J . Phys. Chem. 1992, 96, 2118-2122
2118
I' J.
T
I/
-16.4
-20.5
Figure 3. MR-CISD+Q energy profile in kcal mol'l.
barrier height and the frequencies as indicated above, the rate constant at 298.15 K is 2.5 X cm-3 molecule-I s-', thus one-sixth the experimental constant5 2.0 X cm-3 molecule-l s-I. In order to compare the preexponential factor with the experiment, a set of 11 rate constants k( T ) calculated in the 220-420 K temperature range using eq 3 has been fitted to the Arrhenius equation: k(T) = A exp(-E,/RT). From the slope of the plot, the value of the activation energy is 3.64 kcal mol-', in agreement with that deduced using eq 2. In turn, the theoretical preexponential factor A is 1.63 X lo-" cm-3 molecule-' s-I, in quite good agreement with the experiment: 9.0 X cm-3 molecule-' s-l. This result suggests that although the calculated activation energy is somewhat overestimated, the theoretical analysis reported in this work seems to be essentially correct. In other words, the chlorine abstraction by the HO radical in this process appears to be a bimolecular homolytic substitution (SH2) of the type classified by Ingoldz3as synchronous.
Summary and Conclusions We report in this paper a theoretical study of the chlorine abstraction process occurring in the reaction of HO radical with nitrosyl chloride. The reaction is assumed to occur in a plane, and we have argued from symmetry considerations that the A' potential energy hypersurface should be favored. Three stationary points have been located from CASSCF calculations. The first one is a van der Waals complex in which a small interaction between the radical H O and NOCl is observed. The second stationary point has been properly characterized as a transition state, which appears early according to an exothermic reaction. A third stationary point on the potential energy hypersurface has been found in which the products HClO and N O are separated by 3.37 A. A summary of the calculated potential energy profile for the reaction is shown in Figure 3. The reaction enthalpy and activation energy, calculated at the MR-CISD+Q level, including the ZPE and thermal corrections, are -15.3 and 3.6 kcal mol-', in agreement with the experimental values of -18.2 and 2.25 kcal mol-', respectively. The kinetic analysis of the process agrees with a bimolecular homolytic substitution (SH2) type reaction, and its mechanism appears to be fairly similar to that generally accepted for the SN2 nucleophilic ~ u b s t i t u t i o n . ~ Our ~ ~ ~reactive ' and product van der Waals complexes would play the same role as that of ion-dipole adducts. Acknowledgment. This work was supported by the Direccidn General de InvestigaciQ Cientifica y Tknica (PB89-0561). We are grateful to M. Dupuis for a copy of the HONDO-7 code and to F. Diez for his help in implementing HONDO-7 on a C-210 Convex computer. We also thank a referee for useful suggestions on symmetry aspects. Registry No. OH, 3352-57-6; NOCI, 2696-92-6. (23) Ingold, K. U. In Free Radicals; Kochi, J. K., Ed.; Wiley: New York, 1976; Vol. I, p 67. Ingold, K. U.; Roberts, B. P. Free-Radical Substirution Reactions; Wiley: New York, 1971. (24) Larson, J. W.; McMahon, T. B. J . Am. Chem. SOC.1984,106, 517. (25) Tucker, S.C.; Truhlar, D. G. J . Phys. Chem. 1989, 93, 8138 and references therein.
Theoretical Study of the Bonding of the First-Row Transition-Metal Positive Ions to Ethylene M. Sodupe, Charles W. Bauschlicher Jr.,* Stephen R. Langhoff, and Harry Partridge NASA Ames Research Center, Moffett Field, California 94035 (Received: August 19, 1991)
Ab initio calculations have been performed to study the bonding of the first-row transition-metal ions with ethylene. While Sc+ and Ti+ insert into the T bond of ethylene to form a three-membered ring, the ions V+ through Cu+form an electrostatic complex with ethylene. The binding energies are compared with those from experiment and with those of comparable calculations performed previously for the metal-acetylene ion systems.
