11406
J. Phys. Chem. 1994, 98, 11406-11410
The Metal Carbon Double Bond in Fischer Carbenes: A Density Functional Study of the Importance of Nonlocal Density Corrections and Relativistic Effects Heiko Jacobsen, Georg Schreckenbach, and Tom Ziegler* Department of Chemistry, University of Calgary, 2500 University Drive N. W., Calgary, Alberta, Canada T2N IN4 Received: June 20, 1994; In Final Form: August 25, 1994@
Fischer type carbenes of the chromium triad (C0)5M=CH2, M = Cr, Mo, W, have been subjected to a density functional study. It was found that the self consistent treatment of nonlocal density corrections has a substantial influence on the M=C geometry with bond extensions of 5 pm for all three metals. Further, for the tungsten compound the contributions from relativistic corrections to the W-C bond distances amounts to 7-8 pm. As far as bond energies are concerned, it is sufficient to optimize the geometries within the local density approximation and to calculate the final energies with nonlocal corrections added as a perturbation. The relativistic corrections to the M=C bond energy are of special importance in the tungsten case.
Introduction About 30 years ago, Fischer and Maasboll reported for the first time the existence of a transition metal complex possessing a carbene ligand. The chemistry of the so called Fischer type complexes2 has since developed rapidly with extensive studies of their structures and r e a c t i ~ i t y . ~Fischer .~ type compounds are utilized in a variety of transformations and have been established as a useful synthetic tool in organic and organometallic ~hemistry.~ In contrast to the so called Schrock type complexes,6 Fischer carbenes are characterized by low-valent transition metal fragments, typically formed by late transition metals. Transition metal carbene complexes have been the focus of theoretical considerations for a long time, but so far only a few ab initio studies on coordinatively saturated complexes have been reported. The first application of nonempirical molecular electronic structure calculations to a transition metal carbene was reported by Spangler and c o - ~ o r k e r s ,who ~ chose (C0)3Ni=CH2 as their model compound. Further important theoretical studies on Fischer type complexes have been performed by Nakatsuji and co-workers*on (CO)~CFCH(OH) and (CO)Pe=CH(OH), as well as by Taylor and Hall9 on (C0)5Mo=CH(OH) and (CO)sMo=CH2. The interest in the electronic and molecular structures of Fischer type complexes has recently been reviewed by MArquez and Femandez Sanz,lo who presented calculations on (CO)sMo=EH2, E = C, Si, Ge, Sn. We have initiated” a density functional study on Fischer type complexes (C0)5MEER2, in order to investigate the nature of the M=E bond in relation to the transition metal M,lla the main group representative E,” as well as the substituents R.IIb Our geometry optimizations are based on the local spin density approximation, where the final bond energies are calculated with nonlocal corrections added as a perturbation. However, it has been shown that the self consistent treatment of nonlocal corrections12a%c has a substantial influence on the geometries of transition metal complexes.12bscIn a recent study of transition metal carbonyls, Li and c o - ~ o r k e r shave ~ ~ demonstrated the importance of relativistic effects for geometry calculations of heavy metal carbonyl complexes. It is the goal of the present work to probe the importance of nonlocal corrections and quasi-relativistic contributions on the @
Abstract published in Advance ACS Abstracts, October 1, 1994.
0022-365419412098- 11406$04.50/0
geometries of Fischer type carbenes. Here, we present a case study on the methylene complexes of the chromium triad (C0)5Cr=CH2 (Ia), (C0)5Mo=CH2 (Ib), and (CO)sW=CH2 (IC). Of further interest are the changes in the M-C bonding energies, induced by the improved molecular geometries as well as the self consistent treatment of nonlocal corrections.
