4453
J. Am. Chem. SOC.1985, 107, 4453-4459
-
2 1 isomerization to be within f 5 kcal of our single point DZP-CI result of 39.1 kcal. It appears that aluminum, or possibly other metals, may be useful in isolating and identifying vinylidene. As discussed by Trenary,, the features exhibitedin the energy surface of AI + C2H2 are likely to be important in Other hydrocarbon rearrangements where a metal is introduced. A rather interesting result in this regard is found here in comparison with the naked vinylidene -, acetylene rearrangement, which (as noted) has a negligible barrier. In contrast, Figure 1 shows (follow arrows in reverse direction) that the Al-vinylidene complex 1 has a substantial barrier (-52 kcal) for rearrangement t o t h e Al-acetylene complex. Thus the
attachment of the aluminum atom, while reducing the barrier height relative to non-interacting A1 H C C H -,A1 CCH2, effectively introduces an inhibitive barrier to a reaction [l 21 which otherwise proceeds very rapidly.
+
+
-
Acknowledgment. This research was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the u,s. Department of Energy under Contract No. DE-AC03-76SF00098. The Berkeley theoretical chemistry minicomputer is supported by the U S . National Science Foundation, Grant CHE-8218785. Registry No. C2H2,74-86-2; AI, 7429-90-5.
Theoretical Study on the Quadruple Metal Bond in d4-d4 Binuclear Tetracarboxylate Complexes of Chromium, Molybdenum, and Tungsten by the Hartree-Fock-Slater Transition-State Method Tom Ziegler Contribution from the Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N l N 4 . Received December 20, 1984
Abstract: Hartree-Fock-Slater calculations are presented on the metal-metal bond distance RMoand metal-metal stretch force constant kMMofor M2(C02H)4(M = Cr, Mo, W) as well as the three states 2B2, (u2a46),2E, ( u ' T ~ ~and ~ ) ,2A,, ( ~ 7 ~ ~ 6 ~ ) of M2(C02H),+ (M = Cr, Mo, W). The three states 2B2,, 2E,, and 2 ~ l corresponding g to the ionization of an electron out of the 6, a,and u metal-metal bonding orbitals, respectively, were calculated to be at lower energy than the ion states corresponding to ionizations from the ligand-based orbitals. It is shown from calculations on W2(C02CF3)4that the photoelectron spectrum of this molecule is consistent with u, a,6 being at higher energy than the ligand-based orbitals, and a similar interpretation ) ~ . ionization of an electron from 6 results in is offered, based on HFS calculations, for Cr2(C02CH3),and M o ~ ( C O ~ HThe a modest (0.04 A) elongation of the metal-metal bond, whereas the increase in metal-metal bond length is more substantial (0.10 A) for an ionization out of the a orbital. The ionization of an electron out of the strongly metal-metal bonding n orbital does on the other hand not significantly change the metal-metal bond distance contrary to what one might have expected. This surprising result is explained in qualitative terms. It is finally shown that u, a, 6 in M2(PH3)&I4 (M = Mo, W) and u, T in M o ~ ( O H )as ~ ,for the tetracarboxylates, are at higher energy than the ligand-based orbitals, and this result is reconciled ~ ~ change ) ~ . in RMoon ionization with the recorded photoelectron spectra of M2(PMe3),C14(M = Mo, W) and M o ~ ( O C H ~ C MThe of an electron from u, a, 6 in M2(PH3)4C14(M = Mo, W) and a, u in M o ~ ( O Hwas ) ~ calculated to follow the same trend as for the tetracarboxylates.
I. Introduction The structure of the dimolybdenum tetracarboxylate complex Mo2(C02CH3),was determined' shortly after the recognition of a quadruple metal-metal bond by Cotton in Re2Cls2-. Cotton accounted for the quadruple bond in Re2Cls2-in terms of metal-metal bonding orbitals of local u, 7,6 axial symmetry, and the same bonding scheme was adopted for Mo,(CO~CH,),.~ The complex Mq(CO,CH,), has according to Cottons bonding picture the electron configuration with the same formal bond order of four as Re2Cls2-. The neutral dimolybdenum tetracarboxylates Mo2(CO2CH,), and Mo2(C02H), have4s5 been used widely to further our understanding of the quadruple metal-metal bond since their volatility makes them well suited for experimental investigations even in the gas phase, and Mo2(C02H), is further amiable for theo( 1 ) Lawton, D.; Mason, R. J. A m . Chem. SOC.1965, 87, 921. (2) Cotton, F. A. Inorg. Chem. 1965, 4 , 334. (3) Cotton, F. A.; Walton, R. A. "Multiple Bonds Between Metal Atoms"; Wiley: New York, 1982. (4) Reference 3, pp 84-135 and pp 390-435. (5) (a) Coleman, A. W.; Green, J. C.; Hayes, A. J.; Seddon, E. A,; Lloyed, D. R.; Niwa, Y. J. Chem. SOC.,Dalton Trans. 1979, 75, 485. (b) Green, J. C.; Hayes, A. J. Chem. Phys. Lett. 1975, 31, 306. (c) Hino, K.; Saito, Y.; Benard, M. Acta. Crystallogr. 1981, B37,2164. Lichtenberger,D. L.; Blevine, C. H., I1 J. A m . Chem. SOC.1984, 106, 1936.
