14
J. Phys. Chem. 1983, 87, 14-17
Bonding vs. Antibonding States in Transitlon-Metal Bond Activation: Energetic Grounds and Stereochemical Implications Evgeny Shustorovich Research Laboratories, Eastman Kodak Company, Rochester, New York 14650 (Received: September 15, 1982; I n Final Form: November 9, 1982)
An analytical LCAO MO perturbation model has been developed to treat the M-X2 (and M-YZ) interactions where Xz (YZ) is a closed-shell diatomic molecule and M a transition-metal atom. In a linear fragment M-X-X (M-Y-Z), the metal orbitals have larger off-diagonalmatrix elements IP*l with the antibonding MO’s than 101 with the bonding MO’s. The model predicts that the vacant antibonding molecular states typically play the dominant role in bond activation, especially by metal surfaces. The predominance of the antibonding-state contribution to the M-X, (M-YZ) bond energy and charge transfer seems to determine some basic stereochemical patterns as well.
Introduction In recent years there has been a great deal of interest in the mechanism of bond activation by transition metals.’ The common notion’ is that the vacant antibonding states may contribute predominantly in conventional acceptors (unsaturated a-bonded molecules with low-lying vacant a* MO’s) but that bonding-state contributions prevail in conventional donors (saturated u-bonded molecules where the vacant antibonding u* MO’s lie very high, typically above vacuum).2 However, the recent computations3 have shown the u* contribution to be important for the oxidative addition of H,to various transition-metal complexes, and Muetterties’q has argued that metal surfaces might be especially efficient to activate the C-H bonds through their u* orbitals. The main purpose of the present work is to give a simple analytical explanation of why the u* contribution may be crucial for the bond activation of saturated molecules chemisorbed on transition-metal surfaces (and in many transition-metal compounds as well). Furthermore, we will show that the bonding- vs. antibonding-state contributions to the heat of chemisorption (to the metal-ligand bond energy) may determine some basic stereochemical regularities of chemisorption (coordination) of diatomic molecules and fragments. We start with a common LCAO MO scheme for a homonuclear diatomic XZ4where the bonding $ and antibonding $* MO’s (either u or a) have the form ,
e($) =
(1) See, for instance, recent books and reviews: (a) Collman, J. P.; Hedegus, L. S. ‘Principles and Applications of Organotransition Metal Chemistry”; University Science Books: Mill Valley, CA, 1980. (b) Somorjai, G. A. ‘Chemistry in Two Dimensions: Surfaces”; Cornell University Press: Ithaca, NY, 1980. (c) Muetterties, E. L.; Rhodin, T. N.; Band, E.; Brucker, C. F.; Pretzer, W. R. Chem. Reu. 1979, 79, 91. (d) Muetterties, E. L.; Stein, J. Chem. Reo. 1979, 79, 479. (e) Muetterties, E. L. Pure A p p l . Chem. 1982, 54, 83. (D Muetterties, E. L.; Wexler, R. M. Sum. Progr. Chem. In press. (g) Muetterties, E. L. Chem. SOC.Rev. In press. (2) For energies of various u* and s* MO’s, see, for instance: Jorgensen, W. L; Salem, L. “The Organic Chemist’s Book of Orbitals”; Academic Press: New York, 1973. (3) (a) Dedieu, A.; Strich, A. Inorg. Chem. 1979, 18, 2940. (b) Sevin, A. Nouu. J. Chim. 1981, 5, 233. (4) See, for instance: Coulson, C. A. ‘Valence”; Oxford University Press: London, 1961; Chapter 4.
+a
€*($*) = a - A*
A=-!...-
l+s
(3)
(4)
(5)
Y
A* = 1-s A* 1+S - =A 1-S
(7)
Here y = /3 - a s , where a , P, and S are the Coulomb, resonance, and overlap integrals, respectively. Remember that it is S # 0 that produces an unsymmetric splitting of the MO energies E and e* about the A 0 energy, a, displacing t* upward more than t downward (cf. eq 7). We will show, however, that the very mechanism (the overlap S > 0) which pushes the antibonding MO’s $* higher in energy makes the xM- $* interactions larger, and that this increase, combined with orbital-energy considerations, can make the o* contribution predominant for many transition-metal forms, especially for surfaces.