I. Introduction Activation of hydrocarbons by transition-metal ions is currently an area of active experimental research.'-'* The determination (1) Sunderlin, L. S.; Armentrout, P. B. J . Am. Chem. SOC.1989, 1 1 1 , 3845. (2) Sunderlin, L. S.; Aristov, N.; Armentrout, P. B. J . Am. Chem. Soc. 1981, 109, 78. ( 3 ) Sunderlin, L. S.; Armentrout, P. 9. Inr. J . Mass Spectrom. Ion Processes 1989, 94, 149. (4) Aristov, N.; Armentrout, P. B. J . Am. Chem. SOC.1986, 108, 1806. (5) Georgiadis, R.; Armentrout, P. B. Int. J . Mass Spectrom. Ion Processes 1989, 89, 227.
0022-365419212096-2118$03.00/0
of bond energies of isolated metal-ligand bonds is important for predicting stable structures and reaction mechanisms. Experi(6) Schultz, R. H.; Elkind, J. L.; Armentrout, P. B. J . Am. Chem. Soc. 1988, 110, 411. (7) Fisher, E. R.; Armentrout, P. B. J . Phys. Chem. 1990, 94, 1674. (8) Tolbert, M. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1984,106,8117. (9) Armentrout, P. 9.; Beauchamp, J. L. J . Am. Chem. SOC.1981, 103, 6628. (10) Hanratty, M. A.; Beauchamp, J. L.; Illies, A. J.; van Koppen, P.; Bowers, M. T. J . Am. Chem. SOC.1988, 110, 1 . (1 1 ) Jacobson, D. B.; Freiser, B. S . J . Am. Chem. SOC.1983, 105,7492. (12) Burnier, R. C.; Byard, G . D.; Freiser, B. S . Anal. Chem. 1980, 52, 1641.
0 1992 American Chemical Society
Bonding of Transition-Metal Positive Ions to Ethylene mental binding energies (or lower bounds) are available for all of the first-row transition-metal-ethylene ions except MnCzH4+; for VCzH4+,only an estimate is available on the basis of a comparison with analogous systems such as VCzHz+.4 A recent theoretical study of the bonding between the first- and second-row transition-metal ions and acetylene showedI3 that the early transition-metal ions of each row insert into the A bond of acetylene, while the late ones bind electrostatically. Although the computed binding energies agreed reasonably well with the experimental data for the late-transition-metal ions, the experimental values are much larger than the computed results for the early ones. Interestingly, while a previous theoretical study14 showed a large discrepancy with experiment for ScC2H2+,the computed ScCzH4+binding energy agreed satisfactorily with experiment. In this work we extend our study of the transitionmetal-ethylene ions to the entire first row, to contrast the bonding between the metal-ethylene and metalacetylene ions and to better assess the accuracy of the experimental binding energies. 11. Methods For the transition-metal atoms we use an [8s4p3d] contraction of the (14s9p5d) primitive sets of Wachters,I5 supplemented with two diffuse p and one diffuse 3d function.I6 This is further augmented by a single contracted set of f polarization functions that is based on a three-term fit” to a Slater-type orbital, with exponents varying in steps of 0.4 from 1.6 for Sc to 4.8 for Cu. The transition-metal basis sets are of the form (14sl lp6d3f)/ [8s6p4dlfl. For Sc and Cu,larger (20sl5plOd6f4g)/[7~6pkl2flg] atomic natural orbital (ANO) basis sets18 are used to test the completeness of the smaller transition-metal basis sets. These sets are derived from the (20s12p9d) sets optimized by Partridge.lg The Cu basis set is described in detail in ref 20, and the Sc basis set is constructed in an analogous manner. For C and H, we use both valence double-S; VDZ, and A N 0 basis sets. The C and H VDZ basis sets are the (9s5p)/[3s2p] and (4s)/[2s] sets, respectively, developed by Dunning and Hayz1 from the primitive set of Huzinaga.22 The C and H A N 0 basis sets are the (1 3s8p6d4f)/ (Ss4p2dlfl and (8s6p4d)/ [3s2pld] sets described in ref 23. These are the same basis sets as used in an earlier study of the metal-acetyleneI3 systems. Calculations are carried out at the self-consistent-field (SCF) and modified coupled-pair functionalz4 (MCPF) levels of theory. We also use the single and double excitation coupled-cluster methodzs with a perturbational estimate of the triple excitationsz6 [CCSD(T)] approach to calibrate the accuracy of the MCPF treatment. The geometry of the transition-metal-ethylene cation is fully optimized at the SCF level. In these calculations, we used the C and H VDZ basis sets. The metal f function is not included, but the s combination of the 3d functions is included. The binding energies are calculated at the S C F optimal geometry with the essentially