Quintuple Bonds Wagner & Kempe Nat Chem 09

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review articlePublished online: 23 sePtember 2009 | doi: 10.1038/nchem.359

Chemical bonding, in particular the nature of a chemical bond, the electronic structure and its reactivity, is of fundamental interest1. Reactivity expresses the significance of reaction

pathways (it is a ‘projection’ of reaction rates) and the electronic structure allows us to understand why some of the reaction path-ways a bond can take are relevant while others are not. Chemical bonding is the basis of chemistry, the science of synthesis. It is more than 90 years ago that Lewis introduced the idea of electron pair-ing and sharing between neighbouring atoms2, in the first model of covalent bonding (see ref. 3 for a summary of Lewis’s work). Remarkably, this simple model is still the basis of teaching in school and academia, and lies behind the bonding dash we draw between two atoms to describe the structure of a compound. A little more than ten years later, Heitler and London provided the first theoreti-cal evidence supporting Lewis’s model by showing that the energy of the H–H bond is due to the resonance between the electrons as they exchange positions between the two atoms4,5. The question arises as to how many of such covalent bonds can be formed between two atoms (of the same kind). A maximum of three has been found between main-group elements, for instance in acetylene and dini-trogen, and a greater number, up to six, could be expected for bonds involving transition metals, owing to the participation of not just s and p orbitals but s and d orbitals. Stable molecules with fourfold bonding have been known for a little more than 40 years and have been investigated experimentally and theoretically in detail since then6. In 2005, Power and co-workers provided the first experimen-tal evidence of quintuple bonding in a stable molecule7. Here we summarize experimental and theoretical work related to quintuple bonding initiated by this work.

bond orders and quantum mechanical calculationsBecause bond order is a chemical concept, and not an observable in the quantum mechanical sense, there does not exist a unique defini-tion of bond multiplicity in quantum chemistry. Thus, it is charac-teristic of the situation that in the recent papers on Cr–Cr quintuple bonding, different methods of studying the bonding and, in par-ticular, evaluating the bond order have been used. There follows a general, brief overview of the different concepts used in the analysis of the bond order of the molecules highlighted in this Review.

ultrashort metal–metal distances and extreme bond ordersFrank r. Wagner1*, awal noor2 and rhett Kempe2*

Chemical bonding is at the very heart of chemistry. Although main-group-element E–E′ bond orders range up to triple bonds, higher formal bond orders are known between transition metals. Here we review recent developments related to the synthesis of formally quintuply bonded transition metals in coordination compounds, and their theoretical description. The quadruple bond fascinated chemists for about 40 years. Recently, a stable molecule containing a formal quintuple bond initiated a ren-aissance in synthesizing and understanding bonds with high bond orders. Ultrashort metal–metal distances as low as 1.73 Å are one of the outcomes. First results indicate that the relevance of these bimetallic platforms to synthetic chemistry can be addressed through quintuple-bond reactivity studies. The theoretical description of the bonding situation in molecules with extreme bond orders has only just begun.

There is a common idea that the covalent bond is the result of electron sharing between two atoms8, as already proposed by Lewis2 in 1916. However, concerning the role of spin pairing itself, the direct interaction of the spins, in the sense of an interaction between mag-netic dipoles, is entirely negligible9. Thus, the Lewis two-electron cov-alent bond “is essentially the cumulative result of the effects of each electron being shared individually between two atoms (tempered, of course, by the effect of the interelectronic repulsion)”8. From this it becomes clear that the primary goal of a definition of bond order is to give a measure of the number of electrons shared between two atoms. For this purpose, a definition of an atom within a polyatomic unit must be made, and unfortunately this is not possible in a unique and unambiguous quantum mechanical way (see, for example, ref. 10).

The common concepts used in defining an atom within a polya-tomic unit can be divided into Hilbert-space and position-space concepts. In Hilbert space, an atom is defined using its basis set and the engagement of it in the wavefunction. In position space, an atom is defined as an entity on the basis of some space-partitioning scheme. Two principally different schemes are used: non-overlap-ping, space-filling atomic units, the most prominent ones being the basins of electron density in Bader’s quantum theory of atoms in molecules (QTAIM)11; and fuzzy atoms with overlapping regions, the most prominent ones being the Hirshfeld atoms12. Both have been shown to possess a general physical meaning10.

Quantum chemical calculations are typically done in Hilbert space. Historically, there are two types of wavefunction representa-tion, the molecular-orbital and valence-bond types, each of which influences how chemical bonding is considered in a specific way. Although at present the representations of the wavefunction can be at least approximately transformed into one another, they give rise to different types of bonding analysis in Hilbert space that are more-or-less specific to the wavefunction method13. The advantage of these procedures is that chemical bonding analysis can be done in terms of the immediate basic quantities used to generate the wavefunction, that is, basis sets, molecular orbitals and valence-bond structures. Notably, the position-space representation of chemical bonding, which is based on the one- and two-particle density matrices, is essen-tially independent of the type of wavefunction used. These matrices contain the essential information about the physical particles under

1Max-Plank-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany, 2Anorganische Chemie II, Universität Bayreuth, 95440 Bayreuth, Germany. *e-mail: [email protected]; [email protected]

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review article NATURE CHEmisTRy doi: 10.1038/nchem.359

consideration, that is, the electrons: the one-particle density matrix (the diagonal part of which is the electron density) describes the dis-tribution of electrons and the two-particle density matrix describes the distribution of electron pairs. Ideally, the different methods of position-space analysis of chemical bonding each focus on specific aspects of the electronic behaviour without introducing new artificial objects (‘unicorns’14). In this respect, they are not competing with each other, but synergistically construct a view on the chemical bond complementary to the various Hilbert-space views.