0002-7863/85/1507-4453$01.50/0
retical treamenk6 One of the experimental technics with the strongest bearings on the nature of the quadruple metal-metal bond is low-energy photoelectron spectroscopy5" which in conjunction with theoretical calculations6 can provide information on the states generated from ionizations of electrons out of the u, a,6 and metal-metal bonding orbitals. Different interpretations of the recorded photoelectron spectra on Mo2(C02R), system^^^.^ have, however, been provided by the H F ab initio6a,bmethod and the SCF-Xa-SW scheme6c in connection with theoretical calculations on Mo2(C02H),. A recent ab initio calculation by Atha et a1.6dseems, however, in our view, to have resolved the controversy. The nature of the quadruple metal-metal bond has also been probed by low-energy photoelectron experiments on the homologous and equally volatile dichromiumsa and ditungsten tetracarboxylates.' The interpretation of the recorded spectra of Cr2(C02R), systems by theoretical calculations6a,8has, however, (6) (a) Benard, M. J. Am. Chem. SOC.1978, 100, 2354. (b) Hillier, I. H.; Garner, C. D.; Mitcheson, G. R.; Guest, M. F. J. Chem. SOC.,Chem. Commun. 1978, 204. (c) Norman, J. G.; Kolari, H. J.; Gray, H. B.; Trogler, W. C. Inorg. Chem. 1977, 12, 987. (d) Atha, P. M.; Hillier, I. H.; Guest, M. F. Mol. Phys. 1982, 46, 437. (7) Bancroft, G. M.; Pellach, E.; Sattelberger, A. P.; McLaughlin, K. W. J. Chem. SOC.,Chem. Commun. 1982, 752. ( 8 ) Cotton, F. A,; Stanley, G. G.Inorg. Chem. 1977, 16, 2668.
0 1985 American Chemical Society
4454 J . Am. Chem. SOC.,Vol. 107, No. 1.5. 198.5 Table I. Calculated and Experimental Ionization Potentials (eV) for HCOOH assignmento IP(ca1cd) IP(calcd)b 7a' 11.63 11.51 2a" 12.59 12.5 6a' 1 a" 5a'
13.90 15.57 16.7
14.7 15.7 17.1
OThe symmetry point group of H C O O H is C,. *From ref 5b.
been hampered by lack of experimental information on the length of the Cr-Cr bond,9 and no calculations have to date been presented to aid the interpretation of the photoelectron spectra' of W2(C02R)4complexes. We present in the first part of this study Hartree-Fock-Slater calculations on the energies of M2(COzH)4and the three states of M2(C02H)4+corresponding to the ionization of a single electron out of the u, R, 6 orbitals as a functionlo of the metal-metal bond distance for the entire triad M = Cr, Mo, W. The calculated potential energy curves provide not only information on the relative energies of the three states but also equilibrium metal-metal bond distances RMoand metal-metal stretching frequencies vMM. The relative energies as well as the spectroscopic constants RMoand uMM can be determined experimentally from low-energy photoelectron spectroscopy, but the constants RMo,and uMM have to date only been inferredMfor one tetracarboxylate ion state, namely ~ + assignment . of the recorded the state u2r46 of M O ~ ( C O ~ H )An low-energy photoelectron spectra of Mo2(C02H)4,5aand W2(CO2CF3)2is given in the second part based on H F S calculations on the three molecules. We compare finally in the last part the results from the present study on the tetracarboxylates to theoretical" and experimentalllaqcinvestigations on other binuclear complexes of group 6 metals with a quadruple or triple metal-metal bond.
Ziegler ( M = Cr, Mo, W) given the same geometry as determined experimentally in M O ~ ( C O ~ Hand ) ~ ,the metal-oxygen distances were the same as determined in C T ~ ( C O ~ C HM~O) ~ (, C O ~ H ) ~ , and W2(C02CF3)4,respectively. A standard value of a = 0.70 was used for the exchange scale factor.12 We give in Table I, in order to demonstrate the adequacy of the H F S method and assess the quality of the basis set, a comparison between calculated and experimental ionization potentials for HCOOH. It follows that the accord between theory and experiment is fair in particular for the two ionizations of lowest energy. 111. M2(C02R)4( M = Cr, Mo, W). (a) The Bonding in M2(C02H)4(M = Cr, Mo, W). The metal-metal bond in binuclear complexes was first accounted for by Cotton2 in terms of metal-metal bonding orbitals with local u, T , 6 axial symmetry 1 as well as the corresponding metal-metal antibonding orbitals u*, T * , 6*. The order of energy for the orbitals was assumed based on overlap considerations to be t(u) < t ( T ) < t(6) < €(6*) < €(R*) < c(a*), 1.
-
U*
f -
-?I*
-6*
1
11. Computational Details The d4-d4 tetracarboxylates M 2 ( C 0 z H ) ) 4(M = Cr, Mo, W) All calculations were based on the HFS method as implemented of D4hpoint group symmetry 2 have in Cotton's original model by Baerends et a1.I2 The relativistic calculations were based on the quadruple metal-metal bonded configuration ( O ) ~ ( T ) ~ with ( ~ ) ~ the method due to Snijders et al.13 The many electron wave 6* as the unoccupied orbital of lowest energy (LUMO). functions for the binuclear complexes were represented as discussed PH~)~ in ref 11b. The computational details for M O ~ C ~ ~ ( and c, WzC14(PH3)4can be found in ref 1l b and those of Mo2(OH), in /O 0 1 ref 1Id. All atoms on the carboxylate ligands were represented by an uncontracted double-{ STO basis set.I4 The 1s orbitals on C, 0, F were taken as core and frozen according to the procedure by Baerends et al.I2 On the metal atoms ns and np were L represented by an uncontracted double-{ STO basis14 whereas nd, Fi (n l)s, (n l ) p were represented by an uncontracted triple-{ STO basis.I4 Orbitals of lower energy were frozen according to the method by Baerends et al.Iz 2 The experimentally determined geometries were adopted for The metal-metal bonded orbitals of u, 6, T symmetry are in calculations on Cr2(C02CH3)4,15 M O ( C O ~ H ) ~and , ' ~W2(C02Cour HFS calculations identified as the 7al,, 7eU,and 2b2, orbitals F3)4.17The C02H-ligand was in the calculations on M2(C02H)4 respectively 3 whereas 2blu represents the 6* orbital.