size-extensive MCPF method, which provides an accurate treatment of electron correlation, because the SCF occupation is a good zeroth-order representation in all cases. In these calculations we use the C and H A N 0 basis sets and include the metal f function. Only the spherical harmonic basis functions are retained. Binding energies are calculated using the SCF-optimized (13) Sodupe,M.; Bauschlicher, C. W. J . Phys. Chem. 1991, 95, 8640. (14) Rosi, M.; Bauschlicher, C. W. Chem. Phys. Lett. 1990, 166, 189; Bauschlicher, C. W.; Langhoff, S. R. J . Phys. Chem. 1991, 95, 2278. (15) Wachters, A. J. H. J . Chem. Phys. 1970, 52, 1033. (16) Hay, P. J. J . Chem. Phys. 1977,66, 4377. (17) Stewart, R. F. J. Chem. Phys. 1970, 52, 431. (18) AlmlBf, J.; Taylor, P. R. J . Chem. Phys. 1987, 86, 4070. (19) Partridge, H. J . Chem. Phys. 1989, 90, 1043. (20) Bauschlicher, C. W.; Roos, B. 0. J . Chem. Phys. 1989, 91, 4785. (21) Dunning, T. H.; Hay, P. J. In Methods of Electronic Structure Theory; Schaefer, H. F., Ed.; Plenum Press: New York, 1977; pp 1-27. (22) Huzinaga, S. J . Chem. Phys. 1965, 42, 1293. (23) Bauschlicher, C. W.; Langhoff, S.R.; Taylor, P. R. J . Chem. Phys. 1987, 87, 387. (24) Chong, D. P.; Langhoff, S.R. J. Chem. Phys. 1986,81, 5606. See also: Ahlrichs, R.; Scharf, P.; Ehrhardt, C. J . Chem. Phys. 1985, 82, 890. (25) Bartlett, R. J. Annu. Rev. Phys. Chem. 1981, 32, 359. (26) Raghavachari, K.; Trucks, G. W.; Pople, J. A,; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479.
The Journal of Physical Chemistry, Vol. 96, No. 5, 1992 2119 TABLE I: Symmetry Properties of the Valence Orbitals of MC2H,+ symmetry a1 a2 b, b2
metal 3d,z, 3dxlyz, 4s 3dxy 3% 34,
C2H4
r bond, CC u bond, CH bond CH bond C H bond ?y*, CH bond
geometries. It was shown in previous workI4on similar compounds that, if a consistent set of ligand and metal-ligand geometries is used,the MCPF binding energies agree to better than 1 kcal/mol, regardless of whether the equilibrium structures are taken from the S C F or the MCPF level of theory. MCPF calculations are carried out correlating the 4s and 3d electrons of the metal ion and all the electrons of the ethylene except the 1s-like electrons of the C atoms. For all open-shell systems, we impose the first-order interacting space to reduce the codiguration interaction (CI) expansion length.z7 This constraint is not expected to affect the accuracy of the computed 0,values. For example, the Mne 3d6 to CzH4 binding energy is reduced by less than 0.18 kcal/mol, in spite of reducing the number of configurations from 1.83 X i o 6 to 3.47 x 105. The SCF geometry optimizations were performed using the GWCF program.28 The MCPF and CCSD(T) calculations were performed using the MOLECULE-SWEDEN” and TITAN3’ program systems, respectively. All calculations were performed at NASA Ames using the CRAY Y-MP/832. 111. Results and Discussion
A. Qualitative Considerations. At the S C F level, the equilib rium structure found for all the MCzH4+cations has C , symmetry with the metal ion approaching the A bond along the line perpendicular to the C-C bond. The C - C bond midpoint is at the origin, with the C-C bond along the x axis and the metal atom is on the z axis. To aid in the discussion, we have listed in Table I the symmetry properties of the CzH4 and the metal ion valence orbitals. As for the transition-metalacetylene cations,13our results show two different bonding mechanisms between the metal ion and ethylene. The early-transition-metal ions insert into the A bond of ethylene to give a three-membered ring. The C-C bond length increases to a value similar to that of C&, and the H atoms bend away from the metal ion, which is consistent with the change in the C hybridization to sp3. The two m e t a l 4 bonds formed have a l and bz symmetry and contain more metal 3d than metal 4s character. The strength of the interaction depends on the overlap of the metal 3d orbitals with the C sp3 hybrid orbitals, on the loss of 3d-3d exchange energy, and on the energy necessary to promote the metal ion to the appropriate state. For the late-transition-metal ions, the bonding mechanism is mainly electrostatic. The ligand geometry in the complex is only slightly changed from free ethylene, and the H atoms bend away from the metal ion by only a small amount. The size of the ion largely determines the metal-ethylene distance, and because the bonding