9794 J. Phys. Chem. 19!

32,96, 9794-9800
(34) Czerminslri, R.; Kwiatkowslri, J. S.;Person, W. B.; Szczepaniak, K. (49) Hush, N. S.;Cheung, A. S.Chem. Phys. Lett. 1975,34, 11.
J . Mol. Strucr. 1989, 198, 297. (50) Aktekin, N.; Pamuk, H. 6. Chim. Acta Turc. 1982, I .
(35) Langlet, J.; Claveric, P.; Caron, F.; Bceuve, J. C. Int. J. Quantum
- (51) Berthold, H.; Giessner-Prettre, G.: Pullman, A. Theor. Chim. Acta
Chem. 1981; 19, 299. 1966,5, 53.
(36) (a) Boys, S.F.; Bemardi, F. Mol. Phys. 1970, 19, 553. (b) Yang, (52) Pullman, B.; Pullman, A. Quantum Biochemistry;Wdey-Interscience:
J.; Kestner, N. R. J. Phys. Chem. 1991, 95, 9214. London, 1963.
(37) Hobza, P.; Sandorfy, C. J. Am. Chem. Soc. 1987, 109, 1302. (53) Younkin, J. M.;Smith, L. J.; Compton, R. N. Theor. Chim. Acta
(38) F6rner. W.; Otto, P.; Ladik, J. Chem. Phys. 1984, 86,49. 1976, 41, 157.
(39) Kang, Y. K.;Jhon, M.S. Theor. Chim. Acta 1982, 61, 41. (54) Compton, R. N.; Yoshioka, Y.; Jordan, K. D. Theor. Chim. Acta
(40) Szczginiak,M.M.;Scheiner, S.;Hobza, P. J. Mol. Struct. (THEQ 1980, 54, 259.
CHEMI 1988.179. 177. (55) Wiley, J. R.; Robinson, J. M.;Ehdaie, S.;Chen, E. C. M.;Chen. E.
(4 1) ‘Sasaengk, W. Princplcs of Nucleic Acid Structure; Springer-Verlag: S.D.; Wentworth, W. E. Biochem. Biophys. Res. Commun. 1991,180,841.
New York, 1984; p 123.
(42) Doughty, D.;Younathan, E. S.;Voll, R.; Ahdulnur, S.;McGlynn, (56) Gregoli, S.;Olast, M.;Bertinchamp, A. Radiat. Res. 1982,65,202.
S . P. J. Electron Socctrosc. Relat. Pheom. 1978, 13. 379. (57) Sevilla, M.D.; Clark, C.; Holroyd, R. A.; Pettei, M. J. Phys. Chem.
(43) Lin, J.; Yu;C.; Peng, S.;Akiyama, I.; Li, K.; Li Kao Lee;LeBreton, 1976, 80, 353.
P. R. J. Am. Chem. Soc. 1980, 102,4627. (58) Sevilla, M. D. In Excited States in Organic Chemistry and Bio-
(44)Dougherty, D.;McGlynn, S.P. J. Chem. Phys. 1977,67, 1289. chemistry;Pullman, B.; Goldblum, N., Eds.;Reidel: Baston, 1977; pp 15-26.
(45) LeBreton, P. R.; Yang, X.;Urano, S.;Fetzer, S.;Yu, M.;Leonard, (59) Mulliken, R. S.;Person, W. B. Molecular Complexes;Wiley-Inter-
N. J.; Kumar, S . J. Am. Chem. Soc. 1990, 112, 2138. science: New York, 1969.
(46) Bodor, N.; Dewar, M.J. S.;Harget, A. J. J. Am. Chem. Soc. 1970, (60) Szabo, A.; Ostlund, N. S. In Modern Quantum Chemistry;
92, 2929. McGraw-Hill: New York, 1989; p 151.
(47) Lifschitz, C.; Bergmann, E. D.; Pullman, B. Tetrahedron Lett. 1967, (61) Hinchliffe, A. Ab Initio Determination o j Molecular Properties;
46, 4583. Adam Hilger: Bristol, 1987; p 152.
(48) Orlov, V. M.;Smirnov. A. N.; Varshavsky, Y. M. Tetrahedron Lerr. (62) Grislund, A.; Ehrenherg, A.; Rupprecht, B.; Tjilldin, B.; Strijm, G.
Downloaded by UNIV NACIONAL AUTONOMA MEXICO on August 31, 2015 | http://pubs.acs.org

1976, 48,4377. Radiat. Res. 1975, 61, 488.

Theoretical Study of the Blnding of Ethylene to Second-Row Transition-Metal Atoms

Publication Date: November 1, 1992 | doi: 10.1021/j100203a040

Margareta R. A. Blomberg,* Per E. M. Siegbahn, and Mats Svensson

Institute of Theoretical Physics, University of Stockholm, Vanadisviigen 9, S - 1 1 346 Stockholm, Sweden
(Received: May 14, 1992)

The binding between ethylene and all second-row transition-metal atoms from yttrium to palladium has been studied by
using size-consistent correlation methods and large basis sets. The binding energy curve as a function of atomic number
of the metal shows the usual characteristic minimum in the middle of the row. This minimum is mainly due to the logs of
exchange when the bonds are formed. The strongest bonds are formed by the atoms to the right, for which covalent and
donation-back-donation bonding is optimally mixed. The atoms to the left form metallacyclopropanes in which the C-C
bond is entirely broken. Comparisons are made both to the componding reaction with methane and to the bonding between
metal cations and ethylene.