+
b?
+
~~~
~
LUMO
(9) (a) Reference 3, pp 150-159 and p 177. (b) Wiest, R.; Benard, M. Chem. Phys. Lett. 1983, 98, 102. (10) The metal-metal distance RMM was varied under the constrain of
fixed M - O distances, with the rest of the molecule rigid. We note that a variation without this constrain in which R,, is changed with the rest of the molecule fixed relative to the center of mass gave nearly the same potential curve for M o ~ ( C O ~ HThus ) ~ . the exact way in which the "free movement" of the two metal atoms is defined is not crucial. (1 1 ) (a) Cotton, F. A.; Hubbard, J. L.; Lichtenberger, D. L.; Shim, I. J . Am. Chem. SOC.1982, 679. (b) Ziegler, T. J . Am. Chem. SOC.1984, 106, 5901. (c) Bursten, B. E.; Cotton, F. A.; Green, J. C.; Seddon, E. A,; Stanley, G.G.J. Am. Chem. SOC.1980,102,4579. (d) Ziegler, T. J. Am. Chem. SOC. 1983, 105, 7543. (12) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (13) (a) Snijders, J. G.;Baerends, E. J.; Ros. P. Mol. Phys. 1979,38,1909. (b) Relativistic calculations were only carried out on Sd complexes. (14) Snijders, G. J.; Baerends, E. J.; Vernooijs, P. At. Nucl. Dara Tables 1982, 26, 483 and private communication. (15) Ketkar, S. N.; Fink, M. J . Am. Chem. SOC.,in press. (16) Cotton, F. A,; Norman, J. G.,Jr.; Stults, B. R.; Webb, T. R. J. Coord. Chem. 1976, 5, 217.
HOMO
7eu-
-2blu
-2b29 -
-7a~ ( a 2 on C O ~ H - { , * ~
/*Jw
on ~ 0 2 ~ -
-6alg 3 ~~
(17) Sattelberger, A. P.; McLaughlin, K. W.; Huffman, J. C. J . Am. Chem. SOC.1982, 104, 2880.
J . Am. Chem. Soc., Vol. 107, No. 15, 1985 4455
Binuclear Tetracarboxylate Complexes of Cr, Mo, and W 12
10
0
5 6
$ 4 p: 0
3 2
Figure 1. Energies (eV) of the [A,, ground state for M2(C02H)4(M = Cr, Mo, W) and the three states 2B2, (6n4u2),2E, (62n302), and 2Al, (62a4a) of M2(C02H),+ ( M = Cr, Mo, W) as a function of the metal-metal bond distance RMM(A).
Table 11. Calculated Spectroscopic C o n s t a n t P for M2(C02H), (M = Cr, Mo, W) and the 2B2,, 2E,, and 2A,, States of M2(C02H),+ (M = Cr, Mo, W) Cr2(C02H)4
Mo2(C02H)4
state IAI,
RMO kMMO YMM' 5.26 586 1.87 562 4.84 2B2, 1.92 2.90 435 2E" 2.03 3.92 505 2A,, 1.87 a RMois the calculated metal-metal equilibrium distance in is the calculated metal-metal stretching frequency in cm-l
RMa 2.12 2.16 2.23 2.10
VMMO
RMO
kMMO
YMMO
5.83 5.80 3.93 5.12
454 453 313 450
2.26 2.30 2.37 2.26
5.68 5.37 3.89 4.29
324 315 268 282
A. kMMois the calculated metal-metal stretching force constant in mdyn/A.
The 7a,, orbital 4a is an in-phase combination between dz2 on the two metals, antibonding with respect to the 4al orbital 5a on COZH-.
4
d o
8%
v
W2(C02H)4
kMMO
c~MMo
and lb2, primarily are ligand based with la,,, 2a,, representing in-phase combinations of ns and np, on the metal centers, respectively. The 7e, orbitals 4c, antibonding with respect to 4a, on C 0 2 H 5a and the in-phase d,-d, combination, has more than 60% metal character whereas 6e, 6b, the corresponding metalligand bonding orbital, has less than 25% metal character. The orbitals 2e, to 5e, are primarily ligand based, and le, is the np,-np, metal combination.
