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

Physical, Spectroscopic and Theoretical Results 747

Cotton

all of these, but a few are worth mentioning, such as the following ones (cm-1) for homoleptic species:208

There are two classes of compounds in which β2Αββ* transitions which might naively have been expected are not seen. In Mo2(O2CAr)4 compounds, strong LMCT transitions occur in the region where the relatively weak β2Αββ* transitions must be and completely cover them up.209 In compounds of the type shown in Fig. 4.40 in Section 4.5.6, the β bonds that were originally present on the two short, unbridged edges of the rectangles have opened and the β orbitals and their electrons have become engaged in forming Mo-Mo single bonds along the two long, bridged edges. No simple β2Αββ* transitions remain.210

While the behavior of the [M2X8]n- ions is conventional and fairly easily interpreted, that of the carboxylato species M2(O2CR)4 and some others is not. In fact, several of these species present examples of complicated vibronic interactions that were previously so rare that it was some time before the true situation was recognized and the spectra were correctly interpreted. We may begin the discussion as it began in the literature, namely, with the low-temperature, oriented single-crystal spectra of [Mo2(O2CCH2NH3)4](SO4)2·4H2O,211 shown in Fig. 16.29. This compound forms tetragonal crystals in which the Mo–Mo bonds are all aligned with the crystal c axis, thus making cleanly polarized spectra quite easy to record.

Fig. 16.29. Single crystal polarized spectra of [Mo2(O2CCH2NH3)4]4+ at 15 K.

In view of the fact that for [Mo2Cl8]4- the β2Αββ* transition is found at 18.0-20.0 x 103 cm-1, it had seemed natural to suppose that the weak transitions exhibited by Mo2(O2CR)4 compounds in the range 20.0-23.0 x 103 cm-1 should be similarly assigned. It will be recalled, however, that this transition was expected to appear exclusively in z polarization. As Fig. 16.29 shows, in the glycinate it is present with comparable intensities in both z and xy polarizations. This was taken as evidence that, contrary to expectation, the absorption in this region could not be assigned to the β2Αββ* transition, but must be assigned to some electronically forbidden transition, with several different vibrations being involved in conferring vibronic intensity upon it. Some specific suggestions were made as to the assignment.211

748Multiple Bonds Between Metal Atoms Chapter 16

It was soon shown that Mo2(O2CH)4 has very similar behavior,198 with vibrational progressions of comparable intensities appearing in both xy and z polarizations, again implying that the transition should not be assigned to the bAb* transition. A very detailed investigation212 of the acetate, Mo2(O2CCH3)4, then showed that not only was there intensity in xy polarization, but that this was predominant. From a detailed analysis of the observed vibrational structure, the temperature dependence of hot bands, and the characteristics of the emission spectrum of Mo2(O2CCF3)4, it was concluded that the absorption band at c. 23.0 x 103 cm-1 in Mo2(O2CCH3)4 was best assigned to an orbitally forbidden, metal-localized bA/* transition, which derived its intensity from vibronic coupling.

The trouble with having all of this evidence against assigning the bands at c. 23.0 x 103 cm-1 in Mo2(O2CR)4 molecules to the b2Abb* transition was that there are no bands at lower energy in the visible spectrum, and it hardly seemed likely that this transition could come at an energy below the visible (i.e. at < 12 000 cm-1). On the other hand, the next higher bands are at 30.0 x 103 cm-1 and above, which seemed too high. For a short time, the problem appeared to have no reasonable solution, until, in 1979, Martin, Newman, and Fanwick provided the definitive explanation.213 They showed that the characteristics of the band in Mo2(O2CCH3)4 at c. 23.0 x 103 cm-1 and similar bands in other Mo2(O2CR)4 compounds are not inconsistent with their being assigned to the b2Abb* transition. They pointed out that there were inconsistencies in the earlier study212 of Mo2(O2CCH3)4 and that all observations could be explained in the following way.

