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

Physical, Spectroscopic and Theoretical Results 727

Cotton

Fig. 16.14. A comparison of the energy levels in [Re2Cl8]2- and Re2Cl4(PH3)4, both calculated by the SCF-X_-SW method with relativistic corrections. HOMOs are indicated by paired arrows and percentage metal character is given for some. The two diagrams have been vertically aligned to match the lowest Cl lone-pair orbital energies.

The first tests of DFT on compounds with multiple bonds between transition metal atoms were made by Cotton and Feng.135 The molecules included in the first study were M2(O2CH)4, (M = Nb, Mo, Tc), M2(HNCHNH)4 (M = Nb, Mo, Tc, Ru, Rh), M2(HNNNH)4 (M = Mo, Ru, Rh), and M2Cl4(PH3)4 (M = Nb, Mo, Tc). In all cases where real molecules of the same or similar types were known, the calculated structures were generally quite accurate provided the most appropriate functional (B3LYP) was used and all-electron calculations were done. For example, for M2(O2CH)4 the following results were obtained:

For M2(O2CH)4, M2(O2CH)4(H2O)2 and Mo2(O2CCH3)4 (M = Mo, Rh) vibrational spectra were also calculated, and again in very good agreement with experiment.

For the calculation of electronic spectra, it is advantageous to use an extension of DFT called time-dependent DFT.136 This method provided helpful results in assigning the spectra of [Mo2(DAniF)3](O2C(CH=CH)nCO2)[Mo2(DAniF)3] (n = 0-4) molecules,137 although quantitative agreement was not attained.

Mo2Cl84- and Mo2Cl4(PR3)4.

These species have also been treated theoretically several times, beginning with SCF-X_-SW calculations on Mo2Cl84- as already noted.123 From these calculations emerged the first orbital contour diagrams for multiple metal–metal bonds. They are shown in Fig. 16.15. Although there is some mixing of metal and ligand orbitals in the Mo2Cl84- ion, the pictures clearly show that the mixing is not great and these M–M bonding MOs display their metal orbital parentage very clearly.

728Multiple Bonds Between Metal Atoms Chapter 16

In connection with PES studies of Mo2Cl4(PMe3)4 and W2Cl4(PMe3)4, to be discussed in Section 16.5, relativistic SCF-X_-SW calculations were done.138 These gave results that fitted well with the experimental data including even the spin-orbit splitting of the / ionization peak. Hypothetical molecules containing PH3 were used for these calculations.

Fig. 16.15. Contour diagrams for the μ (left), / (center), and β (right) bonding orbitals of [Mo2Cl8]4- from SCF-X_-SW calculations.

Two particularly careful and important calculations have been done on the electronic structure of Mo2Cl4L4 ( L = PH3139 or ½H2PCH2CH2PH2140) type compounds as a function of rotation about the Mo-Mo bond. CASSCF calculations139 on the model Mo2Cl4(PH3)4 showed that the 1A1g - 3A2u gap decreases to 1550 cm-1 at the exactly staggered conformation while DFT calculations140 on the model Mo2Cl4(H2PCH2CH2PH2)2 molecule gave values in the range 700-1600 cm-1. The experimental data indicate a value of c. 1300 cm-1. Thus, even though the β–β overlap goes to zero at 45°, the singlet (1A1g) ground state persists. This point is pursued further in Section 16.4.1.

16.3.3 The M2(O2CR)4 (M = Cr, Mo, W) molecules

The first attempt to deal rigorously with such molecules was the SCF-X_-SW calculation on Mo2(O2CH)4 by Norman.141,142 The greater complexity of the four HCO2- ligands as compared to eight Cl- ligands introduces a few additional features, but the Mo–Mo bonding picture remains basically the same. Eight of the sixteen C–O / and O 2p lone-pair orbitals of the formate ions mix with metal atom orbitals, and thus eight MOs responsible for Mo–O bonding are engendered. These bonds, in which considerable charge transfer from the HCO2− ions to the Mo24+ unit occurs, greatly reduce the charge on the metal atoms, thereby expanding the metal orbitals and enhancing the Mo–Mo bonding interactions.