Results Consider a linear fragment M-X(l)-X(2) where, by symmetry (Cmo),both $ and $* belong to the same irreducible representation and interact with the same metal orbital xM,for instance u and u* interacting with d,z or a(%) and a*(%*)interacting with d,, (dJ. Introducing the twocenter M-Xi matrix elements Pi
with the relevant energies (see Figure 1)
a
= (xMIHIxx,)
(8)
we have for the three-center M-X, interactions
so that
Within a reasonable range of conventional Hiickel-type parameters (see Table I), the ratio (/3*//3)2remains larger than unity and may closely approach the extreme value of (1 + S)/(l- S) corresponding to Pz 0 (neglect of the
0022-3654/83/2087-0014$01.50/0 0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 1, 1983
Letters
15
TABLE I: Values of Some Parameters in Eq 11' XM
single
r
b
M-X(,)
((01
distance,c A
2.00 2.50 3.00
PliP2
2.00 2.00 2.00 2.00 2.50 3.00 2.00 2.50
double { = 4.95 (0.50581) 5, = 1.80 ( 0 . 6 7 4 7 1 )
r1
3.36 4.29 4.99 3.00 3.56 4.02 7.96 10.90 14.10 5.88 9.11 12.40 13.97 17.77 20.60
3.00 2.00 2.50 3.00 2.00 2.50 3.00
-
P2)/
(il, + P 2 ) I Z
(P*/P)'
0.29 0.39 0.44 0.25 0.32 0.36 0.60 0.69 0.75 0.50 0.64 0.72 0.87 0.89 0.91
Sc,d
XAd
Is
0.636
Is
0.636
2s
0.387
1.00
2P 0
0.332
1.29 1.44 1.38 1.42 1.45
2P,
0.228
1.32 1.74 2.00 1.13 1.41 1.62 1.36 1.56 1.70
r
a Overlap matrix elements used were taken from ref 24. Both single and double sets were tried, T h e single f values varied = 2.0-3.0). The double values are the conventional ones for Cr. The distances X(l)-X(2)were taken as 0.74 A for H-H and 1 . 2 0 A for N-N. Standard extended-Huckel orbitals for H ( l s , 5 = 1.30) a n d N(2s, 2p, = 1 . 9 5 ) were used.
(r
r
r
non-near-neighbor interaction). In this extreme case, we have (cf. eq 7) In other words, the overlap S > 0 changes not only A*/ A but also (fi*/p)2in the similar way. From Table I, we see that eq 12 will be better justified for larger M-X distances (in particular, when X2just begins to interact with M) and for the first-row atoms X = C, N, 0, Le., better for the H-C, H-N, C-C, C-N, C-0, etc. bonds but worse for the H-H bond. In this respect, M-H, may not be a good model for transition-metal coordination and activation of other X,(YZ) entities (see below). For closed-shell molecules X2, one can assume the M-X2 bonding to be weak compared with the X2 bonding, so that the former can be treated as a perturbation of the latter. Indeed, dissociation energies of X2 (H2,N2,CO, etc.) exceed the bond energies M-X2 on transition-metal surfaces and in complexes by factors of 5-20.lWr5 To first order, neglecting the M-X2 overlap integral S M (SM 0 is explicitly included,' we have Q+ < Q- < Q+* < Q-*(cf. Figure l), so that the following conclusions for SM = 0 are further e n h a n ~ e d . ~ (7) Shustorovich, E. To be published. (8) For an excellent summary of the perturbation formalism, see: (a) Hoffmann, R. Acc. Chem. Res. 1971,4, 1. (b) Libit, L.; Hoffman, R. J . Am. Chem. SOC. 1974,96, 1370. (9) The perturbation treatment of other three-orbital cases: (a) Shustorovich, E. J. Am. Chem. SOC.1978, 100,7513. (b) Reference 11. (10) Shustorovich, E. Solid State Commun. 