Methods for theoretical ‘bond-order’ analysis. In the very early days of molecular-orbital theory, even before it had been named, the first definition of the number of bonds between two atoms in a symmetric diatomic molecule was given by Herzberg15: in its original form, it is equal to half the difference between the number of bonding electrons and the number of ‘loosening electrons’ in the molecule.

For conceptual reasons, this counting scheme was adopted shortly after also by Mulliken16, but he considered more fundamen-tal a continuous conception of chemical bonding in which a non-integral bonding power of either sign is attributable to every outer electron. The Mulliken population analysis (see below) developed 20 years later contained such a quantity. Although Herzberg wrote in terms of electrons in his original paper15, it was becoming more and more recognized that the objects obtained from certain elec-tronic-structure methods were one-electron wavefunctions, which Mulliken chose to term ‘orbitals’17. From then on, in the framework of the developing molecular-orbital theory, bonding, non-bonding and antibonding orbitals were increasingly used to describe the bonding scenario in molecules. The Herzberg scheme of deter-mining the bond order from molecular-orbital occupations is now taught in general chemistry textbooks and the resulting bond order is sometimes called the Herzberg number. The Herzberg number, defined on the basis of a monodeterminantal wavefunction, is now accepted as the molecular-orbital definition of the formal bond order. Also, for explicitly correlated wavefunctions, the antibond-ing molecular orbitals that were empty in the initial Hartree–Fock wavefunction become partially occupied. In the resulting natu-ral orbitals, this happens at the expense of the occupation of the initially fully occupied bonding orbitals. Applying the Herzberg definition also in these situations generally leads to fractional bond orders. This possible generalization of the Herzberg definition was described and applied to a metal–metal multiple-bonding situation in 198718. Recently19, the idea was revived and proposed as the defi-nition of the effective bond order (EBO), which has been applied to characterize the bonding in diatomic molecules and in bimetallic complexes with formal metal–metal multiple bonding (see above).

The Herzberg scheme is restricted to either diatomic molecules or to polyatomic molecules with strongly localized orbitals between a pair of atoms. The first definition of bond order in the framework of molecular-orbital theory applicable to delocalized orbitals was given by Coulson in terms of the Hückel model20. The application of the new definition to conjugated hydrocarbons resulted in fractional C–C bond orders, for example 1.67 for benzene and 1.5 for graph-ite. Although not mentioned in ref. 20, this yields total valences of 4.33 and 4.5 for the respective carbon atoms, which were certainly considered less ‘chemical’ than the bond orders given by Pauling21 several years before.

In the competing valence bond method of Heitler, London, Slater and Pauling, the electronic structure was considered to be a super-position of wavefunctions of Lewis-type structures with perfectly paired electrons. For quantitative purposes, the inclusion of ionic structures even for classical covalent bonds was soon discovered to be necessary to obtain reliable results. On the conceptual side, fractional bond orders were considered to arise as a result of resonating bonds. Three years before Coulson’s20 molecular-orbital definition of the bond order, the resonance between the two (benzene) and three (graphite)

Kekulé-type structures led Pauling21 to assign a C–C bond order of 1.5 to benzene and 1.33 to graphite, which yields a total valence of four for both types of carbon species. In this framework, Pauling set up an empirical function from four basic values expressing the depend-ence of the (experimentally known) C–C interatomic distance on the assumed amount of single-bond–double-bond resonance, that is, on the amount of double-bond character. From this function, the intera-tomic C–C distances in other organic molecules were predicted and compared with experimental data. The idea of there being a simple relationship between the bond distance and the bond order is still in use today, also for heavier elements, despite the existence of various counter-examples. One interesting counter-example concerning Tc–Tc multiple bonding in Tc2Cl8 units with variable charge is discussed in ref. 6. On the methodological side, there is a connection between the old resonance concepts of chemical bonding and the modern idea of natural resonance theory22 (NRT) presented in 1998 as an extension of the then-established natural-bond-orbital analysis23. The basic quantity of this method is the (possibly correlated) one-particle density matrix, which is considered to be constructed as a weighted superposition of one-particle density matrices from Lewis-type structures already including bond polarity. In practice, the generation of the structures and their weights from the given one-particle density matrix (typically obtained from a molecular-orbital calculation) occurs automatically by a complex process. For monodeterminantal wavefunctions, bond orders very close to the corresponding Herzberg numbers are obtained for prototype molecules H2, N2 and F2. Interestingly, a decomposition of the total bond order in terms of only additive covalent and electro-valent (ionic) contributions has been defined.