r. ~atrodu~ti~n tion-metal atoms. In the first of these bonding types, the back-
The coordination of alkenes to transition-metal centers con- donating d-orbital on the metal is initially doubly occupied. In
stitutes the starting point in several important catalytic reactions, the second bonding type this orbital is only singly occupied. In
e.g., the saturation of unsaturated hydrocarbons and the polym- the third bonding type, finally, the binding has a normal covalent
erization of ethylene and other olefins. The polymerization of character and a metallacyclopropaneis formed. In the latter case
ethylene, catalyzed by transition-metal compounds in the Zie- the reaction between ethylene and the metal atom can be described
gler-Natta process, has been thoroughly studied the past decades,’ as an oxidative addition reaction in which the r-bond of ethylene
but the reaction mechanisms are still not well understood. For is broken and two metal-carbon a-bonds are formed. This reaction
example, the mechanism for the carbon-carbon bond-forming has many similaritieswith other oxidative addition reactions that
polymer chain propagation step is still controversial. It is expected have been studied previously, such as the reaction between methane
that the strength of the metal-ethylene bond influences the C< and second-row transition-metal atoms.* It should be added that
bond-forming step, which is described as insertion of the ethylene the distinction between the three types of bonding is not entirely
moiety into the metal-alkyl bond. A starting point in an inves- strict. It is, for example, clear that the purely covalent bonding
tigation of the mechanisms for ethylene polymerization is therefore in the metallacyclopropane is just an extreme of the donation
to determine the variation in the metal-ethylene binding energies bonding with doubly occupied donating orbitals. In the analysis
over different metals. In this paper we summarize the results from below we have, nevertheless, still found it useful to discuss the
such a study for the second-row transition-metal atoms. binding mechanisms in terms of these three different bonding
The interaction between a transition-metal complex and types.
ethylene is often described by the Chatt-Dewar-Duncanson The binding between ethylene and transition metals has been
mechanism in which ethylene donates parts of the r-electrons to systematically studied previously both theoretically3and exper-
an empty a-orbital of the metal. This weakens the *-bond of imentally: for the case of positively charged metal ions. By
ethylene, which makes the r*-orbital lower in energy so that charging the metals it has been possible to study the reactions
electrons will be accepted from a backdonating d-orbital of the by mass spectrometric methods, which has given important in-
metal atom. This is a very general binding mechanism, which formation about both reaction pathways and enthalpies. Detailed
can broadly describe practically all metal-ligand bonds. If the comparisons have then provided valuable information about the
metal-olefin bonding is studied more in detail, it is possible to accuracy of both the calculations and the experiments. The
characterize at least three rather different bonding types that are positively charged transition metals are of considerable interest
preferred, as will be demonstrated below, by different transi- by themselves, but one of the major goals of these studies has also
0022-36S4/92/2096-9794S03.00/00 1992 American Chemical Society
 Ethylene Binding to Transition-Metal Atoms The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9795

TABLE I: Geometries and Energies (Relative to Free Ethylene and Ground-State Atoms) for the Ground States of Second-RowMC2& Systems
atomic AE, AE + corr,
M ground state state config M-CZH4, A C-C, A kcal/mol kcal/mol
Y 2D(5s24d') 2Al a'dk 2.15 1.54 -18.3 -22.3
Zr 'F( 5s24d2) 'B1 a'd2d' 2.07 1.52 -19.0 -23.0
Nb 6D(5s'4d4) 4B1 ald?d?dl
bz bl 81 2.07 1.51 -19.6 -23.6
Mo 7S( 5S14d5) 'B2 u'd&d&df,d~, 2.03 1.48 -2.5 -6.5
Tc %(5s24d5) 4B2 a'd&d;,df,d:, 2.01 1.45 +3.6 -0.4
RU"~ 5F(5s'4d7) 'A2 u'd&d&df2dil 1.99 1.44 -22.8 -26.8
Rh"J 4F(5s14d8) 2A1 u'd&ddfdf,d:, 1.97 1.44 -30.9 -34.9
Pd" 'S(5SO4d'O) 'A1 dd&d~,d:,di, 2.01 1.43 -26.7 -30.7
" MCPF optimized geometry. Optimized for the 'B2 state. Optimized for the 2A2state.
been to increase the understanding of the mechanisms involved
in important catalytic processes such as the ones mentioned above.
In these processes neutral metal complexes are involved and some
of the pure electrostatic binding mechanisms, which are present
for the metal ions, are then essentially missing. An interesting
question in this context is to what extent the metal ions still
Downloaded by UNIV NACIONAL AUTONOMA MEXICO on August 31, 2015 | http://pubs.acs.org

resemble neutral complexes. One important objective of the

present study is therefore to compare the present results for the
binding of ethylene to the neutral atoms with previous results for
the positive ions.
This paper is one of a series of papers in which simple model
reactions involving second-row transition-metal atoms and com-
Publication Date: November 1, 1992 | doi: 10.1021/j100203a040

