52 J . Phys. Chem. 1993,97, 52-58

Co+*(H& Clusters: Binding Energies and Molecular Parameters

Paul R. Kemper,’ John Busbnell, Cert von Helden, and Michael T. Bowers’ Department of Chemistry, University of California, Santa Barbara, California 931 06

Received: July 13, 1992; In Final Form: September 10, 1992

Temperature-dependent equilibrium measurements of mass-selected Co+ ions reacting with H2 were used to determine binding energies and entropies for Co+.(H2),, clusters. Clusters with one to seven H2 ligands were examined. The observed binding energies decrease with cluster size in a pairwise fashion. The first and second H2’s have roughly equal binding energies (18.2 and 17.0 kcal/mol); the third and fourth binding energies are also equal (9.6 kcal/mol); the fifth and sixth cluster binding energies are 4.3 and 4.0 kcal/mol; the seventh H2 is very weakly bound (-0.8 kcal/mol). The observed pattern and magnitude of the cluster binding energies can be largely explained with a simple model of electrostatic attraction and steric interference. The results on the first three clusters agree well with high-level calculations by Partridge et al. The calculations give valuable insight into the cluster bonding and structure and allow reasonable predictions of structures for all clusters.

I. Introduction

High-pressure, temperature-dependent equilibrium measure- ments have been used for many years to determine thermodynamic quantities (AJYand AS) of ion-neutral complexes and A very large body of data exists for the hydration of atomic and polyatomic ions; smaller amounts of work have been done on clusters involving rare gas and organic neutrak2 In our own group, for example, we have recently reported temperature- dependent equilibrium measurements of Co+, Ni+, and Cr+ binding with He, Ne, and Ar neutral^.^ Our results agree well with high-level theoretical calculations by Partridge and Baus- ~ h l i c h e r , ~ as well as photodissociation work by Lessen and Brucat where overlaps e x i ~ t . ~ * ~ Using the technique of electronic state chromatography (EX): we were able to determine the presence of electronically excited metal ions and, in the case of Ni+, separately measure the ground- and excited-state binding energies to He and Ne. These latter results are in good agreement with independent measurements made by using ion mobility tech- niques.8

Activation of a-bonds is, of course, an extremely important endeavor in the area of catalysis. This is especially so for C-H bonds in alkanes due to their importance in the petroleum industry. The factors that govern such activation are thus of broad fundamental and practical interest. An excellent model for a-bond activation is the H-H bond in the H2 molecule. Consequently, one would expect a high degree of activity in this area. In the gas phase this simply is not the case. For example, very little data exist on the energetics of metal ion-hydrogen clusters with only the Li+.H2 system reported in the l i t e r a t ~ r e . ~ Armentrout and co-workers1° have measured thresholds of endoergic M+/H2 reactions forming MH+/H products to extract M+-H bond energies. They deduced 3d - 4s promotion energies were import- ant in activating the H2 bond for first-row transition metals. Since these reactions are all strongly endoergic it was not clear whether or not the metal actually inserted to form M+(H)2 intermediates, an unlikely proposition for 3dn-14s1 metals (due to electron repulsion of the 4sl orbital) but possible for electronic states with dn configurations.

There have been a limited number of very interesting studies of the reactivity of transition-metal clusters with H2I1-l3 where the emphasis has been on reactivity and total coverage. Of particular interest is the workof Smalley and co-workers’3 where H2 is observed to attach to (Nb)n+ clusters as small as Nb4+. Both attachment rate constants and total coverages (saturation levels) are observed to be strongly size dependent. They assume the

0022-3654/58/2097-0052%04.00/0

cluster acts like a miniature surface and the H2 molecule dissociatively absorbs. Since the experiments operate in the 10-’-Torr range, collisional cooling is not a viable option. Consequently, radiative cooling is then thought to compete with backdissociation, a t least for the smaller clusters. Still, a question must remain as to whether or not the H2 molecule dissociates and, if it does, how large a cluster is required for dissociation to occur?

In more traditional neutral solution organometallic chemistry, dihydrogen complexes with transition metals have been confirmed only in the past decade by the pioneering work of Kubas and co-workers.I4 Of interest is the fact that d6 metals appear to provide the majority of host metal centers for “nonclassical” H2 addition.15 For reasons that will becomeapparent, it is interesting that d8 metal centers tend tooxidatively add H2 to form “classical” M(H)2 dihydride compounds.I6 The ability of a transition-metal center to add intact H2 ligands appears to be related to its oxidation state; that is, to the electronegativity of the remaining ligands attached to the metal: thegreater theelectron-withdrawing power of the ligand, the more positively charged the metal, the easier it adds H2. Presumably, this occurs because donating electrons from the metal to the H2 a* orbital increases in energy as the oxidation state of M increases.17 Consequently, bare transition- metal ions in the gas phase appear to make superb candidates for nonclassical H2 addition.