In molecular-orbital theory, the Mulliken population analysis developed in the 1950s for wavefunctions calculated using linear combination of atomic orbitals (LCAO) has had a big impact (and still has) on the conceptual aspects of chemical bonding. It defines a decomposition of the molecular orbitals’ electronic population into net atomic populations and diatomic overlap populations24,25. Summed up over all occupied orbitals, the latter can be either posi-tive or negative. As an indicator of covalent bonding between two atoms, Mulliken overlap populations characterize the accumula-tion of charge density in the region between the chemically bonded atoms, but they do not represent a bond order.

The bond-order index was defined independently by Giambiagi et al.26 and Mayer27 for Hartree–Fock-like electronic-structure methods. It was initially defined as a generalization of the Wiberg index28, which has found widespread use in semi-empirical electronic-structure theory using an orthonormal basis set. With respect to the partitioning of the two-centre overlap density it is related to the Mulliken population analysis, and the whole method is therefore sometimes called Mulliken–Mayer population analysis (MMA). It has been proven that under certain conditions the bond-order index of a homonuclear diatomic molecule exactly equals the Herzberg number29. In actual applications, the values normally reproduce the classical bond orders for C2H6, C2H4, C2H2, N2 and F2, for example, very well. One big conceptual and practical drawback is its strong dependence on the basis set (inherited from the Mulliken type of partitioning), which affords the use of well-balanced, not-too-diffuse atomic basis sets in practical applications. Despite this known drawback, the method is conceptually very interesting. The bond-order index between two atoms has been shown to be equal to the diatomic contribution to the integral of the exchange den-sity, which is a part of the same-spin pair density. It measures the degree to which the fluctuations of the atomic populations from their average values in both atoms are correlated with each other30. This means that the bond-order index represents a measure of the electronic delocalization between two atoms in Hilbert space.

There is an important connection between the Hilbert-space MMA method and the position-space analysis of chemical bonding. The integrals of the exchange density within a single atomic domain




review articleNATURE CHEmisTRy doi: 10.1038/nchem.359

and between a pair of atomic domains in position space had already been shown31 to measure the extent of electron localization in the single domain and the extent of delocalization between the pair of domains, respectively. The decision to choose the QTAIM basins as the basis for the position-space partitioning of the exchange-density integrals gave rise to the topological definition of a bond order32 that represents the position-space counterpart of the MMA bond index. In contrast to its Hilbert-space analogue, the topological definition does not explicitly suffer from unbalanced and diffuse atomic basis sets. Unfortunately, the initially proposed extension of the topologi-cal bond-order index to the case of correlated wavefunctions lessens its physical content31,33, and the question arises of whether this price is worth paying. To describe the situation more completely, as a continuation of the original work31 a so-called delocalization index between two QTAIM atoms was defined in a physically transparent way using the general exchange-correlation density34. Both electron-sharing indices, the topological bond order and the delocalization index, are identical at the monodeterminantal level, but they differ for correlated wavefunctions35. The calculation of the delocalization index at the correlated level is quite complicated and time consum-ing, and only a few studies have been published so far.

The results for monodeterminantal wavefunctions are quite promising. For symmetric diatomic molecules such as, for exam-ple, H2, N2 and F2, the two definitions yield identical values close to the Herzberg number. For unsymmetrical ones such as, for exam-ple, LiH, the resulting values are much smaller than one, which is consistent with the significant ionic component of the bonding. Additionally, for polyatomic molecules it is found that the values between atoms A and B is significantly influenced by the other atoms connected to A or B, which leads to a reduction of the values relative to the Herzberg number36. These observations point to the chemical interpretation (in addition to the clear physical interpreta-tion of the delocalization index) of both of these electron-sharing indices being effective covalent bond orders.

historical backgroundThe first quadruple bond. About 120 years after the first report37 on a compound which is now known to contain a formal metal–metal quadruple bond, namely Cr(ii)2(O2CCH3)4(OH2)2, the existence of metal–metal quadruple bonding is supported by strong experimental and theoretical evidence. In 1964, on the basis of a careful chemical characterization of several synthesized dirhenium octahalide com-pounds38, the experimental crystal structure39 of K2[Re2Cl8]·2H2O and simplified molecular-orbital calculations40, Cotton and co-workers presented the first strong evidence for the notion of metal–metal σ2π4δ2 quadruple bonding in [Re2Cl8]2− molecular units41. The δ-bond inter-pretation was strongly suggested by the observed eclipsed arrange-ment of the chlorine ligands and the simultaneous unusually short Re–Re distance (2.24 Å). This type of compound had in fact been obtained several years before42, and the experimental crystal structure with the correct Re2Cl8 units had been published43. However, owing to the erroneous assignment of the Re(ii) oxidation state during the characterization studies41, the bimetallic units had been formulated as [Re2Cl8]4−, and additional H+ ions had been supposed to be present in the crystal structure. Mainly, though, the authors, like many of their colleagues, were not yet mentally prepared for the notion of metal–metal multiple bonding. It was therefore Cotton and co-workers, working on similar compounds and being aware of these previous publications, who put the pieces together in the right way and created the prototype picture of a metal–metal quadruple bond. The whole story has been told in several places (see, for example, ref. 6).

