Multiple Bonds Between Metal Atoms / 16-Physical, Spectroscopic and Theoretical Results

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a In a monoclinic form there are two independent molecules with 3% and 8% secondary orientations. In a cubic polymorph there is a three-way disorder.

b Two molecules in the asymmetric unit.

Molecules of the type M2X4(µ-LL)2 also display disorder, of a type that can be approximately described as two orientations of the M24+ unit relative to a given configuration of the ligands.

This is illustrated for the case of Mo2Cl4(dppe)2 in Fig. 16.7.58 It is important to note that the two differently oriented molecules are different molecules. They are geometric isomers, and they also have opposite chiralities with regard to the helical twist about the Mo–Mo axis. This form of disorder has been found for numerous other M2X4(µ-LL)2 compounds as well, as shown in Table 16.3.

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Fig. 16.7. Disorder in the structure of Mo2Cl4(dppe)2; phenyl groups are omitted for clarity. Note that the ligand arrangement is the same in both molecules and only the orientation of the Mo2 units is changed.

Table 16.3. Orientational disorder in M2X4(µ-LL)2 compounds

16.1.6 Rearrangements of M2X8 type molecules

As soon as two to six of the X ligands in an M2X8 type ion or molecule are replaced by other ligands, isomers of the mixed-ligand complex must be considered. This, in turn, raises the question of whether, and if so how, isomers may be interconverted. In general, as already noted in Section 16.1.2 barriers to rotation about the M–M bond axis are low (c. 40 kJ mol-1) so that in any multistep rearrangement process where the rate-determining step has a significantly higher barrier, such a rotation (or rotations) may be a step in the overall process. The crucial question is what sort of processes with activation energies greater than about 60 kJ mol-1 are plausible.

An early suggestion69 was an internal flip of the M2 unit within the box of eight ligand atoms, as shown in Fig. 16.8. Such a net change could occur by either of two pathways, as also shown in Fig 16.8. The most intensively studied rearrangement processes have been those in which _-M2X4(diphos)2 isomers are converted to equilibrium _/` mixtures, or in some cases completely to the ` isomers.70-74 In solution these reactions are unimolecular, with rates independent of excess diphos and activation energies in the range of 80-120 kJ mol-1. In each case the flip mechanism is consistent with but not necessarily required by the facts. The flip mechanism has also been invoked in other cases.75-82

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With the advent of efficient computer codes for the application of density functional theory (DFT) to relatively large molecules, a quantitative avenue for computationally testing rearrangement pathways became available. DFT studies84,85 have found that calculated activation energies for the flip mechanism are much higher than those measured for _-Mo2Cl4(diphos)2 Α `-Mo2Cl4(diphos)2 processes in solution. An alternative process in which one end of the phosphine slips into a bridging position and then continues on to give a transition state in which one metal atom is three-coordinate (MoCl2P) which the other is five-coordinate (MoCl2P3), was found preferable. By the way, the calculated activation energy (c 360 kJ mol-1) for a flip process was not inconsistent with that measured 335 ± 30 kJ mol-1) for the _Α ` isomerization in the solid state.58

Another type of isomerization is shown in Fig. 16.10 for the three isomers of W2Cl4(NHEt)2(PMe3)2.78-80 In the reports of the experimental results, mechanisms featuring internal flips were proposed. It should be noted that an extra factor comes into play in this case, because in each isomer there are two N–H···Cl hydrogen bonds and for a reaction path in which these must be broken there will accordingly be a significant increment to the activation energy. The entire problem is too complex to be recapitulated in detail here, but DFT calculations86,87 militate against the suggested internal flip pathways and favor others in which hopping of chloride ligands as well as hopping and/or dissociation of phosphine ligands are the rate-determining steps.

Fig. 16.10. Unimolecular trans to cis transformations. Note that vertical N–H···Cl hydrogen bonds are present in each isomer.

