either sandwich-like structures for early transition metals (Sc, Ti, and V) or rice-ball structures for late transition metals (Fe, Co, and Ni)Kurikawa et al. (1999). TM-Bz compounds look promising for future applications. For instance, sandwich-like molecules have been proposed as conductors involving spin transportOrmaza et al. (2017), either isolated bridging the tips of a Cu nanocontactsKarolak and Jacob (2016); Ormaza et al. (2017) or pile up building infinite wires having Sc, Ti, V, Cr, and MnXiang et al. (2006). Sandwiched molecules and infinite wires containing V, Nb, and Ta have been found to provide strong magnetic anisotropy Mokrousov et al. (2006). We are interested in characterizing larger clusters with rice-ball structures, specifically in the study of Mn-Bz compounds, to gain knowledge on their still unfamiliar structures and properties.

The field of organometallics was recently boosted following a breakthrough in the synthesis of binuclear metallocenes, so-called dimetallocenes, such as decamethyldizincoceneResa et al. (2004); Grirrane et al. (2007) Zn2($\eta^{5}$C5Me5)2) and (Zn2($\eta^{5}$C5Me4Et)2). Compounds containing Mn with many nuclei have plenty of uses in organometallicsCahiez et al. (2009). Some previously described molecules containing Mn-C bonds are dimanganese decacarbonylBrimm et al. (1954); King et al. (1968); Dahl et al. (1957) Mn2(CO)10 and methylcyclopentadienyl manganese tricarbonyl (CH3C5H4)Mn(CO)3, which has been used to increase the octane level of gasolineDavis (1998). Experiments on TM-Bz compounds have been performed, leading to their synthesis in the gas phase and their characterization using spectroscopic methods Duncan (2008); Kurikawa et al. (1999); Zheng et al. (2008); Buchanan et al. (1999) and in magnetic experimentsMiyajima et al. (2007); Akin et al. (2016). TM-Bz compounds are present in many types of molecular clusters. Small Mn-Bz compounds, such as MnBz2, have been synthesizedKurikawa et al. (1999); Zamudio-Bayer et al. (2015). As for Mn adatoms in graphene, Mn sandwiched between Bz molecules prefers to be in a hollow positionSevinçli et al. (2008); Mao et al. (2008). Theoretical studies are required to understand larger complexes of inner Mn clusters surrounded by Bz molecules as to be produced experimentally.

Dimetallocenes and multimetallocenes have been largely investigated using density functional theory (DFT) calculations. Different external molecules have been considered, such as Bz, cyclopentadiene, and even fullerenesGao et al. (2009). Similarly, many different central metal atoms have been studied, leading to alkaline-earth dimetallocenesChattaraj et al. (2008); Kan (2009); Li and Xu (2006); Velazquez et al. (2007), transition metal dimetallocenesZhou et al. (2006); Zhu et al. (2011); Meng et al. (2015), heterodinuclear compoundsHe et al. (2008); Hu et al. (2015) and zinc isoelectronic elements, such as Cd and Hg Carmona and Galindo (2008). Although multinuclear metallocenes of Co, Cu, and Ni, and other transition metals have been described Zhou et al. (2006); Zhu et al. (2011); Meng et al. (2015); Rao and Jena (2002); Froudakis et al. (2001); Zhang and Wang (2008); Valencia et al. (2011); Kua and Tomlin (2006); Gonzalez et al. (2017), the study of larger manganese benzene compounds is still to be done.