plexes will be systematically studied. In a previous study we have

compared the reactivity of these metal atoms (and cations) to
methane2 and it will be demonstrated that there are many sim-
ilarities between that reaction and the present one for ethylene.
By these systematic studies for an entire row of transition metals," Figure 1. Structureof the MC2H4complexes, shown by the example of
a different route has been started toward the understanding of niobium.
transition-metal chemistry. Until now, the normal approach has
been to study one particular complex or reaction and make com- TABLE Ik Mnlliken Populations (MCPF)for the Ground States of
parisons to experimental findings. There are several factors that the Second-Row MC2& Systems
make the present more ambitious systematicstudies possible. The M state qM 5s 5P 4d
first of these factors is the finding that single configuration based
correlation methods are usually quite adequate for accurately Y +0.31 0.94 0.36 1.31
Zr +0.30 0.76 0.35 2.52
describing relative energies for different transition-metal systems. Nb +0.29 0.76 0.19 3.71
This is particularly true for complexes involving second-row Mo +0.20 0.97 0.46 4.32
transition metals and this is one of the reasons this row has been Tc +O. 18 0.71 0.12 5.94
selected for the present series of studies. The second factor making Ru +O. 14 0.38 0.10 7.32
these studies possible is the finding that geometry optimization Rh +0.08 0.34 0.11 8.41
at a lower level, such as the SCF level, is usually adeq~ate.~ Again, Pd +0.05 0.33 0.11 9.45
this appears to be particularly true for the second transition-metal
series. The final factor is, of course, that efficient methods have studies on this system have shown that sd hybridization in the d9s
been developed and fast computers are now available, which allow state is important for reducing the repulsion and for simplifying
the use of adequate basis sets and which still leads to manageable electron donation to the metal.' Calculations on FeC2H48have
computation times. A final comment should be made about these shown that also sp hybridization can be important when the ground
model studies. Until recently it has not been entirely clear how state of the metal atom has an s2 occupation, yielding a quintet
relevant these simple models, sometimes including only a single ground state of FeC2H4. Calculations have also been performed
metal atom, are for real catalytic reactions. Promising results on ethylene coordination to ligated metal complexes; see, for
in this context were, however, given by the previous study on the example, the recent review article by Koga and M ~ r o k u m a . ~
methane dissociation reaction? It was first shown that the rhodium In the present paper the ethylene binding energies to the sec-
atom has the lowest activation bamer for breaking the C-H bond, ond-row transition metals are calculated by using the modified
which is in line with the experimental finding that rhodium coupled pair functional method (MCPF). A few calculations are
complexes are the only ones of the second-row transition-metal also performed by using the coupled cluster method (CCSD(T))
complexes that dissociate methane. Second, when ligands were to estimate the size of higher correlation effects. The details of
added to the rhodium atom, mimicking the actually observed the calculations are given in the Appendix. Preliminary results
rhodium complex that dissociates methane, the whole potential for the metal-ethylene binding energies were published in ref 10.
energy surface was found to be extremely similar to the one For some of the metals, more strongly bound states were found
obtained for the single atom. These findings may not be com- since then, therefore the binding energies are larger in the present
pletely general for all types of reactions but are at least promising paper.
enough for these model studies to be pursued.
Besides the above-mentioned theoretical study there have been It. Results and Discussion
many other studies performed on the binding between ethylene a. General Comments. The general structure investigated for
and transition metals. Only a few of these will be mentioned here. the second-row transition-metal-ethylenecomplexes is depicted
The nickel-ethylene complex NiC2H4has been a standard model in Figure 1. The geometries, binding energies, and electronic
system for testing new quantum chemical methods. The most configurations for the ground-state MC2H4molecules are given
recent study uses the CCSD(T) (coupled cluster singles, doubles, in Table I. The corresponding populations are given in Table
and triples) method, and results close to the most reliable ex- 11. For yttrium and niobium there are two low-lying states very
perimental value for the binding energy are obtained.6 Previous close in energy, and we have chosen to include the state with a
 9796 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 Blomberg et al.

TABLE UI: Geometries and Ewrgies (Relative to Free Ethylene and Ground-State Atom) for Differeot States of the Second-Row MC2H4
Systems
AE, AE + corr.
M state config Mc2H4, A c c ,A kcal/mol kcal/mol
Y 2AI 2.15 1.54 -18.3 -22.3
Y' 2.46 1.42 -18.3 -22.3
ya.6 2.46 1.42 4.0 0.0
Zr 2.07 1.52 -19.0 -23.0
Zf 2.39 1.42 -7.7 -11.7
Nb 2.07 1.51 -19.6 -23.6
Nb' 2.34 1.41 -19.8 -23.8
Mo 2.03 1.48 -2.5 -6.5
Tc 2.41 1.37 +4.1 +o. 1
Tc 2.01 1.45 +3.6 -0.4
Ru"*~ 1.99 1.44 -22.8 -26.8
Ru" 1.99 1.44 -18.4 -22.4
Ru"ve 1.99 1.44 -18.2 -22.2
Rh"vd 1.97 1.44 -30.9 -34.9
Downloaded by UNIV NACIONAL AUTONOMA MEXICO on August 31, 2015 | http://pubs.acs.org

Rh" 1.97 1.44 -28.9 -32.9

Pd" 2.01 1.43 -26.7 -30.7
"MCPF optimized geometry. boptimized for the 2Bzstate. Coptimizedfor the 'B2 state. dOptimized for the 2A2state.

rABLE I V MlllliLcs Popuiatioas (MCPF) for Different States of M + c ~ H ~ + A E = M : :CH

II
Publication Date: November 1, 1992 | doi: 10.1021/j100203a040

the Second-Row MC2H4Systems AE 'CH,

Ikcollmoll
M state QM 5s 5P 4d
Y 'AI +0.31 0.94 0.36 1.31
Y ZB2 +0.01 1.58 0.43 0.93
Y 4A2 +0.11 0.82 0.51 1.40
Zr
Zr
'BI
5AI
+0.30
+0.06
0.76
0.90
0.35
0.26
2.52
2.72 O t A
Nb
Nb
Mo
'BI
6AI
5B2
+0.29
-0.01
+0.20
0.76
0.79
0.97
0.19
0.15
0.46
3.71
4.03
4.32
-I0 t / \
Tc 6B2 +0.09 0.97 0.27 5.63
Tc 4B2 +0.18 0.71 0.12 5.94
Ru 'A2 +0.14 0.38 0.10 7.32
Ru 'B2 +0.13 0.60 0.10 7.10 -40-
Ru 'BI +0.13 0.60 0.10 7.11
Rh 2AI 0.08 0.34 0.11 8.41 , / / i I I I I