The highest filled orbital is again the b2g β bonding orbital, and this has 89% metal d-char- acter. The next orbital down is the 6eu-orbital, which has 65% metal d/-character, but also 32% oxygen character; it contributes substantially to Mo–Mo /-bonding, but also to Mo–O /-bonding. The next eu level down, 5eu, has 38% metal character and 48% oxygen character, and it too makes significant contributions to both Mo–Mo and Mo–O / bonding, but in this case, the Mo–O bonding is preponderant. The Mo–Mo /-bonding obtains substantial contributions from both the 6eu and the 5eu MOs. The Mo–Mo μ-bonding is also provided by two MOs. This is in contrast to the case of [Mo2Cl8]4-, where the highest filled a1g orbital, with 83% metal character, is mainly responsible. In this case it is actually the second-highest filled a1g orbital, 4a1g, with 75% metal character, that makes the principal contribution, while the 5a1g orbital (48% Mo) makes a smaller contribution and is more involved in Mo–O μ-bonding.

A few years after the SCF-X_-SW calculations appeared, the first of a series of Hartree-Fock calculations were published.143 It was found that the single configuration of lowest energy was the quadruple bond configuration (μ2/4β2). After the introduction of a moderate amount of

Physical, Spectroscopic and Theoretical Results 729

Cotton

configuration interaction (CI), the μ2/4β2 contributed about 66% to the ground state of the molecule.

Numerous other HF-CI calculations have been reported for Mo2(O2CH)4 and comparisons with the Cr2(O2CH)4 molecule have also been stressed.144-149 For example148,147 calculations done in the same way for the two systems gave the results shown in Table 16.6. It is clear that while the μ2/4β2 configuration makes only a small (16%) contribution to the ground state of Cr2(O2CH)4 it makes up such a large fraction (67%) in the Mo2(O2CH)4 case that by itself it can be considered a useful description of the electronic structure.

Table 16.6. Contributions of various configurations to ground state wave functions of M2(O2CH)4 molecules

For the mixed species, CrMo(O2CH)4, two calculations have been reported. Both show that the bonding closely resembles that in Mo2(O2CH)4. In one calculation121 the method was conventional Hartree-Fock with extensive inclusion of configuration interaction, whereas the other calculation was done by the CASSCF method.150 It appears that the polarizability of the molybdenum 4d orbitals leads to a substantial overlap with the contracted 3d orbitals of chromium.

The inadequacy of the HF-CI method for describing the electronic structure of Cr2(O2CH)4 or any other Cr24+ complexes151 has not yet been remedied, even by much more elaborate methods.152

16.3.4 M2(O2CR)4R'2 (M = Mo, W) compounds

These compounds, first reported and extensively investigated153 by Chisholm and co-work- ers, are remarkable because in spite of the presence of strong axial M–C bonds (W–C 5 2.2 Å), the M–M bonds remain essentially the same length as they are in the corresponding M2(O2CR)4 compounds. Normally, axial ligation causes a lengthening of the M–M multiple bond, but a theoretical analysis154,155 has shown why the present examples are exceptions. We have already referred to this in Section 16.1.3.

The problem was treated by the SCF-X_-SW method and the essential results are shown in Fig. 16.16. It is evident, and not surprising, that the formation by W2(O2CH)4 of the two axial W–C bonds leaves the W–W /, /*, β, and β* orbitals essentially unaltered. The important

730Multiple Bonds Between Metal Atoms Chapter 16

consequences of introducing the two CH3 units result from the interaction of their frontier orbitals (which form ag and bu combinations) with the various μ orbitals of the W2 unit.

Fig. 16.16. MO energy level diagram from relativistically corrected SCF-X_-SW calculations, showing the correlation of orbitals in W2(O2CH)4 and 2CH3 with those in W2(O2CH)4(CH3)2.

