J. Am. Chem. SOC.1992,114, 7851-7860 Using the Rodrigues formula, the first term of (1 1) becomes: II - (n-l)Po
785 1
n'n - 1 = 0
+
+cos ( e l f ,
+(l-cos (e)(n"*PI)A
+sin (e)(n"xP1)
+(l SH2> SF,. The opposite order will be obtained by classifying the ligands with respect to their acceptor ability. It is further notable that an important amount of charge is donated back to the sulfur ligand, up to 0.5 electron for SF,. For the .?r donation, we find that SF2and SMe, are much better donors than SH2. In the latter case,the donation is exclusively due to the single p orbital at the sulfur, la. For the first two ligands we have additional antibonding contributions from p orbitals of the fluorine substituents as well as from appropriate combinations of hydrogen s orbitals of the metal group, as indicated in 7a and 7b.
I
I
H
H
7a
7b
By donating electrons to the metal system, the electron density at the sulfur is reduced and therefore also the antibonding interaction between the sulfur and its substituents. We conclude that not only the electronegativity of the substituents at SR2 determines the bonding ability of the ligand, but also secondary influences due to additional orbital interactions. Finally, we will include steric effects in our discussion. Above, we introduced the term hEp, which denotes energy contribution can be written as due to steric interaction. The electrostatic term AEelstand the change in the exchange are in general stabilizing, whereas the correlation energy hEdlxc exchange repulsion energy AEexrpis the mainly destabilizing component of A,??.66 hEexrp is directly related to the so-called "four-electron twosrbital" interactions. We see, from Table 111,
Jacobsen et al.
that for the sulfur ligands the trends in orbital interactions and steric interactions are correlated. As the orbital interaction increases, the distance between metal fragments and SR2 ligand decreases, which induces a stronger destabilizing steric interaction. The interesting result is, however, that for C1- in a bridging position the steric interaction is almost negligible. One of the reasons for this is certainly the larger metal-metal distance in Ia. The net result is that C1-, in spite of its smaller orbital interaction, by a factor of 3.5, surpasses SH2 in overall bonding strength. We now shall return to the isomerization reaction (SH2)C12Mo(p-Cl),MoCI(SH2)2(IIa) (SH2)Cl2Mo(p-C1),(SH2)MoC12(SH2)(IIIa) (Scheme I). To account for the small isomerization energy, the key point is not whether SH2 or C1- holds the bridging Y position, since we have seen that the bonding energies for both cases are comparable, with preference for C1-. It is rather important to address the question of energy differences between terminal and bridged thioethers. Because of the longer metal-ligand distance, both the electronic as well as the steric contributions are significant smaller for SH2 in a terminal position. The decomposition analysis for IIIa shows the bonding energy for a terminal SH2ligand to be -82.9 kT/mol. It is therefore 52.3 kJ/mol less stable than the bridging thioether. The contribution due to back-bonding decreases from 16.3% for the bridging case to 10.8% for the terminal case. Furthermore, we have to take into account the contributions from the chloride ligand. We recall that we form a less stable bond if we substitute SH2 by C1- into the bridging position. The difference in energy between the terminal and bridging position is less significant for C1-. Using the isomerization energy for the process discussed in Scheme I and the bonding analysis for bridging ligands, we found the bonding energy for terminal chloride to be -101.2 kJ/mol. C1- is to be considered solely as a a donor. The bonding interaction for a bridging chloride is increased by 42% with respect to a terminal chloride. For a bridging SH2 the bonding energy is increased by 68% compared to a terminally bonded thioether. In both cases, the chloride is bonded more strongly to the metal fragment than SH2. It is the larger increase in the bond energy of the bridging thioether that can be used to rationalize the small difference in energy between compounds IIa and IIIa, with IIIa being the thermodynamically more stable complex. This section is concluded with a bond analysis of the (p-C13) system la, optimized for different spin states. Recalling that the change in the metal-metal distance is the most important geometrical difference in these complexes, it was seen that an elongation of the metal-metal bond makes a high-spin configuration plausible, but leads to an overall decrease in terms of the electronic interaction energy A& of eq 1. The elongation, on the other hand, will lead to a decrease in steric interaction, mainly due to a reduced exchange repulsion term. The difference in the change of the stabilizing electronic interaction energy, hEd,and the destabilizing steric energy, A,??, determines the geometry of Ia. Figure 7 illustrates the trends