Rh 2Az +0.08 0.51 0.12 8.24 Y Zr Nb Mo Tc Ru Rh Pd

Pd !Al +0.05 0.33 0.11 9.45

doubly occupied db,-orbital in Table I. For both yttrium and

niobium this state is expected to become the lowest in a better
calculation since it is the state with the largest correlation effects,
in the case of yttrium due to a higher d-population and in the case
of niobium due to one more doubly occupied orbital. The results nation to the ethylene n*-orbital can be made from a doubly
for different electronic states are given in Tables 111and IV. The occupied &-orbital. A similar mechanism to the left would require
ground-state binding energies are also displayed in Figure 2. Two a costly 4d spin pairing and the binding mechanism for yttrium
values are given for the metal-ethylene binding energies. The to niobium is therefore quite different from that to the right. The
first value is the actually calculated binding energy at the MCPF binding for the atoms to the left is best characterized as normal
level using the standard basis set of the present paper, and the covalent bonding forming a metallacyclopropane. The definite
second is a corrected value where higher correlation effects are breaking of the ethylene n-bond is clearly seen on the long C-C
estimated based on CCSD(T) calculations on PdC2H4using a bond distance characteristic of a single bond. It is noteworthy
larger basis set (see further section IIIf). A few of the more that because of the required promotion energies and the loss of
general results in these tables should first be mentioned. The first exchange, the M-C2H4binding energies are not proportional to
notable result is that the binding energies go through a marked the perturbation on the ethylene geometry. Concerning the ge-
minimum in the middle of the row for molybdenum and tech- ometries, it should also be noted that the formation of the me-
netium. The main origin of this minimum is loss of exchange tallacycle requires shorter metal-carbon bond distances, which
energy when the bonds are formed. This loss is largest in the leads to a larger repulsion between nonbonding electrons than for
middle of the row since there is a large number of unpaired the donation bonding modes. The shorter M-C bond distances
4d-electrons in this region. This result is quite general and has for the metallacycles are best seen in the results in Table I11 for
been noted in most previous similar studies also for other lig- the different bonding modes for the same atom. It is not directly
ands.**" The largest binding energies are obtained to the right. seen in the geometries in Table I for different atoms since the pure
The main reason for this is that the atoms to the left have larger metallacycle bonding w a r s for the atoms to the left. The radii
promotion energies to reach the binding 4dn+15s1 state. The of these atoms are much larger than they are to the right and still
exchange loss is also somewhat larger to the left. A third reason the M-C bond distances are about the same.
the atoms to the right have larger binding energies is that the The occupation of the valence orbitals as one goes from the left
mixture of the donation bonding and the purely covalent bonding to the right is systematic and is determined by the covalent in-
can be efficiently maximized to reduce the promotion and ex- teractions in the Al(n) and B2(**) symmetries and also by the
change loss energies. This can be accomplished since back-do- ligand field. The first orbitals that are filled are thus the a1 and
 Ethylene Binding to Transition-Metal Atoms The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9797

the b2 orbitals. To the left in the periodic table, these orbitals covalent bonds. For the previously studied systems of MRlRz type,
are covalent M-C bonds. To the right, these orbitals are instead where R is an alkyl or a hydrogen atom>11the bonding is strictly
the a-orbital on ethylene in AI symmetry and a back-donating covalent and the promotion energy to a bonding state with two
doubly occupied 4d-orbital in Bz symmetry. The remaining in- open-shell orbitals directly enters the strength of the bonds that
teractions on the metal center are repulsive and the 4d-orbitals are formed.
are occupied to minimize this repulsion. The first 4d-orbital The C-C bond length is remarkably constant at 1.44 f 0.01
occupied is a b ] , which points perpendicular to the MCC plane. A for all the atoms that donates through a doubly occupied
The next 4d-orbitals to be occupied are the 4ddd-type orbitals in 4db2-orbital. It is interesting that about the same C-C bond length
the AI and Az symmetries. The final 4d-orbital to be occupied is obtained also for the atoms to the left for the bonding mode
is the 4d,-type orbital. The fact that the metal atoms prefer to with one singly occupied 4dbz-orbital. This bond distance is
adopt a 4d occupation that as much as possible obeys spherical precisely in between that of a double and a single C-C bond and
symmetry requirements is a slight complication in this simple it thus appears as if there is an intermediate stability of a C-C
orbital-filling scheme. For example, for this reason the 4dbl-orbital bond that is halfway broken.
becomes doubly occupied rather than the 4db(Az)-orbital for There are no metallacyclopropanesformed by the atoms to the
RuCZH~. right, which can be understood in the following way. The for-
b. The Metnl Atom Y-Tc. The transition-metal atoms to the mation of purely covalent bonds requires promotion to an s1 state
left in the periodic table have two different ways to bind ethylene. and is accompanied by a loss of exchange. The metals to the right
In the low spin state, two covalent bonds are formed, leading to can avoid these costs by mixing in the so state, which gives rise
a metallacyclopropane. In the other way of binding ethylene, to the donation type of bonding. The actual bonding to the right
usually a high spin state, a donation-back-donation binding is is a compromise between the covalent and the donation forms of
Downloaded by UNIV NACIONAL AUTONOMA MEXICO on August 31, 2015 | http://pubs.acs.org

obtained with a singly occupied back-donating 4dbz-orbital. These bonding. For these atoms the same state that forms the metal-
two bonding modes have quite different geometries. The me- lacyclopropane can dissociate all the way to the atomic limit and
tallacyclopropane has short M-C distances and a long C-C thus optimize the balance between covalency and loss of exchange.
distance, whereas for the donation mode the C-C bond is shorter This is not possible for the atoms to the left where the state that
and the M-C distances are substantially longer. Since both the forms the metallacyclopropane dissociates to strongly excited states
Publication Date: November 1, 1992 | doi: 10.1021/j100203a040