I
7%
4Q
2b2g
7%
4b
4c
The 2bzgorbitals 4b consists of an in-phase combination between d, on the two metals, bonding with respect to the unoccuppied 2b2 ligand orbital 5e of CO,H- and antibonding with respect to the occupied 1bz orbital 5d of CO,H-. 6%
6a 4.1
3'1
5b
"2
'4
2'2
5c 5d 5e The orbital pair 7eux, 7e, is made up from in-phase combinations between d,, or d,, on the two metals, respectively, antibonding with respect to the occupied 4a, orbital 5a on C02H-, 4c. The 7al,, 2bzg orbitals 4a, 4b, metal-metal bonding, and metal-ligand antibonding have more than 75% metal character. The 6alg orbital 6a is metal-metal bonding as well as metal-ligand bonding with less than 15% metal character, whereas 3al, to 5al,
5a
6%
6b
It is perhaps interesting to note that the X a model without the muffin-tin approximation, as it is used here in the implementation by Baerends et a1.,I2 provides level orderings and orbital compositions in accord with recent H F a b initio calcultions,6a~b~d whereas previous X a calculations in which the muffin-tin approximation was applied gave quite different orderings and compositions.6c (b) The Energy of Mz(CO2H), (M = Cr, Mo, W) and M2(C02H).,+as a Function of the Metal-Metal Bond Distance R M M . We present in Figure 1 the ground-state energy of M 2 ( C 0 2 H ) 4 as well as the energies corresponding to the 2A,,, 'B,,, and 'E, states of Mz(C02H)4f as a function of the metal-metal bond
4456 J . Am. Chem. SOC.,Vol. 107, No. 15, 1985
Ziegler
distance RMM, where ,A,,, 2B2g,and ,Eu are the states resulting Table 111. Experimental Spectroscopic Constants for Cr2(COCH3)4,‘ from an ionization of one electron out of the u, 6, and a metal Mo2(C02CH3),,*and W2(C02CF3),‘ bonding orbitals of M2(C02H)4,respectively. ~ M M ’(mdyn/A) vMM’ (cm-I) complex RM’ (A) It follows from Figure 1 and Table I1 that the ionization of one 3.8d 498‘ C r d C O C H d 4 1.97 electron from the weakly bonding 6 orbital results (2Bz ) in a 4.6 404 Mo2(C0CH3)4 2.08 modest elongation of the metal-metal bond distance (0.04 and 5.3’ 313 W2(C02CF3)4 2.21 a modest change in the force constant kMMo, whereas an ionization ‘Reference 15. Reference 23. Reference 17. Determined from from the stronger bonding a orbital gives rise to (2E,Ja substantial the mean amplitude of the metal-metal stretch in ref 15. eEstimated elongation of the metal-metal bond distance as well as a conhere from kcrcr given in ref 15 by assuming a pure metal-metal siderable reduction in the force constant kMMo (see Table 11). stretch. ’Estimated here from vMMo assuming a pure metal-metal Ionization of one electron from the strongly metal-metal bonded stretch. u orbital gives rise to (,Eu) a substantial elongation of the metal-metal bond distance as well as a considerable reduction in the RMoocalculated for Mo2(CO2H),+ in the ZB2,state is too short force constant kMMo (see Table 11). Ionization of one electron compared with RM: calculated for M o ~ ( C O , H ) ~ .We note, from the strongly metal-metal bonded u orbital 7al, does, on the ) Re2C14(PMe2Ph)4+ however, that RezCl4(PMezPh);+ (u z ~ 4 6 2and other hand, not, according to our calculations, elongate the (u2a46)both are observed22to have a metal-metal bond distance metal-metal bond distance as M2(C02H)4+in the 2A,, state is of RR2 = 2.22 A, and that we in reasonable agreement with this calculated to have nearly the same equilibrium distance as M2observation in a previously HFS studyIlbhave calculated R R 2 for (CO2H)4 in the ground state (Table TI). We note in order to Re2C14(PH3)42+ at RR; = 2.24 A only to be 0.01 8, shorter than explain this somewhat surprising result that the in-phase d, RR> for Re2(PH3)4C14+at RRe+ = 2.25 A. combination 4a in contrast to the d, and d, combinations 4b, 4c The calculated metal-metal stretching force constants kMMo has strong overlaps with metal orbitals of lower energy, notably and frequencies uMMO seem somewhat large in comparison with ns, np,. Such overlaps will weaken the metal-metal quadruple the experimental values for kMMo and uMMO compiled in Table I11 bond of M 2 ( C 0 2 H ) 4through repulsive interactions (exchange for Crz(C02CH3)4,M O ( C O ~ C H ~and ) ~ W2(C02CF3)4, , respecrepulsion) between the electron pair of the in-phase d, combination tively. The complexity of the tetracarboxylate excludes a complete and the electrons in ns, np,. The removal of one electron from experimental force field analysis, and it is assumed in the comthe a-orbital 7a1, will reduce the u bond order as well as the parison that the observed frequencies uMMO correspond to a pure exchange repulsion. The reduction of the u bond order and the metal-metal stretch without significant couplings from other exchange repulsion have adverse effects on the metal-metal bond vibrational modes. distance of the 2A1, state, which largely cancels according to our The three states of W2(C02H)4+,corresponding to ionizations calculations. of an electron out of the 6, a, u metal-metal bonding orbitals, The calculated metal-metal bond distances RMofor the two have in Figure 1 and Table I1 been classified according to their quadruple bonded species M o , ( C O ~ H )and ~ W2(C02H)4are R:, symmetries in the D4h single point group as 2B2g,2El,and ,Al,, = 2.12 A and RWo= 2.26 A, respectively, in fair agreement with respectively, although W2(COzH)4+as well as W2(C02H)4were R M 2 = 2.09 A observed for M o ~ ( C O , H ) , ’ ~ and Rwo = 2.21 subject to relativistic calculation^.