for Ia in the spin states S,, = 0, 1,2. The low-spin singlet geometry (Smx= 0) has been optimized with a metal-metal bond distance of 228.6 pm. This corresponds to a strong coupling of the two metal centers. In-phase combinations of the three relevant metal d orbitals are formed and each is occupied with one pair of electrons. These orbitals are shown in 4a-c and are designated as la,, 1b2, and 2a,. Besides the strong coupling of the two metal centers, two different possibilities of realizing weakly coupled systems have been considered. In the case where one electron pair is weakly coupled (S- = l), in-phase combinations of two d orbitals on each metal center are formed and each assigned with one electron pair. This leads to the formation of the orbitals la, (4a) and 1b2(4b). The third pair is described by two different orbitals for the CY and @ electrons, with one orbital polarized on the metal center A and the other one on the metal center B. These orbitals are asymmetric linear combinations of the third set of d orbitals. On going from the system with S,, = 0 to a system with Smx= 1, the metal-metal bond distance increases to 267.8 pm. The steric interaction and the orbital energy terms follow the expected trends. The overall energetic balance favors the singlet (S,,, = 0) over the triplet
-
Density Functional Study of Thioethers -€+-Total
Bonding Energy 50.0
;
I
J. Am. Chem. SOC.,Vol. 114, No. 20, 1992 7859
- 13-- Electronic Interaction . - e - - Steric Interaction I .4 500.0
1Y
t
fa -
la” -
lbi
2a“
i
1 eV
220.0
240.0 260.0 Metal-Metal Distance Ipm
280.0
Figure 7. Electronic and steric contributions, Me, and AI?‘, to the total bonding energy for Ia in different spin states. The metal-metal distances of 228.0 pm, 267.1 pm, and 278.8 pm correspond to spin states S,,, = 0, 1,2, respectively. The energetic contributions for S,, = 0 are set to zero for clarity. Negative energies refer to destabilization. Note the double ordinate representation with a scale from -50 to 50 kJmol-’ for the total bonding energy and a scale from -500 to 500 kJmol-’ for the relative steric and electronic contributions.
state (S,,, = 1) by about 50 kJ/mol. For the two weakly coupled electron pairs (S,,, = 2), both d orbitals on the metal center which give rise to &bonding are treated differently for electrons of different spins. The two electrons of a-spin are polarized toward center A and the two electrons of &spin polarized toward center B. For the quintet high-spin state we find a metal-metal distance of 278.8 pm. The gain in energy due to the reduced steric interaction can overcompensate for the loss of energy due to the electronic interaction. It is remark25le that the energy difference between the low-spin state (S,,, = 0) and quintet high-spin state (S- = 2) amounts to only 6.1 kJ/mol. This indicates the fine balance and equal importance of steric as well as electronic effects for a proper bond description. The theory of Heisenberg spin coupling can result in a ferromagneticcoupling (Jab is positive) or in antiferromagneticcoupling (Jabis negative). For Ia, we find antiferromagneticcoupling in agreement with the experiment.14 However, our theory must then lead to a singlet ground state, which should be about 30 kJ/mol more stable than the quintet state, whereas experimental results14indicate a triplet state to be the ground state. Only a configuration interaction treatment between all possible spin states of S,,, = 2 with the same S = 0,1,2 can lead to the correct result. Such a treatment is not possible within the DFT formalism. For the thioether-bridged systems, we find that the low-spin state (S, = 0) is clearly preferred over the high-spin state (S, = 2) by 31.2 kJ/mol. As we discussed above, this can be rationalized according to the different bonding behavior of thioether systems. Systems Bridged by More Than One Thioetber Ligand. The last point of our discussion deals with the multiple thioether effect, which is the influence of additional thioether ligands in the bridging position. L3M(p-SR2)n(p-Cl)3-nML3 compounds with n = 2, 3 are yet not known for molybdenum, but are well established for :he tungsten system^.^^.^^ Figure 8 displays the energy level diagram for the frontier orbitals of IIIa, VIIa, and VIIIa, which all have one SH2 ligand in the Y position and zero, one, and two SH2 ligands in position X, respectively. The orbitals lal, 1b2, la2, 1bl, and their a’ and a” analogues show a similar energy level pattern for all three complexes. It is the orbital 2al or 3a”, respectively, which is significantlystabilized by introducing additional thioethers in the position X of the bridge. If we look at the contributions of the bridging orbitals separately, we find for the orbitals l a l and 1b2 that an SH2 ligand (75) Boorman, P. M.; Gao, X.; Freeman, G. K. W.; Fait, J. F. J . Chem. Soc., Dalton Trans. 1991, 115. (76) Boorman, P. M.; Gao, X.; Fait, J. F.; Parvez, M. Inorg. Chem. 1991, 30, 3886.