The symmetric combination (ag) of the CH3 frontier orbitals interacts strongly (for both spatial and energetic reasons) with the 5a1g orbital of W2(O2CH)4, resulting in the formation of the 13ag (W–C bonding) and 16ag (W–C antibonding) orbitals of W2(O2CH)4(CH3)2. The former is occupied; the latter is empty. A critical (and perhaps surprising) result of this interaction is that the 4a1g orbital of W2(O2CH)4 is stabilized and increases its metal character in becoming the 10ag MO of the W2(O2CH)4(CH3)2 molecule. Thus W–W μ-bonding is actually enhanced, because in W2(O2CH)4 the 4a1g orbital makes the major contribution to W–W μ-bonding. The new 13ag orbital of W2(O2CH)4(CH3)2, while derived from the 5a1g orbital, differs from it in having a much larger contribution from the tungsten 6s-orbitals. Thus, the new W–C bonds are to a significant extent made possible not by stealing from the W–W μ-bond but by bringing other orbitals, namely, the W 6s-orbitals, into play.

The bu combination of CH3 frontier orbitals interacts mainly with the 5a2u orbital of W2(O2CH)4. It thereby generates the filled 15bu orbital, which is W–C bonding and consists of 6s, 6p, and 5d metal orbitals, but also generates an empty W–C antibonding orbital. This interaction slightly lessens the W–W μ-bond strength. However, together with the increase provided by the 10ag-orbital, the net result of binding the two CH3 groups is to leave the W–W μ-bond strength essentially unaltered.

732Multiple Bonds Between Metal Atoms Chapter 16

Following this early work156 and greatly stimulated by the observations made by EPR (see Section 16.7.1) on the [Rh2(O2CR)4L2]+ ions, where it is possible to get direct experimental evidence as to the nature of the SOMO, which may or may not have been the HOMO in the parent Rh24+ compound, additional theoretical work was done.157-160 An SCF-CI calculation158 showed that for [Rh2(O2CR)4(H2O)2]+ species the odd electron ought to be in the /*-orbital, as indicated by EPR spectra. On the other hand, the observation that for species with PPh3 and AsPh3 as axial ligands the [Rh2(O2CR)4L2]+ ions have the odd electron in an orbital of μ type with strong coupling to the 31P nuclei, occasioned a theoretical investigation of this type of compound.157 Because in PPh3 the lone-pair electrons are much closer in energy to the 4a2u MO of Rh2(O2CR)4, the outcome is quite different from that for H2O as an axial ligand. The essentials of the situation are shown in Fig. 16.18. The much higher lone-pair energy for PH3, as compared to H2O, forces the 17ag MO of Rh2(O2CH)4(PH3)2 to become the highest occupied orbital of the complex. We thus obtain a picture in which the highest occupied orbital is axially symmetric and yet the Rh–Rh bond remains single in complete accord with the EPR results on the Rh2(O2CR)4(PY3)2 cations.161-163 Recent DFT calculations and structural studies have provided additional support for this picture.164

Fig. 16.18. Orbital energies calculated for Rh2(O2CH)4 and Rh2(O2CH)4(PH3)2 by the SCF-X_-SW method.

There have been two calculations, one by the SCF-X_-SW165 and one by the DV-X_166 method on Rh2(HNCHNH)4 and both have shown that the RNCHNR-type ligand has a strong interaction between one of its / MOs and the β*-orbital such that the energy of the latter is driven up well above (c. 1.7 eV) the /*-orbital.

16.3.6 Diruthenium compounds

Diruthenium compounds have a rather curious history. The [Ru2(O2CR)4]X compounds were the first ones discovered (1966) and the presence of three unpaired electrons as well as the stability of the fractional oxidation state were considered puzzling. These questions were not addressed until a dozen years later by an SCF-X_-SW calculation,167 with the results shown in Fig. 16.19. The presence of three unpaired electrons was accounted for by the near degeneracy of the /* and β* orbitals. These calculations also provided a starting point for interpreting the electronic absorption spectra of the [Ru2(O2CR)4]Xn ions.