We herein investigate organometallic compounds in which Bz molecules cage clusters with a few Mn atoms, MnnBzm. The benzene molecules strongly affect the bonding between manganese atoms, differently to other transition metals. Manganese benzene compounds are also interesting because they are in the middle between two trends, sandwich-like structures for early transition metals and rice-ball structures for late transition metals Kurikawa et al. (1999). We find that the clusters contain Mn-Mn multiple (triple) bonds with ultrashort interatomic distances and depleted magnetism. We then focus on the electronic structure of the smaller Mn2Bz2 molecule to further improve our understanding of such molecules. The two Bz molecules covering the Mn2 molecule appear to stabilize a non-magnetic local minimum in the inner Mn dimer. We verify that these results also appear when replacing the caging benzenes with other molecules. Furthermore, ultrashort bonds are also found in larger Mn-Bz compounds, indicating that the effect is robust and that strong dimerization is induced in larger molecules. Because most of experiments work with charged clusters, we have checked that positively charged Mn-Bz clusters also present ultrashort Mn-Mn bonds. Lastly we study the synthesis of the Mn2Bz2 molecule, as a first step towards larger Mn-Bz compounds, and we show that different high local spin magnetic moment states create barriers to such syntheses.

I Results and discussion

I.1 Metallization induced superdimerization

The ground state geometries of the Mn2Bz2, Mn3Bz3, Mn4Bz3, and Mn4Bz4 molecules are shown in Fig. 2. We also consider the roles of isomers for each cluster, and study other geometries and magnetic solutions. We first determine whether a sandwich or rice-ball structure is preferred. The rice-ball geometry has lower energy for each of the four Mn-Bz clusters studied here. The results for the sandwich structures are shown in the Supplemental Material. We perform calculations for several isomers with different magnetic moments. For instance, a symmetric Mn3Bz3 isomer with 5 $\mu_{B}$ has an energy difference of 1 eV from the ground state, and a distorted Mn3Bz3 isomer with 7 $\mu_{B}$ lies 0.5 eV higher in energy. All the isomers are lying higher in energies than the structures presented in Fig. 2.

All the ground state molecules have strikingly short bond lengths between the Mn couples. The Mn2Bz2 molecule is the simplest system to show this effect with a Mn-Mn distance of 1.8 Å. The ultrashort bond lengths are unexpected because larger distances between Mn atoms have been reported, such as 3.4 Å for the Mn dimerYamamoto et al. (2006); Nayak et al. (1998); Baumann et al. (1983), 2.93 Å for dimanganese decacarbonylBrimm et al. (1954); Dahl et al. (1957), 2.4–2.6 Å for manganese carbidesChong et al. (2014); Karen et al. (1991) and the broad distance range of 2.25–2.95 Å for several Mn bulk allotropes Baumann et al. (1983). On the other hand, analogous short multiple bonds have been shown theoretically and experimentally for other transition metals, such as in ultrashort Cr dimers (1.73 Å) within organic molecules Wagner et al. (2009).

We focus on the locally unpolarized Mn2Bz2 molecule with a Mn-Mn distance of around 1.8 Å. The loss of magnetism is a hallmark of the ultrashort bonds between Mn atoms capped with Bz molecules. The magnetic moments of irregular systems, such as Mn3Bz3 and Mn4Bz3, are almost depleted. In the unit consisting of a Mn atom over a benzene molecule, the magnetic moment decreases from 5 $\mu_{B}$ to 3 $\mu_{B}$ Pandey et al. (2000). However, the total elimination of the magnetism for the Mn2Bz2 molecule is still surprising.

When combining two Mn2Bz2 units to form a Mn4Bz4 molecule, the larger compound also has ultrashort bonds, and the total and local magnetic moments remain zero. The Bz molecules around the Mn atoms form a distorted tetrahedron, tilted because of neighboring Bz rings. There are two short bond lengths of 1.94 Å and four larger bond lengths of 2.56 Å. The short bond lengths are between the opposite atom pairs, labeled 1-2 and 3-4 in Fig. 2.