Vllla
Figure 8. Energy level diagram of (SH2)C12Mo(p-Cl)2(p-SH2)MoC12(SH2) (IIIa), (SH2)C12Mo(p-SH2)(p-Cl)(p-SH2)MoCl,(SH,) (VIIa), and (SH2)CI2Mo(p-SH2),MoCl2(SH2) (VIIIa) in illustration of the multiple thioether effect.
in an X position does not participate in the formation of the overall bridging orbital. These orbitals are shown in 8a and 8b for the
9a
8a
8b
9b
(p-Cl)2(p-SH2) bridge and in 9a and 9b for the (p-SH2)(pCl)(p-SH2) bridge. For 8a, substitution of C1- for SH2 to form 9a leads to a stabilization of the bond between the ligand bridge and the metal fragment. On the other hand, the bonding in the bridge itself is weakened, since all three ligands interact in a bonding fashion. The same is true for the 1b2 orbitals 8b and 9b so that the relative energy of 1b2with respect to la, is about the same in all three complexes. For the 3a’ orbital of VIIa, the situation is different. Now the sulfur ligand participates with a localized SH bond orbital in the bridge, as shown in 9c. This orbital is directed toward the p orbital of the C1- in the second X position. This enlarged SH2-C1- interaction in the bridge is responsible for the stabilization of 9c compared to 8c.
ac
9c
For the 2al orbital of VIIIa, where three sulfur ligands are forming the bridge, we find that these SH bond orbitals for both sulfur systems are pointing directly toward each other, as shown in 10. This strong bonding sulfur-sulfur interaction causes
x
n
H
10
7860 J. Am. Chem. SOC.,Vol. 114, No. 20, 1992
Jacobsen et al. EnergyIeV
Scheme I1
n
Y? 2a” la”
-9.a Vb
-- - - -
-
c
c
c
4
lbi
Vlb
additional stabilization of the 2al orbital. It seems that in systems with two thioethers in X pition, a partial, localized bond between these two ligands is formed. Strong sulfursulfur interactions, resulting in short sulfursulfur separations, are well known for thiolato-bridged c o m p l e ~ e s . ~ ~For . * ~tungsten systems bridged by more than one thioether, the sulfursulfur separation is also well within the accepted van der Waals radius of 370 pm.28.81.82 It should be mentioned that this analysis only applies to the relative changes in the electronic structure. Nothing has been said about the relative stabilities of the different systems. As discussed in the previous section, steric influences will be of major importance for the overall bonding energy. Finally, we will include into our discussion VIa, a compound with two thioethers in the X position but none in the Y position. Based on our inspections which we made so far, we can easily predict the changes in the electronic structure for the isomerization reaction (SH2)C12Mo(p-SH2)(p-C1)(p-SH2)MoCl(SH2)2 (VIIa) (SH 2) C1 M (p- SH2) (p- C 1) MoC1 (SH 2) (VIa) (Scheme I I). On going from VIIa to VIa, the 3a’ orbital will turn into the 2a, orbital of lower energy, since we gain energy due to the sulfursulfur interaction as discussed above. On the other hand, we lose the back-bonding from the metal fragment, when we move a SH2 ligand from the Y position into the X position. Therefore, orbital 2a’ will go up in energy to correlate with the lb2 orbital. Figure 9 displays the energy level diagram for the frontier orbitals of VIIa and Via. As expected, the energetic levels of 2a, and 1b2 for VIa are reversed. The same effect can be seen for the empty orbitals la2 and 1b,. la’ remains at almost the same energy to go over into la,. It is more difficult to predict whether complex VIa or VIIa is the more stable isomer. We know that the large bonding contributions of a thioether in the Y position is accompanied by an increase of steric repulsion, due to a short metal-ligand bond. We know further that the metal-ligand bond for C1- in the Y position is stronger than the corresponding bond with SH2in the Y position. Therefore, one might expect VIa to be the more stable compound.