16.1.7 Diamagnetic anisotropy of M–M multiple bonds

It is well known that unsaturated organic molecules (olefins, alkynes, and aromatics) show relatively large diamagnetic anisotropies associated with the /-electrons. An understanding of these is useful in the assignment and interpretation of their NMR spectra. The same considerations apply, a fortiori, to M–M multiple bonds. It was J. San Filippo who first pointed this out for M–M multiple bonds in 1972.88 The most important effect of diamagnetic anisotropy is seen in NMR chemical shifts. The basic theory will be found in a paper by McConnell.89 If ρ represents the magnetic susceptibility parallel to the bond direction and ρ the susceptibility perpendicular to it, ρ -ρ defines the magnetic anisotropy of the bond in the case where the bond has axial symmetry. When axial symmetry is lacking it is necessary to employ two ρ values, ρ ' and ρ ", defined in directions orthogonal to each other. The difference between a measured chemical shift and that which would be expected if there were no anisotropy, is then given by the following equations90 for the axial and non-axial cases, respectively, where subscript i refers to the i-th nucleus located at a distance r along a direction making an angle ε from the M–M bond direction, both measured from the center of the M–M bond:

¨μi = (1/3r3) [ (ρ -ρ ) (1-3 cos2ε)]/4/

¨μi = (1/3r3) [(ρ -ρ ') (1-3 cos2ε' ) + (ρ -ρ ")(1-3cos2ε" )]/4/

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In early work the factor of 4/ was sometimes omitted, leading, naturally, to ρ -ρ values that were too high by this factor. For the axial case the spacial zones of positive (upfield) and negative (down field) shifts are shown in Fig. 16.11. They are separated by a double cone of revolution determined by the value of ε which makes cos2 ε = 1/3, namely 55.44º. Thus, protons (or other resonant nuclei) lying in the equatorial region will be observed downfield from their “normal” position, and those in the axial region will be observed upfield in the NMR spectra.

Fig. 16.11. Zones for positive and negative chemical shifts due to diamagnetic anisotropy about an axially symmetric metal−metal bond.

Examples of the former abound,90-93 the methyl protons of µ-acetate ligands being representative. Only recently has a well-defined instance of protons shifted upfield been reported.94 Table 16.4 provides some values for a range of multiple bonds.

Table 16.4. Diamagnetic anisotropiesa for some M–Mb and otherc multiple bonds

16.2 Thermodynamics

16.2.1 Thermochemical data

Thermochemical data on compounds containing M–M multiple bonds have been gathered primarily because of interest in the M–M bond energies. Since these bonds have such high bond orders and are so short, the question of how strong they may be in a thermodynamic sense naturally arises. However, there are very serious difficulties involved in estimating the bond strengths from measurable thermodynamic quantities. It is even difficult to obtain accurate,

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unambiguous data.95 The most extensive sets of data have been obtained for the following reactions:96-98

W2(NMe2)6 (s) + 24O2 (g) Α 2WO3 (s) + 18H2O (l) + 3N2 (g) + 12CO2 (g)

M2(NMe2)6 (s) + [14H+ + Cr2O72- + H2O] (aq) Α

2H2MO4 (ppt/soln) + [2Cr3+ + 6NMe2H2+] (aq) (M = Mo, W)

Mo2(OPri)6 (s) + [6FeCl3 + 4NaCl + 8H2O] (aq) Α

2Na2MoO4 (ptt/soln) + [6FeCl2 + 6PriOH + 10HCl] (aq)

MM'(O2CMe)4 (s) + [8FeCl3 + 4 NaCl + 8H2O] (aq) Α

[Na2MO4 + Na2M'O4] (ppt/soln) + [8FeCl2 + 4MeCO2H + 12HCl] (aq) (M, M' = Mo, Cr)

Similar reactions were used to obtain enthalpies of formation of several related mononuclear compounds containing comparable metal-ligand bonds, viz. Ta(NMe2)5, W(NMe2)6, and Mo(NMe2)4. Enthalpies of sublimation were measured in a few cases, but were mostly estimated. The available data are collected in Table 16.5.