Finally, studying the interaction of metal ions with H2 in the gas phasecan provide data for comaprison with ab initioelectronic structure calculations. Such calculations are beginning to appear,18-20 but only the Li+.H* system9 has been studied experimentally (to determine a binding energy), and since transition metals are required to activate u-bonds, this system is not of real utility. One of the principal goals of this work, then, is to accurately measure binding energies of H2 to a first-row transition-metal ion via the reaction

Co+(H2),, + H, s Co(H,),,+

Cobalt was chosen because it is simple to make in abundance, is monoisotopic, and, being a d8 ion, might react via oxidative addition rather than dihydrogen addition, although the Co+-H2 bond strength published in the literaturelo makes this unlikely. This paper reports our results for n = 1-7 and compares with theoretical calculations where available. A simple model that rationalizes the change in binding energy as n increases will be discussed.

0 1993 American Chemical Society

Co+.(H2),, Clusters The Journal of Physical Chemistry, Vol. 97, No. 1, 1993 53

uncertainty in the temperature readout is f1.2 K at 80 K, f0.2 K at 273 K, and h1.6 K at 580 K. This contributes minimally to the uncertainty in AGO.

Thereis noeffect due to theCo+ injectionenergy (uponentering the ell).^.^^ This energy is quickly lost by collision and sufficient reaction time is provided for any perturbed equilibrium formed near the cell entrance to thermalize. The effect of the drift field on ion temperature can be easily calculated in the low-field limit by using2'

11. Experimental Technique In these experiments, temperature-dependent clustering equi-

libria are used to determine bonding enthalpies and entropies. The instrument used and the clustering experiments have been described.3JI An overview is given here, along with a discussion of the peculiarities of the Co+ + Hz experiments.

The Instrument. The Co+ ions are formed by electron-impact ionization of ~ p C o ( C 0 ) ~ . After acceleration and mass selection in a double-focusing, reverse-geometry mass spectrometer, the ions are decelerated to approximately 3-4 eV and injected into a reaction cell containing H2 at about 1.3 X lOI7 m/cm3 (4 Torr at 300 K). The excess Co+ kinetic energy present upon injection is quickly lost through collisions with HZ both inside and immediately before the cell entrance.

The ions are drifted through the 4-cm-long cell with a small, uniform electric field. The field is used to vary the ion drift/ reaction time. The ion's kinetic energy due to the drift field is kept small with respect to its thermal translational energy. This point is discussed more fully below. Pressures of H2 in the cell are measured directly with a capacitance manometer. Cell temperatures are varied by using a flow of heated or cooled N2 from 80 to 580 K. The cell body and the electrically isolated exit plate cap are separately heated (or cooled). The flow through the end cap is varied such that the inlet and exit temperatures of the N2 heat exchange gas are identical for both sections of the cell. This procedure should remove any possibility of significant temperature gradients in the cell. Temperatures are read by using a thin-film platinum resistor suspended in the cell bath gas.22 Cell temperatures are generally stable to better than f0.5 K.

Ions that exit the cell are accelerated slightly (2-3 eV), quadrupole mass analyzed, and collected by using standard ion counting techniques. The quadrupole is computer scanned to yield the parent/product mass spectrum. Peak areas are then integrated to give intensities.

TheExperiment. After thecell temperature is stable, product/ parent ion ratios are measured as a function of decreasing drift field (increasing reaction time) until no change in ratio is found. A series of mass spectra are then recorded at this and longer drift times to accurately determine the product/parent ion ratios. These ratios are converted to equilibrium constants by using

where PH2 is the H2 pressure in torr. The corresponding free energy change is calculated by using

AGO = -RT In Kq (3) The experiment is repeated at a series of temperatures to determine the temperature dependence of AGO. Finally, the entire tem- perature series is repeated several times.

Problems and Sources of Error. Sources of error in these experiments include errors in pressure and temperature mea- surement, effects of Co+ kinetic energy due to injection and the drift field, Co+ excited electronic states, collision-induced dis- sociation and clustering in the gas stream exiting the cell, and, lastly, massdiscrimination in thecell, quadrupole, and/or detector. These are discussed in turn.

Pressure measurement errors in the capacitance manometer head are less than 0.05%, according to a recent calibration. Effects due to thermal transpiration are not important, since the temperature gradient between cell and manometer occurs along a tube, whose diameter (6.4 mm) is much larger than the mean free path in the high-pressure H2 (-4 Temperature gradients in the cell are minimized by the massive copper block structure of the cell. Also, the cell and removable end cap are heated individually, rather than relying on conduction. The

(4)

The increase in Teff at the highest drift fields used was less than 3 K, and at typical fields the increase was about 1 K.