is electrostatic, it has a substantial effect on the magnitude of the binding energy. However, the ability of the metal ion to reduce the repulsion with ethylene as well as the difference in the overlap of the metal 3d orbitals with ethylene also make important contributions not only to the determination of the ground state of the complex but also to the bond strength. The transition-metal positive ion can reduce the repulsion with ethylene by several mechanisms. For example, the 4s orbital can (27) Bunge, A. J . Chem. Phys. 1970,53,20. McLean, A. D.; Liu, B. J. Chem. Phys. 1973,58, 1066. Bender, C. F.; Schaefer, H. F. J . Chem. Phys. 1971, 55, 7498. (28) GRADSCF is a vectorid SCF first- and second-derivative code written by A. Komornicki and H. King. (29) MOLECULE-SWEDEN is an electronic structure program system written by J. Almlof, C. W. Bauschlicher, M. R. A. Blomberg, D. P. Chong, A. Heiberg, S. R. Langhoff, P.-A. Malmqvist, A. P. Rendell, B. 0. Roos, P. E. M. Siegbahn, and P. R. Taylor. (30) TITAN is a set of electronic structure programs written by T. J. Lee, A. P. Rendell, and J. E. Rice.
2120 The Journal of Physical Chemistry, Vol. 96, No. 5, 1992 TABLE 11: State-Averaged SCF Calculations for MC,H,+, with M = Sc, Mn, and Ni state
3d,,(b2)
3dX2,i(al)
2AI
2A2 =Al
2 2 2 2
2B2
1
2 2 2 1 2
4B2
2
1
4AI
1 1 1
2
2B,
occupation 3d,(a2) 3d,,(bl) NiC2H4+ 2 2 2 1 1 2 2 2 2 2
3dr2(al) AE" 1
2 2 2 2
0.0 2.1 2.3 2.5 4.1
MnC2H4* )A2
4BI
1
4AI 3A, )A2
'B2 'A,
1
1 1
1 1
2 1 1
1 1 1
2 1
1 1
1 1 2
ScC2H4+(the 4s is singly occupied in all states) 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1
0.0 6.3 6.8 6.8 7.5
0.0 0.1 1.6 2.6 8.2
Energies relative to the ground state (in kcal/mol).
mix in 4p character and polarize away from the ligand. Repulsion can also be reduced by sdu hybridization or by promoting the 4s electron into the compact 3d orbital, leading to a 3dn++'configuration. The relative importance of these effects depends on the ordering of the metal asymptotes. The interaction of the five 3d orbitals with ethylene is not equivalent. By considering the symmetry properties of the valence orbitals given in Table I, one sees that the 3d,,(b2) metal orbital can donate charge into the a * orbital of ethylene. Thus, occupying the 3d, orbital enhances the bonding. The remaining 3d orbitals have a repulsive interaction with the bonding orbitals of ethylene. The 3d+9 and 3d, orbitals have very small overlaps with ethylene, whereas the 3d22 orbital has the largest overlap. Therefore, we expect the 3d orbitals to be occupied in the following order: 3dAb2)
< 3dX2-~z(aJ
3d,(a2)
< 3dY,(bd < 3dAat)
This filling order was confirmed by carrying out state-averaged (SA) SCF calculations for NiC2H4+. Table I1 shows the relative ordering of the five doublet states that arise from a hole in each of the 3d orbitals. As expected, the lowest state is 2AI,where the 3d,z orbital is singly occupied. This configuration minimizes the repulsion with ethylene because the 3d22orbital has the largest overlap with ethylene. The 2B2state lies highest, which is consistent with the preferred occupation of the 3d,, orbital. The other three states are very close in energy and follow the expected ordering. SA-SCF calculations for the quartet states of Mn+(3d6)-C2H4 are also shown in Table 11. In this case one 3d orbital is doubly occupied. It is most favorable to doubly occupy the 3dx,(b2)orbital and least favorable to doubly occupy the 3d,2 orbital, as observed for NiC2H4+. The other three states are close in energy with the 4Alstate being the most stable of the three. This is a consequence of the 3dS4s1occupation being more stable than the 3d6 and the ability of the 3d+2(al) orbital to mix in some 4s character. The final system we consider at the SA-SCF level is ScC2H4+. Since the bonding is derived from the 3D(3d14s') state of Sc', there are five triplet states each having one 3d orbital singly occupied. The 3Al(3d,i) state is much less stable than the rest, as expected. However, the 3Al(3d,2,2) and 3A2(3d,) state are more stable than the 'B2(3d,,) state, even though on the basis of repulsion arguments the 'B2 state, which has the 3d electron in the 3d,,(b2) orbital, would be expected to be the ground state. However, the 3AI state is preferentially stabilized by mixing in the 3dZasymptote, which is 100%3F, whereas the 3B2state mixes In in the 3d2 asymptote, which is 40% 3Fand 60% excited 3P.31