^^ It is of importance for the observed for W,(CO2CF3),.l7 The chromium-chromium bond subsequent discussion in the next sections to note that the doubly distance in dichromium tetracarboxylates was until recently only degenerate state ,Euin the relativistic calculation is split into the known from Crz(C0zCH3)4Lzsystems9 with two axial ligands. two states E,, and E3, of different energies by the spin-orbit The observed distance9 in Cr2(C02CH3)4(H20)z at +? = 2.37 coupling interaction and that the splitting according to our calis rather large, and Cotton9 has suggested that Rcr in Crz(Cculations is AE,, = 0.21 eV at Rwo. Thus, the potential curve 02CH3)4 should be much shorter and at the same order of in Figure 1 for the 2& state of W,(CO,H),+ represents the average magnitude as the “super short” bond in Cr2(PhNC(CH3)0)4with energies of E2, and E3u. Arratia-Perez and Case24have carried Rcr = 1.87 A. Fink et al.15 have now shown from electron-difout a full relativistic calculation on W2ClS4-within the SCFfraction experiments that the metal-metal distance in Cr2(CXa-SW approximation in which they find AE,, = 0.33 eV. The 02CH3)4 is close to “super short” at RcP = 1.97 A. Our calculated two AEsovalues can be reconciled by observing that if the metvalue at Rc? = 1.87 A for Cr2(C02H)4also indicates a very short al-metal bonding a orbital is written in terms of its metal and bond in the dichromium tetracarboxylate systems. ligand components as a = Cl(d,) + C2(L,) then AE,, can, to a Information on the geometries of binuclear systems involving good approximation, be related to the spin-orbit constant Xw of Cr, Mo, and W with a bond order less than 4 as in M2(C02H),+ the W atom by ( M = Cr, Mo, W) is scant. Cotton et aL2I have structurally A&, = CI2Xw (1) characterized Mo,(SO,)~& (u2a462)and Mo2(S04)2- (d7r46). The metal-metal bond distances were R M 2= 2.1 1 8, for M O ~ ( S O ~ ) ~ & We have calculated Xw = 0.41 eV and find with CI2 0.61 for and R M 2= 2.16 A for Mo2(S04)2-,corresponding to a lengthW2(C02H)4+that A,!?, = 0.25 eV in comparison to AE,,= 0.21 ening of the bond by 0.04 8, as one electron is removed from the eV from the full treatment. Arratit-Perez and Case24give C12 6 orbital of M o , ( S O ~ ) ~ ~We - . have, as already mentioned, cal= 0.8 for W2C18&corresponding to AE, = 0.33 eV, in good accord culated a similar elongation for all three metals as one electron with A,!?, = 0.33 eV from the full relativistic treatment of w2cls4-. is removed from the 6 orbital 1 to produce the 2B2, state of The difference in the calculated spin-orbit splitting5 of W2Cls4M2(C02H)4+(see Table 11). and W2(C0zH)4+is thus seen to be a consequence of a different Lichtenberg et al.5dhave, however, inferred from an important participation (C,)from the in-phase d, combination in the work on the photoelectron spectrum of M O ~ ( C O , C Hthat ~ ) ~ the metal-metal bonding a orbitals of the two molecules, and we note ~)~ removal of one electron from the 6 orbital of M O ~ ( C O , C Hgives further that 0.4 eV should be an upper bound for AE,, in the rise to an elongation in the range 0.13 to 0.18 8,. Lichtenberg quadruple bonded binuclear complexes of tungsten. et al. also inferred a considerable reduction in the metal-metal (c) The Photoelectron Spectra of Cr2(C02CH3),,Mo2(C02H)4, stretch (40 cm-I) in going from Mo,(CO,CH~)~ to the “2B2g”state and WZ(CO2CCF3),.The orbital level diagram 3 given for M2of Mo,(CO,CH~)~, in contrast to our results for Mo2(CO2H),and (COzH), has above 2b2,, 7e,, and 7al, a nest of 16 levels repreMo,(CO,H)~P as well as experimental findings on M o ~ ( S 0 4 ) 4 ~ sented by symmetrized combinations of the parent 4al, 3b1, a,, and M o , ( S O ~ ) ~where ~ - a metal-metal stretch of 370 cm-l has and bz C02H- ligand orbitals 5, with laluat the lower energy edge. been found for both species. We can certainly not exclude that We would, in conjunction with the present study on M2(C02H), (M = Cr, Mo, W) and the 2Bzg,2E,, and zAl, states of M2(18) Slater, J. C. Adu. Quantum Chem. 1972, 6, 1. (C02H)4+,like to present a limited assignment of the recorded (19) Johnson, K. H. Phys. Lett. 1968, 27a, 138. , photoelectron spectra of Cr2(COzCH3)4, M o ~ ( C O , H ) ~and (20) Baerends, E. J.; Ros, P. Chem. Phys. 1975, 8, 412. W,(CO2CF3), in which the bands due to ionizations from the 6, (21) Cotton, F. A.; Frenz, B. A.; Webb, T. R. Inorg. Chem. 1975, 14, 391.
A)
J . Am. Chem. Soc.. Vol. 107, No. 1.5, 198.5 4457
Binuclear Tetracarboxylate Complexes of Cr, Mo, and W
Table IV. Assignment for the Photoelectron Spectra of Cr2(C02CH3)a,MO*(CO~H)~, and W2(C02CF3)4 Cr2(C02CCH3)4" MO~CO~H)? W2(C02CF3)4' region IP(expt1) assignm IP(ca1cd) region IP(expt1) assignm IP(ca1cd) region IP(expt1) assignm 8.65
A
b T
9.10(sh)
u
7.97 8.89 9.51
B
A
7.60
6
7.82
A
7.3
B
9.37
n-
8.91 9.56
B1
9.01 9.71
7 4
B2
10.02
c1
12.51
Le
d
CI
10.2 10.51 1 1.04
Le
9.87
Cl
10.95 11.56 11.89khl
Le
IP(ca1cd) 7.79 8.74,8.94 9.38
U
10.22
"Calculate at RMM= 1.97 A. bCalculated at RMM= 2.12 A. cCalculatedat RMM = 2.21 A. dThe calculated ionization potentials at 8.74 and 8.94 correspond to the two spin-orbit components of the n- orbitals. FFirst ionization from ligand-based orbital. a, u metal-metal bonding orbitals are identified and located relative to the peak representing the ionization of lowest energy from the nest of ligand-based orbitals, 3. Binuclear tetracarboxylate complexes of group 6 metals were prior to 1980 only known for M = Cr, Mo, and all interpretations6 of their recordedS photoelectron spectra agreed that the ionization of lowest energy from the ligand-based orbitals should be assigned to the region classified as C I (SeeTable IV). The interpretations differed, however, with respect to an assignment of the region at lower energy than C1. This region was based on a b initio6a,bH F calculations assigned ionizations for all three metal-metal bonding 6 , A, D orbitals whereas only ionizations from 6 , a should be assigned to this region according to SCF-Xa-SW calculations.