Probably the most serious problems in these experiments arose from the Co+ excited electronic state(s). The states present are the a3F 3d8 ground state, along with the a5F and b3F 4s3d7 first and second excited states. The identities, populations, and behavior of these states have been d isc~ssed .~ At present, it is important to note that the 4s3d7 states both cluster poorly (due to the repulsive 4s electron) and are difficult to collisionally deactivate (due to a lack of low-energy curve crossings with the 3d8 ground ~ t a t e ) . ~ ~ . ~ ~ The effect of a few percent of excited (Co+)* might seem negligible; unfortunately, it has a very large effect on the first cluster equilibrium (Co+ + H2 Co+.H2). Because the Co+.H2 bond energies are large, most of the Co+ reacts to form higher order clusters and only a very small amount of Co+ is present in the equilibrium. Further, since the Co+ ground state is far more efficient at clustering,3J3 the remaining Co+ tends to be largely the excited (Co+)*, and the apparent Kq is unrelated to that of the Co+ ground state. The only solution is to work a t reaction times long enough for essentially complete deactivation to occur. The criterion for "complete" deactivation is for the remaining (Co+)* to be much less than the equilibrium amount of Co+ ground state, (Co+),. Since (Co+), increases with temperature, this means working at the highest temperatures and longest times possible. This requirement restricted the temperature range over which we could observe the first clustering equilibrium and increased the associated uncertainty. On the brighter side, the second and higher clusters were completely unaffected by any (Co+)* and were easily brought into equi- librium.

Effects on equilibria have been reported due to 'freezing out" clusters in the gas stream exiting the cell.25 This reduces the slope of the AGO vs T line a t high temperatures. No such effects were seen in any of the equilibria. Collision-induced dissociation (CID) of the clusters has the same effect at low temperatures. Our data did become nonlinear below a certain temperature (different for each reaction). It is not clear the effect was due to CID, however, since different accelerating fields after the cell produced the same nonlinearity. This effect was also seen in our M+.He/Ne equilibrium data. Since a long, extremely linear set of AGO vs T data exists for all the clusters, the few nonlinear points were ignored.

Mass discrimination due to differential collection probabilities at the cell exit has been shown to be nonexistentS2' Likewise, all ions are counted with equal efficiency, since the detector is operated in its plateau response region. Mass discrimination does occur in the quadrupole, however, and is of two types. First there is mass-dependent transmission through the quadrupole. This results in a fixed error factor in the measured Kq's, which, in turn, produces an error in ASo. The binding enthalpies (A@), however, are unaffected. This point is discussed further in the next section. The second effect results from insufficient mass resolution. Although the cluster peaks are 2 amu apart, tailing from a large peak into an adjacent, very small peak can result in significant error. The extent of tailing depends on peak ratios and is consequently temperature dependent. In order to

54 The Journal of Physical Chemistry, Vol. 97, No. I , 1993

eliminate this potential problem, the peaks in the present experiment were absolutely baseline resolved.

In summary, the only significant source of fixed error in our experiment is the quadrupole mass discrimination. The error increases the uncertainty in our entropy measurements but has little or no effect on our reported bond energies (see next section). The reproducibility of individual AGO, points is better than f O . l kcal ( -2 .5% of the normal AGO ranges in the experiment). Uncertainties in our bond energies (Ws) are discussed below.

Kemper et al.

111. Data Analysis

As noted, eqs 2 and 3 are used to convert the observed ion intensities into AGO vs T plots. These are equivalent to van’t Hoff plots; however, the slope equals A$ and the intercept equals A@, since AG: = MT - TA$. Plotting the data this way allows a fairly accurate determination of A@ (binding energy) using the usual heat capacity corrections. However, to obtain highly accurate Aj$‘s (bond energies), a more sophisti- cated extrapolation of AGO to 0 K is required; Le., the temperature dependence of MT and hsT must be included. This is done by using statistical mechanical calculations of In this calculation the total clustering entropy is given by

The observed slope is ASTOT + R In (mass discrimination), where “mass discrimination” is the ratio of collection efficiencies for product and parent ions. The corresponding enthalpy is given by

In the H2 reactant both the high rotational temperature (87 K) and the interaction between the nuclear and rotational wave function prevent a simple calculation of S R ~ T and CROT.’~ Instead, the rotational partition function was calculated with an exact state summation. The ortho and para H2 populations were assumed to be in thermal equilibrium in the extrapolation to 0 K. That is, the resulting &s represent the reaction of the lowest energy H2.

Those few molecular parameters (bond energies, bond lengths and frequencies, and mass discrimination) that are not well fixed by theoretical calculations or comparison with known systems are now varied until the calculated AGO vs T line matches the experimental data points. As will be seen, usually only a few parameters can be varied enough to affect the fit. Despite the relatively small number of variables, a unique solution might seem impossible. This is partly true for the A S calculation. However, we have shown that the A@ values are extremely insensitive to the fitting parameters, since they depend only on the heat capacities, which are essentially parameter independent. Thus, we expect only small uncertainties in the derived bond energies. This was confirmed for each cluster equilibrium by determining the range of e ’ s resulting from a wide range of frequencies, bond lengths, etc. Also note that the translational entropies and heat capacities are known exactly for all the clusters. Because ASTRANS is by far the largest component in ASTOT, even substantial errors in the’ calculated ASROT or ASvre will have only a relatively small effect on the calculated ASTOT.