Computational Details
All calculations were performed utilizing the AMOL program package, developed by Baerends et al.14 and vectorized by Ravenek.15 The numberical integration was performed according to the procedure developed by teVelde et The exchange factor, sex, was given the usual value of 2/3. An uncontracted triple-5 STO basis set1’ was used for the ns, np, nd, (n l)s, and (n l)p shells of the transition metals. For H, a double-g STO basis seti7 was employed, which was extended by one 2p STO polarization function. The ns and np shells of the remaining main group elements were described by a double-5 STO basis set,” augmented by one 3d STO polarization function. Electrons in lower shells were considered as core and treated according to the procedure of Baerends et aLL4 An auxiliary set1*of s, p, d, f, and g STO functions, centered on all nuclei, was used in order to fit the molecular density and present Coulomb and exchange potentials accurately in each SCF cycle. On the lowest level of theory employed in this study, the geometries were optimized within the local density approximation (LDA)I9in the parametrization of Vosko et aLZ0 In a more sophisticated approach, Becke’s2Inonlocal exchange correction as well as Perdew’s2*inhomogeneous gradient corrections for correlation were added self consistently12(NL+SCF). Further, quasi-relativistic corrections (NL+SCF+QR) were taken into account according to the scheme devised by Snijders and coworker~.*~ The extension of this scheme to include geometry optimization is the work of Schreckenbach and c o - w o r k e r ~ . ~ ~ The geometry optimization was based on the method developed by Versluis and Ziegler.25 It has been shown that the LDA method in general overestimates bond dissociation energies.26 Therefore, the final bond energies for the LDA geometries have been determined by adding the nonlocal corrections as a perturbation (LDA/NL). This procedure is computationally much less demanding than a self consistent treatment of nonlocal
+
0 1994 American Chemical Society
+
The Metal Carbon Double Bond in Fischer Carbenes
W
J. Phys. Chem., Vol. 98, No. 44, 1994 11407 ligands and the tungsten center are contracted by 6-8 pm. The remaining structural parameters show only minor influences of relativistic effects. The LDA and NL+SCF calculations result in the following ranking for M=C bond length: W > Mo > Cr. Relativistic effects result in a maximum of the M=C bond length for the molybdenum compound lb, leading to the following order for d ~ * : Mo > W > Cr. Bonding Analysis. We analyze the M=C bond in complexes la-lc by the interaction of a methylene unit with the transition metal pentacarbonyl fragment: (CO),M
Figure 1. Representative eclipsed geometry for (CO)sM=CH* Fischer type carbenes and a description of the relevant geometric parameters.
corrections. Quasi-relativistic corrections to the bond energy have also been included at the LDA level of theory (LDN NL+QR).
Results and Discussion Geometries of (C0)5M=CH2 (M = Cr, Mo, W). We can in principle differentiate between two C2,, arrangements for the (CO)sM=CH2 complexes, namely a staggered conformation S as well as an eclipsed conformation E. These configurations are related by a 45" rotation of the carbene ligand around the C2 axis of the complex. This rotation is essentially free with rotational barriers of about 2 kJ/mo1.8J0J1a The preference of a staggered or an eclipsed arrangement is determined by the substituents of the carbene ligand as well as by the M=C bond distance." In this study, we have adapted an E arrangement. A representative geometry together with the definitions of structural parameters is displayed in Figure 1. In Table 1, we report the bond lengths and bond angles for the complexes lac, obtained at different levels of theory. From Table 1, we see that the angles between the equatorial CO groups and the carbene ligand, ql and al,are comparable for all three complexes under investigation. We also find only small changes with different levels of theory. The overall variation of ql and a1 for all geometries considered in this study amounts to 1.1 and 1.2", respectively. All calculations result in a distorted geometry with q l slightly smaller and a1 slightly larger than 90". This distortion has been rationalized on the basis of molecular orbital arguments.lla Another set of secondary structural parameters defines the geometry of the methylene group. The C-H bond length as well as the angle y are basically transferable between complexes l a and ICand differ only slightly with the improvement of the