Table 16.5. Thermochemical results for triply and quadruply bonded dimetal compounds.

a Estimated.

b Not reported.

From the enthalpies of formation plus collateral data it is possible, and in some cases useful, to derive what have been called enthalpies of disruption, ¨Hdisr, which represent the energy needed to break a mole of the gaseous substance into individual metal atoms and ligands; in

other words, ¨Hdisr is the sum of the M–M and all metal-ligand bond energies. These values are also given in Table 16.5.

One other thermochemical measurement has been reported,99 namely, for Cs2Re2Br8, but there have been no new thermochemical data for many years.

16.2.2 Bond energies

The estimation of individual bond energies from thermochemical data is difficult. Assumptions of highly uncertain accuracy are required. The essential difficulties are clearly evident, in a representative way, for the M2(NMe2)6 molecules.96,100 The disruption energy for such a molecule corresponds to the process

M2(NMe2)6 (g) Α 2M (g) + 6NMe2 (g)

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¨Hdisr and the equation relating this to bond energies is

¨Hdisr = D(M–M) + 6 D(M–NMe2)

Clearly, to calculate D(M–M) it is necessary to know D (M–NMe2), and to know it accurately, since the uncertainty therein is multiplied by six.

Unfortunately, there is no rigorous way to estimate D (M–NMe2), and even the uncertainty in any given estimate is difficult to fix100,101 Thus, for M2(NMe2)6, D(Mo–Mo) values could be as low as 200 and as high as 790 kJ mol-1 although they are likely to be from 350-600 kJ mol-1. Similarly, the likely range for D(W–W) is 550-775 kJ mol-1. No doubt the most definite and useful result of these efforts is that, other things being equal, the W>W bond is appreciably stronger than the Mo>Mo bond. For Mo2(OCHMe2)6, D(Mo>Mo) has been estimated in the range 310-395 kJ mol-1.

For quadruply-bonded species, the problem is even worse since there are eight M–L bonds. By using thermochemical data for M(acac)3 compounds to estimate D(M–O) values, the following D(M–M) values (in kJ mol-1) in M2(O2CCH3)4 compounds were proposed:97 Cr–Cr, 205; Mo–Cr, 249; Mo–Mo, 334. From the measured enthalpy of formation99 of K2Re2Br8 and estimates of lattice energy and D(Re–Br), D(Re–Re) was calculated to be 408 ± 50 kJ mol-1.

A few attempts have been made to estimate the dissociation energies of weaker M–M bonds. From thermodynamic data for solutions, it has been suggested that in the corresponding M2(O2CCH3)4(H2O)2 compounds of Cr and Cu, the Cr–Cr bond is about 45 kJ mol-1 stronger than the Cu–Cu bond.102 The latter is so weak that this may well be tantamount to an estimate of the Cr–Cr bond energy. The dissociation energy of the Rh−Rh bond103 in Rh2(OEP)2 has been shown to be 69 ± 3 kJ mol-1.

Spectroscopic and theoretical methods have also been used to estimate the dissociation energies of some triple and quadruple bonds. There is a procedure in the spectroscopy of diatomic molecules, the Birge-Sponer extrapolation, in which a progression of overtones in the stretching frequency of the diatomic molecule is employed to evaluate τ and ρ, the harmonic stretching frequency and the anharmonicity constant, respectively. With these constants, the bond energy can be estimated as (τ2/4ρ)-τ/2. This is only an approximate relationship and tends to give results that are too high, but it is generally reliable to within 20%.

If the assumption is made that a stretching vibration localized in the M2 unit in the center of a [M2X8]n- ion can be treated like the vibration of a diatomic molecule, the Birge-Sponer procedure can be employed for several [Mo2X8]4- and [Re2X8]2- species that have long progressions in that fundamental mode believed to be essentially a metal-metal stretching motion. Bond energies estimated in this way104 are in the range 530-790 kJ mol-1 for [Mo2Cl8]4-, 635 ± 80 kJ mol-1 for [Re2Cl8]2-, and 580 ± 100 kJ mol-1 for [Re2Br8]2-.