IV. Results and Discussion

The derivation of the molecular parameters used in the statistical mechanical calculations for each cluster (structures, bond lengths, frequencies, etc.) is discussed below and a summary is given in Table I. Table I1 lists the A@’s (bond energies) obtained directly from the AGO vs T data plots (Figure 1) and Table I11 lists those from the more accurate statistical mechanical

TABLE I: Bond Lengths and Vibrational Frequencies for Co+*(Hdn

excited-state bond frequencies? energy level:

kcal/mol cluster lengths,“ A cm-I Co+.H2 H-H 0.791 (0.80) 863‘ (909)’ 1 .o:,;”

Co+*(H2)2 H-H 0.783 86oC (X2) 2.0:;:

CO-Hzd 1.662 (1.66) I 2 8 v 3 7 5 4 (3580)s

CO-Hzd 1.722 1 2 8 6 (X2) 39009 (X2) 465h 170:;: (X2)j

Co+.(H2)3 H-H 0.773 66OC c0-H~~ 1.773 9 5 6 Co-Hi 1.809 40008

500h 1 5 0 2 , (X2)i

Co+*(H2)4 H-H 0.77 66oC CO-Hzd 1.77 9 5 6 Co-Hi 1.81 40009

500h 150:,6,0 (X2)’

Co+*(H2)5 & H-H 0.77 44OC Co+*(H2)6 CO-Hzd 1.77 6 5 6

600h 1402°(X2)i

Co-Hi 1.81 41009

Co+.(H2)7 H-H 0.77 20w CO-H~” 1.77 3 0 6 Co-Hd 1.81 42009 c0-H~~ -2.0 6OOh

40::: (X2)‘

“Bond lengths taken from Bauschlicher et a1.I8 except those in parentheses, which are from Perry et aI.l9 Frequencies for Co+.(Hz) from Partridge’Oand thosein parentheses from Perry et a1.I9 E Thenumber given is the energy of the lowest electronic excited state (3A2 in Co+.H2) from Bauschlicher et aL1* The energy difference in Co+*(H2)2 is about one to two times that in Co+.H2. The excited state is not included in the analysis of the third and higher clusters, since the energy difference is very large (see text). Uncertainties indicate the range that could be fit by using mass discriminations between 0.5 and 2.0. dCo+-H2 bond distance for the first two bonds (first bond in Co+-H2). ‘Co+-H2 symmetric stretch. fCo+-H2 asymmetric stretch (H2 rocking). H-H stretch. Internal rotation (hindered rotation). For Co+.(H2)2 it is estimated from a 1.4 kcal/mol well depth; see text. For larger clusters, the frequency is assumed to rise due to increased steric hindrance. Bending mode. This frequency alone was varied to fit the experimental

data since the higher frequency modes had little effect on the calculated AGO. The range shown corresponds to mass discrimination factors between 0.5 and 2.0. j Bond length for third through sixth Co+-H2 bonds.

Bond length of seventh Co+-H2 bond.

TABLE 11: Experimental A@ and AS; Values for CO+*(HZ),I + H2 + Co+-(H2).

n - MT “ - A$“ temp rangeC 1 19.6 f 1 22.0 f 1.0 450-580 2 18.0 f 0.6 24.5 f 0.8 360-580 3 10.6 f 0.4 20.5 f 0.8 300-580

240-430 4 10.4 f 0.6 24.2 i 1.5 5 5.2 f 0.6 22.5 f 1.5 140-270 6 4.7 f 0.6 23.7 f 1.5 100-190

In units of kcal/mol. 7 1.5 f 0.7 18.0 f 4.0 75-115

In units of cal/(mol K). In kelvin

analysis. The observed entropies (slopes) and those calculated from the parameters in Table I are also listed in Tables I1 and 111.

Entropies in the present experiment [20-25 cal/(mol K)] agree well with the few previously measured H2 clustering entropies2 Significant changes in entropy with cluster number are apparent and are largely due to expected changes in ASROT and Mv~B. This is discussed below. The bond energies ( e s ) in Table 111

C0+4H2),, Clusters The Journal of Physical Chemistry, Vol. 97, No. 1 , 1993 55

and 3d - 5p (5.6 -5.8 eV)27 result in hybridization energy costs of about 2.8 eV/bond (square planar, d2p2 hybridization) or 2.6 eV/bond (octahedral, sd2p3 hybridization). Since the Co+-H2 bond in the unhybridized Co+.H2 is only 0.75 eV, hybridization is energetically unfeasible. One exception to this is a small amount of 3 d o - 4 ~ hybridization expected in the first and second clusters. This has the effect of reducing electron density on the bond axis, reducing Pauli repulsion, and thereby slightly increasing the bond strength. This was both p r e d i ~ t e d ~ , ~ ~ . ~ ~ and observed3 in the Co+.He/Ne/Ar systems.