theoretical model. The major geometrical changes are observed in the M-C and, to a lesser extent, C-0 bond lengths. The self consistent treatment of nonlocal corrections affords M-C distances that are between 2 and 6 pm longer than the corresponding LDA values. This nonlocal bond elongation AINLis about 1 pm larger for the carbonyl ligands than for the methylene group. Further, the average value of Ad:, decreases on going from Cr to Mo and W. All C-0 bonds are stretched by about 1 pm. The influence of quasi-relativistic corrections is negligible for the chromium carbene but noticeable for the molybdenum compound. The relativistic bond contraction Ad for the Mo=C bond amounts to 1.6 pm. For the tungsten cgmplex IC the relativistic contraction becomes a major feature with A i RR given by 7.4 pm. The relativistic bond contraction is larger in absolute terms than the nonlocal bond expansion with the result that the NL-SCF+QR estimate for dw=c is smaller than in the nonrelativistic LDA case. The bonds between the carbonyl
+ CH2 - (CO),M=CH2
(1)
We further describe the bond as dative a/n coupling of two singlet fragments, as shown in Figure 2. Although CH2 possesses a triplet ground state, it has been arguedlOJlathat for the pentacarbonyl fragments of the chromium triad the a/x dative bond description is most appropriate, even for the methylene ligand. We write our bond energy BE as27
The bond-snapping energy BEsnap is the energy associated with the process as shown in Figure 2. The preparation energy AEwp takes into account the geometric distortion of the fragments from their equilibrium geometries to the framework of the final molecule as well as the promotion from the electronic ground state of a fragment into its electronic valence state. In our case, AEprepis dominated by the singlet-triplet splitting AESTof the CH2 group. This is also the most critical component of our bond analysis. Density functional theory (DFT) calculations result in values for AESTof -65 kJ/mol (LDA/NL) and -66 kJ/mol (NL-SCF). These values are too high compared to the experimental result28of AEST= -38 kJ/mol. The optimized geometries for the pentacarbonyl fragments were adapted from the work of Li and co-worker~.'~~ The bond-snapping AEsnap energy can be further decomposed as2729 BE,,,
= -[AP
+ AEint]
(3)
O
The steric repulsion AZF is made up of the stabilizing Coulomb interaction of the fragments as well as the repulsive destabilizing two-orbital four-electron interaction between the pentacarbonyl fragment and the carbene ligand. The destabilizing contribution, which is referred to as the Pauli repulsion, is usually the major contributor to A@. Finally, the orbital interaction term AEint accounts for the stabilizing interactions of virtual and occupied orbitals on both fragments after they are brought together in the final complex. The results of our bond analysis are gathered into Table 2. If we compare the bonding energies for the three different Fischer carbenes at the LDA level of theory, we observe a decrease in the bond strength on going from the chromium compound to the tungsten compound. The same trend can be observed for the values obtained at the LDA/NL level of theory. If we compare the LDA/NL analysis with the NL+SCF decomposition, we find in any case that the NL+SCF calculation results in a higher value for the bond-snapping energy BE,,,. The elongation of the M=C bond leads to reduction in steric repulsion as well as to a decrease in orbital interaction. However, the first effect is more pronounced and results in an overall stabilization in terms of BE,,,. If we now consider the changes in the preparation energy, we find for all three molecules an increase in AEppp, when nonlocal corrections are
Jacobsen et al.
11408 J. Phys. Chem., Vol. 98, No. 44, 1994 TABLE 1: Optimized Bond Distance# and Bond Anglesb for (CO)sM=CHz Complexes (CO)~CFCHZ (CO)~MO=CH~ LDA NL-SCF NL-SCF+QR LDA NL-SCF NL-SCF+QR 188.4 110.7 189.2 185.4 187.6 114.6 115.0 114.5 86.2 91.7 109.9 a
193.3 110.7 195.4 191.3 193.8 115.4 115.7 115.4 86.8 91.0 109.3
193.0 110.6 195.4 191.1 193.7 115.4 115.7 115.2 86.8 91.1 109.4
203.5 110.7 208.7 202.7 205.7 114.6 114.8 114.4 85.7 92.2 109.1
207.7 110.8 214.2 208.3 211.5 115.3 115.6 115.0 85.7 92.0 108.9
206.1 110.9 213.6 206.6 210.4 115.3 115.6 115.1 86.1 91.5 109.1
(C0)5W=CH2
LDA
NL-SCF
NL-SCF+QR
201.7 110.6 214.0 207.2 211.1 114.5 114.7 114.3 86.0 92.1 109.4
210.8 110.8 219.0 211.9 215.1 115.4 115.7 115.2 85.8 92.1 108.8
203.4 110.7 210.7 203.9 209.2 115.4 115.9 115.1 86.1 92.0 109.0
Distances in pm. * Angles in deg.