The two cases Mn2Bz2 and Mn4Bz4 have ultrashort distances and total magnetism depletion. The ultrashort Mn-Mn bonds also occurs for other molecules, such as Mn3Bz3 and Mn4Bz3. The Mn3Bz3 ground state geometry depletes most of the magnetism, and gives an ultrashort distance of 1.88 Å between Mn(1) and Mn(3). The third Mn atom, Mn(2), moves away and remains bonded mainly to Mn(1), with a bond length of 2.22 Å. The side position of Mn(2) bends the Bz molecule associated with Mn(1). The total spin magnetic moment is 1 $\mu_{B}$, localized mainly on Mn(2) with 1.53 $\mu_{B}$. The Mn(1) atom has antiferromagnetic coupling with a magnetic moment of -0.57 $\mu_{B}$, and the Mn(3) local moment decreases to a very small value of 0.28 $\mu_{B}$. 111Small spin polarization is induced in the C atoms (0.06 $\mu_{B}$ being the highest value for one C atom) with opposite sign to the closest Mn atom. The added Mn-Bz unit distorts the Mn2Bz2 geometry, giving nonzero local magnetic moments on the Mn atoms. The peculiar distorted structure is due to the large energy gain because of the ultrashort Mn-Mn bond. The ultrashort bond phenomenon is therefore found partially for Mn3Bz3. The dimerized Mn4Bz4 and Mn3Bz3 structures indicate that the ultrashort bond mechanism is caused by two Mn atoms caged by Bz molecules.

We next consider when the short Mn-Mn bonds accompanied by magnetism quenching occur by removing a Bz molecule from an already dimerized structure. We consider Mn4Bz3 molecule shown in Fig. 2. The structure is obtained by removing a Bz molecule from the final Mn4Bz4 geometry, and fully relaxing the geometry again. The Mn4Bz3 molecule becomes reorganized because the Mn(4) atom has lost its Bz molecule. The Mn(1), Mn(2) and Mn(3) atoms form an equilateral triangle with sides 2.62 Å. The Mn(4) atom is bonded to the other three Mn atoms with short bond lengths of 2.05 Å, which are larger than those found in Mn4Bz4. In this case, the local magnetic moments are antiferromagnetically coupled, with small values of 1.07 $\mu_{B}$ for Mn(1), Mn(2) and Mn(3) and -0.83 $\mu_{B}$ for Mn(4). Most of carbon atoms have a negative induced magnetic moment of 0.02–0.03 $\mu_{B}$. Although the local manganese magnetism is reduced and the bonds are short, it seems that the presence of two Bz molecules caging two Mn atoms is key to the ultrashort Mn-Mn bond scheme.

We now consider the stability these compounds to discuss their possible synthesis. We compute the formation energy, per manganese atom, for MnnBzm clusters toward separated Mn atoms and Bz molecules, using the expression $E_{f}=(n\,E_{\mathrm{Mn}}+m\,E_{\mathrm{Bz}}-E_{\mathrm{total}})/n$. We find that the formation energies are always favorable, in the range 1.76–2.18 eV. Furthermore, the HOMO-LUMO gaps are in the range 1.17–0.72 eV. Taking into account the well-known issue of gap underestimation for generalized gradient approximation, the gap values suggest that the molecules are stable. The gap narrows as the size of the molecule increases. We could have followed the series by looking for larger molecules with ultrashort Mn-Mn bonds, such as Mn5Bz5, Mn6Bz6, and so on. Nevertheless, it appears that placing five or more Bz rings around a nucleus of larger Mn clusters is a real challenge due to the lack of space.

Molecular beam experiments use charged systems, therefore we determine how our neutral Mn-Bz clusters are affected when positively charged. An electron was removed from the structures, which were fully relaxed again. The results show there are two different trends depending on the size. Smaller clusters, Mn2Bz${}_{2}^{+}$ and Mn3Bz${}_{3}^{+}$ preserve the ultrashort distance of the Mn-Mn bonds. Note that the Mn2Bz${}_{2}^{+}$ cluster now has a magnetic moment of 1 $\mu_{B}$ and that the Mn3Bz${}_{3}^{+}$ increases from 1 $\mu_{B}$ for the neutral case to 2 $\mu_{B}$. Larger complexes, Mn4Bz${}_{3}^{+}$ and Mn4Bz${}_{4}^{+}$ lost the ultrashort Mn-Mn bond distance and display bulk-like behavior. The Mn-Mn distances increases to values within the interval 2.3–2.6 Å. The local magnetic moments of Mn increase to values within the range 2.0 – 3.5 $\mu_{B}$ and the Mn atoms are antiferromagnetically coupled.