The Co+.Hz ground electronic state is predicted to be 3Az.18 The 3Al excited state is also present 5 1 kcal/mol above 3A2.18 The Co+ reactant ion is collisionally deactivated to its a3F ground state (see the section on problems and sources of error, above). Further, we have shown that even in Co+-He collisions, excited J levels are relaxed via multiple curve crossings.8 Given the stronger Co+-H2 interaction and the large number of collisions, we expect the Co+ reactant ion to be in its lowest a3F4 state. The ratio of electronic degeneracies is then 3 for each of the low-lying Co+.H2 states. Both these states are populated at high temper- atures in the equilibrium. To account for this in the calculation of AGO vs T , two separate equilibria are calculated (with Ai-@ different by 1 kcal/mol). The product populations are then summed to give an observed equilibrium (and AGO vs T plot), which is compared with and fit to the data. The overall effect is to increase the Co+.H2 product degeneracy slightly, although some temperature dependence is present also.

The three vibrational modes in Co+.H2 are treated as follows. Two calculations exist for the H-H stretch frequency, 375430 and 3580 cm-I,l9 somewhat perturbed from that in the H2 neutral (calculated 4385,30 experimental 4395 cm-1 31). However, the corresponding SV~B and C V ~ B terms nearly cancel. This occurs because the high frequency of this stretch prevents significant contribution to SVIB or CVIB in either H2 or Co+.H2 and any noncancellation is truly negligible. This feature of the analysis is common to all the clusters and actually improves with cluster size, since, in the larger clusters, the H2 ligands are even less perturbed.

The remaining two modes are symmetric and asymmetric Co+- H2 stretches. From theoretical calculations, these frequencies are 863 and 1288 c ~ - I . ~ O Perry et al.I9 calculate a stretch frequency of 909 cm-I. (The small reduced mass and strong bond are responsible for the high frequency.) Because of the high frequency, the vibrational modes contribute only -0.9 cal/ (mol K) to ASTOT (-4%). Thus, even substantial errors in frequency will have only a minor effect on ASTOT and the AGO vs T calculation.

From the abovediscussion it is clear that nearly all the molecular parameters in the AGO vs T calculations are either well-known or unimportant in the Co+.H2 analysis. The mass discrimination and the excited-state energy are the only unknowns and were varied to fit the data. Changes in the excited state energy had very little effect on the calculation. Tlie modes, frequencies, and other parameters used in the analysis are listed in Table I . The resulting value of @ is 18.2 f 1.0 kcal/mol. The theoretically calculated values of D, for Co+.H2 are 17.3Is and 18.3 kcal/ mol.Igb Subtracting the difference in zero-point energies (ZPEs) gives DE'S of 15.1 and 16.1 kcal/mol, corresponding to 83% and 89% of our experimental value. These calculations are expected to give bond energies 280% of the true value and the agreement with experiment is thus good.32

Co+*(H2)2. Calculations indicate that bonding in the second cluster is similar to the first.'* The H2-Co+-H2 bond axis is linear. The H2 ligands are staggered to allow electron donation from separate, filled d s orbitals on Co+ (dxz and dJ. The barrier to internal rotation is about 1.4 kcal/mol and results not from steric interference but from the loss of a d s orbital for back- donation. The Co+-H2 bond length is slightly longer than in

0 100 200 300 400 500 600

Temperature (K) Figure 1, Experimental AGO vs T plots for Co+.(H2),-1 + H2 - Co+. (H2)" clustering reactions ( n = 1-7).

TABLE 111: Derived Binding Energies (-@) and AS:, for C O + - ( H ~ ) , ~ + H2 - C O + * ( H ~ ) ~

n binding energy" - 1 18.2f 1.0 20.6 f 1.5 2 17.0 f 0.7 24.5 f 1.5 3 9.6 f 0.5 20.5 f 1.5 4 9.6 f 0.6 25.2 f 1.5 5 4.3 f 0.7 21.9 f 1.5 6 4.0 f 0.7 23.8 f 1.5 7 0.8>0: 18.0 f 4.0

" I n units of kcal/mol. * I n units of cal/(mol K).

show an obvious decrease with cluster size. Perhaps more interesting is the similarity in bond energies between first and second, third and fourth, and fifth and sixth clusters. This can be explained in terms of d-orbital structure and steric interference in the individual clusters.

In the following section we discuss the clusters one by one. It is useful, however, to first briefly present our picture of the bonding as H 2 ligands are added to Co+. Justification for this picture is given in the following sections. The first and second H2 moieties will attach to the half-filled do (d9) orbital, with the H-H bond perpendicular to the bond axis. The H2 ligands three through six attach to the other half-filled orbital, in this case the d6 (dx2+). Again, the H-H bond will be perpendicular to the bond axis. The remaining three filled d orbitals (dxy, dyz, dxz) will be available for A back-bonding into the unfilled o* orbital of the H2 ligands. The details of how the H2 moieties orient relative to themselves and the energy balance between steric interference and maxi- mizing R overlap will be discussed on a case by case basis.