To characterize the strength of the δ bond, the optical absorption spectrum of the alkylammonium compound (NR4)2[Re2Cl8] was analysed to find the energy of the δ–δ* absorption band. Owing to its observed low oscillator strength, the 14,000 cm−1 (1.7 eV) band was ruled out and the transition was attributed with more than

twice the energy (4–5 eV)40. However, in the 1970s the δ–δ* transi-tion was uniquely identified as the 14,700 cm−1 (1.82 eV) band and the low oscillator strength was explained to be due to poor δ-orbital overlap44. A similar energy for the δ–δ* transition was theoreti-cally obtained in a 2003 computational study45 that employed an explicitly correlated treatment of the electronic structure in the ground and excited states using the complete-active-space method with additional second-order perturbative treatment of dynamical correlation (CASPT2), an advanced technique in transition-metal computational chemistry. The spectral features were obtained with good accuracy. Re–Re bonding has been characterized by means of the effective bond order described above. An EBO of 3.2 has been obtained from the sum of the partial bond orders 0.92 (σ), 1.74 (π) and 0.54 (δ). The strongly reduced δ-bond contribution (0.54) is con-sistent with the small δ–δ* energy difference mentioned above, and does not invalidate the formal picture of the quadruple bonding.

Owing to the established weakness of the δ bond, another reason for the eclipsed arrangement of the chlorine atoms, on which Cotton and co-workers put so much emphasis, has been sought. As the result of density functional theory (DFT) calculations in combination with coupled cluster calculations, hyperconjugation has been proposed46 to be the true reason for the observed rotomeric preference.

The shortest metal–metal bond in coordination compounds for decades. Bond lengths of main-group elements become signifi-cantly shorter as bond order increases1. This trend should also occur in bonds involving transition-metal homobimetallic complexes. The shortest metal–metal bond in a stable molecule has been of interest to natural scientists, in particular chemists, for decades. The ele-ment chromium has an important role in the search for such a bond. Owing to their electron configurations, chromium and the higher homologues of group-6 metals can form metal–metal bonds of high formal bond orders. Within group 6, chromium has the smallest ion radius and is ideally suited to form exceptionally short metal–metal bonds. For nearly 30 years, an aryl Cr(ii) compound, structurally characterized in ref. 47 and first prepared by Hein and Tille more than 40 years ago48, was thought to have the shortest experimentally

a

b

Cr−Cr, 1.830(4) Å Cr−Cr, 1.828(2) Å

2

N

O

Figure 1 | Quadruple bonding in chromium homobimetallic complexes. a, Molecular structures of the two coordination compounds that for decades held the record for the shortest metal–metal distance in stable molecules. b, Reversible cleavage of an unsupported Cr–Cr multiple bond by pyridine (red, Cr; orange, C; blue, O; green, N; purple, Li; brown, Br).





obtained metal–metal distance in a stable molecule, namely 1.830(4) Å (Fig. 1a, left). Hein and Tille also proposed the dimeric structures for this compound, which were verified by structure determination. Interestingly, a little more than a month before the submission of ref. 47, tetrakis(2-methoxy-5-methylphenyl)dichro-mium (Fig. 1a, right), a homobimetallic Cr(ii) compound with a Cr–Cr distance of essentially the same length, 1.828(2) Å, was sub-mitted for publication49. It appeared in print one issue after ref. 47. Both publications are recognized by the community equally.

Owing to the better availability of X-ray crystal structure analysis in inorganic laboratories, a great interest in synthesizing homobime-tallic complexes with short metal–metal contacts evolved6. A criti-cal review50 of the role of the bridging ligands in alkoxo, amido and aryl Cr(ii) homobimetallics with regard to the formation of short Cr–Cr quadruple bonds concluded that divalent chromium show a surprisingly passive behaviour compared with the dominance of the ligand. The Cr2 unit in such complexes seems to respond to the lig-and by overlapping orbitals and coupling electrons. It seems almost chemically nonsensical for extremely short metal–metal distances to suggest the existence of stronger bonds or a higher degree of metal–metal bond multiplicity. Very important in this regard are Cr(ii) atoms multiply bonded without a bridging ligand, that is, chromium homobimetallics with unsupported metal–metal bonds. Examples are rare. A metal–metal distance of 2.096(1) Å was observed for a tetramethyldibenzotetraaza[14]annulene derivative (Fig. 1b, left)51. This compound undergoes reversible metal–metal bond cleavage upon the addition of pyridine, forming a bispyridine adduct (Fig. 1b). It was concluded that the energy of such Cr–Cr multiple bonds are in the same range as the sum of the energies of the generated pyridine chromium bonds52. Dissolution of the pyridine adduct in tetrahy-drofuran leads back to the dimer. These findings are indicative of the weakness of multiple bonding between Cr(ii) atoms. Very recently, it was shown53 that homobimetallic chromium complexes can have metal–metal distances of less than 1.80 Å. This indicates that for-mally quadruply bonded complexes can have much shorter metal–metal distances than was thought to be the case for many years. The key to this compound is an organometallic synthesis in which AlMe3 acts as an N-ligand acceptor and a methyl donator.

