The recent report of a stable, crystalline compound with a quintuply bonded chromium–chromium core1 may reopen the debate on the nature of the multiple bonds between transition metals2 that was initiated by the discovery of a stable, quadruple bond by Cotton et al. in 1964.3 Although a recent study of a quintuple bond in the uranium dimer4 U2 provided strong support for the existence of such bonds, the isolation of the stable [Ar′CrCrAr′] species (Ar′=2,6-(2,6-iPr2-C6H3)2-C6H3), which has a planar, trans-bent rather than a linear CipsoCrCrCipso core and weak temperature-independent paramagnetism, has raised new questions about multiple bonding. Such a trans-bent structure was recently predicted for the simple [HCrCrH] dimer by Weinhold and Landis on the basis of DFT calculations and a natural-bond analysis.5
The simplest molecule containing a CrCr bond is Cr2. Its experimental bond length, obtained from laser-induced fluorescence spectroscopy, is 1.679 Å, and this extremely short CrCr bond has a formal bond order of six, although its significance was questioned6 because of its low dissociation energy (1.53±0.06 eV). According to different theoretical studies, the description of the CrCr interaction in Cr2 ranges from a sextuple bond,7–10 through a single bond,11 to a complete absence of bonding between the chromium atoms.6 It is now well established that a proper description of the bonding in this species requires a multiconfigurational treatment. A description of the bonding in Cr2 that is in full agreement with the experimental data was obtained in a recent study.12 Formally, a sextuple bond is formed, but the effective bond order is only about four because of mixing of excited, less-bonding states into the ground state. Similar behavior was also observed for [Re2Cl8]2−, in which a formal quadruple bond was found to have a bond order of only about three for similar reasons.13, 14
The bonding scheme in the [Ar′CrCrAr′] complex resembles that found in the Cr2 dimer: The interaction of two CrI centers with d5 electron configurations leads to five, rather than six, metal–metal bonding molecular orbitals, along with their antibonding counterparts. The questions that arise are: which electronic configurations dominate the ground-state wave function, and how important is the contribution of the bonding (σg)2(πu)4(δg)4 configuration? The main difference between the bonding in Cr2 and [Ar′CrCrAr′] lies in the fact that two additional metal–ligand orbital combinations involving the participation of mainly 4 s orbitals in the metal–carbon(ligand) bond are present in [Ar′CrCrAr′]. Despite this apparent similarity, the situation in the real complex is more complicated because of the size of the ligands, and also because of the presence of the “indirect” metal–ligand interactions. Because of the presence of the flanking aryl groups in the vicinity of the chromium centers, a weak, but non-negligible interaction occurs.1 This interaction, along with the large size of the ligand, can lengthen the CrCr bond in the [Ar′CrCrAr′] compound.
We now report the results of a theoretical study of a simplified model compound for [Ar′CrCrAr′], namely [PhCrCrPh] (Ph=phenyl). The complete active space (CAS) self-consistent field (SCF) method15 was used to generate molecular orbitals and reference functions for subsequent multiconfigurational second-order perturbation calculations of the dynamic correlation energy (CASPT2).16 Additional DFT calculations were performed on the [PhCrCrPh] model and on the experimentally observed [Ar′CrCrAr′] compound. The results show that the trans-bent and linear geometries at the CASPT2 level are essentially degenerate but are separated by an appreciable barrier (Figure 1). Fivefold bonding with filled bonding orbitals (σg)2(πu)4(δg)4 is the predominant configuration in the wave function.
The most-significant structural parameters for the trans-bent (A) and linear (B) [PhCrCrPh] structures are reported in Table 1. The computed bond distances for the trans-bent structure (CrCr=1.75 Å, CrC=2.018 Å) are somewhat shorter than the experimentally determined values (CrCr=1.83, CrC=2.15 Å).1 As will be shown below, this difference can be attributed to the extra aryl substituents in [Ar′CrCrAr′], which because of steric and electronic factors as well as the presence of an additional Cr–ring interaction weaken both the CrCr and CrC bonds somewhat. The application of the same computational methodology to Cr2 also affords a shorter CrCr bond (1.662 Å) than the experimental value (1.679 Å). We computed the CrCr bond energy by comparing the energy of the complex with that of two CrPh units (with DFT-optimized geometry) and found it to be 76 kcal mol−1. In comparison, the bond energy of Cr2 is 36 kcal mol−1. The bond in [PhCrCrPh] is thus twice as strong. The reason is most likely that, in Cr2, the interaction of the 4 s is repulsive at equilibrium geometry.
The trans-bent planar structure is only 1 kcal mol−1 higher in energy than the linear structure. However, the compound [Ar′CrCrAr′] has a trans-bent structure, and we presume that this preference is a result of the secondary interaction between the chromium and the flanking ring of the ligand. This behavior is not possible in our model compound. A reaction path between A and B was determined by interpolating the extreme values of the CrCr bond length, CrC bond length, and C-Cr-Cr angle. A barrier of 20 kcal mol−1 with respect to the linear structure B exists for a Ph-Cr-Cr angle of 131°.