Co+.Hz. A coherent picture of the bonding in Co+.H2 comes from the calculations of Partridgeand Bauschlicher.l* The ground state of the Co+ ion has a d8 configuration. The Hz moiety bonds to the half-filled do (d9) orbital. The H2 internuclear axis is perpendicular to the Co+-H2 bond axis, which maximizes the chargequadrupole interaction. The half-filled orbital maximizes H2 - Co+ electron donation and minimizes Pauli repulsion. Back- donation to the H2 u* orbital is maximized by a filled d r orbital (dxz or dyz) in the Co+-H2 plane. The other half-filled orbital is then a d6 (d, or dxi-p). The two lowest Co+.H2 electronic states arise from these two possible d6 configurations. The energy difference is small ( I 1 kcal/mol). The Co+-H2 bond distance (to the H2 bond midpoint) is calculated to be 1.662 A; the H-H bond length is 0.791 A. The latter is slightly longer than that calculated for neutral H2 (0.740 A), showing the effect of Co+ d r to H2 u* donation. The cluster SROT was easily calculated from the predicted s t r ~ c t u r e . ~ , ~ ~

It is important to note that the Co+-Hl bonds do not involve hybridized 3d/4s/4p orbitals, even in the C O + . ( H ~ ) ~ and Co+. (H2)6 complexes. Promotion energies for 3d - 4 s (0.2-0.5 eV)

56 The Journal of Physical Chemistry, Vol. 97, No. 1 , 1993

Co+.H2 (1 -72 vs 1.66 A), and the H-H bond is slightly shorter (0.781 vs 0.789 A). Despite these indications of weaker Co+-H2 bonds, the calculated De(Co+.H2-H2) is 17.7 kcal/mol, about 0.4 kcal/mol greater than De(Co+-H2) in the first cluster. The reasonprobablyliesin thesmallamount of 3du+4s hybridization discussed above.lBJB.29 The hybridization occurs in the first cluster, but, because the axial electron density reduction is symmetric, the second ligand obtains the increased bond energy without the energy promotion cost. The result is a greater well depth. The effect has been seen in Co+.He2 as welL3 Although the De for removal of the second H2 is greater than that of the first, the observed BE is about 1 kcal/mol less. This is due to the greater zero-point energy in Co+.(H2)2.

The theoretical structure and electronic ground state term (3B2)18allow accuratecalculations OfSRoTandSELfor thecluster. Thus, ASTRANS, ASROT, and ASEL are well determined for the second cluster reaction. No calculation of excited-state energies is available. One might expect a splitting about twice that in the first cluster, however, since two similar H2-d16 interactions are present. In our calculation of AGO we varied the Co+-(H2)2 excited-state energy from 2 to 4 kcal/mol and the ratio of (Co+.H2)* to (Co+.(H2)2)* energies between 1 and 2. No significant effect on I@ was found.

The cluster has nine vibrational modes. Given the large Co+/ H2 mass difference, the individual HZ modes are assumed to be separable. Since the binding energy of the second H2 is very nearly equal to the first, this means the vibrational modes present in the first Co+.H2 clusters are also present in Co+*(H2)2. The contribution from these modes to ASVIB is then near zero. This leaves six new modes to consider. The new H-H stretch in Co+. (H2)2 is again similar to that in the H2 reactant, and again no measurable contribution to QVlB is expected due to the high frequency. Two new Co+-H2 stretches are expected, again with frequencies of -870 and 1280 cm-’ (since the first and second H2 BEs are about the same). An internal rotation is present. It was treated by calculating harmonic oscillator energy levels below the barrier on the basis of the known potential form and barrier height33 and by using free rotor levels above the barrier. Because of the small H2 reduced mass, both sets of levels are very widely spaced. Only one vibrational level exists in the well (w - 465 cm-I) and no levels are near the barrier energy. This validates (largely) our “either vibrationor rotation” analysis. The partition function was then calculated directly from the individual levels. The resulting contribution to is small. The remaining two modes form a degenerate HrCo+-Hz bend. The frequency is expected to be low, given the flat potential and results with Co+- (He)z.3J8 This frequency and the mass discrimination were varied to fit the experimental AGOvs T data since the other parameters are either well-known or have little effect on ASTOT. A bend frequency of 170_:8,0 cm-I was required to fit the data. A summary is given in Table I. The resulting A@ is 17.0 f 0.7 kcal/mol. After subtracting ZPE contributions from the the- oretical &,I8 a predicted A@ of 14.3 f 0.5 kcal/mol for the second clustering reaction is obtained. This is about 84% of the experimental value and again agreement is satisfactory. The individual Co+-H2 bonds are, of course, equivalent with individual bond strengths equal to the average of the first and second @s (17.6 kcal/mol).

A significant increase in the magnitude of AS occurs between the first and second clustering reactions [-24.5 cal/(mol K) vs -20.6 cal/(mol K)]. This is due to a decrease in the positive ASROT term, due in turn to the presence of rotational modes in the Co+.H2 reactant (absent in the Co+ reactant). The effect is reduced by an increase in the positive ASvle for the second cluster. A similar increase in A S increase was found in the Co+ + He/Ne systems.3

CO+-(H~)J. Both theory and experiment show that the third H2 is bound much less strongly than the first two (experimental

Kemper et al.