Because of the small overlap of the dxy orbitals, b2Abb* transitions have rather low intensities, even though they meet the symmetry requirements to be orbitally allowed in z polarization. In other words, while there is a purely orbital dipolar intensity mechanism, it is an unusually week one. To understand how this affects the appearance of the absorption band (other than making it very weak), we must consider in detail the following expression for the transition moment:

This expression takes account of vibronic coupling to first order and must be squared to give the intensity values for each vibrational component. When this is done using the adiabatic Born-Oppenheimer approximation we obtain:

The functions g0| and |fi'i denote the zeroth vibrational level of the electronic ground state and the ith vibrational level of the upper electronic state, respectively. As a normal rule, when a transition is orbitally dipole-allowed, M0 is so large that M02 >>M0mi >>>mi2 and we see only the vibrational progression in a totally symmetric frequency represented by the first term on the RHS of the equation. Moreover, this occurs only in parallel polarization. For dipole-for- bidden transitions (M0 = 0) only the third term survives; we then see vibronic progressions in one or both polarizations, but not in the totally symmetric frequencies. The curious situation we have with the weaker bAb* transitions is that M0 5 mi so that all three terms in the equation are of similar importance.

It is therefore possible to see in z polarization not only the “expected” progressions in one or more totally symmetric vibrations, but also one or more other progressions in which the

Physical, Spectroscopic and Theoretical Results 749

Cotton

Franck-Condon factors (that is, the relative intensities of the lines in the progression) may be different from those in the totally symmetric progressions. In addition, vibronic components of similar intensities will also be seen in xy polarization.

Subsequent study of other amino acid complexes214 has further confirmed the general applicability of Martin, Newman, and Fanwick’s analysis to all Mo2(O2CR)4 compounds. Moreover, this sort of situation has been shown to prevail in several other compounds, and it now appears to have been only a happy accident that in the [M2X8]n- systems first examined, no ‘anomalous’ features were present. This is because in the [M2X8]n- ions the βΑβ* type transitions have molar intensities of 800 M-1 cm-1 or greater, and the conventional allowed-band characteristics (i.e. z polarization and all progressions having identical Franck-Condon factors) dominate. In the tetracarboxylates, however, the intensities are only about 100 M-1 cm-1, and this leads to the complex behavior characteristic of these species.

While the assignment of the β2Αββ* transition in Mo2(O2CR)4 compounds to the absorption band at c. 23 x 103 cm-1 was placed almost entirely beyond doubt by the work of Martin, Newman, and Fanwick,213 as just explained, there have been several more recent experimental studies that also contribute, in varying degrees, to supporting this conclusion.200,215-218 The polarized crystal spectra of Mo2(O2CCF3)4 and Mo2(O2CCF3)4py2 display well-developed vibrational progressions on this band that can be interpreted in a manner fully consistent with the β2Αββ* assignment.200 In two new crystal forms of Mo2(O2CCMe3)4, a wealth of vibronic structure is observed and can be fully explained by employing the β2Αββ* assignment.217 Similarly, in a study of Mo2(O2CCPh3)4·nCH2Cl2, the vibronic structure is extremely rich and detailed, and all of it entirely consistent with the β2Αββ* assignment.218

A study of Re2(O2CCMe3)4Cl2 has provided corroboration of the analysis of the Mo2(O2CR)4 β2Αββ* bands.219 This compound forms tetragonal crystals which, as in the case of Mo2(O2CCPh3)4 and several others, makes the interpretation of polarized crystal spectra as straightforward as possible. A band maximizing at 20,200 cm-1 is strongly but not totally z-polarized; there is a weak (15%) band at 20, 500 cm-1 in xy polarization. The intensity of the z-polarized band is also temperature independent (from 300 to 6 K). Thus, assignment to the β2Αββ* transition is indicated. The weak xy-polarized absorption at slightly higher energy can be attributed to vibronic activation of the same transition. Because the allowed transition (z-polarized) is here about four times as strong as in the Mo2(O2CR)4 molecules, the vibronic contribution is much less important.

It is interesting that the appearance of progressions with two different sets of Franck-Con- don factors for a single vibration is observed in an even more startling and unequivocal fashion220 in the compound Mo2[(CH2)2P(CH3)2]4, as shown in Fig. 16.30. It can be seen that there are five origins for vibrational progressions, all of which are built on the excited state ι'(M–M) of 345 cm-1 (the ground state value is 388 cm-1). It is obvious, however, that the two series, labeled 0 and a, have very different Franck-Condon factors: the former has its strongest peak second (02), while the latter has it third (a3). From a detailed interpretation of these results it has been deduced that the Mo-Mo distance in the excited state β2/4ββ* is about 0.09 Å longer than that in the β2/4β2 ground state.