the first quintuple bond in a stable moleculeDespite the fact that transition metals can formally form bonds with six shared electrons, only quadruply bonded coordination compounds had been isolated until 2005. Transition metal dimers,

such as Cr2 trapped in inert matrices at low temperature54,55 gener-ated by vaporization of the metals56 or as short-living intermedi-ates through pulsed photolysis of chromium hexacarbonyl57, were the only existing evidence for molecules with formal bond orders higher than four58. These species are ligand free and all valence electrons can be used to form multiple bonds. Designing a com-pound with bond orders higher than four involves the reduction of the coordination number of covalently bonded ligands to allow as many electrons as possible to participate in metal–metal bond-ing. Sterically demanding ligands such as the monovalent terphe-nyl ligand C6H3-2,6-[C6H3-2,6-(isopropyl)2]2

− are able to provide these features59. The first quintuple bonding in a stable compound was observed by Power and co-workers in a chromium complex stabilized by this ligand (Fig. 2)7. Those authors defined quintuple bonding as follows: “The description ‘quintuple bond’ is intended to indicate that five electron pairs play a role in holding the metal atoms together. It does not imply that the bond order is five or that the bonding is very strong, because the ground state of the molecule necessarily involves mixing of other higher-energy con-figurations with less bonding character. This gives lower, usually noninteger, bond orders”.

The dark-red crystalline compound studied in ref. 7 is very air and moisture sensitive. The weak temperature-independent paramag-netism is consistent with an S = 0 ground state and strongly coupled d5–d5 bonding electrons. Surprisingly, the bimetallic compound is characterized by a metal–metal bond of 1.8351(4) Å, which is long in comparison with the shortest formal quadruple Cr–Cr bonds known at the time (Fig. 1a)47,49. The secondary arene interaction has an important role in this compound. Quantum mechanical calcula-tions, using both CASPT2 and DFT methods, were undertaken for chromium, iron and cobalt (model) complexes to provide a multi-reference description of the metal bond and to determine the extent of secondary metal–arene interaction in 1 (ref. 60). The studies indi-cate that the arene interaction in the chromium complexes causes only a slight weakening of the quintuple bond and that in the iron and cobalt complexes strong arene coordination precludes signifi-cant metal–metal bonding.

We note that the quintuple-bond character in 1 has been pre-dicted61 to be theoretically controversial because of the trans-bent structure of the C–Cr–Cr–C entity, which differs from the trans-linear arrangement expected for a quintuple bond. Trans-bent geometries in quintuply bonded molecules have been proposed62 to originate in the preference of a strong σ bond from sdz2 hybridi-zation. Bending does not destroy the δ bond: the hybridization scheme proposed even leads to the creation of a more favoura-ble δ bond through sd4 hybridization as well as a pure dδ orbital. Even more generally, a subsequent computational DFT study63 on bending isomers of simple model compounds R–Cr–Cr–R with various monodentate ligands reported a remarkable persistence of the qualitative quintuple-bond picture for the various bending geometries representing minima of the corresponding potential hypersurface. More specifically, at the level of CASPT2 calcula-tions on a model compound PhCr–CrPh (Ph, phenyl), only a tiny energy difference between the trans-linear and the trans-bent structure (but an appreciable energy barrier) was obtained64. The preference for the trans-bent structure in the experimental com-pound 1 was ascribed to secondary interactions of chromium with the true ligand. For the Cr–Cr bonding in the model compound, an EBO value of 3.5 was calculated. Despite this, it has been emphasized that the formal bond order is still 5. A bond energy of 76 kcal mol−1 was computed, which is about twice as large as for a Cr2 molecule with a formal sextuple bond. This counterin-tuitive result has been mainly attributed to the destabilizing 4s–4s interactions in the dimer. From supplementary DFT calculations, certain bond-weakening interactions between chromium and the flanking aryl groups have been detected. It has been concluded

1

Figure 2 | molecular structure of the first stable compound in which quintuple bonding was observed. The aryl chromium dimer 1 has a Cr–Cr distance of 1.8351(4) Å (colour code as in Fig. 1). The metal–metal bond is supported by a metal arene interaction (thin line).





that the Cr–Cr bond length found in 1 is not the shortest possible for this type of system, allowing for exciting new possibilities.