1982,44, 567. (11) For a detailed discussion see: Shustorovich, E. J. Phys. Chem. 1982,86, 3114. (12) Obviously, if the metal d*z orbital is vacant (for example, in many ML, Cb complexes such as Cr(CO),), the acceptor bond X2 M cannot be formed. Typically,however, d,z is filled, for example, in square ds ML4 complexes which are common for X2 coordination and oxidative addition.'~~ (13) Dunitz, J. D.; Orgel, L. E. J. Chem. Phys. 1955, 23, 954. (14) Hundreds of p-dinitrogen complexes are known: (a) Chatt, J.; Dilworth, J. R.; Richards, R. L. Chem. Rev. 1978, 78,589. (b) Burt, R. J.; Leigh, G. J.; Hughes, D. L. J. Chem. SOC.,Dalton Trans. 1981, 793. (15) (a) For a review of N2 on Fe, Ni, Ru,Pd, W, Ir, and Pt surfaces, see: Ertl, G.; Lee, S. B.; Weiss, M. Surf. Sci. 1982, 114, 515. (b) N2/ Ni(ll0): Horn, J.; DiNardo, J.; Eberhardt, W.; Freund, H.-J.; Plummer, E. W. Ibid. 1982,118,465. (c) N2/Ru(001): Feulner, P.; Menzel, D. Phys. Reu. B 1982, 25, 4295, and references cited therein. (16) Though CO is always found to be normal to atomically flat surfaces (though in various coordinated sites1btct3,it can be tilted17or even lie down'* on some atomically rough surfaces. (17) (a) CO/Pd(210): Madey, T. E.; Yaks, J. T., Jr.; Bradshaw, A. M.; 1979,89,370. (b) CO/Pt(llO): Hofmann, P.; Hoffman, F. M. Surf. SCC. Bare, S. R.; Richardson, N. V.; King, D. A. Solid State Commun. 1982, 42, 645.
-
z
F
W
M
XW Y
X Z
X(2)
YZ
2
Figure 1. The interaction of energy levels in X2 (YZ) and in a linear fragment M-X(,)-Xt2) (M-Y-2). See text.
contributions to the energy stabilization of M-X, from 1)
1/48)and #*(Q*) will beG9 (see Figure
(18) CO/Cu(311): Shinn, N. D.; Trenary, M.; McClellan, M. R.; Feely, F. R. J . Chem. Phys. 1981, 75, 3142. (19) Friend, C. M.; Muetterties, E. L.; Gland, J. L. J . Phys. Chem. 1981,85, 3256. (20) When CO can be chemisorbed in both normal and parallel configurations, the latter is weaker bound.18 A similar situation may occur for Nz.lk (21) For a detailed discussion of alternative coordination modes of diatomic ligands Li2-F2in transition-metal complexes, see: Hoffman, R.; Chen, M. M.-L.; Thorn, D. Inorg. Chem. 1977, 16, 503. (22) For the discovery of organotransition-metal systems capable of intermolecular oxidative addition to single C-H bonds in saturated hydrocarbons and a comprehensive list of references, see: (a) Janowicz, A. H.; Bergman, R. G. J . Am. Chem. SOC. 1982,104,352. (b) Hoyano, J. K.; Graham, W. A. G. Ibid. 1982,104, 3723. (23) For chemisorption of alkanes and C-H bond cleavage, the reconstructed Ir(ll0) (1X 2) surface (which may be pictured as a series of two-layer-deep troughs) seems to be especially efficient: Wittrig, T. S.; Szuromi, P. D.; Weinberg, W. H. J. Chem. Phys. 1982, 76, 716-23, 3305-15, and references cited therein.
16
The Journal of Physical Chemistry, Vol. 87,No. 1, 1983
Letters
3112 d,, = dZ,2- sin 2 w 2
where
+ ...