In Tc2(hp)4Cl (hp = anion of 2-hydroxypyridine the βΑβ* type transition has a more complex plethora of vibrational components than in any other case.221 Fortunately, this compound forms tetragonal crystals, with the molecules all parallel to the c-axis, and the polarized spectra were therefore cleanly accessible. It would probably have been impossible to separate the many components had the molecules not been entirely parallel to one another. The results are shown in Fig. 16.31. In z polarization only, there is a peak at 12,194 cm-1 and this must be the 0-0 component of the orbitally allowed β2β*Αββ*2 transition, but following it there are clearly

750Multiple Bonds Between Metal Atoms Chapter 16

other progressions of equal or greater intensity. There are also numerous progressions in xy polarization that are as strong, or stronger. Again, we have a case where vibronic intensity is equal to or greater than the orbital dipole intensity.

Fig. 16.30. The β2Αββ* transition in polycrystalline Mo2[(CH2)2PMe2]4 at 5 K.

A complete analysis of the z-polarized spectrum and a partial analysis of the xy-polarized spectrum showed that not only the ι1'(Tc–Tc) vibration (339 cm-1), but also the Tc–O and Tc–N vibrations ι2' and ι3' (264 and 298 cm-1) are involved. Thus, after the 0-0 band we have peaks corresponding to ι1', ι2', and ι3'. Following this, however, we have not only the expected continuation of progressions in all possible overtones of ι1' and ι2' but also in their combinations. Thus, for example in the fifth collection of peaks we identify 5ι2', 4ι2' + ι1', 3ι2' + 2ι1', 2ι2', 3ι1', ι2' + 4ι1', and 5ι1'. This spectrum may well be the most complex example of vibronic coupling yet observed and analyzed.

It is interesting to note that while the [Mo2(SO4)4]4− ion, with which we began this discussion, shows no vibrational structure for the β2Αββ* transition even at 15 K, the [Mo2(SO4)4]3− ion (like [Tc2Cl8]3-) shows such structure even at room temperature222 and in solution.223 At low temperature (5.3 K) the resolution is enormously enhanced and the details are found to be complex, which is, in part, a result of there being two crystallographically distinct [Mo2(SO4)4]3- ions present in the compound K3[Mo2(SO4)4]·3.5H2O. All data, including polarization, are consistent with the βΑβ* assignment. The energy of the electronic transition is c. 6400 cm-1, which is very similar to that for [Tc2Cl8]3-. Thus we see again, now for the β2/4β case, that when electron correlation effects are not involved, βΑβ* transitions have energies of c. 6000 cm-1, whereas, when correlation effects come into play, as they do for the quadruply bonded β2/4β2 configuration, the energies are 14,000 ([Re2Cl8]2-) to 23,000 cm-1 (Mo2(O2CR)4).

The M2(mhp)4 (M = Cr, Mo) molecules also display β2Αββ* transitions, with origins at about 21,000 and 19,400 cm-1, respectively.224 For the Mo compound a vibrational progression of 344 cm-1 separation is assigned to ι'(Mo-Mo), while a progression of 305 cm-1 in the Cr compound was not considered to have this assignment, but the situation is ambiguous. The related Mo2(mhp)2Cl2(PEt3)2 has its β2Αββ* transition225 with an origin at c. 17,600 cm-1 (maximum at c. 18,500 cm-1) and shows progressions in ι'(Mo-Mo) 5 370 cm-1.

Physical, Spectroscopic and Theoretical Results 751

Cotton

Fig. 16.31. Polarized crystal spectra of the β2β*Αββ*2 transition of Tc2(hp)4Cl at 5 K.

16.4.3 Other electronic absorption bands of Mo2, W2, Tc2 and Re2 species

The literature records a vast array of other electronic absorption spectra in addition to those due to βΑβ* type transitions. Some of these results will be presented here, more or less briefly.

[Re2X8] n- ions.