ultrashort metal–metal bondsA way of comparing the shortness of bonds across the periodic table, and thus establishing what a ‘short bond’ is, is the formal shortness ratio (FSR)6. The FSR is a dimensionless number given by the ratio of the atom–atom distance, d, of a bond and the sum of the radii1 of the two atoms involved, rA + rB: FSR = d/(rA + rB). The advantage of this formalism is its interelement applicability. The FSR is a use-ful tool for comparing formal quintuple bonding and short metal–metal distances within the group-6 metals, for instance. Because here we mainly discuss the distances in chromium homobimetal-lic complexes, we write in terms of the distances and not the FSRs. Quintuple bonds could naively be expected to be shorter than quad-ruple bonds, considering general trends that have been observed for increasing bond orders in main-group chemistry1. However, the first formal quintuple bond observed in a stable molecule was longer than the shortest Cr–Cr distances observed in formally quadruply bonded Cr(ii) homobimetallic complexes at that time. The Cr–Cr bond length of laser-evaporated Cr2 in the gas phase is about 1.68 Å (ref. 56). Spectroscopic studies of Cr2 generated from pulsed photolysis of Cr(CO)6 are indicative of a distance of 1.71 Å (ref. 57), and the calculated minimum of the ground-state potential is comparable in distance65. The Cr2 molecule can be regarded as formally sextuply bonded. Interestingly, the potential curve is rather flat around the minimum65 and should, if it is similarly flat in multi-ply bonded Cr(i) dimers, allow drastic shortening by rational ligand design. A quintuply bonded complex should reach a Cr–Cr distance between those observed for 1 and Cr2, namely between 1.84 and 1.68 Å. Consequently, efforts have been made to find formally quin-tuply bonded complexes that have metal–metal bond lengths within this range. The first report in this regard66 considered an N-ligand-stabilized homobimetallic chromium complex (Cr–Cr bond length, 1.8028(9) Å). The compound, 2 (Fig. 3a), was synthesized by addi-tion of an excess of sodium and a Cr(iii) chloride to a sterically demanding diazadiene, affording a chromium monochloride that was further reduced using potassium graphite.

The problem with the diazadiene used, and other imine ligands, is its redox ambiguity, which makes it difficult to judge the oxida-tion state of the chromium atoms66. The DFT electronic-structure calculations reported in ref. 66 showed that one of the five occu-pied Cr–Cr bonding orbitals, a dδ orbital, is highly delocalized over the ligand. NRT analysis was used to investigate the conse-quences of the delocalization on the metal–metal bond order. The NRT-based bond order of 4.3 indicates a rather significant effect, to be compared with the NRT-based bond order of 4.6 obtained

for trans-bent HCr–CrH (ref. 62). In an independent bonding analysis of the same compound using the QTAIM methodology at the Hartree–Fock level of theory, a Cr–Cr bond order of 3.6 was obtained67 on the basis of the delocalization index. The difference between the NRT and QTAIM results has been attributed to the physically different definitions used by the two methods of analy-sis. On the basis of a multiconfigurational CASPT2 wavefunction, a bonding analysis of this compound yielded a Cr–Cr EBO of 3.4 (ref. 68), which is identical to the one obtained for 1 (ref. 60) at the same level of theory. Interestingly, the authors of ref. 68 encoun-tered some difficulties with the EBO formalism owing to the delo-calization of one chromium dδ orbital, and the reported EBO was obtained only after an additional localization procedure. Thus, three different types of bond-order analysis have been reported for this compound, two at the monodeterminantal level of theory but fully including delocalization effects, and one at the multiconfigu-rational level but with a weakness with respect to the full separa-tion of metal–metal interactions from metal–ligand interactions. It seems that, with both delocalization and correlation effects being significant, the method of analysis has an important role as well. This makes the analysis of chemical bonding of these types of compounds a real challenge. Clearly, NRT and QTAIM analysis at the multiconfigurational level of theory for this and similar com-pounds would be very interesting.

As a continuation of ref. 7, Power and co-workers synthesized derivatives of 1 with varying substitution patterns, finding metal–metal distances of between 1.8077(7) and 1.8351(4) Å. Packing forces rather than electronic effects were thought to control the dif-ferent distances69.

Inspired by 2 and the potential of three-atom bridging ligands to establish short metal–metal distances6, introduced as the Hein–Cotton concept70, two groups independently synthesized compounds stabilized by such ligands, and respectively observed metal–metal distances of 1.75 and 1.74 Å, for instance, 3 and 4 (Fig. 3b,c)70,71,72. The N–N distances within the ligands listed in Fig. 3 demonstrate the importance of the ligand in terms of establishing short metal–metal bonds. These N–N distances clearly correlate with the Cr–Cr bond lengths. The examples shown in Fig. 3b,c represent the class of ultrashort metal–metal-bonded homobimetallics. Calculations indicate quintuple bonding. The Cr–Cr bond lengths of these com-pounds are intermediate between the quadruply bonded Cr(ii)–Cr(ii) complexes and the gas-phase Cr2 molecule with its formal sextuple bond. Interestingly, in one of the compounds71 chromium is three-coordinated with respect to the ligand, which is difficult to understand in the context of formal quintuple bonding, as the number of metal d orbitals involved in metal–ligand bonding is con-sidered to be minimized60. A comparison of the Cr–N bond lengths

a b cN−N, 2.84 ÅCr−Cr, 1.80 Å

N−N, 2.26 ÅCr−Cr, 1.75 Å

N−N, 2.24 ÅCr−Cr, 1.74 Å

2 3 4

Figure 3 | Homobimetallic chromium compounds in which unusually short metal–metal distances were observed. a-c, Molecular structures of 2, 3 and 4, respectively. Complexes 3 and 4 represent the class of compounds that contain ultrashort metal–metal bonds. Quintuple bonding and metal–metal distances nearly as short as for the transient Cr2 molecule, which could be considered formally sextuply bonded, have been observed in them. Colour code as in Fig. 1.