Sodupe et al. addition, it should be noted that repulsion between the occupied 4s orbital and ethylene increases the metal-ethylene distance thereby weakening the 3d-ethylene interaction. Thus, the atomic parentage is a more important factor in determining the ground state than is maximizing the 3d-a* interaction. Nevertheless, since the metal to ?r* donation is increased at the correlated level, the 'B2 state is only 0.9 kcal/mol higher than the 'A, state at the MCPF level. B. Detailed Analysis of the Bonding. In Table 111 we present the equilibrium geometries, the binding energies, the net metal charge, and the 3d population of the first-row transition-metalethylene cations. The ground state of ScC2H4+is 'Al, in analogy with the ScC2H2+m~lecule.'~In this state the metal ion inserts into the a bond of ethylene. Our results are consistent with the study of Sarasa et al.,32who also find the most stable structure to involve the perpendicular approach of Sc+ to the bond midpoint of the C-C bond. The metal-C bonds contain more metal 3d than 4s character, although this is somewhat obscured by the large metal to ethylene charge donation. The lowest triplet is the 'A, state derived from the 3d'4s1 occupation of Sc+. The 3d electron is primarily in the 3dX~-y2 orbital. The bonding in the triplet state is electrostatic in origin, and the binding energy is about 8 kcal/mol less than that of the covalently bound lA, ground state. For TiC2H4+we find a 2Alground state, where again the metal ion has inserted into the a bond of ethylene to form a threemembered ring. This state is derived from the 'A, state of ScC2H4+by adding an electron to the 3d,2+(al) orbital. For TiC2H2+we found a 2A2ground state'' where the extra electron was in the 3d,(a2) orbital. The difference in the ground states is due to the fact that in TiC2Hz+the 3d, orbital has a stabilizing interaction with the out-of-plane a * orbital of acetylene, whereas in TiC2H4+both the 3d,~-~zand 3d, orbitals have a repulsive interaction with the orbitals of ethylene. The lowest quartet state of TiC2H4+is the 4B2state derived from the 3d24s' configuration of Ti'. The 3d,,(b2) and 3dX2+(a,) orbitals are singly occupied, which is consistent with the filling order of the 3d orbitals previously mentioned. The electrostatically bound 4B2state is about 5 kcal/mol less stable than the covalently bound 2Al ground state. The SA,ground state of VCzH4+,derived from the 3d4(sD) state of V+, consists of V+ electrostatically bound to ethylene. Consistent with minimizing the repulsion with ethylene, the 3d,z orbital is empty. The lowest lying triplet state, 'A2, arises from the 2AI state of TiCzH4+by adding an electron to the 3d,(az) orbital. In this state the metal ion inserts into the a bond of ethylene. Although further basis set expansions and improvements in the treatment of correlation energies are expected to stabilize the 3A2 relative to state, the computed energy difference at the present level of calculation is sufficiently large, about 15 kcal/mol, that we are confident that the ground state is the electrostatically bound state. This differs from VC2H2+where the ground state is the 'A2 covalently bound state." The difference in the ground state is related to the stronger a bond in ethylene than in acetylene. A more detailed comparison of the acetylene and the ethylene systems will be given below in the Trends subsection. The ground state of CrC2H4+is a 6AI state derived from the %(3d5) asymptote of Cr'. The lowest quartet state is a 4B2state with the expected occupation based on minimizing repulsion. As for C T C ~ H ~ +both , ' ~ the sextet and quartet states are electrostatically bound. As a result of the large loss of 3d-3d exchange energy, the quartet state lies well above the 6A, ground state. For MnC2H4+we considered the 'A, state derived from the 3dS4s'('S) ground state of the metal ion and the 5B2state derived from the 3d6(SD)excited state. As expected the doubly occupied orbital in the quintet state is the 3d,,(b2) orbital. In both the quintet and septet states, the metal ion binds electrostatically to ethylene. Although the electrostatic interaction is stronger for the 3d6 occupation due to the smaller size of the ion and smaller repulsion with ethylene, the very large 7S-5Dseparation for Mn+ ~
(31) Walch, S. P.; Bauschlicher, C. W. J . Chem. Phys. 1983,78, 4597.