In the [Re2Cl8]2- ion there are several absorption bands that occur below 50,000 cm−1 but above the β2Αββ* transition in these species and attempts to assign them began as early as 1975.125 Two strong bands (ϒ = 5000-10000) at 30,900 and 39,200 cm-1 were reported to have xy polarization and to show MCD A-terms. Both of these characteristics imply that the excited states have Eu symmetry and the high intensities indicate that allowed transitions are responsible. It was therefore proposed that the first band is due to an egΑb1u transition and it was described as a charge-transfer transition where electron density from an orbital mainly occupied by Cl lone pair electrons is transferred to the metal-based β* orbital.

Support for this assignment has since come from RR excitation profile studies,204 which also suggest that bands in [Re2Br8]2- (23,800 cm-1) and [Re2I8]2- (14,800 cm-1) can be given the same assignment. The other band was assigned 125 to the /Α/* transition but it has been suggested 130 that this is incorrect.

Between the βΑβ* and the /(Cl)Αβ* transitions in [Re2Cl8]2- there are several other transitions, all weak and presumably forbidden. This region of the spectrum is shown in Fig. 16.32. It has been suggested that bands I and II are not singletΑtriplet transitions,226 but only on the basis of negative evidence. The earliest set of assignments104 are unreliable due to uncertainties in the (nonrelativistic) calculations, inadequacies in the data, and a simplistic approach.

752Multiple Bonds Between Metal Atoms Chapter 16

Fig. 16.32. The visible absorption spectrum of (NBun4)2[Re2Cl8] in acetonitrile.

At the present time the best interpretation of the region shown in Fig. 16.32, is to be found in a later paper130 in which a relativistically corrected SCF-X_-SW calculation is employed as well as calculations of actual transition energies by the transition state method (as opposed to mere subtraction of orbital energies). To illustrate the importance of this, the energy of the egΑb1u (/Αβ* ) LMCT band at 31.4 x 103 cm-1 in [Tc2Cl8]3- is calculated to be about 22.0 x 103 cm-1 by using only orbital energy differences, but when a relaxation correction using Slater’s transition state method is introduced, a value of c. 29 x 103 cm-1 is predicted. In addition new measurements of crystal spectra were made whereby errors in the older data were corrected. These new measurements failed to confirm the existence of the questionable-looking band III in Fig. 16.32. Bands I and II were examined under better resolution and their polarizations correctly determined.

Band I was assigned to two overlapping transitions, /Αβ* and βΑ/*, and band II to a spin forbidden 3(/Α/* ) transition. The assignment of the pair of bands labeled IV remains uncertain. One suggestion104 was that these might be singlet-triplet transitions related to the strong, spin-allowed LMCT band at 30,800 cm-1, but other assignments are possible in the absence of further experimental data.

Some work on [Re2Br8]2- has also been published 125,227 but it is inconclusive. It was carried out before the existence of disorder in the (NBun4)2[Re2Br8] crystals was recognized and thus the interpretation of polarization data requires reconsideration.

Other dirhenium species.

For Re2(O2CCMe3)4Cl2, in addition to the firm assignment of the 1(β2Αββ*) transition at 20,200 cm-1, a much weaker band at 16,500 cm-1 with xy polarization was tentatively assigned to the spin-forbidden 1A1g(β2)Α3A2u (ββ*) transition.219 Bands at 24,700 and 29,000 cm-1 have been assigned to the vibronically activated /Αβ* and βΑ/* transitions, respectively.

There have been some spectroscopic data reported for the Re2Cl5(PR3)3 and Re2Cl4(PR3)4 species.228 The former are μ2/4β2β* species and would be expected to have β2β*Αββ*2 transitions at quite low energy, by analogy with [Tc2Cl8]3-. In fact, all such species have absorption bands at c. 7000 cm-1 that can be so assigned. The Re2X4(PR3)4 compounds often appear

Physical, Spectroscopic and Theoretical Results 753

Cotton

to have similar bands, but it has been shown that these come not from such molecules, but from their oxidation products, the [Re2X4(PR3)4]+ ions, and they may again be assigned as β2β*Αββ*2 bands. The spectrum of the compound [Re2Cl4(PPr3n)4]PF6 has been investigated in detail at 5 K and a complete assignment proposed.133 The band at c. 6600 cm−1 is, indeed, the β2β*Αββ*2 transition, and assignments in keeping with the general picture developed for [Re2Cl8]2- have been made for the entire spectrum on the basis of an SCF-X_-SW calculation with relativistic corrections.133

The [Tc2Cl8]3- ion.