in a series of structurally analogous chromium amidinates, in which the distances are roughly equal, is indicative that the Cr–N bond lengths are independent of the steric demand of the ligand72. For the aminopyridinate70, chemical bonding analysis at the DFT level has been done using position-space quantities, the electron localiz-ability indicator73,74 and the delocalization index. Even at the mono-determinantal level, indications of a Cr–Cr bond order significantly reduced relative to the Herzberg number owing to weak interatomic electron sharing of one of the δ bonds in particular are reported. The other δ bond can be seen to be of the more favourable sd type already discussed62. The calculated bond order of 4.2 based on the delocalization index between the QTAIM chromium atoms supports the notion of a formal quintuple bond. The majority of the contri-butions (62%) are found to originate in the chromium third atomic shell region in position space, which is consistent with earlier results obtained for Mo2(formamidinate)4 displaying a formal quadruple bond75. We note that a significantly lower value of the delocalization index, of 3.6, was obtained for the Cr–Cr bond in 2 in a later study67, which may indicate a substantial difference in Cr–Cr bonding.

By comparing the two ligand families used to stabilize ultrashort Cr–Cr bonds, namely aminopyridinates and amidinates (Fig. 4a,b), the ‘two-wings-up’ arrangement observed for amidinates (Fig. 4b) apparently causes much less interligand repulsion within the bimetallic complex than the ‘wing-up–wing-down’ arrangement observed for aminopyridinates (Fig. 4a). This allows the generation of a closer N–C–N pincer and/or an alignment of the ligand orbit-als (lone pairs) that bind with chromium towards each other. Both structural consequences may result in a shorter Cr–Cr distance. As a result, ‘steric pressure’ generated through the introduction of a bulky substituent at the bridging carbon atom should give rise to a further reduced distance between the metal atoms (Fig. 4c). Guanidinates appear to be ideally suited for this purpose. The π system is delocalized and thus prefers a planar arrangement of the three N atoms and their residues (Fig. 4c). This planar arrange-ment can be embedded between two bulky 2,6-alkyl groups of the phenyl ‘wings’. Consequently, the substituents of the non-metal-bonded N atom push both wings further down. A ligand intro-duced recently, (CH3)2N-C(N-2,6-diisopropylphenyl)2

−, seems to be ideal in this regard76 and was used successfully to shorten the Cr–Cr bond length to 1.73 Å (ref. 77). The molecular structure of this compound, 5, is shown in Fig. 5. The space-filling model (Fig. 5b) indicates the steric pressure of the methyl groups (brown carbon atom) towards the ‘wing’.

The Cr–Cr distance of 5 is 0.1 Å shorter than the distances observed in complexes that held the 30-year record for the short-est metal–metal distances in a stable molecule (Fig. 1a). The stud-ies discussed here indicate that the shortening of the metal–metal

bond of ultrashort chromium homobimetallics is primarily deter-mined by the ligand. This has also been one of the conclusions of a very recently published article78. Cr–Cr δ bonding competes with Cr–ligand π bonding, yielding lower Cr–Cr bond orders and in principle larger Cr–Cr distances for substantial ligand π-bond par-ticipation. The Cr–Cr distance effect may be hidden by the brack-eting effect of the ligand. A stimulating model calculation at the CASPT2 level on the hypothetical complex FCr–CrF, in which lig-and delocalization is maximally excluded, yielded a Cr–Cr distance of 1.65 Å. This is similar to that obtained for Cr2, which sets the benchmark for rational ligand design.

outlook for other metals and quintuple bond reactivityDimers of the 4f and 5f metals could in principle form bond orders even higher than the transition metals. The crucial point is the itinerancy of the f states. For this reason, not the lanthanides, with their atomic-like localized 4f states, but the actinides are considered the interesting can-didates. On the experimental side, evidence for these types of species comes from matrix isolation and gas-phase detection79 (U2).

Electronic structures of the U2 dimer have been calculated80 at the CASPT2 level of theory including either scalar relativistic effects or even spin–orbit coupling. Ten of the 12 valence electrons are found to be chemically active, displaying an exotic bonding pattern with a classical bonding part consisting of one σ (7sσg) and two π (6dπu) doubly occupied bonding orbitals, and a ferromagnetic bonding81 part with four singly occupied bonding orbitals (6dσg, 6dδg and 5fπu, 5fδg). In total, a formal bond order of 3 + 4/2 = 5 is obtained. The remaining two electrons are found to be situated in localized 5f

a bCr–Cr, 1.7293(12) Å

5

Figure 5 | molecular structure of the coordination compounds with the shortest metal–metal bond so far observed. a, Ellipsoid plot of 5. b, Space-filling model indicating the steric pressure provided by the methyl moieties (brown carbon atom) towards the aryl wing. Colour code as in Fig. 1.