Attempts have been made to estimate bond energies directly from theory;105 the reliability of the results is difficult to assess but unlikely to be high. The final conclusion105 was that the best theoretical estimate for the dissociation energy of the Mo>Mo triple bond in Mo2X6 compounds is about 284 kJ mol-1. A generalized valence bond method106 especially adapted to the particular difficulties presented by M–M multiple bonds, gave a bond energy of 367 kJ mol-1 for the [Re2Cl8]2- ion. This is appreciably lower than the Birge-Sponer estimates but in fair agreement with the thermochemical estimate 408 ± 50 kJ mol-1 for [Re2Br8]2-. This same calculation indicated that the β-bond contributes only 25 ± 12 kJ mol-1, which is probably too low. SCF-X_-SW calculations on Mo2, [Mo2Cl8]4-, and Mo2(O2CH)4 gave 305 and 406 kJ mol-1 for [Mo2Cl8]4- and Mo2(O2CH)4, respectively.107

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The preceding summary of the published efforts to estimate D(MM) values for triple and quadruple bonds suggests that the results obtained, at least individually, are very unreliable. However, when they are taken all together, the results show a moderate degree of consistency. It is very likely (in our opinion) that the highest estimates are, in fact, too high. Most likely, the D(Mo>Mo) values are around 300 kJ mol-1, and the D(W>W) ones somewhat higher, say about 350 kJ mol-1. For quadruple bonds, it is likely that D(Mo Mo) is about 350 kJ mol-1 while D(Re Re) is between 400 and 450 kJ mol-1.

To put these values in context, they are somewhat above the range, 250-350 kJ mol-1 of single bonds between lighter elements. Suitable comparisons are provided by D(C–C) = 350, D(S–S) = 265, D(Cl–Cl) = 244 kJ mol-1. However, they are well below the values for such multiple bonds as C=C (622), C>C (715) and N>N (950). Thus, in spite of the exceptional shortness of M–M multiple bonds (in relation to the atomic sizes) they are not exceptionally strong. They probably are adversely affected by the rather large cores and consequent core-core repulsions that come into play at these short distances.

16.3 Electronic Structure Calculations

16.3.1 Background

Multiple bonds between transition metal atoms pose exceptional challenges to the quantitative theory of molecular electronic structure. At the time these bonds were first recognized and qualitatively described, and for some years thereafter, these challenges were insuperable.

Early attempts were made to employ approximate semiempirical methods110-113 to the quadruple bond, but the results were then of doubtful reliability and are today of little value or interest. We shall not discuss them here at all, nor shall we consider qualitative valence bond,114 or other less rigorous treatments.115-118

The first encouraging developments began in the early 1970s with the modification of certain theoretical techniques, originally developed by Slater’s school for dealing with the band theory of metals, to make them applicable to molecular problems. This work, pioneered by John C. Slater and Keith Johnson, resulted in what became known as the SCF-X_-SW method; the abbreviation means self-consistent field X_ scattered wave.

The term X_ refers to an approximate way of evaluating the mean exchange energy. This way of setting up the problem led to equations that lent themselves to machine solution even when the atoms have many electrons and the molecule is large. More recent advances in both theory per se and computer codes for its implementation, make it possible to employ the Har- tree-Fock equations, including the density functional modifications, to the whole field of multiple bonds between metal atoms. In general the SCF-X_-SW method has been superceded, but many of the results previously obtained have not been and are still an excellent guide to electronic structures.