We further test when ultrashort Mn-Mn bonds would appear by replacing the caging benzenes with other organic molecules, such as cyclopentadiene C5H6, and even inorganic molecules, such as borazine B3H6N3 Zhu and Wang (2009); Li et al. (2013); Wilkinson et al. (1956) . After careful atomic relaxations, both types of caging compounds for Mn2 present ultrashort Mn-Mn bonds accompanied by magnetism depletion. 222For the cyclopentadiene-caged Mn2, the ultrashort Mn-Mn distance is 1.85 Å. The Mn local magnetic moments become about 0.1 $\mu_{B}$, which are not fully depleted in comparison to Bz-Mn molecule because a H atom from cyclopentadiene is bound to a Mn atom. For the borazine-caged Mn2, the Mn-Mn distance is 1.82 Å and the local and total magnetic moments are fully depleted. Then, the ultrashort Mn-Mn bond effect, accompanied by a significant decrease in the magnetic moment of Mn, seems to be robust, and it is expected to be found for other molecules caging manganese atoms.

I.2 Simplest case: Mn2Bz2

We focus on the smaller Mn2Bz2 molecule to investigate the ultrashort Mn-Mn bond, also found in larger molecules. The fully relaxed Mn2Bz2 molecule has an unexpected Mn-Mn bond length of 1.8 Å, as shown in Fig. 2. However, the Mn dimer has been found to be stabilized by van der Waals interactions Yamamoto et al. (2006) and to have a bond length of more than 3 Å. Bulk metallic Mn is predicted to have interatomic distances of between 2.25 Å and 2.95 Å, depending on the allotropic structure. The Mn-Mn distance decreases when shifting from van der Waals-like bonds to metallic-like bonds. However, our results are surprising because the Mn-Mn bonds can be ultrashort. This means that the Mn-Mn bonding mechanism in hybrid Mn-Bz molecules is different from the one seen in Mn clusters and bulk Mn Nayak et al. (1998). We find a non-magnetic solution for the Mn2Bz2 molecule that contrasts with the high-spin solutions obtained from most DFT calculations for the Mn dimer Qing-Min et al. (2007); Bobadova-Parvanova et al. (2005); Longo et al. (2005); Kabir et al. (2006); Nayak et al. (1998); Baumann et al. (1983). Benzene molecules reduce spin-splitting in the Mn atoms, and electrons fill the minority-spin bonding molecular orbitals instead of the majority-spin antibonding molecular orbitals. The ultrashort Mn-Mn distance is therefore related to the loss of magnetism. For spin-compensated solutions, the Mn dimer in Mn2Bz2 can be further compressed because electrons between the Mn atoms suffer less electronic repulsion when they fill the same Mn-Mn molecular levels with opposite spins. Note that high-spin solutions for Mn2Bz2 require larger distances because of the larger electronic repulsion between Mn levels.

To improve our understanding of the ultrashort Mn-Mn bonds, we carry out spin-polarized single point calculations for the Mn2Bz2 molecule. The Mn atoms are separated by 0.1 Å in each step, and the Bz rings are maintained in the same relative positions with respect to the Mn atoms. We plot the energy against Mn-Mn distance in Fig. 3(a). The local magnetic moments of Mn are zero up to a distance of 2.4 Å, and there is a deep minimum at a distance of 1.8 Å. The energy increases sharply by more than 2 eV as the Mn atoms separate. Two different DFT codes gives the minimum at 1.8 Å, even when the Mn2Bz2 molecule is distorted and allowed to relax again. The large energy gain is associated to the multiple (triple) bond between Mn atoms, as shown by considering the molecular orbitals and electron localization function, as described in the Supplemental Material.