CrCr

N N

NN

a

CrCr

N N

N N

b

CrCr

N N

N

N N

N

c

Figure 4 | The role of the ligand in stabilizing ultrashort metal–metal bonds. a, In aminopyridinates, the ‘wing-up–wing-down’ arrangement may cause interligand repulsion limiting the ‘compression’ of the two metals by the ligands. b, In amidinates, a ‘two-wings-up’ arrangement allows the ‘wings’ to be put further down, aligning the N-centred lone pairs to provide shorter metal–metal bonds. c, In guanidinates, the steric pressure on top of the ligand initiates a process that pushes the ‘wings’ down, resulting in a further shortening of the Cr–Cr distance.





orbitals on each U atom. The calculations predict all six electrons to be ferromagnetically coupled.

As a continuation of this work in a broader and more refined study19 of Ac2, Th2, Pa2 and U2, the concept of the EBO has been additionally applied to characterize chemical bonding. EBO values of 1.7, 3.7, 4.5 and 4.2 have been obtained for Ac2, Th2, Pa2 and U2, respectively. The Pa2 molecule displays the highest EBO, the highest computed bond energy (4.0 eV) and the shortest distance (2.37 Å). Despite being close to Pa2 in EBO value, U2 has a much lower bond energy (1.2 eV), whereas Th2, which has a lower EBO, is found to have much higher bond energy (3.3 eV). There is no direct relation between the EBO and the bond energy, because the latter is a compli-cated energy difference that depends on variable electronic properties of the actual molecule and the isolated atoms. The study has not been continued to heavier homologues. Owing to increasing 7s promotion energies and the increasing localization of the 5f electrons, bond ener-gies and bond orders are expected to be generally smaller than for the early actinides. Thus, the question arises of what is the highest cova-lent-bond bond order between any atoms of the periodic system.

On the basis of CASPT2 calculations (at least at scalar relativistic level) it has been argued82 that the maximum bond order between two transition metal atoms can be six, with two σ, two π and two δ bonds. In contrast to the main-group elements, high effective bond orders have been found to be more favourable for the heavier homologues. Scalar relativistic effects give rise to more itinerant (n − 1)d orbitals, leading to higher effective EBO contributions from the δ bonds and to more contracted ns orbitals, yielding more optimal σ-bonding con-tributions. Thus, although for Cr2 an EBO of 3.5 and a dissociation energy of only 1.65 eV (calculated) have been obtained, EBO values of 5.2 have been computed for Mo2 and W2 molecules with dissocia-tion energies of 4.41 (calculated) and 5.37 (calculated), respectively. Likewise, to achieve high EBOs for formal quintuple bonds, it has been proposed that the molybdenum and tungsten homologues of the Cr(i) compounds be synthesized. Another candidate for a strong quintuple bond has been predicted to be Nb2, because the niobium atom is already fully polarized (d4s1 configuration) in its ground state. The heavier homologue, Ta2, is less favourable owing to the higher promotion energy of the tantalum atom (d3s2 configuration) to a valence state with five unpaired electrons.

Because stable, formally quintuply bonded species are now avail-able, the investigation of the reactivity of these diamagnetic Cr2 plat-forms can be started. The first results are available and, for instance, the carboalumination of a Cr–Cr quintuple bond has been observed (Fig. 6)83. Carbometallation and especially carboalumination reac-tions of C–C double and triple bonds are a well-established syn-thetic protocol in organometallic chemistry and organic synthesis. Analogous reactivity patterns of Cr–Cr quintuple bonds indicate that such quintuple bonds are not as exotic as was assumed before-hand. However, the peculiarites of these reactions reflect the spe-cific nature of the high metal–metal bond orders. The reactions of 1 with N2O and adamantanyl azide resulted in the formation of com-pounds that have no metal–metal bonding84.

These studies are the final step in the journey from establishing stable quintuple bonds through an understanding of their electronic structure(s) to investigating their reactivity and chemistry to find potential applications.

At this early stage, it is rather difficult to judge the impact coordi-nation compounds containing formal quintuple bonds may have, or to foresee possible applications, as only a few reactivity studies are available. They show the potential for small-molecule activation, par-ticularly on a diatomic platform that can provide from two to eight (in principle even ten) electrons. In addition, one could also expect a potential for homogeneous catalysis, because a monoligand-stabi-lized Cr(i) species can be provided which is not coordinatively satu-rated by other ligands, for instance by solvent molecules. Selective ethylene tri- and tetramerization might be examples. What we can

really do with these high-bond-order platforms may become clear if more examples with other metals are available. In fact, during the proofing process for this article, the first examples of molybdenum–molybdenum quintuple bonds have appeared85. Understanding chemical bonding better is another important aspect. Quintuple bonding is only a small part of understanding chemical bonds, and we must now seek to place it into a common conceptual framework encompassing all types of chemical bonds.

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Figure 6 | Carboalumination of a Cr–Cr quintuple bond. This carboalumination proceeds in analogy to carboalumination reactions observed for C–C double and triple bonds, and thus indicates similarities between these classical bonds and quintuple bonding. The blue bonds indicate the unprecedented binding of the (H3C)2Al− moiety to the two chromium atoms. Aluminium, white, plus colour code as in Fig. 1.





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