(32) Sarasa, J. P.; Poblet, J. M.; Anglada, J.; Caballol, R. Chem. Phys. Lert. 1990, 167, 421.
The Journal of Physical Chemistry, Vol. 96, No. 5, 1992 2121
Bonding of Transition-Metal Positive Ions to Ethylene TABLE III: Summary of Geometries, Dissociation Energies, Transition-Metal-Ethylene Cations"
M
state
sc
"41
sc Ti Ti
'Al 2Al 'B2
V V
5AI 'A2
Cr
6Al 4B2
Cr Mn Mn Fe Fe co Ni cu
'Al Q2
4B2 6A, 'A2 2Al
"The bond lengths are in
r(C-C)
r(C-H)
1.49 1.35 1.42 1.35 1.35 1.40 1.35 1.36 1.35 1.36 1.35 1.35 1.35 1.35 1.36
1.08 1.07 1.os 1.07 1.07 1.os 1.07 1.07 1.07 1.07 1.08 1.08 1.07 1.07 1.07
D, Net Metal Charge, qM, and 3d Population for the First-Row
r(M-BMP)b 1.98 2.89 2.03 2.82 2.69 2.07 2.60 2.26 2.82 2.26 2.34 2.70 2.31 2.29 2.25
L(HCH)
H bend
4
4M
3d
111.3 116.3 113.8 116.3 116.3 114.9 116.4 116.0 116.4 115.9 116.4 116.5 116.4 116.5 116.5
35.0 5.8 24.5 6.0 6.6 19.5 6.3 11.0 5.8 10.3 7.8 6.0 7.1 7.2 7.3
24.8 16.9 24.2 19.0 25.2 10.5 22.0 -27.0 16.1 -6.7 25.7 20.5 36.4 37.6 36.0
1.48 0.89 1.30 0.91 0.93 1.19 0.91 1.03 0.87 1.00 0.90 0.84 0.86 0.83 0.78
1.28 1.10 2.37 2.10 3.95 3.45 4.93 4.71 5.00 5.68 6.83 6.00 7.90 8.93 9.89
A, the angle and H bend in degrees, and the binding energies in kcal/mol. b B M P denotes the
(41.6 kcal/m01)~~ leads to a 7A1ground state. For FeC2H4+we find the ground state to be the 4B2state derived from the excited 3d7 atomic asymptote. As manifested by the 3d population in Table 111, there is some contribution from the 3d64sl occupation. The two doubly occupied orbitals are the 3d,(b2) orbital and an a, orbital (primarily 3d,~9),as expected on the basis of the filling order discussed previously. The quartet states of the other symmetries were computed to be 4-5 kcal/mol higher in energy. The lowest sextet state arising from the 3d64s1(6D)ground state of Fe+ is the 6AI state, where the doubly occupied 3d orbital is 3d,z+(al). Based on repulsion arguments, one would expect the 6Bz state with the 3d,, orbital doubly occupied to be the most stable sextet state. However, we find this state to be 0.8 kcal/mol higher in energy. For the sextet states the repulsion with ethylene is larger because the 4s orbital is occupied. This leads to a quartet ground state for FeC2H4+,even though the sextet state arises from the ground state of the metal ion. It must be noted, however, that the difference between the 6D and 4F states of Fe+ is only 5.8 kcal/moL3' The ground state of CoC2H4+is a 'Az state derived from the 3d8(3F)ground state of Co'. In this state the 3d,,(bq), 3d+~(a,), and 3dy2(bl)metal orbitals are doubly occupied. This state is not the one expected to be the most stable on the basis of the filling order mentioned earlier, as the 3d,(a2) orbital would be expected to be doubly occupied instead of the 3dy,(bl) orbital, leading to a 'B, state. This SB1state is computed to lie 1.3 kcal/mol above the 'A2 ground state a t the MCPF level. This is similar to the triplet states of ScC2H4+where the atomic parentage is an important factor in determining the ground state. This is especially important on the right side of the row where the contraction of the 3d orbital leads to a weaker interaction with ethylene. Therefore, it becomes more important to occupy the 3d orbitals so that they correspond to an asymptotic dissociation of 100% ground-state ion than it is to minimize the metal-ethylene