We further explore the nature of Mn2Bz2 bonding to determine when both inner Mn atoms are locally spin-compensated. We study the isolated Mn2 molecule, varying the Mn-Mn distance from 1 Å to 4 Å, as shown in Fig. 3(b). When the magnetization is released, the total magnetic moment varies from 2 $\mu_{B}$ for distances shorter than 1.7 Å to 10 $\mu_{B}$ for distances larger than 2.4 Å. We have also calculated the energy versus distance curves for fixed total spin values of 0, 2, 6, and 10 $\mu_{B}$. We find that each spin curve has a different minimum. The global minimum for Mn2 is around 2.5 Å, as previously reported at this level of calculations (LDA/GGA)Qing-Min et al. (2007); Bobadova-Parvanova et al. (2005); Longo et al. (2005); Kabir et al. (2006). The antiferromagnetic curve is almost degenerated to that of 10 $\mu_{B}$ for long distances, in agreement with previous calculationsTzeli et al. (2008),333There is a delicate balance between exchange and splitting, and small changes in distance can modify the magnetic characteristics of the Mn dimerMejía-López et al. (2008). Although DFT has been shown to be successful for many systems, the choice of exchange correlation functionals is key for some systems, such as the Mn dimer. Note, for example, that obtaining the minimum caused by van der Waals interactionsMorse (1986); Nayak et al. (1998); López-Urías and Díaz-Ortiz (2003) at distances larger than 3 Å requires using hybrid functionalsYamanaka et al. (2007) or even the casscf (Complete Active Space Self-Consistent Field) methodYamamoto et al. (2006), which reproduces the antiferromagnetic coupling and the bond length larger than 3 Å obtained in experimentsCheeseman et al. (1990); Baumann et al. (1983); Rivoal et al. (1982); Van Zee et al. (1981); Bier et al. (1988).. The strong Mn-Mn bonding in the Mn2 molecule at short distances can therefore be computed accurately enough using generalized gradient approximation (GGA) functionals. The low spin solutions (with 0 and 2 $\mu_{B}$) shrink to local minima at bond lengths of about 1.8 Å, as reported previously Wolf and Schmidtke (1980); Paul and Misra (2009). The minimum at short distances is also favored in the bonding in Mn2Bz2 because the magnetic moment in the 3d Mn levels is decreased by the Bz molecules, so the Mn-Mn distances are dramatically reduced.

I.3 Implications for the synthesis of Mn2Bz2

The MnBz2 molecule has been synthesized and identified using spectroscopic techniques in the same way as for other TM-Bz compounds Kurikawa et al. (1999). Larger Mn-Bz compounds are, however, difficult to synthesizedYasuike et al. (1997). It seems that electron spin restrictions may prevent their synthesis. Here, we investigate the path for the synthesis of Mn2Bz2 by estimating energy barriers. The possible barriers are extracted from the energy versus Bz-Bz distance curves for different total magnetic moments, as shown in Fig. 4. Further computational details are given in the Supplemental Material. The total magnetic moment decreases from long to short distances, and a barrier appears as the Mn2Bz2 molecule forms at high spin. We can overcome this barrier by, for instance, bringing the Mn-Mn core into a low spin state sandwiched between distant Bz molecules. We propose that using thermal or optical pumping techniques on the Mn cluster and Bz molecule precursors could help to find routes for synthesizing the Mn2Bz2 molecule and larger Mn-Bz clusters.

II Final remarks

We studied Mn-Bz molecules with rice-ball configurations. We found a multiple (triple) bond between the inner manganese atoms in the core metal cluster. Two hallmarks of this effect are a strikingly short Mn-Mn bond length of about 1.8 Å and a lack of magnetism. These can be explained because every two Bz molecules stabilize the two neighboring Mn atoms with no spin polarization. Furthermore, other molecules such as borazine and cyclopentadiene have a similar effect on manganese atoms. We also found that the ground states of larger molecules, such as Mn3Bz3 and Mn4Bz4, stabilize the irregular structures of the molecules with ultrashort Mn-Mn bonds. Last, we investigated the roles of different spins, looking at the Mn2Bz2 energy as the Bz-Bz distance varied. There are energy barriers that could be overcome by canceling local Mn spins using optical or thermal techniques. These results suggest that further experimental progress can be made in synthesizing larger Mn-Bz clusters that are of interest in the field of organometallic compounds.

