3777
J . Phys. Chem. 1985,89, 3111-3118
D. P. Onwood* and A. L. Companion Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506-0055 (Received: June 18, 1985)
There exists experimental evidence that the reactivity of some metal clusters with dihydrogen is very sensitive to cluster size. This work uses the ASED theoretical method to attempt to rationalize this effect in the case of small clusters of cobalt. The results suggest that the stability of the first-formed hydride may be a strong factor in determining reactivity; purely kinetic considerations are unlikely to be important for those clusters with many degrees of internal freedom.
A recent report' of results obtained from metal clusters in supersonic beams suggests that, while dihydrogen will not react with clusters of from 1 to 20 copper atoms, reaction does occur with clusters of cobalt or of niobium atoms of certain masses, which differed from cobalt to niobium, and that the probability of reaction with these is very sensitive to cluster mass: cobalt clusters of one or two atoms did not react at all, tricobalt reacted extensively, tetra- and pentacobalt reacted to a substantial extent, hexa- to nonacobalt did not react, decacobalt and up reacted extensively. Similar, but different, variations were shown by niobium. The former observation was rationalized, and apparently prompted, by the high activation energy for dissociative adsorption of hydrogen on copper surfaces, and the latter were presented as a provocation for theoretical studies in this are$. While we do not claim to have a complete explanation for the results cited, we have attempted to explore a relatively accessible aspect of the problem, in the hope that the results obtained will be applicable, at least in principle, to more complex clusters. The scope of the present work is expressed by the title of this Letter, in the context that, while both the solid metals may dissociatively adsorb hydrogen, copper is reported to show a large activation energy for this process.2 Since the geometries of the clusters and likely hydrides are not generally known, it was necessary to employ a method which gives some guidance toward those configurations which might be important. Semiempirical methods are useful for initial approaches to problems of this kind; a review of some yolecular orbital (MO) calculational methods commonly used is given in ref 3. In the present work, the ASED approach4 was employed, in order to give indications of bond length, bond angle, and the energy of a cluster. We emphasize that, while bond lengths obtained by this approach are usually reasonable, the exact numerical results are not to be viewed as definitive; rather, we believe that differences in the energies of related clusters at energy minima, as calculated by this method, will be of interest, together with the analysis of the combination of atomic orbitals (as modeled by basis set functions) to form MOs. An essential feature of this method is the use of Slater-type Functions (STFs) to form a limited basis set for the MOs. The parameters used to specify thesp functions are readily available for first-row transition metals; this study is confined to Co and Cu clusters. Although the ASED method does not explicitly incorporate bond correlation energy, the effects of bond correlation may be mimicked by modifying the effective ionization energies of electrons in valence shell atomic orbitals which are modeled by STFs. Since the effects we wish to rationalize are substantial, it was (1) M.E. Geusic, M. D. Morse, and R. E. Smalley, J . Chem. Phys., 82, 590 (1985). (2) M. B a l m h , M. J. Cardillo, D. R. Miller, and R. E. Stickney, Sur!. Sci., 46,358 (1974). (3) B. Bigot and C. Minot, J . Am. Chem. SOC.,106, 6601 (1984). (4) A. B. Anderson, J. Chem. Phys., 60,2477 (1974); 62, 1187 (1975); J . Am. Chem.Soc., 100, 1153 (1978).