LDA/NL+QR. The relativistic contribution is crucial for an adequate estimate of BEw-. Anywise, the LDA/NL+QR value for B E w e represents already a good estimate of the bond energy obtained at the more sophisticated NL-SCF+QR level of theory. If we rank the metal carbene bond strengths at the nonrelativistic NL-SCF level of theory, we find that the bonding energy decreases on going down the triad: Cr > Mo > W. Relativity considerably stabilizes the W=C bond, and we obtain the following order with respect to BE: W > Cr > Mo. Comparison with ab Initio Studies. We will conclude our (CO)sM (C0)5M=CHz CHl discussion with a short comparison of our DFT properties for the M=C bond with those obtained by ab initio calculations. Figure 2. ~ J dative C coupling scheme for the (C0)sM fragment with We restrict our discussion to metal carbonyl compounds with CHI. The carbene has been promoted to its electronic valence singlet state. the carbene ligand CH2. The values for dM=c and BeMe are collected in Table 3. included in the geometry optimization. This change is caused To our knowledge, for the first transition metal row, the only by a higher geometric preparation energy for the metal fragment. ab initio calculation on (CO),M=CH2 complexes to compare As a result, the LDA/NL bond energies are slightly higher than the NL-SCF values. However, the deviation between B E L D ~ with is the study by Spangler and co-workers' on (C0)3Ni=CH2. The bond length for our chromium compound is 5 pm (LDA) and BENL-SLFamounts only to 2-4 kJ/mol. Thus, the LDA/ or 10 pm (NL-SCF) longer than that obtained for the nickel NL bond energies are already very good estimates for the true carbene complex. This difference seems reasonable, keeping M=C bond dissociation energy. in mind that experimentally known nickel carbenes have We now consider the influence of relativistic effects. For substantially shorter M=C bonds than the Fischer complexes the chromium complex l a we find that relativistic effects with the chromium pentacarbonyl fragment: dNi-c = strengthen the CFC bond by 4-6 kJ/mol. The LDA/NL+QR 18532a-190 pm,32bdcpc = 200-216 Spangler et al. do and the NL-SCF+QR values for BEc- are quite similar. not report a value for the bond dissociation energy for the Ni=C For the molybenum compound lb, we observe as a major link. relativistic effect an increase in the orbital interaction energy For the molybdenum carbene lb, we can compare our results mint. This can be rationalized by the relativistic destabilization30 of the metal d orbitals, which minimizes the energy gap with the calculations of Taylor and Hall as well as with the between interacting orbitals forming the n bond, as shown in study of Mkquez and Femhdez Sanz. The SCF value for the Figure 2. Thus, the orbital interaction between those orbitals MO=C bond length obtained by Mhquez and FemPndez Sanz is increased. The LDA/NL+QR calculation overestimates this compares reasonably well with our LDA result. An advanced stabilizing interaction, since the LDA value for is too treatment of electron correlation leads in the SCF case to a short. At the NL-SCF level of theory, this correction amounts contraction of the Mo=C bond (CASSCF), whereas the DFT to 16 kJ/mol. study at the NL-SCF level of theory results in an increase of For the tungsten compound IC, we observe a second d~,,-c. Since no experimental data are available for lb, it is relativistic effect. The steric interaction term is now effectively hard to judge which calculation gives a more appropriate reduced. This has been shown by Ziegler and co-workers3' to description of the Mo=C geometry. Looking at the two be related to a relativistic reduction in the electronic kinetic experimentally determined Mo=C bond distances of 21833aand energy. The