geometries and the electronic structures are SO different for these of the atoms with doubly occupied 4dbz-orbitals. Since the freedom
bonding modes, it appears as a coincidence that the binding en- to optimize the binding is larger for the atoms to the right, the
ergies for the two modes for yttrium, niobium, and technetium binding energy is largest for these atoms even though there are
are so extremely similar. For these atoms the binding energies more repulsive nonbonding electrons present.
of the two modes differ by less than 1 kcal/mol. The exception d. Comparisons to Methane Dissociation. The general shape
to this behavior is zirconium, which has a substantially more bound of the binding energy curve for the insertion product of the
metallacyclopropaneform. In this context it is interesting to note methane dissociation reactionZ is quite similar to the curve in
that the metal complex that most efficiently polymerizes ethylene Figure 2. The loss of exchange for the atoms molybdenum and
in the homogeneous phase is a zirconium complex.' This could technetium in the middle of the row is even more pronounced for
be due to the efficient breaking of the ethylene r-bond by zir- the methane case, giving strongly unbound insertion products. For
conium but needs to be investigated more. methane the complexes that are most strongly bound are found
For the atoms to the left in the periodic table, one of the orbitals to the left for zirconium and niobium, rather than to the right
in the AI symmetry, a a-orbital, is usually dominantly of 5s as for ethylene. The reason for this difference is the following.
character. For both yttrium and zirconium in the state with a The bonding both in the case of methane and in the case of
singly occupied donating 4dbz-orbital, this u-orbital is doubly ethylene is dominated by the 4dn+'Ss' state on the metal. For
occupied to mix in the ground states of the atoms, which have methane the bonding is more strictly covalent and for the atoms
s2 occupations. For the metallacyclopropane state, this a-orbital to the left there are in this case also large contributions from the
is singly occupied. For this reason and others the dissociation of 4dn5s15p'state, which increases the stability of these insertion
the metallacyclopropane will adiabatically go to excited states of products. In the ethylene case it is the atoms to the right that
the atoms. In fact, there could in principle be a barrier for increase their stabilities by mixing in other states, in this case the
formation of the metallacyclopropane. In order to test this, a 4dn+2state. The situation is best illustrated by comparing the
geometry optimization for the low-spin metallacyclopropanestate binding energies of methane and ethylene for rhodium and pal-
was started at the outer minimum for the other bonding mode ladium. The insertion product of the methane reaction is bound
of ZrC2H4. However, this geometry search converged to the inner by 5 kcal/mol for rhodium but unbound by 9 kcal/mol for pal-
minimum without any barrier. ladium. This difference is rather well explained by the difference
The populations on the metallacyclopropanesof Y-Nb indicate in promotion energies to reach a state with two singly occupied
that the d"+'s' state is the main bonding state. It is interesting orbitals. Such a state is needed to form two strictly covalent bonds.
that the binding energies for these three atoms are practically the For palladium there is an excitation energy of 21 kcal/mol to reach
same, even though the promotion energies to the d"+'s' state are this state, whereas the ground state of rhodium already has two
different. For the niobium atom this state is the ground state, open shells. For ethylene this excitation energy does not enter
whereas for zirconium and yttrium there are excitation energies the difference in the binding energies, which are about equal for
of 13.6 and 31.4 kcal/mol, respectively, to reach this state. rhodium and palladium. With a donation type of bonding this
Apparently the loss of exchange (mainly), which increases toward is not surprisiig since there are no requirements on singly occupied
the middle of the row, happens to exactly cancel the effect of orbitals in this case. The back-donation from a 4d'O state should
electronic promotion. For molybdenum and technetium, the loss be at least as efficient as from a 4d95s1state. It is interesting to
of exchange is a dominating factor, as already indicated above. note that the energy difference between rhodium and palladium
c. The Metal Atoars Ru-Pd. The bonding for the metal atoms for the transition state of the methane reaction is more similar
Ru-Pd is the one that best fits the normal donation-backdonation to the difference for ethylene. The barrier height of the methane
picture. The amount of donation is about 0.4 electrons in each reaction is for rhodium 14 kcal/mol and for palladium it is 16
direction. These atoms also have the strongest metal-olefi bonds kcal/mol. It was emphasized in ref 2 that an important re-
in this row. The populations indicate that the bonding state is quirement for a low barrier for the methane reaction is access to
a mixture of the d"+'s' and the d"+Zstates with some dominance a 5so state (4d"+Zstate). This state is also a suitable state for
of the former state. It thus appears as if the d"+*state can form back-donation and explains the similarity between the binding
the bonds to ethylene almost as well as the d"+'s' state. This is energy region of ethylene and the transition-state region for
interesting since for palladium the dn+2state cannot form any methane. It is further true for the whole row of metals that the
covalent bonds, since it lacks open-shell orbitals. This illustrates variation of the ethylene binding energies is more similar to the
the qualitative difference between donation bonds and normal variation in bamer heights for the methane insertion reaction than
 9798 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 Blomberg et al.
to the variation in binding energies for the methane insertion TABLE V Relrtivbtic .ad Correlath Effects on the Relative
products. To the left of the periodic table this can be understood Eaegkrr of tbe MeW-Ethykse Complexes (in k d / d )
from the properties of the s2 state, which is low lying in this region. M state relativistic effect correlation effect
In the methane insertion products this state can improve the
bonding by mixing in the SIP' state, leading to a linear distortion Y +0.7 -8.8
Zr +0.9 -13.2
of the strongly bound MHCH, products. In the metallacyclo- Nb -6.7 -35.2
propane complexes this type of bonding cannot be involved due Mo -3.4 -44.5
to the ring structure and therefore the s2state has rather a repulsive Tc +10.3 -46.8
effect, as it has in the transition-state region of the methane Ru +1.8 -48.8
reaction. Rh +2.9 -50.1
The above-mentioned differences between the binding to Pd -11.0 -26.9
methane and ethylene are also seen on the populations. The
4d-population for the insertion product of the methane reaction in discussions of differences between cations and neutral atoms
is 8.2 for rhodium and 9.2 for palladium, indicating the importance is the effect the positive charge has on the strength of the bonds.
of the 4d95s' state in the bonding. For the ethylene complex the Covalent bonds formed by transition metals are often accompanied
4d-populations are higher with 8.4 and 9.5, respectively, showing by electron donation to the ligand. When the positive charge is
the importance of the mixing with the 4d9 and 4dI0 states, re- present this donation is hampered and the strength of the covalent
spectively. The equilibrium 4d-populationsin the case of ethylene bonds is significantly reduced. This effect was noted in our
are quite close to those found for the transition state of the methane previous studia on the interaction between transition-metalcations
reaction. Larger 4d-populations for the ethylene complex than
Downloaded by UNIV NACIONAL AUTONOMA MEXICO on August 31, 2015 | http://pubs.acs.org

and methan$-I2 and in studies on the interaction between CO and

for the insertion product of the methane reaction is a general result Ni and Ni+.I3 The exothermicity of the methane reaction was
across the entire row. The explanation for this result to the left in general found to be smaller for the cations than for the cor-
of the row is different from the explanation to the right of the responding neutral atoms, even though the initial interaction is
row. The methane insertion products to the left are found to have much stronger for the charged systems. The u complex between
large 5s, 5p contributions in the bonds and this leads to larger the cation and molecular methane is sometimes bound by up to
Publication Date: November 1, 1992 | doi: 10.1021/j100203a040