Physical, Spectroscopic and Theoretical Results 733

Cotton

As indicated in Fig. 16.19, it was suggested that the accidental degeneracy of the /* and β* orbitals should persist in the Ru2(O2CR)4 molecules with a /*3β* arrangement of the top four electrons being preferred. This, however, has turned out not to be true, according to a detailed magnetic study168 of such compounds. The magnetic data are well accommodated by a 3A2g ground state derived from a β*2/*2 configuration. It is probable that the calculation is not seriously in error since interelectronic interactions may become the controlling factor in such a situation. With the Ru2(Xhp)4 (X = CH3, Cl, Br) compounds the same ground state was again indicated by magnetic data.169 As noted in Chapter 9, in certain cases, magnetic and structural data have been able to distinguish between alternatives such as /*4, /*3β* and /*2β*2, or /*3, /*2β* and β*2/*, or /*2, /*β* and β*2.

Fig. 16.19. Orbital energies calculated for Ru2(O2CH)4, [Ru2(O2CH)4]+ and [Ru2(O2CH)4Cl2]-.

An SCF-X_-SW calculation165 on Ru2(HNCHNH)4 showed that this type of ligand has the capacity (not found for RCO2- ligands) to drive the β* orbital well above (c. 1 eV) the /* orbital, thus causing such a compound to have a diamagnetic ground state derived from the μ2/4β2/*4 configuration.

The most recent theoretical work170 on Ru2(O2CH)4, Ru2(O2CH)4L2 and Ru2(O2CH)4X molecules, employing a semiempirical INDO method as well as DFT reconfirms that the /* and β* orbitals have very similar energies and that unambiguous, a priori assignment of the ground states of these molecules is generally likely to be difficult.

16.3.7 M2X6 molecules (M = Mo, W)

Calculations by the SCF-X_-SW method on the Mo2X6 species (X = OH, NH2, NMe2, and CH3) have given a very detailed and satisfactory (as judged by comparison with PES) account

734Multiple Bonds Between Metal Atoms Chapter 16

of the bonding in these molecules.171,172 Of the four species mentioned, only Mo2(NMe2)6 is known, the others being only models for real molecules (i.e. Mo2(OH)6 for Mo2(OR)6 compounds, Mo2(NH2)6 for Mo2(NR2)6 compounds, and Mo2(CH3)6 for Mo2R6 molecules in general). These models were chosen to lessen the expense of the calculations. Comparison of the results for Mo2(NMe2)6, which can be checked against the PES, with those for its model, Mo2(NH2)6, confirms that the chosen models are valid, provided due allowance is made for the greater inductive effects of R groups compared to H atoms.

The results for the three model compounds are shown as energy level diagrams in Fig. 16.20. In addition, the numerical wave functions for all three compounds have been resolved into contributions from atomic orbital basis sets. These results are given in Table 16.7 for Mo2(OH)6. We shall discuss here only this molecule in detail, but complete discussions of all three will be found in the literature.172 It must be noted that in the D3d symmetry of these molecules, both / and β AOs and MOs belong to the same representations, eg or eu, and thus, in contrast to the X4MMX4 molecules with fourfold symmetry, / and β character is not rigorously differentiated.

Fig. 16.20. SCF-X_-SW energy levels for Mo2L6 model compounds. Only the higher filled orbitals are shown. The percentage metal character is shown for some levels.

On the basis of the information contained in Fig. 16.20 and Table 16.7, the following statements can be made concerning Mo2(OH)6. First, the valence orbitals of Mo2(OH)6 are grouped energetically into four sets:

1.the Mo–Mo bonding orbitals, 5eu and 4a1g;

2.oxygen lone-pair levels;

3.Mo–O μ-bonding orbitals;

4.O–H μ-bonding and Mo–O /-bonding orbitals.