0022-3654/85/2089-3777%01SO10
TABLE I: Valence Shell STF Parameters
'orbital" 4s 4p 3d A. Cobalt and Hydrogqn -H(ii)/eV 8.76 4.93 7.53 1.7 1.05 5.550, 1.90 l coefficients for 3d 0.555, 0.646
1s
9.36 1.3
B. Copper and Hydrogen
-H(ii)/eV
9.08 1.95
l
5.01 1.20
coefficients for 3d
8.12 5.950, 2.10 0.580, 0.620
9.79 1.3
TABLE XI: Energies of Formation of Dihydrides (eV) M, Hz = M,H,
+
cobalt -0.85 -0.03 -0.36 -0.70'
n
1 2
3 1O b
copper, -0.46' -0.04 0.31 -0.18'
'See text. 'Based on closest-packed 10-atom (7.3) metal cluster and a single H atom. Values shown are obtained by multiplying that result by two, to preserve comparability with the other values shown herein. TABLE 111: Geometry of Dihydrides'
cobalt n
S
1 2 3 10
v
I v h
R
r
1.555 2.44 2.45 2.50'
1.55 1.54 1.53
copper a
b
S
R
137 1 180 z 2.11 66 202 v 2.23 2.56'
r
a
b
1.55 180 1.57 151.5 1.54 62 198 1.53
" S = symmetry class: I = linear, v = C,, z = C,,, h = C3";R = M-M distance, r = M-H distance (A); a = M-M-M angle, b = XM-H angle (degrees). bLiterature values, to enable this (7,3) 10-atom cluster to mimic a solid surface.
sufficient to employ a straightforward algorithm for this process; for the present studies involving hydrogen reacting with metal clusters, parameterization was accomplished by modeling the diatomic hydride molecule M H (M = Co, Cu) at the experimental interatomic distanceS using a readily available M O program.6 Charge iteration using the default parameters of this program was run until convergence was reached. This gave adjusted parameters H(ii) for M and H. These were rounded to the nearest 0.01 eV and used throughout the ensuing calculations. They are sbown in Table I. Off-diagonal terms, H(ij), are obtained by the usual ~~
~
( 5 ) B. Rosen, "Spectroscopic Data Relative to Diatomic Molecules" (International Tables of Selected Constants, 17), Pergammon, New York, 1970.
(6) J. Howell, A. Rossi, D. Wallace, K. Haraki and R. Hoffmann, QCPE,
No. 344. Q 1985 American Chemical Societv
3718
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985
Wolfsberg-Helmholz formula' which is based on the Mulliken approximation.8 STFs for 3d orbitals were of the "double-S" type, with one set of 3d orbital parameters for each transition-metal atom. Low spin states, likely to be of some interest chemically? were considered initially. Many of the cobalt clusters which do react absorb more than one molecule of dihydrogen. Since three-body collisions will not be an important consideration for these gas-phase reactions, the reaction with hydrogen must proceed through the bimolecular interaction of the pure metal cluster with a single molecule of dihydrogen to form M,H2, which may subsequently react with more dihydrogen. We have therefore performed calculations to model the energetics of the process M, HZ = M,H,; M = CO, CU; n = 1, 2, 3
+
The energies of formation of these hydrides from the metal cluster and H2 are shown in Table 11, and geometries in Table 111. While CuH, is found to be linear, a nonlinear geometry is indicated for CoH,; similar results have been reported from calculations invoking configuration interaction.I0 Within the ASED approximation, we also find that CoH, is predicted to be stable. The lack of evidence for CoH, in the beam experiment must be rationalized by kinetic considerations unique to its reaction pathway. Fortunately, such considerations are neither difficult to find nor scientifically unattractive; we need merely recognize that, at many transition states, energy carried in various internal modes within the reactants may flow into the reaction coordinate to provide energy at least equal to an activation energy, and may flow back into new internal modes after reaction is complete. The reactants Co H2 are singularly ill-provided for in this respect. Dihydrogen has such a high vibrational frequency that only the two rotational degrees of internal freedom are appreciably excited; and in this case the other reactant has no internal degrees of freedom at all. We thus have a mean thermal energy, for the reacting complex, of about 4RT, or some 0.1 eV at 300 K. Since our calculations further suggest a transition state with activation energy about 1.5 eV, it is apparent that kinetic considerations are dominant. The approach to the transition state is accompanied by a weakening of the correlation of the H-H bonding M O to the lowest-lying M O and an increase of that correlation to higher MOs, in particular, to a virtual MO, the lowest unoccupied (LU)
+
MO. CuH2 might also appear to be stable, being seemingly 0.46-eV exothermic, based on the parameters of dIos1ground-state copper. Analysis of the MOs, as H2 approaches Cu, shows that the highest occupied (HO) "spd" M O is strongly bonding between the H atoms, while the LUMO correlates to the H-H antibonding orbital, and that no viable reaction pathway exists. Insight to this process is gained by examining orbitals in the The hydride itself; the orbital occupancy is found to be four degenerate HOMOs are pure "d", and one is half-filled; we see that the state from which this hydride is formed is d9s2, as found by other (7) M. Wolfsberg and L. Helmholtz, J . Chem. Phys., 20, 837 (1952). (8) R. S. Mulliken, J . Chim. Phys., 46, 497, 675 (1949). (9) C. A. Baumann, R. J. Van Zee, and W. Weltner, Jr., J . Phys. Chem., 88, 1815 (1984). (10) P. E. M. Siegbahn, M. R. A. Blomberg, and C. W. Bauschlicher, Jr., J . Chem. Phys., 81, 1373 (1984).