bond angles. For the metallacyclopropanes the bond angle is 20 kcal/mol, whereas the corresponding neutral system is seldom
restricted by the u-bond between the carbon atoms and the 5s, bound, but for the final product of the C-H dissociation reaction,
5p contributions are therefore smaller than for the methane case. where the covalent bonds are formed, the situation is usually
Another general result across the row is that the positive charges reversed. The fact that covalency is not present for most of the
are larger for the methane insertion products than for the ethylene cationic systems studied in ref 3 is thus due not only to the large
complexes. The reason for this to the left of the row is that the size of the electrostatic interaction but also to a large part due
5s, Sp orbitals, which are more diffuse than the 4d orbitals, in to the weaker covalency for the cationic than for the neutral
general tend to donate more electrons to the ligands. To the right system.
of the row the contribution from donation-back-donation bonding f. Correlation and Relativistic Effects. In the present study,
tends to even out the charge distribution and make the complexes SCF calculations are always performed initially and the "elation
almost neutral. The largest charges are for both methane and effects are therefore available. It is well-known that the correlation
ethylene found to the left of the row, which is in line with the lower effects on the absolute binding energies are usually very large,
ionization energies for the metals to the left. but not many investigations have been made to systematically
e. Comp"s to the Metal-Ethylene Cations. There are no study the correlation effects on the relative binding energies be-
previous theoretical studies of second-row metal-ethylene cations tween different transition metals. The correlation effects for the
but the binding of ethylene to first-row transition-metal cations MC2H4systems obtained in the MCPF calculations are therefore
has been studied previously by Sodupe et al., The computational given in Table V. Since relativity is treated by perturbation
methods were quite similar to the ones used in the present study. theory, relativistic effects on the binding energies are also available
There are some immediate similarities between the results of that and are given in the same table.
study and ours but also some notable differences. The binding Starting with the correlation effects, it is clear from the results
energies for the first-row cations are in the range 16-37 kcal/mol, in the table that the relative effects are nearly as large as the
which is a little bit larger than that for the neutral second-row absolute effects. The total correlation effects on the binding
atoms, but the order of magnitude is the same. There is also a energies for ruthenium and rhodium are as large as 49.8 and 51.1
marked minimum in the binding energies for the cations in the kcal/mol, respectively. Since the total correlation effect for yt-
middle of the row, exactly as for the neutrals in the present study. trium is only 8.8 kcal/mol, the relative effects are over 40
However, the main origins of these minima are somewhat different. kcal/mol. In general, the absolute correlation effects are much
In the present study, the loss of exchange when the bonds are larger to the right in the series since there are more 4d-electrons
formed is responsible for the minimum in the binding energy. For for these atoms. However, for palladium the correlation effect
the cations, the minimum for manganese occurs because it is the is relatively small since there are more 4d-electrons for the free
only cation between Cr+ and Cu' that has the repulsive 4ssrbital atom than for the complex. In general, the difference in the
occupied. The direct loss of exchange is only of secondary im- correlation effects between different metals will be smaller if the
portance for most of the cations. correlation effect is always computed relative to an asymptotic
The nature of the binding for most of the metal cations is quite state with the same number of 4d-electrons as for the complex.
different than it is for the neutral atoms of the present study. In However, the relative correlation effects will still be substantial,
fact, for all cations except Sc+ and Ti+ the binding is almost purely at least in the present case where the binding in the complex is
electrostatic. For the cations V+ to Ni+, most of the particular sometimes a mixture of states.
properties of the d-electrons of the transition metals, which make In order to estimate the size of the correlation effects not
them so useful catalytically, are replaced by strong electrostatic included in the present standard calculations, a few calculations
forces. The most notable exception is Sc', which binds strongly were performed by using the single- and double-excitation cou-
covalently with ethylene in a metallacyclopropane form similar pled-cluster (CCSD) method that includes a perturbational es-
to that of the second-row atoms to the left of the periodic table. timate of triple excitations, denoted CCSD(T). In these calcu-
The C 4 distance in Sc'C2H4 is 1.49 A. Already for Ti+ the C< lations a larger basis set was used, including three uncontracted
distance is reduced to 1.42 A, and for the other cations, ethylene f-functions on the metal and two d-functions on carbon (see
is essentially unperturbed by the metal cation. Appendix). Since the CCSD(T)14 program at present only can
It is interesting to note that the binding energies for the first-row handle closedahell systems, these calculations were only performed
cations studied in ref 3 are not much larger than they are for the for the case of palladium. The enlargement of the basis set
neutral atoms studied here. One effect that is often neglected increases the MCPF binding energy of PdC2H4 by about 1
 Ethylene Binding to Transition-Metal Atoms The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9799

kcal/mol, from 26.7 to 27.6 kcal/mol (the SCF binding energy The present binding energy curve for ethylene in Figure 2 shows
is unchanged). This small effect is probably the result of cancelling many similarities to the curves obtained for methane dissociation?
effects, a decreased superposition error, which decreases the In fact, the ethylene curve is more similar to the curve obtained
binding energy, and an improved description of the bonding, which for the transition-state energies for methane than to the curve for
increases the binding energy. The CCSD binding energy is the methane product energies. The reason for this is that for the
somewhat smaller than the MCPF binding energy, 25.6 kcal/mol atoms to the right there is a similar mixing between the s1 and
using the largest basis set. The triple excitations, fmally, increase so states. However, the origin of this mixing is different for
the binding energy by about 5 kcal/mol, yielding a CCSD(T) ethylene and for the methane transition states. For ethylene the
binding energy of 30.7 kcal/mol for PdC2H4. The difference in mixing between malent- and donation-type bonding is maximized,
the result from the standard calculation on PdC2H4 and the best whereas for methane so is mixed into the bonding s1 state at the
calculation is thus an increase in the binding energy of 4.0 transition state to minimize repulsion from the electrons on
kcal/mol. It is assumed that a similar increase of the binding methane. One important difference between the ethylene and
energy would be obtained for all the MC2H4systems if higher methane reactions is that for ethylene the strongest bonds are
correlation effects could be included and therefore a correction found to the right, whereas for the methane products they occur
of 4.0 kcal/mol is added to all the binding energies in Tables I to the left. The reason the leftmost atoms form strong bonds to
and 111. It can be expected that a further improvement of the methane is that the sp state can efficiently contribute to the
basis set and the description of higher excitations would increase bonding since the H-M-C angle is without strain. For the me-
the binding energies by another 1-2 kcal/mol. tallacyclopropanes formed to the left in the ethylene case the
The conclusion drawn here is that the SCF results are not useful C-M-C angle is forced to be smaller by the presence of the C-C
even for the relative energy differences between different metals. bond and is therefore much less optimal for the sp state.
Downloaded by UNIV NACIONAL AUTONOMA MEXICO on August 31, 2015 | http://pubs.acs.org