For the [Tc2Cl8]3- ion a complete assignment has been proposed,199 in part on the basis of guidance provided by an SCF-X_-SW calculation.127 The observed spectrum is shown in Fig. 16.33 (except for the β2β*Αββ*2 transition, which is off-scale at c. 1600 nm), and the proposed assignment is give in Table 16.8. Again there are no allowed transitions between β2β*Αββ*2 and the first LMCT transitions in the near-UV, except that here, because of the presence of a β* electron, there is an allowed β*Α/* transition that cannot occur for [Re2Cl8]2- and other such species. In general, the fit of calculated and observed energies is very good. It will be recalled that for [Re2Cl8]2- this was not the case. While part of the problem with [Re2Cl8]2- may have been the result of relativistic effects, it is likely, in view of the work on [Tc2Cl8]3-, that the underestimation of the actual energy is largely attributable to the failure to include relaxation energy in the calculation.

Fig. 16.33. The absorption spectrum of the [Tc2Cl8]3- ion in aqueous HCl solution.

The spectrum of the [Mo2Cl8]4- ion was first reported and assigned by Norman and Kolari,123 and subsequent work200,227 has only served to confirm their proposals, which are shown in Table 16.9. The polarization of the band at 31.4 x 103 cm-1 was shown to be in accord with the assignment,200 and the absorption band at about 37.0 x 103 cm-1 has been shown to have an MCD A term as required for a 1A1gΑ1Eu transition. It should be noted that there is again good agreement between calculated and observed energies (except for β2Αββ*), as in the case of [Tc2Cl8]3-, because here too the transition state method of Slater was used. The assignments suggested for the weak absorption at around 24.0 x 103 cm-1 are like those proposed for similar bands in [Re2Cl8]2-.

754Multiple Bonds Between Metal Atoms Chapter 16

Table 16.8. Spectrum of [Tc2Cl8]3- and possible assignments

a Energies in cm-1 x 103; ϒ in liters mol-1 cm-1; f is the oscillator strength (dimensionless). b Bold numbers indicate electric dipole-allowed transitions.

c Energy of first vibrational component. d Estimated; see text.

Table 16.9. Calculated and experimental electronic spectrum of [Mo2Cl8]4- below 40 kcm-1a

aBand positions in kcm-1, obtained using the relation 1 hartree = 219.4746 kcm-1. All calculated spinand dipole-forbibben transitions that should not be obscured by dipole-allowed bands are listed. All observed

peaks in the range 4.8-40 kcm-1 are listed plus the strong unresolved absorption that begins above 34 kcm-1 and apparently maximizes above 40 kcm-1.

b Largely metal orbitals are denoted μ, /, β, β*, /*, μ*, and dx2-y2 according to their character. Largely ligand orbitals are represented by Cl.

c From the mineral oil mull spectrum of K4Mo2Cl8·2H2O.

The bands in [Tc2Cl8]3- at 13,600 (ϒ 35) and 15,700 cm-1 (ϒ 172) were assigned as 2B1uΑ2Eu (/Αβ*) and 2B1uΑ2Eg (β*Α/*), respectively. The weakness of the /Αβ* transition can be attributed to its being Laporte-forbidden in D4h symmetry. Although the β*Α/* transition is fully allowed, the extinction coefficient of 172 M-1 cm-1 indicates that it is quite

Physical, Spectroscopic and Theoretical Results 755

Cotton

weak. The transitions at 17,000 and 18,000 cm-1 are broad and weak, and it was not possible to obtain definitive polarization data from the crystal spectrum.

Mo2(O2CR)4 molecules.