reduction in steric repulsion, A,!?', together with 219.5 pm,33brespectively, the values for both calculations an increase in orbital interaction leads to a major stabilization fall short compared to the X-ray structures. However, it has of the W=C bond. The NL-SCF-tQR calculation results both been argued that the M=C double bond can be expected to be in an increased steric interaction and in a more efficient orbital shorter for CH2 than for a CR1R2ligand, possessing a singlet interaction. This effect is caused by the relativistic bond ground state and sterically demanding substituents.ll Calculacontraction. The bond-snapping energy is 12 kJ/mol less than tions for the Fischer complex (CO)sCr=CMe(OMe)' l b resulted in the LDA/NL+QR case. However, on the NL-SCF+QR in Cr=C bond lengths of 193 pm (LDA) and 198 pm (NLlevel of theory, the preparation energy only amounts to 76 kJ/ SCF), respectively. Thus, the modification of the carbene ligand mol, compared to 96 kJ/mol for LDA/NL+QR. Thus, the total leads to a further Cr=C bond elongation of 5 pm. The NLbond energy is 8 kJ/mol higher for NL-SCF+QR than it is for SCF value for the CFC distance now approaches reasonably
"I
a-
I +\
The Metal Carbon Double Bond in Fischer Carbenes
J. Phys. Chem., Vol. 98, No. 44, 1994 11409
TABLE 2: Bond AnalysitP for (CO)sM=CH2 Complexes (CO)SCFCH~
AE" "t
BEsnap AEprep
BE
LDA/ NL
LDA/NL +QR
113 -469 356 75 28 1
111 -472 361 76 285
NL-
(CO)sMo%Hz LDA/
SCF
NL-SCF +QR
15 -438 363 84 279
75 -445 370 85 285
NL-
(C0)5W=CHz
NL
LDA/NL +QR
SCF
NL-SCF +QR
104 -440 336 82 254
108 -480 372 86 286
69 -422 353 101 252
-439 369 100 269
70
NL-
LDA/ NL
LDA/NL +QR
SCF
NL-SCF +QR
89 -429 340 86 254
53 -455 402 96 306
62 -416 354 104 250
91 -481 390 76 3 14
Energies in kJ/mol.
TABLE 3: Theoretical DFT and ab initio Bond Distances and Bond Dissociation Energies for the Metal Carbon Double Bond in (CO)sM=CHz Complexes
dM=c" BEM-c~
(CO)sCrCH2 this work
(C0)3Ni=CH2 Spangler et al.'
188.g 193.38 2799 3079.'
183*
m
(CO)~MO=CH~ this work 203.9 207.78 2528 2809.'
(CO)~MO=CH~ Taylor and Halld
(CO)sMo=CHz Mhquez and Femindez Sanze
i
202.021 198.55k 320'" 282k,'
234"
Bond lengths in pm. Bond dissociation energies in kllmol. If necessary, literature values have been transformed. Reference 7. Reference 9. e Reference 10. f LDA. NL-SCF. * HF-SCF. Not optimized. j HF-ECP. CASSCF. Corrected with the experimental value for A&(CHz). Not reported. GMO-CI. Refers to a dissociation into two singlet fragments.
well the lower end of the spectrum of experimentally known Cr=C bond lengths (vide supra). Considering the bond dissociation energy, we already mentioned that the singlet-triplet splitting for methylene is the most critical parameter in our analysis. A correct assessment of A& still provides a challenge to density functional theory. We therefore included in Table 3 optimized bond dissociation energies, corrected by the experimental value for A&. Further, the BE value for lb, reported by Mirquez and FemAndez Sanz refers to a dissociation into two singlet fragments. We also corrected this energy with the experimental AESTfor electronic preparation. If done so, the result of the present DFT study, BE(MO=C)NL-SCF= 280 kJ/mol, is in excellent agreement with the ab initio calculation, BE(MO=C)CASSCF = 282 kJ/mol. Both results are about 50 kJ/mol higher than the bond energy obtained by Taylor and Hall. Accurate experimental M=C bond energies for neutral Fischer carbenes are not available. However, for the carbene systems of the chromium triad, it has been that chromium compounds are less stable than similar tungsten derivatives but more stable than analogous molybdenum compounds. This stability ranking W > Cr > Mo is in accord with our calculated trend for M=C bond strengths.