& Bancroft et aL7 have, following the successful synthesis after 1980 of W2(C02R), systems by Sattelberger et al.17 as well as Cottonzs and Wang, recorded the photoelectron spectrum of W2(C02CF3)4,where three bands can be clearly identified in the region below C , (see Table IV). Bancroft et al. assigned 6 to A (7.3. eV) and A, u to BI (9.01 eV), B2 (9.71 eV), respectively, and this assignment is supported by the present HFS calculation on W2(C0,CF3), where ionizations from 6 , a, u are calculated to be at lower energy than the first ionization from a ligand-based orbital (Table IV). Bancroft et al. found that the large slitting (0.7 eV) and difference in intensities (2:l) between B, and B2 ruled out an assignment of the two bands as due to ionizations from the spin-orbit components of the two a-orbitals, and we note that the calculated spin-orbit splitting of the two a-orbitals at 0.20 eV is much smaller than the observed splitting (0.7 eV) between BI and Bz. It is of interest to note that BI is much broader than either A or B,. The broadening of BI can aside from the spin-orbit splitting be accounted for when we observe that an ionization from the *-orbitals in section IIIb was calculated to result in a much larger elongation of the metal-metal bond than ionizations from the 6 and u orbitals. We calculate, as in the case of WZ(C02CF3),,the ionizations from 6 , A, D to be at lower energy than the ionization from the first ligand based orbital for both CrZ(C02CH3)4and Mo2(C02H), and offer the same assignment, Table IV, for the photoelectron spectra of the two molecules as given previously based on a b initio6a*b*d calculations on Cr2(C02H), and Mo2(C02H),. Our relativistic calculations on W2(C02CF3),thus indicate that the assignment of the three first ionization potentials to 6 , A, u for tetracarboxylate complexes of Molybdenum, based on ab initio calculations6d on Mo2(C02H),, can be extended to tungsten systems as well. The assignment of the first three ionization potentials to 6 , a,u for Cr2(C02R), systems has been based on a b initio calculations on the model system Cr2(C02H), corresponding to a metal bond distance (2.20-2.36 A) much larger than that observed (1.97 A)IS in Cr,(C02CH3), for which a photoelectron spectrum in fact has been recorded. However, H F S calculations on Cr2(COZCH3)4 with RMo= 1.97 A, Table IV, confirm the original6d assignment of 6, a, u to the first three ionization potentials of Cr2(C02R), systems. (4V2(C02H)4, Nbz(COzH),, M ~ z ( C O Z Hand )~,TCACO~H)~ We have also carried out calculations on the unknown d3-d3 systems V2(C02H),, Nb2(C02H)4of configuration u2r4as well as the unknown ds-dS systems Mn2(C02H),, Tc2(CO2H), of
Table V. Calculated Metal-Metal Bond Distances (A) RMofor Various M2(C02H)4Complexes M ~-
Ru0
V
Cr
Mn
1.95
1.87
1.87
~
Nb-
Mo
Tc
2.35
2.12
2.16
configuration ( ~ ) ~ ( ~ ) ~ ( 6 ) ~all( with 6 * ) a~ triple , metal-metal bond. The two metals V and N b in the d3-d3 systems have relatively diffuse d orbitals and the calculated metal-metal bond distances are as a consequencesomewhat larger than the calculated distances for the corresponding d4-d4 and ds-dS complexes (Table V). It is not easy to define the metal-metal bonding energy for the tetracarboxylate systems Mz(COzH)4. We have for the various metals compared the energy of M2(C02H), with the energy of two M(CO,H), units of structure 7 in their electronic high-spin configuration. The d3-d3complexes have according to this comparison a somewhat stronger metal-metal bond, and the ds-ds complexes a somewhat weaker metal-metal bond, than the corresponding d4-d4systems, indicating perhaps that at least V2(CO2R)4 and Nb2(CO2R), systems might be isolated. The calculated metal-metal bonding energies according to the procedure given above were 207 and 486 kJ mol-' for Cr2(C02H), and Mo2(C02H),, respectively.
7 IV. M O ~ C I ~ ( P HWzC14(PH3)4, ~)~, and M O ~ ( O H ) ~ We have in previous studies investigated the quadruple bond"b of M2C14(PH3)4(M = Mo, W) as well as the triple bondlId in M O ~ ( O Hby ) ~ way of our energy-decomposition scheme. We present in Figure 2, as a function of RMM, the energies for the 2Bl, 'E, and 2Al states of M2C14(PH3),+( M = Mo, W), corresponding to ionizations out of the 6 , a , u orbitals, respectively, as well as the energies for 2El ($a3) and ,A,, (or4) of Mo,(OH)~+. It follows from Figure 2 and Table VI that the changes in the metal-metal bond distances on ionization of an electron out of the 6 , a , u orbitals in M2CI4(PH3),( M = Mo, W) and the u, a orbitals in M O ~ ( O Hgive ) ~ rise to the same trends as calculated for the tetracarboxylates in section IIIb, and we expect in general for binuclear complexes with a multiple metal-metal bond that the removal of one electron from the S orbital will result in a modest elongation of the metal-metal bond length, whereas the removal of an electron from the T orbital will give rise to a larger increase in RMo.The ionization of an electron from the u orbital should, on the other hand, in contrast to what one might expect, not significantly increase the metal-metal bond length for reasons given in Scheme IIIb. It is in this respect interesting to note that (22) Cotton, F. A,; Dunbar, K. R.; Falvello, L. R.; Tomas, F.; Walton, R. A. J . Am. Chem. SOC.1983, 105, 4950. (23) Kelley, M. H.; Fink, M. J . Chem. Phys. 1982, 76, 1407. (24) Arratia-Perez, R.; Case, D. A. Inorg. Chem. 1984, 23, 3271. (25) Cotton, F. A.; Wang, W. Inorg. Chem. 1982, 21, 3859.