Second, the Mo–Mo bonding orbitals are largely made up of metal d-orbital contributions and conform closely to what is expected from the simple d-orbital overlap picture.

Physical, Spectroscopic and Theoretical Results 735

Cotton

Table 16.7. Energies and percent characters of the highest occupied orbitals of Mo2(OH)6

a μ = 4dz2; / = 4dxz, 4dyz; β = 4dxy, 4dx2-y2.

bSpaces indicate contributions less than 0.4%. Hydrogen 1s contributions are not listed but are the difference between the sum of the contributions shown and 100%.

The HOMO, i.e. the 5eu orbital, has 89% metal character, most of which (81%) is metal d/ character. Fig. 16.21 shows a contour plot of one component of the MO, and it is clear that it is essentially the result of overlapping of two dxz (or two dyz) orbitals of the metal atoms, although slight Mo–O /*-antibonding character is also evident both from the plot and from the oxygen 2p percentage in Table 16.7.

The next lowest MO is the 4a1g orbital, which is strongly Mo–Mo bonding, as can be seen from the contour diagram in Fig. 16.22. The total metal contribution here is 75%, although 12% is derived from the Mo 5s-orbital. It can also be seen in the contour plot that the 4a1g orbital is Mo–O antibonding.

The clean separation of the Mo–Mo μ- and /-bonding orbitals from all the lower-lying MOs that we find for Mo2(OH)6 is lost when we go to the Mo2(NH2)6 and Mo2(CH3)6 cases, as can be seen in Fig. 16.20. The lower effective nuclear charge felt by the valence-shell electrons of nitrogen atoms causes the lone-pair electrons of these atoms to lie at energies equal to, and even slightly above, those of the metal d-orbitals. Thus, in Mo2(NH2)6 the two highest filled orbitals, 1a2g and 1a1u, are 100% nitrogen 2p in character. The 5eu MO, which is responsible for Mo–Mo /-bonding, comes next, and it has now only 72% Mo character and 24% nitrogen 2p character. It is not until we reach the sixth highest filled orbital, 4a1g, that the principal Mo–Mo μ-bonding orbital is found.

In the case of Mo2(CH3)6, the result of the carbon AOs being of comparable energy to that of the Mo d-orbitals is that Mo–C bonding orbitals are in the same energy range as the Mo-Mo /- and μ-orbitals. The mixing is now quite extensive in all respects, and no simple account of the bonding suffices. The Mo–Mo /-bonding is now effected by two MOs, 5eu and 4eu; moreover, in both of these the d/ and the dβ type AOs make substantial contributions. It is again the sixth highest MO (now 3a1g rather than 4a1g, since the totally symmetric Mo–C bonding orbital is 4a1g) that constitutes the principal instrument of Mo–Mo μ- bonding.

736Multiple Bonds Between Metal Atoms Chapter 16

Fig. 16.21. A contour plot of the 5eu orbital of Mo2(OH)6. Full and broken contours represent positive and negative regions.

Fig. 16.22. A contour plot of the 4a1g orbital of Mo2(OH)6.

The question of how well the model compounds, containing only hydrogen atoms appended to the ligating atoms, serve their purpose was addressed by comparing the results of the Mo2(NH2)6 calculation with those for Mo2(NMe2)6. As will be shown later, the photoelectron spectrum of the latter shows that the theoretical results for it are essentially correct. The computational results for the two compounds are juxtaposed in Fig. 16.23.

Since there are many more MOs in the case of Mo2(NMe2)6 that in Mo2(NH2)6, the numbers of orbitals with corresponding character in the two compounds do not correspond. Three of the six highest orbitals, including the two highest that are of a2g and a1u symmetry, are essentially pure nitrogen lone-pair orbitals in both cases. Two other orbitals in this group of six are, in each case, two eu-orbitals that jointly provide the Mo–Mo /-bonding. However, the apportionment