(18)
and assuming the same distances M-X,,, in the linear (L) and triangular (T) fragments, we have
Bearing in mind eq 3, 4, and 12, we have Q*/Q
> 1 if
tM
> CY
(16a)
Q/Q*
> 1 if
tM
< CY
(16b)
or
For the majority of ligands (adsorbates) coordinated with transition metals, tM > a, so that in the case described by the inequality 16a, the antibonding #* state contribution Q* prevails. From eq 13-15 it is obvious that the higher tM the larger Q*/Q. For surfaces, the heats of chemisorption of donor (lone pair) and acceptor (vacant orbital) adsorbates are Q 0: P2/(& - tA) and Q* 0: P * 2 / ( ~ ~- *EF), respectively,10i.e., they are similar to eq 13 and 14 where tM is replaced by the Fermi level EF, which is higher than tM by 5 eV or more." In other words, the pattern Q*/Q > 1 may be persistent for many metal forms, enhancing from atoms and clusters to surfaces, which are excellent donors.'- However, in molecular cases when M is of high oxidation state ( t M < a ) and/or of low d occupancy,12it is possible that the bonding $ state contribution Q (eq 16b) will prevail. One more comment concerning the difference between the surface and molecular regimes might be useful. In closed-shell molecules, the discrete metal orbital X M may be either vacant or occupied, resulting in the donor X2 M (Q, eq 13) or acceptor X2 M (Q*, eq 14) bonding. On surfaces, the same XM band participates in both donor and acceptor bonding, Q being proportional to the d hole count (Nh) but Q* to the d occupancy (Nd = 2 - Nh) or to the product NhNd.l0 To first order, the values of Q and the relevant charge transfer q are proportional."l' So, the inequality 16a may be restated as follows: in a linear fragment M-X-X (provided P, N 0), the antibonding x1 - x2 states contribute more significantly to the M-X, bonding energy and charge transfer than the bonding x1 + x2 states. (The reverse is true for the inequality 16b.) If the linear fragment M-X(l)-X(2) is getting bent, lPal increases, reducing Q*/Q (cf. eq 11). In the extreme case of the isosceles triangle
-
M...
+
( c ~symmetry) "
the $ and #* will belong to different irreducible representations, so that they will interact with different metal d orbitals, say dZzand d,, ( x z is the fragment plane) for u and u*, respectively. Now, to compare Q* with Q, we will express all the matrix elements in terms of P1 = P,. Also, now we know that one can neglect S. By using the relevant trigonometric transformations (w is the angle between the coordinate axes z and z313 d22 = dz,2(cos2w - y2 sin2 w )
+ ...
(17)
(24) Our model conclusions are also in agreement with the straightforward band-structure calculations on chemisorption of H2, CH,, and CBHB on metal films: Baetzold, R. C. J. A m . Chem. Soc., submitted for publication. (25) In principle, xM will not be of the pure d character (as we assume) but will have some sp admixture. However, even in comprehensive theoretical treatments of reaction mechanisms, this admixture is sometimes neglected, for instance, for reductive elimination of ds organotransition-metal complexes: Tatsumi, K.; Hoffman, R.; Yamamoto, A,; Stille, J. K. Bull. Chem. SOC.Jpn. 1981, 54, 1857. (26) Shustorovich, E.; Baetzold, R. C.; Muetterties, E. L. J . Phys. Chem., submitted for publication.