The correct assignment of the βΑβ* transition in Mo2(O2CR)4 molecules, at c. 23.0 x 103 cm-1, was achieved only after considerable effort, with much confusion along the way, as already recounted in Section 16.4.2. So much attention has been concentrated on this question that the rest of the spectrum has not yet been studied very thoroughly. The SCF-X_-SW calculation142 suggested several assignments of the solution spectrum, but agreement between calculated and observed peaks is not especially good. There is a band at 26.5 x 103 cm-1 in the spectrum of Mo2(O2CCH3)4, which may be the βΑ/* transition,213 that had previously been erroneously assigned to the 23.0 x 103 cm-1 band. The spectra of the Mo2(O2CR)4 species need further experimental (and perhaps also theoretical) study.

The [Mo2(HPO4)4] 2- ion.

The [Mo2(HPO4)4]2- ion is doubtless the best characterized example of a μ2/4 configuration within the M2X8 D4h structural context. It has been carefully studied and the principal features of its electronic absorption assigned229 as shown in Table 16.10. From these assignments one calculates a separation of ~ 5500 cm-1 between the one-electron β and β* orbitals, in reasonable accord with expectation from theory. The separation between the / and /* orbitals is then about 40,000 cm-1 (5 eV), also in agreement with the strength of the /-bonding indicated by MO calculations.

Table 16.10. Electron transitions in [Mo2(HPO4)4]2-

Mo2X4(PR3)4 compounds.

We conclude this section by citing work on the Mo2X4(PR3)4 compounds, which have been rather extensively investigated197,230-232 and provide some important insight into the relationship of the β2Αββ* transition (energy and intensity) to the other properties of the molecule, as well as data on other electronic transitions. For a series of Mo2Cl4(PR3)4 molecules, the position of the β2Αββ* transition is sensitive to the /-acidity of the phosphine.230 It moves to lower energy as the /-acidity of the phosphine increases. However, it is not clear how to account for this. When the phosphine is kept constant (as PMe3) and the halide is changed197,231 from Cl to Br to I, the position of the β2Αββ* transition is little affected but the intensity increases markedly. This has been attributed to borrowing from an LMCT band at 30,860 (Cl), 29,990 (Br), and 25,320 (I) cm-1. The nature of this LMCT transition was described as μ(M–P)Αβ* (Mo2) with substantial XΑM character as well. In addition, there are several weak bands lying between the β2Αββ* and the LMCT bands, one of which lies in the 20,000-23,000 cm-1 range and has been assigned to the /Αβ* transition.

756Multiple Bonds Between Metal Atoms Chapter 16

16.4.4 Spectra of Rh2, Pt2, Ru2 and Os2 compounds

Rh2(O2CR)4L2 molecules.

All such molecules have two principal electronic absorption bands: band A around 17,000 cm-1 and band B around 23,000 cm-1, whose assignments have been controversial. The polarized crystal spectra of Rh2(O2CCH3)4(H2O)2 are shown in Fig. 16.34 for band A.

Fig. 16.34. Polarized crystal spectra of Rh2(OCCH3)4(H2O)2 in the region of band A.

As early as 1970 it was proposed that band A, on the basis of its xy polarization, tempera- ture-independent intensity, and sensitivity to changes in the axial ligand, should be assigned to a /*(Rh2)Αμ*(Rh2), 5egΑ4a2u transition.110 The MO calculations of Norman and Kolari156 as well as further measurements of crystal spectra233,234 supported this assignment. One of the observations used to support this assignment was the appearance of a vibronic progression with a frequency of 297 cm-1. This was assumed to be due to ι(Rh–Rh) in the excited state and such an assignment seemed consistent with the then accepted assignment of ι(Rh–Rh) in the ground state of 320 cm-1. The moderate (23 cm-1) lowering of the frequency was considered reasonable for a /*Αμ* transition, where an electron goes from one antibonding orbital to another (presumably) more strongly antibonding one. Finally, a further theoretical treatment167 also supported this assignment.

In 1984, however, the assignment of this electronic transition was challenged and a change proposed.235 The main reason given was that a ι(Rh–Rh) frequency in the ground state of 320 cm-1 was considered to be too high. By attributing this ground state Raman frequency to the A1g Rh–O stretching mode these authors235 were led to reassign band A as a /*(Rh2)Αμ* (Rh–O), 5egΑ4b2u, transition. However, it is now known that the Rh–Rh stretching mode is in the neighborhood of 300 cm-1 (see Section 16.6.1).