Letters
Our results suggest that both MzH2are of marginal stability, with little driving force available for their formation. If we invoke a monotonic energy relationship (exemplified by, for instance, the linear variety beloved of organic chemists) to give a correlation between overall energy change and the activation energy, the nonappearance of these products is rationalized. The difference in the geometries, found by this model, is of some interest. The calculated energies of formation of M3H2, found by this model, show a substantial difference. While M = Cu is predicted to be unstable, M = Co is predicted to be stable. These results suggest that the experimental results for these clusters may need to be rationalized in terms which include thermodynamic considerations. In order to obtain an insight to the interaction of the hydrogen orbitals with the metal orbitals, calculations were performed a t various H-H distances, with the H-H moiety at various distances from the M3 residue. We find no mixing of the H-H bond with the HOMOs in the case of cobalt, and only slight mixing in the case of copper, though we emphasize that we did not perform a complete geometry optimization to identify a transition state, and that no heavy atom relaxation from the locations occupied in the dihydride was performed in this part of the work. Rounding out this study, the energetics of the dissociative chemisorption of dihydrogen on the solid metals was also modeled. A 10-atom (7,3) closest-packed cluster, with metal internuclear distances corresponding to published values,I2 served to model the solid. Our results were obtained from a hydrogen atom at a onefold site atop a central atom of seven. They suggest that the process is much less favored energetically on copper than on cobalt; similar trends have been found with a muffin-tin-based calculation on clusters embedded at the surface of an effective jellium-like medium. In summary, while the results obtained by this approximate method should be viewed with some circumspection (especially with regard to geometries which are driven by relatively small energy differences), given that metal clusters have proven intractable in the past to far more complicated computational approaches, they do nontheless suggest that the dependence of reactivity upon cluster size may involve factors other than activation barriers. This is consistent with the findingI4 that measured physico-chemical quantities of clusters may show strong, even periodic, dependence on cluster size. This work supports the view established in earlier workI5that results gained from small clusters may not offer much insight to the properties of surfaces. It is apparent that clusters represent a novel, stimulating aspect of metal chemistry in which atoms, freed from the symmetry constants associated with a requirement to pack efficiently in three space, are enabled to more fully manifest their unique chemical properties. Registry No. Co, 7440-48-4; Cu, 7440-50-8; H, 1333-74-0; CoH2, 33485-99-3; C U H ~33486-01-0. , (1 1) A. B. Kunz, M. P. Guse, and R. J. Blint, Nurl. Bur. Stand. Spec. Publ., No. 455, 53 (1976). (12) A. F. Wells, "Structural Inorganic Chemistry", 3rd ed, Oxford University Press, Oxford, England, 1962, p 984. (13) J. P. Muscat and D. M. Newns, Surf. Sci., 99, 609 (1980). (14) D. E. Powers, S.G. Hansen, M. E. Geusic, D. L. Michalopoulos, and R. E. Smalley, J . Chem. Phys., 78, 2866 (1983). (15) J. Demuynck, M.-M. Rohmer, A. Strich, and A. Veillard, J . Chem. Phys., 75, 3443 (1981).