-
(77) Benson, I. B.; Knox, S. A. R.; Naish, P. J.; Welch, A. J. J . Chem. Soc., Chem. Commun. 1978, 878.
(78) Weidenhammer, K.; Ziegler, M. L. 2.Anorg. Allg. Chem. 1979,422, 29. (79) Stiefel, E. I.; Miller, K. F.; Bruce, A. E.; Corbin, J. L.; Berg, J. M.; Hodgson, K. 0. J . Am. Chem. Soc. 1980, 102, 3624. (80) Boorman, P. M.; Codding, P. W.; Kerr, K. A.; Moynihan, K. J.; Patel, V. A. Can. J . Chem. 1982.60, 1333. (81) Moynihan, K. J. Ph.D. Thesis, University of Calgary, Calgary, Alberta, Canada, 1983. (82) Gao, X. Private communication. (83) Dahl, J. P., Avery, J., Eds. Local Density Approximations in Quantum Chemistry and Solid Stare Physics, Plenum Press: N e w York, 1984. (84) Parr, R. G.;Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989.
AI
-10.0
la’$+
Vlla
- - - - - -ff f a t Vla
Figure 9. Correlation diagram for the isomerization reaction between ( S H2)C12Mo(p-SH,) (p-C I ) (p-SH ,) MoCl,( SH,) (VI Ia) and (SH2)C12Mo(p-SH,),(p-Cl)MoCI,(SH2) (VIIa).
The calculations shows that this is indeed the case. The isomerization energy for this process is calculated to be 22.1 kJ/mol. The complexes VIa and VIIa are close in energy and VIa is thermodynamically favored. 4. Summary and Conclusions We have demonstrated that density functional theoryI3is able to account quantitatively for the fine balance between metal-metal bonding and metal-ligand bonding interactions in bridged binuclear complexes with respect to different ligands. Our main objective in the present investigation has been to elucidate the bonding of thioethers to the metal centers in d3-d3 Mo-Mo bioctahedral frameworks. We have found that thioethers in general have to be seen as good cr donors. In contrast to common belief, the orbital on the thioether responsible for back-bonding is not an empty d orbital on the sulfur, but rather, as is the case for phosphines, it is a low-lying cr* orbital of the thioether that accepts electron density from the metal center. For the special case of our bioctahedral molecules, the ?r acceptance is greater for thioethers in the bridging position. The variation in donor and acceptor strength exhibits the expected influence of the substituent on the thioether. The bridging position is generally the preferred position, as it has been demonstrated by the calculation of the ligand isomerization process thioethertminal(IIa) versus thioetherbridging (IIIa). The isomerization is accompanied by a significant shortening of the Mo-Mo bond, due to a decrease in repulsion for the bridging region of the bioctahedron. Further work is under way addressing the question of ?r-acceptor strength, making use of the comparison with known ?r acceptors.
Acknowledgment. This investigation was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). We thank Professor E. J. Baerends and Professor W. Ravenek for a copy of their vectorized LCAO-HFS program system and the University of Calgary for access to their IBM6000-RISC facilities.