H

Figure2 Proposed structures for first six Co+.(HZ),clusters. Structures for n = 1 , 2, and 3 are taken from the calculations of Bauschlicher et a1.18

bond energy = 9.6 f 0.5 kcal/mol vs 17.6 kcal/mol). This decrease in bond energy suggests a substantial change in bonding mechanism may have occurred, a conclusion consistent with Partridge and Bauschlicher’s calculations.18 Their predicted structure is a slightly distorted “T” with the third Co+-H2 distance (1.81 A)slightlygreaterthanthefirst two(1.77A). Theoriginal HrCo+-H2 bond angle of 180° is now 157O. Further, the first two H2 molecules are now eclipsed and the third is perpendicular to them (Figure 2). It is clear from this structure that H2-H2 steric interference is significant, since what was the top of a 1.4- kcal/mol internal rotation barrier (the eclipsed form of the first two H2 ligands) is now a minimum on the potential surface.

The third H2 is undoubtedly located at a lobe of the other half filledd orbital (3d6 in Co+-H2). This minimizes electron repulsion on the bond axis and allows A - u* donation from a filled d r orbital as in Co+.H2 and Co+.(H2)2. Compared with the first two Co+-H2 interactions, this configuration gives less electron repulsion (since the single Co+ electron is dispersed over two orbital lobes) but less H2/Co orbital overlap (allowing less H2 electron donation to Co+). The benefit of 3d u- 4s hybridization, which was important for the first two H2 ligands, is now largely lost, since the third H2 is located at the electron density maximum of the 3du/4s hybrid orbital. Thus, at least three factors may be contributing to the weaker third Co+-H2 bond: steric interference, a reduced bonding interaction and reduced r-u* donation to the first pair of H i s due to the eclipsed configuration. Examination of the bond energies in the larger Co+*(H2),, clusters indicates the majority of the reduction is due to steric effects (see discussion of Co.(H2)5+).

It is unlikely that a low-lying excited electronic state similar to those in Co+.H2 and Co+.(H2)2 is present in Co+.(H2)3. Since the third H2 approaches the half-filled d orbital perpendicular to the first bonding axis of the two Hz’s, the two states corresponding to the two possible half-filled d orbitals are widely separated in energy in the Co+*(H2)3 molecule. Similar arguments should also pertain to higher clusters.

Once again, an accurate calculation of ASTRANS, A!~RoT, and ASEL for the cluster is possible. The vibrational analysis is similar to that of the second cluster; Le., that the existing Co+.(H2)2 modes cancel and only five of the six new modes need to be considered. These include two Co+-H2 stretches, an internal rotation, and two bends. The stretch frequencies are scaled down

Co+.(H2), Clusters

to 660 and 950 cm-I to reflect the reduced bond ~t rength .3~ The hindered rotor potential has clearly changed, but no new barrier height is available. Consider, however, that as more H2’s are added, the steric effects will increase. This will increase the internal rotation barrier height, turning these modes into higher frequency vibrations with less and less effect OnSViB. The internal rotation mode frequency was thus increased to 500 cm-I. This again leaves a low-frequency bend as the single important fitting variable. As in the above clusters, its frequency (and the mass discrimination) was varied over a wide range to see the effect on ~. The resulting parameters are listed in Table I. The experimental binding energy was determined to be 9.6 f 0.5 kcal/mol. The theoretical D, for the third H2 is 10.7 kcal/mol.I8 Making the usual ZPE correction gives a predicted bond energy of about 7.4 kcal/mol, about 78% of the experimental value. The ZPE correction becomes increasingly uncertain in these larger clusters, especially for internal rotation (where the barrier is now unknown). Also, the theoretical calculations for the Co+*(H2)3 cluster were not as exacting as those for the first two clusters.I8 These factors may account for the greater discrepancy between theory and experiment.

The A S for the third clustering reaction is significantly smaller than that for the second [20.5 cal/(mol K) vs 24.5 cal/(mol K)]. This is due primarily to the large increase in the (positive) ASROT term, due, in turn, to a large increases in the third moment of inertial in the T-shaped Co+.(H2)3. The addition of the lower frequency bends is also responsible.

CO+. (H~)~ . In the absence of calculations, a structure for Co+. ( H Z ) ~ must be assumed. The similarity between the binding energies of the third and fourth hydrogens indicates a similarity in bonding. The large influence of steric effects in the third cluster indicates that minimizing steric interference will be a large extent determine the structure of the fourth cluster. The most likely structure is then approximately square planar. The H2 ligands on each bond axis are eclipsed and perpendicular to those on the other axis (Figure 2). This configuration minimizes steric interaction at a cost of about 1.4 kcal/mol for each pair of H2 ligands due to loss of A back-bonding. The bond length between the third and fourth H2 ligands and Co+ was assumed equal to that of the third H2 in Co+-(H2)3. The slightly shorter Co+-H2 bond length for the first two H2 ligands was taken from

Some uncertainty exists in this structure. However, the effect on ASROT is suprisingly small due to an increasing cancellation of product and reactant cluster SROT. The SROT from the H2 reactant becomes the dominant term in the equilibrium between larger clusters. As discussed above, the Hz SROT is calculated exactly. Furthermore, errors in cluster structures that lead to errors in SROT lead to constant, non-temperature-dependent errors in ASROT. These require small adjustments in the mass dis- crimination factor used but do not affect the extrapolation to 0 K or the values of A@ (bond energies).