repulsion. As was discussed in detail above, the 2AI ground state of NiC2H4+is derived from the Ni+ 3d9 occupation with the hole in the 3d2zorbital to minimize the repulsion. CuC2H4+has a IA, ground state in which the metal ion retains the 3d1° occupation of the ground state of the free ion. Previous theoretical studies of the copper-ethylene cation, such as the studies of Kelber et al.,34Boge1,3Sand Merchln et al.36.have shown that the bonding is electrostatic in origin with little A back-donation. This is at variance with the results obtained by Ziegler et al.,37 which indicated an important contribution of A back-donation. (33) Moore, C. E. Aromic Energy Levels; Circular No. 467; U. S. National Bureau of Standards: Washington, DC, 1949. (34) Kelber, J. A.; Harrah, L. A.; Jennison, D. R. J . Organomet. Chem. 1980, 199, 281. (35) B6ge1, H. Srud. Biophys. 1983, 93, 263. (36) Merchin, M.; Gonzalez-Luque, R.; Nebot-Gil, I.; Tomas, F. Chem. Phys. Lett. 1984, 112, 412. (37) Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 28, 1558.
C-C bond midpoint.
C. Trends. In the ground states of ScC2H4+and TiC2H4+,the transition-metal ion inserts into the A bond of ethylene. The geometrical parameters and binding energies show that the strength of the interaction is larger for Sc+ than for Ti+. As for ScCzHz+and TiCZH2+,I3this decrease in the binding energy with increasing Z is due to the larger loss of 3d-3d exchange energy as the number of open shells increases. However, the binding energies of the ethylene systems are about 16-19 kcal/mol less than the corresponding binding energies of the acetylene ions. Moreover, whereas the ground state of VC2H2+resulted from the insertion of the metal ion into the A bond of acetylene, the bonding in the ground state of VC2H4+is mainly electrostatic. These differences can be explained by considering the weaker A bond for acetylene. At a similar level of c a l ~ u l a t i o nit, ~requires ~ 88.0, 169.0, and 222.5 kcal/mol to break the C-C bond in CzH6,C2H4, and CzHz, respectively. Thus it requires about 28 kcal/mol more energy to break the A bond in ethylene than that in acetylene. The actual difference (16-19 kcal/mol) between the binding energies of MC2H4+and MC2Hz+ is less than 28 kcal/mol, probably due to the extra strain for the metal-acetylene cations arising from the shorter C-C bond length. For VC2H2+the covalently bound ground state is only 3.2 kcal/mol more stable than the electrostatically bound SAl state." Thus it is not surprising that the stronger ?r bond the ethylene leads to an electrostatically bound ground state for VCzH4+. From Cr+ to Cu+, the bonding to ethylene is electrostatic in origin, as it was found for the analogous MC2H2+molecules. Since the binding energy mainly depends on the metal-C2H4 distance and thus on the size of the ion, the binding energy generally increases with increasing 2. Mn+ is an exception to this trend because it has the 4s orbital occupied and has, therefore, a larger radial extent than Cr+. Cu+ is also an exception since it has a smaller binding energy with ethylene than Ni+. This can be explained in terms of increased shielding of the metal nucleus, since the 3d,z orbital in Cu+ is doubly occupied. When comparing the binding energies of the ethylene and acetylene electrostatically bound systems, one finds that although the M+