Underlying all Hartree-Fock calculations on M–M multiple bonds is the fact that a oneelectron orbital picture, so familiar and so straightforwardly useful in many other types of chemistry, is often a poor approximation for these very electron-rich systems. The idea behind the usual Hartree-Fock MO treatment is that the energies of interaction between electrons are much smaller than orbital energy differences. As more electrons (upwards of 6 to as many as 14)

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are crowded together in the space between two close (1.8-2.4 Å) metal atoms, this idea becomes less valid. The most difficult problems have been encountered with the simple diatomics (e.g., Cr2, Mo2) and among isolable compounds, with those of Cr24+ and others formed by metals in the first transition series. There are several papers that specifically deal with this so-called ‘electron correlation’ problem.119,120

16.3.2 [M2X8]n- and M2X4(PR3)4 species

The first quantitative calculations performed on metal-metal multiple bonds were carried out by the SCF-X_-SW method on the [Mo2Cl8]4- ion123 and the [Re2Cl8]2- ion.124,125 These calculations are major landmarks because they provided reliable, detailed, and quantitative descriptions of the ground state electronic structures of these ions (along with descriptions of the lower unoccupied MOs) and verified the essential correctness of the qualitative description of the quadruple bond originally given.126 Later, calculations for the [Tc2Cl8]3-, [W2Cl8]4- ions,127 and the [Os2Cl8]2- ion128 were presented. In addition, a calculation129 on [Re2Cl8]2- was done by the discrete variational X_ method, giving results in good general agreement with those by the SCF-X_-SW method. A pictorial comparison of all SCF-X_-SW results for [M2X8]n- species, taken from the paper128 dealing with the osmium compound is shown in Fig. 16.12. It can be seen that all the electronic structures are qualitatively similar.

Fig. 16.12. Selected energy levels for the [M2X8]n- species that have been calculated by the SCF-X_-SW method. Levels drawn with heavier lines have > 50% metal character.

In all these [M2Cl8]n- species the pattern of orbitals has 2b1u (β*) > 2b2g (β) > 5 eu (/), with a rather large gap from the β* orbital up to the next lowest antibonding orbital. Below the eu (/)

type orbital, there is a fairly dense array of closely spaced orbitals of mainly M–Cl and Cl lone pair character, but among them are three a1g-orbitals which must, in varying degrees, enter into M–M and M–Cl μ-bonding. This can be better discussed by employing the energy level diagrams in Fig. 16.13 for [Re2Cl8]2-.

In more recent years improvements in computer hardware and increasing sophistication in software have permitted more accurate and sophisticated calculations (at least in principle) to be made. One obvious improvement is to include relativistic effects, at least approximately, for compounds of third-transition series metals. This was done for [Re2Cl8]2- in 1983,130 by a

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method that was believed to be about 90% effective. As shown in Fig. 16.13 some levels are shifted significantly, although the qualitative picture is not changed. Subsequently full inclusion of relativistic effects became possible, including the calculation of spin-orbit coupling.131 One of the first of such calculations was done on the [W2Cl8]4- ion, where a change from the nonrelativistic to the relativistic calculation had about the same results as those in Fig 16.13. Another interesting result in the relativistic [W2Cl8]4- calculation is that spin-orbit coupling is predicted to split the eu (/) orbitals by 0.33 eV, which is very close to the splitting observed by PES for W2(mhp)4 (c. 0.4 eV).

Fig. 16.13. Energy levels of [Re2Cl8]2- calculated by the SCF-X_-SW method without (left) and with (right) relativistic corrections.

Various other calculations have more recently been done on [Re2Cl8]2-, by a variety of methods.132 While these have illuminated certain details, from the point of view of the chemist the essentials are unchanged.

The effect of replacing four Cl- ligands in [Re2Cl8]2- by phosphine ligands was investigated by relativistic SCF-X_-SW calculations.133 As shown in Fig. 16.14 the pattern of the frontier orbitals is not much changed on going to the model phosphine compound Re2Cl4(PH3)4.

Beginning in the late 1990s efficient computer programs for a computational methodology called density functional theory (DFT)134 have become available, and DFT is now a popular choice for ground states of molecules. The computational efficiency of DFT methods is very high and it has the ability to provide computed bond lengths, bond angles and vibrational frequencies that usually approximate very closely to experimental values, especially when large basis sets and well crafted functionals are used.