In fact, it is our opinion that the present type of MCPF calcu- The present study, involving an entire row of transition-metal
lations, using one f-function on the metal and one d-function on atoms or complexes, is a type of investigation that will be more
carbon, are a minimal requirement for obtaining reasonably re- common in the future. The main advantage with this type of
liable energy differences. Probably, in a few years time, much approach is that the different transition-metal atoms of a row have
larger basis sets and methods including the effects of triple ex- a variety of different spectral and other properties that can be
Publication Date: November 1, 1992 | doi: 10.1021/j100203a040

citations will be routinely used for these systems. At present, such directly compared for the interaction with a ligand of interest.
calculations are too time consuming for this type of systematic This is, in our opinion, a much more fruitful procedure than to
study. try to analyze the components of the bonding in detail by studying
The relativistic effects on the binding energies are much smaller the wave function for one isolated system. By the latter approach
than the correlation effects. Still, these effects can be substantial it is in general possible to see the different aspects that contribute
and need to be included for obtaining a reliable binding energy to the bonding, such as the bonding state and the presence of
trend. A procedure where the relativistic effect is computed electron donations, but it is quite difficult to estimate exactly how
relative to an asymptote with the same number of 4d-electrons important these aspects are energetically. In the near future
is fairly successful and can, for example, account almost quan- several other model reactions involving transition metals will be
titatively for the large relativistic effect for the case of palladium presented, such as C-C bond breaking, olefin insertion, and C-H
of 11.O kcal/mol. In general, a relatively rough procedure to obtain bond breaking in unsaturated hydrocarbons. The goal is to build
the relativistic effects, such as the use of perturbation theory or up a piece by piece understanding of real catalytic reactions.
the use of relativistic ECPs, appears quite adequate. For the
description of the transition-metal atomic spectra, which is im- Acknowledgment. We are grateful to Andrew Komomicki for
portant for obtaining the correct mixing of states in molecules, the use of the GRADSCF program package.
the perturbation approach gives results very close to numerical
relativistic Hartree-Fock results for the first- and second-row Appendix A. Computational Details
metals.I5 For these metals the spin-orbit effects are furthermore In the calculations reported in the present paper for the reaction
rather small. The perturbation approach has also been tested in of ethane with second-row transition-metal atoms, large basis sets
molecular calculations16 and was shown to agree well with Di- were used in a generalized contraction scheme" and all valence
rac-Hartree-Fock calculations. electrons were correlated. Relativistic effects were accounted for
by using first-order perturbation theory, including the mass-ve-
111. Conclusions locity and Darwin terms.I6
The present calculations on the entire second-row transition- For the metal atoms the Huzinaga primitive basis'* was ex-
metal atoms have allowed a systematic investigation of the dif- tended by adding one diffuse d-function, two p-functions in the
ferent effects that are of importance for the binding to ethylene. 5p region, and three f-functions, yielding a (1 7s, 13p, 9d, 3f)
It is found that the largest binding energies are found to the right primitive basis. The core orbitals were totally contracted except
of the row. For these atoms the bonding is an optimized mixing for the 4s- and 4p-orbitals, which have to be described by at least
between purely covalent bonding and donation-back-donation two functions each to properly reproduce the relativistic effects.lg
bonding. The purely covalent bonding in general requires pro- The 5s- and 5p-orbitals were described by a double-[contraction
motion to an excited state of the atom and is also accompanied and the 4d by a triple-[ contraction. The f-functions were con-
by a loss of exchange energy when the bonds are formed. The tracted to one function giving a [7s,6p, 4d, lfl contracted basis.
optimization of the bonding is accomplished by a mixing between For carbon the primitive (9s, 5p) basis of Huzinaga20 was used,
the de2 and the d"+lsl states. A similar mixing to the left of the contracted according to the generalized contraction scheme to [3s,
row is not possible, since in that case the bondings involving these 2p] and one d-function with exponent 0.63 was added. For hy-
states have different spin. To the left of the row there are instead drogen the primitive (5s) basis from ref 20 was used, augmented
two other psibilities. The first one is a purely covalent bonding with one pfunction with exponent 0.8 and contracted to [3s, Ip].
leading to the formation of metallacyclopropanes. In these systems In a few calculations a larger basis set was used. For the metal
the ethylene *-bond is fully broken, leading to a C-C distance the same primitive basis as above was used but the three f-functions
typical for carbon single bonds. The metal to carbon bond distance were kept uncontracted. For carbon and hydrogen extended
is also much shorter than for a donation-back-donation type bond. primitive basis sets were contracted by using atomic natural or-
The second bonding mode for the atoms to the left uses a singly bitals (ANOs). For carbon a primitive (14s, 9p, 4d) basis was
occupied 4d-orbital as a back-donating orbital. As a remarkable used and contracted to give [4s, 3p, 2d] and for hydrogen a (8s,
coincidence, these two modes of binding ethylene are almost 4p) basis was used and contracted to give [3s, 2 ~ 1 . ~ '
exactly equally strong for yttrium, niobium, and technetium. The In the geometry optimizations at the SCF level described below,
exception is zirconium, where the metallacyclopropane form is somewhat smaller basis sets were used. First, for the metal atoms
markedly preferred. a relativistic ECP according to Hay and Wadt22was used. The
 9800 The Journal of Physical Chemistry, Vol. 96, No. 24, 19s'2 Blomberg et al.