The electronic structures of A and B were analyzed. The major configuration in both forms has all the bonding orbitals occupied: (σg)2(πu)4(δg)4 with a total weight of 45 % in the CASSCF wave function for A, which corresponds to a formal quintuple bond. The second dominating configuration has a weight of 9 % and corresponds to a double excitation (δg)2(δu)2. The effective bond order is smaller than five as a result of the large occupation of the antibonding orbitals. It can be estimated as the sum of the occupation numbers of the bonding orbitals, minus the corresponding sum for the antibonding orbitals, divided by two. For the form A, we obtained the following occupation numbers (Figure 2): σg(1.79), σu(0.21), πu(3.54), πg(0.46), δg(3.19), δu(0.81). These values yield an effective bond order of 3.52. The corresponding number for the linear form B is 3.69. The larger number is a reflection of the shorter CrCr bond (see the Supporting Information for a picture of the orbitals of B along with the occupation numbers). Although the calculated bond order is less than five, the bond is formally quintuple, because five orbitals and five electrons on each atom are involved in the bonding.
The geometry optimizations of the model [PhCrCrPh] compound were also performed at the DFT level of theory, and yielded a minimum for the linear optimized geometry with a CrCr bond length of 1.560 Å. The single configurational DFT approach typically underestimates the CrCr bond lengths. Optimization of a planar trans-bent structure with constrained C2h symmetry led to a second-order transition point with the CrCr bond length of 1.658 Å and a Cr-Cr-C angle of 95.0°. A considerable change in the C-Cr-Cr-C core geometry is observed in the DFT-optimized structure of the [Ar′CrCrAr′] molecule. A wider C-Cr-Cr angle (102.7°) and a net elongation of the CrCr bond (by 0.049 Å relative to the [PhCrCrPh] model) clearly indicate that the bulky terphenyl substituents are responsible for these structural changes. Analysis of the DFT results reveals that two different interactions contribute to such behavior: a repulsive interaction between aryl groups in the terphenyl ligands, and a very weak, bonding interaction of the flanking aryl groups with the chromium atoms.
We conclude that a quintuple bond is formed between the Cr atoms in the model compound [PhCrCrPh]. This description is consistent with the pairing of five electrons from each CrPh moiety. The bonding also seems to be stronger than in the formally sixfold bonded chromium dimer Cr2, which we attribute to the absence of the 4 s orbital in the CrCr bond. The geometry of the model compound used in this study is close but not identical to that of the experimentally observed [Ar′CrCrAr′] species. The CrCr bond in [Ar′CrCrAr′] is almost 0.05 Å longer than that in [PhCrCrPh]. When this difference is added to the value of 1.75 Å calculated for [PhCrCrPh] at the CASSCF/CASPT2 level, a CrCr bond length of 1.80 Å results, which is quite close to the experimental value of 1.83 Å. Furthermore, the C-Cr-Cr angle obtained from the DFT-optimized structure (102.7°) of [Ar′CrCrAr′] is identical to the C-Cr-Cr angle determined experimentally in the X-ray structure of this compound. The computed difference in the CrCr bond lengths in [PhCrCrPh] and [Ar′CrCrAr′] is therefore the result of steric repulsion and the extra Cr–ligand bonding that occurs between the metal centers and the flanking aryl groups in the experimental compound. This bonding, even though it is weak, has a significant influence on the structure; it weakens both the CrCr and the CrPh bond.
Further information on this weak interaction can be obtained from DFT calculations, which, because of their monodeterminantal character, cannot properly describe the bonding between the two chromium centers, but can yield important information about the chromium–aryl interaction. The weak chromium–aryl interaction involves mainly chromium centers and the ipso-carbon atoms of the flanking aryl groups. This situation bears some resemblance to that observed in chromocene (bis(cyclopentadienyl)chromium(II)) and related derivatives, which have chromium–aryl(centroid) bond lengths in the range 1.60–1.65 Å.17 In [Ar′CrCrAr′], however, the chromium–aryl(centroid) bond is much longer (2.23 Å). Also, the analysis of the orbital overlaps shows that the chromium–aryl interaction is different and concerns mainly the ipso-carbon atom of the flanking aryl group, rather than the whole aryl ring. This situation is a result of the relative positions of the phenyl rings and the Cr center. The “twist” of the flanking aryl group, which causes a pronounced asymmetry, as well as the different orientation of the chromium d orbitals make this interaction weaker than the η5 complexation observed in chromocene. The DFT calculations suggest that the CrCipso interaction is quite weak and has a value of approximately 1–2 kcal mol−1.
Finally, inspection of the potential-energy surface (PES) scans of the [PhCrCrPh] model (see the Supporting Information) clearly indicates that a trans-bent structure is not a minimum but rather a transition point on the PES. Although the size of the bulky terphenyl ligands precluded frequency analysis of the DFT-optimized structure of [Ar′CrCrAr′], we believe that the sterically bulky terphenyl ligands can stabilize the trans-bent geometry, and turn a transition point into a minimum in a fashion analogous to that observed in [Ar*PbPbAr*] (Ar*=2,6-Ph2C6H3).18
In summary, the number of singly occupied orbitals available for CrCr bonding determines uniquely the formal bond order: six in the chromium dimer, five in the present CrI compound, and four in CrII compounds such as [Cr2(O2CMe)4] (CrCr=1.97 Å,19 calculated bond length=1.94 Å).20