4458 J . Am. Chem. SOC.,Vol. 107, No. 15, I985
Ziegler
Figure 2. Energies of the 'A, ground state for M2C14(PH3)4 (M = Mo, W) and the ,A,, ground state of Mo,(OH)~as well as the 2Bl (S?r4$), 2E(a2r3$), and 2Al (6,r4a) states of M2CI4(PH3),+and the 2E, ( d $ )and 2AI, (7r4a)states of Mo2(0H),+ as a function of the metal-metal bond distance RMM
(A). Table VI. Calculated Spectroscopic Constants',b for Mo2CI4(PH&"+,W2C14(PH3)4n+, and Mo2(0H),"+, with n = 0, 1 Mo~C~~(PHP)~"+ W*CI,(PHJ,"+ Mo2(0H)6"+ n state RMO ~MM' state RMO kMM0 state RMO ~ M M 0 'A, 2.18 (2.13)' 5.18 (3.46)' 'A, 2.28 (2.26)d 4.76 (3.65)d ,A,, 2.24 (2.22)c 3.81 1 2.18 5.01 2B, 2.31 4.54 1 2E 2.22 4.05 2E 2.38 3.70 2Eu 2.33 3.67 1 2A, 2.14 4.99 2Al 2.26 4.65 2Al, 2.25 3.05 RMois the calculated metal-metal equilibrium distance in A. k M M o is the calculated metal-metal stretching force constant in mdyn/A. 'Experimental values for M o , C ~ , ( P M ~from ~ ) ~ ref 3. dExperimental values for W2C14(PMe3)4from ref 3. 'Experimental values for Mo2(OCH2CMe& from ref 3.
Table VII. Assignment for the Photoelectron Spectra of M O , C I ~ ( P M ~W2C14(PMe,)4," ~)~~(~ and Mo2(OCH2CMe3)6(1 Mo~CldPMe3h W2C14(PMe3)4 MO~(OCH~CM~~)~ region IP(expt1) assignm IP(calcd)d region IP(expt1) assignm IP(calcd)' region IP(expt1) assignm IP(calcdy A 6.44 6 6.05 5.81 6 5.89 A A 7.40 X 7.07 B 7.70 X X 7.27, 7.459 8.23 U 8.69 B B, 7.05 7.50 0
Lh
7.52 7.83
B2
7.45 8.36
U
7.57 7.76
C
Lh 9.21 'Reference l l a . bReference 1 IC. 'Calculated and experimental ionization potentials (IP) are all in eV. dFrom calculations on Mo2C14(PHJ4. From calculations on W2C14(PH3)4. /From calculations on M O ~ ( O H )glonization ~. potentials for the two spin-orbit components of the x orbital. First calculated ionization potential from ligand-based orbital. C
8.41
C
N2+of configuration u2a3hasz8 a longer bond than Nz, whereas N2+of configuration ua4has nearly the same bond length as N,. We present in Table VI1 a limited assignment of the recorded photoelectron spectra of M O ~ C I , ( P M ~WzC14(PMe3)4,11a ~)~, and Mo2(0CH2CM3)611C in which we, as for the tetracarboxylates, identify and locate bands due to ionizations from the 6, a, u metal-metal bonding orbitals relative to the peak representing the ionization of lowest energy from the nest of ligand-based orbitals. The assignments are made on the basis of calculations on Mo2(PH3)4C14,W2(PH3),CI4, and Mo,(OH)~. For M o , ( O C H ~ C M ~we ~ )offer ~ the assignment, Table VII, already given by Bursten, Cotton et al.,Ilc in which C is attributed to ionizations from ligand-based orbitals and the bands A and B at lower energies to ionizations from the a and u metal-metal bonding orbitals, respectively. We are in the interpretation of the recordedlla spectra for M o , C ~ ~ ( P Mand ~ ~W2C14(PMe3),, )~ as for the tetracarboxylates, (26) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1 . (27) Noodleman, L.; Post, D; Baerends, E. J. Chem. Phys. 1982, 64, 159. ( 2 8 ) Cade, P. E.; Sales, K. D.; Wahl, A. C. J. Chem. Phys. 1966,44,1973.
Lh
9.46
faced with the task of assigning the region at lower energy than the band C, due to the first ionization from the ligand-based orbitals, to two or three of the metal-metal bonding orbitals 6, a,u. The region has, as in the case of the tetracarboxylates, for M = Mo two bands A and B and for M = W three bands A, B,, and B2, where the splitting between Bl and B, is 0.4 eV (see Table VII). Cotton et al.llBhave from SCF-Xa-SW calculations on MzC14(PH3)4(M = Mo, W ) found u to be of lower energy than 6, a as well as several of the ligand-based orbitals and assigned for this reason only 6, a to the contested region, with Bl and B2 for M = W representing the two spin-orbit components of the a-orbitals. W e find from our calculations on M2(PH,)4C14(M = Mo, W), Table VII, the two orbitals a, u to be of nearly the same energy and the three ionizations of lowest energy to correspond to 6, a, u, respectively. We offer, as for the tetracarboxylates, the assignments A(6), B(a,u) and A(6), B,(a), &(.) for M = Mo, W respectively (Table VII). The relative intensities (2:l) and shapes of BI and B, are closely the same for WzCl4(PMe3), and W,(C02CF3)4with B1being much broader than B2. The different shapes of B, and B, make an assignment of the two bands to the spin-orbit components of the two a-orbitals unlikely.29
J . Am. Chem. SOC.1985, 107, 4459-4465 The observed splitting between B, and B2 of 0.4 eV is further larger than the calculated spin-orbit splitting of AEso = 0.18 eV for W2C14(PHJ4(Table VII). A spin-orbit splitting of 0.4 eV would, according to the discussion in section IIIc, require that the a-orbital is almost pure d, (C12= 1). We find, however, CI2= 0.57 in close agreement with the value of CI2= 0.6 from the SCF-Xa-SW calculations on W2C14(PH3)4.11a
V. Concluding Remarks W e have in this study explored the u, T , 6 orbitals, used by Cotton2' to account for the multiple metal-metal bond in binuclear complexes, by calculating the energies for the 2B2g,2Eu,and 2Al, states of M2(C02H)4+( M = Cr, Mo, W), corresponding to ionization of one electron out of the u, a , 6 orbitals, respectively, as a function of the metal-metal bond distance RMM. The energies for the three states were calculated in the order E('Bzg) E(2EI) (29) It is argued in ref 1l a where B, and B2 are assigned to the a orbitals that the different shapes of B, and B2 are due to differences in the coupling between the two a orbitals with u, 6 as one spin-orbit component of a will interact with 6 and the other with u. We do not in our full relativistic treatment find any significant coupling between x and u, 6. In fact, such a coupling would only be important if either 6 or u was degenerate in energy with the x orbitals. In ref 1la a is separated from 6 and u by 2 eV from above and below, respectively. (30) The calculated trend in RMofor the doublet states of the bridged M2(C02R),+systems, Table I1 and Figure 1, seems not possible to rationalize in terms of changing metal-ligand overlaps with variations in the metal-metal bond distance, as the same trend was calculated for the nonbridged M2C14(PH3)4Csystems, Table VI and Figure 2.