III Computational details

We performed DFT calculations using the Vienna ab-initio simulation package (vasp), based on the projected augmented wave method (PAW)Blöchl (1994); Kresse and Joubert (1999). For the exchange and correlation functionals we used the Perdew-Burke-Ernzenhof (PBE) form of the generalized gradient approximation (GGA)Perdew et al. (1996). We chose a cubic unit cell with sides 30 Å in order to avoid interaction between images. We used an electronic temperature of 25 meV and a cutoff energy of 500 eV. The Mn-Bz molecules were relaxed until the forces were less than 0.006 eV/Å. The results obtained using vasp were reproduced using the siesta package within a GGA and applying the PBE functional for selected cases. We used a mesh cut-off of 250 Ry and sampled at the $\Gamma$-point. The atomic cores were described using nonlocal norm-conserving relativistic Troullier-MartinsTroullier and Martins (1991) pseudopotentials with non-linear core corrections factorized in the Kleynman-Bylander form. The basis set size was double zeta plus polarization orbitals with an energy shift of 0.05 eV. Using the siesta package, the same minima were obtained for the Mn2Bz2 and Mn3Bz3 molecules.

Acknowledgments

This work was partially supported through projects FIS2013-48286-C02-01-P and FIS2016-76617-P funded by the Spanish Ministry of Economy and Competitiveness MINECO, by the Basque Government under the ELKARTEK project(SUPER), and by the University of the Basque Country (Grant No. IT-756-13). TA-L acknowledges a grant provided by the MPC Material Physics Center - San Sebastián. FA-G acknowledges the DIPC for their generous hospitality. The authors also acknowledge the support of the DIPC computer center.

Supplemental Material: Ultrashort Mn-Mn Bonds in Organometallic Complexes

SI Mn-Mn bond in Mn2Bz2

SI.1 Molecular orbitals

We studied the hybridization of the six $p_{z}$ molecular orbitals of benzene (Bz) and the 3d shell of Mn. The properties of benzene orbitals are well known. Three of the four valence electrons of each carbon atom are used to build strong $\sigma$ bonds with neighboring C and H atoms. The extra electrons in the pz orbitals of C atoms form delocalized $\pi$ bonds, which are related to the aromaticity of Bz. These pz electrons are higher in energy than $\sigma$ electrons and close to the HOMO level, and are responsible for the reactivity of Bz with other atoms and molecules. The six pz orbitals are involved in the six well-known molecular orbitals. Some molecular orbitals are degenerated and are divided into four types: $\sigma$ ($\pi_{1}$), $\pi$ ($\pi_{2}$,$\pi_{3}$), $\delta$ ($\pi_{4}^{*}$,$\pi_{5}^{*}$) and $\phi$ ($\pi_{6}^{*}$). For Mn2Bz2, the degenerate Bz levels are, however, split in energy because the Bz molecules are slightly bent toward the Mn atoms.

In the presence of a Bz molecule, the Mn 3d orbitals split into three different energies, according to the orbital symmetry, in the energy order d$\sigma$ (3d${}_{z^{2}}$), d$\pi$ (3dxz,3dyz), and d$\delta$ (3dxy,3d${}_{x^{2}-y^{2}}$). The Mn orbitals hybridize with the Bz orbitals when they have the same symmetry, to produce $\sigma$, $\pi$ and $\delta$ molecular orbitals, as has been found in similar analyses Yasuike and Yabushita (1999); Karolak and Jacob (2016). The Mn 3d${}_{z^{2}}$ orbitals are not expected to interact much with the Bz because they point toward the center of the Bz ring. Regarding the Mn 4s orbitals, $\sigma$ bonds with the Bz $\pi_{1}$ molecular orbitals are expected.