Conclusion We will summarize our present study in a few final remarks. The self consistent treatment of nonlocal correction is important in the description of molecular geometries. M=C bond distances evaluated by the LDA method are in general 4-6 pm shorter than NL-SCF results. The relativistic bond contraction is of major importance for complexes with a third-row transition metal. When bond energies are concerned, it is sufficient to add nonlocal corrections as a perturbation. LDA/NL as well as NL-SCF bond dissociation energies are of comparable quality. Relativistic effects are crucial in a correct assessment of the M=C bond length and bond energy for the tungsten complex. Whereas the relativistic bond contraction is a major contributor to the W=C geometry, the LDA/NL+QR as well as the NLSCF+QR bond energies are again comparable. For the calculation of computationally more demanding complexes, we recommend the LDA/NL+QR method as the most appropriate one. Relativistic effects prohibit an interpolation of structural data and chemical properties amongst analogous complexes of one
transition metal triad. Nonrelativistic calculations result in monotone trends for ~ M - C(W > Mo > Cr) and for BE(M=C) (Cr > Mo > W). Relativity, however, changes this order in a way that the second transition row element forms the longest and the weakest M=C bonds. The relativistic bond lengths increase as Cr < W -= Mo whereas the relativistic bond energies decrease as W > Cr > Mo.
Acknowledgment. This investigation was supported by the National Science and Engineering Research Council of Canada (NSERC) and by the donors of the Petroleum Research Fund, administered by the American Chemical Society (Grant ACSPRF#27023-AC3). References and Notes (1) Fischer, E. 0.;Maasbol, A. Angew. Chem., Int. Ed. Engl. 1964,3, 580. (2) Fischer, E. 0. Angew. Chem. 1974, 86, 651. (3) Dotz, K. H.; Fischer, H.; Hofmann, P.; Kreissl, F. R.; Schubert, U.; Weiss, K. Transition Metal Carbene Complexes; Verlag Chemie: Weinheim, Germany, 1983. (4) Schubert, U. Coord. Chem. Rev. 1984, 55, 261. (5) (a) Dotz, K. H. Pure Appl. Chem. 1983,55, 1689. (b) Dotz, K. H. Angew. Chem., Int. Ed. Engl. 1984,23,587. (c) Brookhart, M.; Studabaker, W. B. Chem. Rev. 1987, 87, 411. (d) Hegedus, L. S. Pure Appl. Chem. 1990, 62, 691. (e) Schmalz, H. G. Angew. Chem., Int. Ed. Engl. 1994,33, 303. (6) Schrock, R. R. Acc. Chem. Res. 1979, 12, 98. (7) Spangler, D.; Wendoloski, J. J.; Dupuis, M.; Chen, M. M. L.; Schaefer, H. F., III. J . Am. Chem. Soc. 1981, 103, 3985. (8) Nakatsuji, H.; Ushio, J.; Han, S.; Yonezawa, T. J . Am. Chem. SOC. 1983, 105, 426. (9) Taylor, T. E.; Hall, M. B. J . Am. Chem. SOC. 1984, 106, 1576. (10) Mirquez, A.; Femhndez Sanz, J. J . Am. Chem. SOC. 1992, 114, 2903. (11) (a) Jacobsen, H.; Ziegler, T. Inorg. Chem., submitted for publication. (b) Jacobsen, H.; Ziegler, T. Organometallics, submitted for