-
4459
E(2Alg),indicating with out energy-decomposition analysis on several M2C14(PH3)4n+complexes'Ib of group 6 and group 7 metals. We have found in line with the 6 bond being weaker than the a bond that ionization of one electron out of the a-orbital results in a larger elongation of the metal-metal bond than the ionization of an electron out of the &orbital. The ionization of an electron from the a-orbital does, on the other hand, not change the metal-metal bond distance substantially, and this somewhat surprising result30 is explained in section IIIb. The HFS calculations indicate, in contrast to previous studies4 based on the X a model, that ionizations from the 6, a , u orbitals occur at lower energy than ionizations from the ligand-based orbitals and that the ionization potentials for u, T are close in energy. W e have attempted to reconcile the H F S results with record photoelectron spectra of tetracarboxylate complexes5~'and other binuclear systems11awith a quadruple metal-metal bond and find that the spectra of W2(C02CF3),and W2C14(PMe3)4 clearly show three bands that can be assigned to the metal-metal bonding orbitals 6, a, u, at lower energy than the first peak due to ionizations from ligand-based orbitals.
Acknowledgment. The investigation was supported by the National Sciences and Engineering Research Council of Canada. Registry No. Cr2(COzH)4,63448-51-1; Mo2(C02H),, 51329-49-8; W2(C02H),,96482-79-0; W2(C02CF3),,77479-85-7; Cr2(C02CH3),, 15020-15-2; Moz(Ph3)4CI,, 80485-12-7; W2(PH,),Cl,, 80485-13-8; M o ~ ( O H )64438-94-4. ~,
Comparative Studies on the Electronic Structures of W2(02CH), and W,( 02CH),( CH3)*by the Relativistic Xa-SW Method: A d3-d3 Metal Dimer with a Quadruple Metal-Metal Bond? M. D. Braydich,'" B. E. Bursten,*+lBM. H. Chisholm,lb and D. L. Clark" Contribution from the Department of Chemistry, The Ohio State University, Columbus, Ohio 43210, and the Department of Chemistry and Molecular Structure Center Indiana University, Bloomington, Indiana 47405. Received November 16, 1984
Abstract: The bonding in W2(02CR)4and in the recently characterized W2(02CR)4R'2molecules is compared via Xa-SW calculations with quasi-relativistic corrections on the model system W2(02CH)4(I) and W2(02CH),(CH3), (11). Several questions concerning the electronic structure of I1 have been addressed; in particular, the apparently strong W-W bond in the presence of strong W-C bonds was of interest. It has been found that I1 is best considered as a W,(02CH), fragment interacting with two CH, radicals, a description consistent with the photochemical decomposition of W2(02CEt)4(CH2Ph)2.The resulting W-W bond still retains the essential components of the quadruple bond in I. The W-W bonding remains strong in spite of strong axial ligation because of involvement of a higher-lying s-s u-bonding orbital, an orbital whose contribution is more important in I1 than in I. It is the presence of this orbital, which is lower-lying for third-row metals than for first, which is believed to account for the structural differences between Cr2(02CR)4L2and the W2(OZCR)4R2 systems.
The rapid growth is the synthetic and structural chemistry of dinuclear transition-metal complexes containing strong metalmetal bonds has provided a wealth of information about the nature of metal-ligand and metal-metal interactions2 The elegant story of the Cr-Cr quadruple bond as told by Cotton and Walton3 beautifully emphasizes this point. The general conclusion gained through the structural studies of these C r compounds is that it is not the electronic properties of the chelating ligands that determines the Cr-Cr bond lengths but rather the presence of or absence of axial ligands. Indeed, the unfailing Occurrence of axial 'Camille and Henry Dreyfus Foundation Teacher-Scholar (1 984-1989) and Fellow of the Alfred P. Sloan Foundation (1985-1987).
0002-7863/85/1507-4459$01.50/0
ligation in the dichromium tetracarboxylates and the enormous range of Cr-Cr distances has posed exceptional challenges to the theory of the electronic structure of these compounds. Numerous electronic structural calculations have appeared in the 1iterature3-l0 ( I ) (a) Ohio State University. (b) Indiana University. (c) 1984-1985 Indiana University SOH10 fellow. (2) Cotton, F. A. Acc. Chem. Res. 1978, 11, 225. (3) Cotton, F. A.; Walton, R. A. "Multiple Bonds Between Metal Atoms"; Wiley: New York, 1982; Chapter 4. (4) Benard, M. J . Am. Chem. Sot. 1978, 100, 2354. (5) Benard, M.; Veillard, A. N o w . J . Chim. 1977, I , 97. (6) Garner, C. D.; Hillier, I. H.; Guest, M. F.; Green, J. C.; Coleman, A.
W. Chem. Phys. Lett. 1976, 41, 91.
0 1985 American Chemical Society