frozen 4s- and 4prbitals are described by a singlet contraction, ethylene, 74-85-1.
the valence 5s- and Sporbitals by a double-f basis, and the 4d
orbital by a triple-t basis, including one diffuse function. The Refereaces pad Notea
rest of the atoms are described by standard double4 basis sets. (1) Pasquon, 1.; Giannini, U. In Caralysis, Science a d Technology; An-
The correlated calculations were performed by using the derson, J. R., Boudart, M. Eds.; Springer-Verlag: Heidelberg, 1984; Vol. 6,
modified coupled pair functional (MCPF) method,z3which is a pp 65-159.
(2) (a) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M. J . Am.
size-consistent, single reference state method. The metal 4d-and Chem. Soc., in press.
5s-electrons and all electrons on the C2H4 unit except the C (3) Sodupe, M.; Bauschlicher, C. W., Jr.; Langhoff, S.R.; Partridge, H.
1s-electrons were correlated. Calculations were also performed J. Phys. Chem. 1992, 96, 2118.
by using the single- and double-excitation coupled-cluster (CC- (4) (a) Sunderlin, L. S.;Aristov, N.; Armentrout, P. B. J. Am. Chem. Sa.,
1987,109.78. (b) Aristov, N.; Armentrout, P. B. J . Am. Chem. Soc. 1986,
SD)14method that includes a perturbational estimate of connected 108, 1806. (c) Tolbert, M. A.; Beauchamp, J. L. J . Am. Chem. Soc. 1984,
triple excitations, denoted CCSD(T). These calculations were 106.8117. (d) Armentrout, P. B.; Beauchamp, J. L. J. Am. Ch" Soc. 1981,
only performed for the palladium system, since the present version 103, 6628. (e) Jacobson, D. B.; Freiser, B. S.J . Am. Chem. Soc. 1983, 105,
of the program can only handle closed-shell wave functions. In 7492.
( 5 ) Bauschlicher, C. W.; Langhoff, S.R. J. Phys. Chem. 1991,95,2278.
these calculations the largest bask sets described above were used. (6) Blomberg, M. R. A.; Siegbahn, P. E. M.; Lee, T. J.; Rendell, A. P.;
All geometries used in the calculations are optimized, either Rice, J. E. J. Chem. Phys. 1991,95, 5898.
at the SCF level or at the MCPF level. At the SCF level full (7) Widmark, P.-0.; Roos, B. 0.;Siegbahn, P. E. M. J . Phys. Chem. 1985,
optimizations are performed, while in the MCPF optimizations 89, 2180.
(8) Widmark, P.-0.; Roos, B. 0. Theor. Chim. Acra 1989, 76, 33.
the C-H bond distanee is kept constant at the value for free (9) Koga, N.; Morokuma, K.Chem. Rev. 1991, 91, 823.
ethylene (1.085 A), and the H-C-H angle is kept at 116", which
Downloaded by UNIV NACIONAL AUTONOMA MEXICO on August 31, 2015 | http://pubs.acs.org

(10) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M.; Wennerberg,

is the value obtained in a CASSCF optimization on NiC2H4.24 J. In Energefics of organomerallic Species; NATO AS1 Series; Martinho
In the MCPF optimization, furthermore, the C-C bond distance Simo&, J. A., Ed.; Kluwer Academic Publishers: Amsterdam, 1992; pp
387-421.
and the out of the ethylene plane bending of the C-H bonds are (ll)Rosi, M.; Bauschlicher, C. W., Jr.; Langhoff, S.R.; Partridge, H. J .
assumed to be linearly coupled, based on the results from some Phys. Chem. 1990, 94, 8656.
previously performed optimization^.^-^*^^ For all metals except ( 12) Blomberg. M. R. A,; Siegbahn, P. E. M.; Svensson, M. New J. Chem.
1991. 15. 727.
Publication Date: November 1, 1992 | doi: 10.1021/j100203a040

palladium and rhodium, the states listed in Table I could be (13) Blomberg, M.; Johansson, J.; Siegbahn, P.; Wennerberg, J. J . Chem.
optimized at the SCF level. For ruthenium optimizations were Phys. 1988,88, 4324.
performed at both the SCF and the MCPF level and the results (14) The coupled cluster calculations are performed by using the TITAN
were found to be very similar. For palladium and rhodium the set of electronic structure programs, written by LAX, T. J., Rendell, A. P., and
SCF optimizations gave only very weakly bound systems, and the Rice, J. E.
(15) Martin, R. L.; Hay, J. J . Chem. Phys. 1981, 75, 4539.
optimization had to be performed at the MCPF level. The main (16) Martin, R. L. J . Phys. Chem. 1983,87, 750. See also: Cowan, R.
reason for this difference between rhodium and palladium on the D.; Griffin, D. C. J . Opf. Soc. Am. 1976,66, 1010.
one hand and the rest of the metals on the other is that the (17) (a) Almbf, J.; Taylor, P. R. J . Chem. Phys. 1987, 86, 4070. (b)
HartreFock codiguration for the metal-ethylenemolecule can Raffenetti, R. C. J. Chem. Phys. 1973, 58, 4452.
(18) Huzinaga, S.J. Chem. Phys. 1977, 66, 4245.
dissociate correctly to a low-lying state of the metal atom for (19) Blomberg, M. R. A.; Wahlgren, U. Chem. Phys. Left. 1988,145,393.
rhodium and palladium, which is not the case for the rest of the (20) Huzinaga, S.J. Chem. Phys. 1965,42, 1293.
metals. The geometries for the other states were optimized at (21) Widmark, P.-0.; Malmqvist, P.-A.; Roos, B. 0. Theor. Chim. Acra
the MCPF level (since these optimizations were performed before 1990, 77, 291.
(22) Hav. P. J.: Wadt. W. R. J. Chem. Phvs. 1985.82. 299.
we had access to the SCF-gradient program). The SCF opti- (23) Chong, D. P.; Langhoff, S.R. J . Chem. Phys.'1986, 84, 5606.
mizations were performed by using the GRADSCF programz6 (24) Blomberg, M. R. A.; Siegbahn, P. E. M.; Schiile, J., unpublished
and the MCPF optimizations were performed by pointwise cal- results.
culations. (25) Bauschlicher, C. W., Jr.; Langhoff, S.R. J . Phys. Chem. 1991,95,
2278.
Registry No. Y, 7440-65-5; Zr, 7440-67-7; Nb, 7440-03-1; Mo, (26) GRADSCF is a vectorized SCF first- and second-derivative code
7439-98-7; Tc, 7440-26-8; Ru, 7440-18-8; Rh,7440-16-6; Pd, 7440-05-3; written by A. Komornicki and H. King.