so that
(&/PL)~= 4(cos2 w - y2 sin2 w)' (&*I&*) = 3 sin2 2w
(22) (23)
For a typical value of sin w N 0.25 (which would correspond to the X2 distance of 1.0 8, and the M-X distance (&I&,)'N 3 but N In other of 2.0 8, ) , 1 b9cf*5 words, while going from the linear to the triangular fragment M-X2, the bonding # contribution (to Q and q ) substantially increases but the antibonding $* contribution decreases, i.e., we gain in the donor X2 M bond energy QD but we lose in the acceptor X2 M bond energy QA. Assuming P, < P, < P6 < 0 for the u, a,6 components of the M-X2 bond and using just the more intricate trigonometry,'J3 we can obtain similar conclusions for the T bonded X2 as well.' The above arguments have obvious stereochemical implications. If Q* > Q, the linear M-X, geometry will typically be more favorable than the triangular geometry; if Q* < Q, the reverse will be true. We saw that in most cases our model projects Q* > Q, so that the linear geometry M-X-X, "end-on" in complexes or "normal" to surfaces (rather than "side-on" or "parallel"), is predicted to be typical. Conversely, the observed linear geometry M-X-X may be taken as an indicator of Q* > Q. If we have several metal atoms interacting with X2, the rule of thumb to maximize Q* is to minimize the l&l terms in eq 10, Le., to keep the non-neighbor M-X distances as large as possible. It means that in complexes the M-XX-M geometry will typically be favored over
--
On surfaces, this mechanism will make the different sites (on-top, bridge, hollow) close in energy for the upright X,, one of these geometries corresponding to the ground chemisorption state. But in the excited chemisorption states, the same mechanism would favor the formation of multicenter metallocycles, say
/x-x\
M
M
Remember that of two possible geometries of X,, with the molecular axis perpendicular or parallel to the surface plane, only the latter may be productive for dissociative chemisorption.'b-p Thus, our model predicts that the favored chemisorption geometry and the favored reaction (the X-X bond cleavage) geometry will typically be not the same. Consider now a heteronuclear diatomic YZ where Y is a little less electronegative but Z is more electronegative than X (Figure 1). The MO's will be
ic. = aXY + bxz ic.* = CXY - d x z where
(1')
(2')
The Journal of Physical Chemistry, Vol. 87, No. 1, 7983
Letters
(25) Repeating all the above arguments (for simplicity, one can take S = 0, leading to a = d , b = c , b > a > 0, a < 2-'i2, b > 2-'12, a b < 2lI2), we obtain the following:' 1. In a linear fragment M-YZ, the coordination through Y further increases Q* and decreases Q, so that
+
(Q*/Q)yz
> (Q*/Q)x,
Q*YZ> Q*x,
(1W
2. While going from the linear to the triangular fragment M-YZ, both Q* and Q decrease. This makes the linear ("end-on", "normal") geometry for YZ even more favored over the triangular ("side-on", "parallel") one than it is for x2.
3. If YZ is a fragment of some molecule RZY, its coordination in both metal complexes and metal surfaces w i l l also be such that to minimize the interaction between the nonneighbors.
Discussion So far, the thermochemical and stereochemical regularities have been established mostly for the a-bonded molecules such as N2,1a-c,f95*14,16 C0,1a-f35J6CH3CN, and CH3NC,1a~c@~fJg and these data are in encouraging agree-
17
ment with OUT simple arguments.mi21Regarding the a-bond activation, in particular the C-H bond breaking, there is growing evidence, for both complexes 1a,eg*4,22 and metal ~ u r f a c e s , lthat ~ * ~the ~ net process is oxidative addition with smooth charge transfer from the metal center to the ligand (adsorbate). Also, in the computational analysis of H2 oxidative addition3 it was concluded that H2 initially approaches the metal center end-on and only later tips over to give a side-on configuration. Our model expectation^^^ are consistent with these findings (as seen from Table I, the smaller the M-H distance, the larger the bonding state contribution Q favoring the side-on geometry) and further elaborate the suggestion by Muettertiesl-g that the C-H bond coordination occurs through the M-H(C) interaction and the C-H bond breaking on metal surfaces may include the multicenter M-H-C-M bonding. Though the interactions between real molecules and real metal centers (especially in the endless variety of complexes) might be rather complicated and affected by details of the electronic and geometric s t r u c t ~ r e s , ~ we, ~hope ,~~~~~ that the model patterns described will remain as the major factors. A detailed discussion of the above topics will be given
Acknowledgment. I am grateful to Earl L. Muetterties and Roger C. Baetzold for numerous discussions and valuable comments and the reviewer (Roald Hoffmann) for insightful remarks and constructive criticism.