publication. (12) (a) Fan, L.; Ziegler, T. J . Chem. Phys. 1991, 94, 6057. (b) Fan, L.; Ziegler, T. J . Chem. Phys. 1991, 95, 7401. (c) Fan, L. Ph.D. Thesis. University of Calgary, 1992. (13) (a) Li, J.; Schreckenbach,G.; Ziegler, T. J . Phys. Chem. 1994, 98, 4838. (b) Li, J.; Schreckenbach, G.; Ziegler, T. J. Am. Chem. SOC., submitted for publication. (14) (a) Baerends, E. J.; Ellis, D. E.; Ros, P. E. Chem. Phys. 1973, 2, 41. (b) Baerends, E. J. Ph.D. Thesis. Vrije Universiteit Amsterdam, 1975. (15) Ravenek, W. In Algorithms and Applications on Vectorand Parallel Computers; Riele, H. H. J., Dekker, Th.J., van de Horst, H. A., Eds.; Elsevier, Amsterdam, The Netherlands, 1987. (16) tevelde, G.; Baerends, E. J. J . Comput. Phys. 1992, 99, 84. (17) (a) Snijders, G. J.; Baerends, E. J.; Vemoijs, P. At. Nucl. Datu Tables 1982, 26, 483. (b) Vemooijs, P.; Snijders, G. J.; Baerends, E. J. Slater
11410 J. Phys. Chem., Vol. 98, No. 44, 1994 Type Basis Functions for the Whole Periodic Table. Internal Report; Vrije Universiteit Amsterdam: 1981. (18) Krijn, J.; Baerends, E. J. Fitfunctions in the HFS-Method. Internal Report; Vrije Universiteit Amsterdam: 1984. (19) Gunnarson, 0.;Lundquist, I. Phys. Rev. 1974, BlO, 1319. (20) Vosko, S. J.; Wilk, M.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (21) (a) Becke, A. J . Chem. Phys. 1986, 84, 4524. (c) Becke, A. J . Chem. Phys. 1988, 88, 1053. (22) Perdew, J. P. Phys. Rev. 1986, B33, 8822. (23) (a) Snijders, J. G.; Baerends, E. J. Mol. Phys. 1978, 36, 1789. (b) Snijders, J. G.; Baerends, E. J.; Ros, P. Mol. Phys. 1979, 38, 1909. (c) Ziegler, T.; Tschinke, V.; Baerends, E. J.; Snijders, J. E.; Ravenek, W. J . Phys. Chem. 1989, 93, 3050. (24) Schreckenbach, G.; Ziegler, T.; Li, J. Int. J . Quantum Chem., submitted. (25) Versluis, L.; Ziegler, T. J . Chem. Phys. 1988, 88, 322. (26) Ziegler, T. Chem. Rev. 1991, 91, 651.
Jacobsen et al. (27) Ziegler, T. NATO Adv. Study Inst. Ser. 1991, C378, 367. (28) McKellar, A. R. W.; Bunker, P. R.; Sears, T. J.; Evenson, K. M.; Saykally, R. J.; Langhoff, S. R. J . Chem. Phys. 1983, 79, 5251. (29) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1. (30) Pykko, P. Chem. Rev. 1988, 88, 563. (31) Ziegler, T.; Snijders, G. J.; Baerends, E. J. In The challenge of d andf Electrons; Salahub, D. R., Zemer, M. C., Eds.; ACS Symposium Series 395; American Chemical Society: 1989; p 322. (32) (a) Sellmann, D.; Prechtel, W.; Knoch, F.; Moll, M. Organometallics 1992. 11. 2346. (b) Dean. W. K.: Charles. R. S.: Van Derveer. D. G. Inorg. Chem'. 1977, 16; 3328.' (33) (a) Dai, X.; Li, G.; Chen. Z.; Tang. Y.; Chen, J.; Lei, G.; Xu, W. Jiegou Huaxue 1988, 7, 22. (b) Erker, 6.;Dorf, U.; Kriiger, C.; Tsay, Y.-H. Organometallics 1987, 6, 680. (34) Kirtley, S. W. In Comprehensive Organometallic Chemistry, 1st ed.; Wilkinson, G., Stone, F. G. A,, Abel, E. W., Eds.; Pergamon Press: Oxford, U.K., 1982; Vol. 111, p 899.