The energy levels for Mn2Bz2 near the Fermi energy are shown in Fig. S1. The $\sigma$, $\pi$, and $\delta$ molecular orbitals are found by considering the number of nodal planes, (0, 1, and 2, respectively). The two $\pi$ orbitals have lower energies than the $\delta$ orbitals, and are occupied by more electrons. Figure S1 shows that the $\pi$ and $\delta$ molecular orbitals have bonding or antibonding character that alternates as the energy energy increases. The number of hybrid orbitals expected in each symmetry can also be explained. For $\pi$ symmetry, there are four $\pi$ orbitals from two Bz molecules and four 3d orbitals (3dxz and 3dyz from each atom). As a result, there are eight molecular orbitals. The same argument can be applied to the $\delta$ orbitals.

To summarize, a spin compensated structure was found with electrons filling the $\sigma$, $\pi$ and $\delta$ hybrid molecular orbitals built from the Bz pz levels and Mn 3d levels, following symmetry considerations. Therefore, the ultrashort Mn-Mn bond is a triple bond, with $\sigma$, $\pi$ and $\delta$ bonds.

SI.2 Electron localization function

The Mn-Mn bond is studied in detail using the electron localization function, as shown in Fig. S2. There is a direct $\sigma$ metallic bond between the Mn atoms, composed of 3d${}_{z^{2}}$ orbitals. The disk around the bond center indicates the presence of $\pi$ and $\delta$ molecular orbitals and bonds. The basins in the Mn-Mn bonds have an electron localization function value of 0.125, which is small and typical of metallic bonds. The electron localization function results agree completely with the energy levels, hybridization, and wave-functions described above, confirming the triple-bond characteristics of the bonds between the Mn atoms.

SII Energy barriers

We next comment on the barrier that prevents the formation of the Mn2Bz2 molecule. We carried out calculations for Mn2Bz2 for a set of spin magnetic moments and distances. The energy barrier is calculated using the geometrical arrangement shown in Fig. S3. The total magnetic moment is fixed to 0, 6, 8, and 10 $\mu_{B}$. For each spin value, the molecule is computed using several Bz-Bz distances dBz-Bz between 4.8 and 10 Å at steps of 0.2 Å. The C and H atoms are relaxed in the $xy$ plane, keeping the Bz-Bz distance frozen. For each calculation, the Mn atoms are initially set in the center with a distance dMn-Mn of 2 Å, as shown in Fig. S3. The Mn atoms are allowed to relax along the $z$ axis. For large dBz-Bz values, the Mn atoms can either bind to Bz molecules or form a Mn-Mn core in the center. These two geometries explain the abrupt step seen for some energy curves in Fig. 4 in the main article, for instance at 6.4 Å for 6 $\mu_{B}$, and at 7.2 Å for 8 $\mu_{B}$. At these distances, the Mn-Mn forces are at maxima, and for larger distances the Mn-Mn atoms prefer to bond together remaining separated from the Bz molecules.

SIII Mn-Bz sandwiches

We also considered sandwiched structures for the four Mn-Bz clusters, as shown in Fig. S4. The rice-ball structures presented in the main text are more stable than the sandwiched structures, with energy differences larger than 1 eV. Furthermore, the total magnetic moments are larger for the sandwiched structures than for the rice-ball structures.

SIV Mn-Bz: charge state

We studied local charges using the Mulliken scheme within the siesta package. For the Mn2Bz2 molecule, there is a small charge transfer of 0.18 electrons from each Mn atom towards C atoms. For Mn3Bz3, the charge transfers of Mn(1) and Mn(2) are almost negligible, and the charge transfer reaches a threshold of 0.11 electrons for Mn(3). For Mn4Bz3, Mn(1), Mn(2), and Mn(3) lose 0.07 electrons each, and Mn(4) gains 0.42 electrons; globally each Mn atom therefore receives 0.21 electrons from Bz molecules. For Mn4Bz4, each Mn atom gains almost 0.04 electrons, meaning that, in total, 0.16 electrons move from Bz molecules to Mn atoms. We therefore find that increasing the Mn cluster size causes the charge transfer between Mn atoms and Bz molecules to change sign. In general, charge transfer values are small. We can assume that the Mn oxidation state is zero for the calculated Mn-Bz clusters, and specifically for the ultrashort Mn-Mn bond in Mn2Bz2.