The vibrational analysis in this cluster follows that of Co+. (H2)3. Five active modes are assumed to add in the clustering reaction. Two are Co+-H2 stretches which have frequencies that scale with bond energy. One mode is an internal rotation, treated as above, and two are low-frequency bends. The bend frequency and the mass discrimination arevaried to match the experimental AGO vs T plots. As usual, the fitting parameters are listed in Table I.

The resulting experimental A@ for this clustering reaction is 9.6 f 0.6 kcal/mol-equal to that of the third cluster. This is expected since, in the proposed square-planar structure, the third and fourth H2 ligands have essentially identical Co+-H2 bonds and Hz-H2 steric interference.

The increase in A S for the fourth cluster (Table 11) again reflects a decrease in the positive ASROT relative to the third cluster. In this and succeeding clusters, ASvle is nearly constant

Co+*(H2)3.

The Journal of Physical Chemistry, Vol. 97, No. 1, 1993 57

since Co+.(H2)3 through Co+.(H2)7 each add five new active vibrational modes (neglecting the high-frequency H-H stretch). The modes and frequencies are similar for all the clusters (Table I). Thus changes in ASROT cause nearly corresponding changes in ASTOT.

Co+.(H2)s+. The experimental binding energy of the fifth H2 (4.3 * 0.7 kcal/mol) is much lower than that of the third and fourth H2 ligands (9.6 kcal/mol). The expected structure is a slightly distorted square pyramid with the fifth H2 at the apex. The bond axes of adjacent H2.s are again expected to be perpendicular to minimize steric interference (Figure 2). For the same reason, the four base H2’s are probably pushed below the true base plane (similar to the distortion in CO+.(H~)~) . The bond length and vibration analyses follow those in CO+. (H~)~ , with the fifth Co+-H2 bond length assumed equal to the fourth. The usual cancellation in SVIB occurs, leaving only the low- frequency vibration (and the mass discrimination) as data fitting parameters. This procedure is followed for the remaining clusters.

In this assumed structure, the orientation of d orbitals with respect to the fifth H2 is similar to that of the third and fourth H2 ligands. The H2 ligands all approach lobes of the same half- filled d orbital and have a filled d orbital available for A back- bonding. The bonding of the third through sixth H2’s is thus very similar. It appears then that the observed reduction in bond energies is due largely to steric effects. We can calculate what the expected reduction in binding energy would be for the fifth H2, assuming that the observed reduction in bond energy for Co+.(H2)3 and Co+.(H2)4 is due entirely to steric interference. In Co+*(H2)4 there are four identical H2-Hz interactions. If we assume that, without steric interference, the third and fourth H2 ligands (which are eclipsed) have bond strengths about equal to the average of the first and second minus the internal rotation barrier (17.6 kcal/mol- 1.4 kcal/mol = 16.2 kcal/mol) and we note that with steric interference the observed bond strengths are each 9.6 kcal/mol, then steric interference reduces bonding by about 3.3 kcal/mol per Hz-H~ interaction. In Co+*(H2)5 the fifth H2 interacts with four H2 ligands and a binding energy of 17.6 kcal/mol - (4 X 3.3 kcal/mol) = 4.4 kcal/mol is predicted-close to the experimental value of 4.3 kcal/mol. This indicates that the observed bond energy reduction in C O + . ( H ~ ) ~ is apparently due more to steric interference rather than to a change in bonding.

Co+-(H&+. Similar bond energies are found for Co+*(H2)4- H2 and Co+-(H2)s-H2 (4.3 and 4.0 kcal/mol). The only reasonable structure for Co+-(H2)6 is an octahedron. All six bonds are probably not equivalent (since the necessary d2sp3 hybrid- ization is energetically unfeasible). The two original Co+-H2 bonds are most likely equivalent and somewhat stronger than the last four. On the basis of the Co+.(H2)3 calculations,l8 the difference in bond lengths is probably small (less than 5%).

A predicted binding energy of 3.0 kcal/mol can be calculated by using the steric interference model above. The H2 ligand added to Co+*(H2)5 interacts with four H2 ligands (those in the plane) and is eclipsed with the H2 ligand along its bonding axis. The resulting bond energy predicted is 17.6 - 4(3.3) - 1.4 = 3.0 kcal/mol. The model thus predicts a decrease in bond energy between Co+-(H2)4-H2 and Co+.(H2)s-H2, but the predicted magnitude is rather too large.

One more interesting point about this cluster. If one assumes each HZ ligand contributes two electrons to this complex, a 20- electron complex is formed. This is an apparent violation of the 18-electron rule.

Co+-(H2)7. Very limited data are available since the cluster is formed only at the lowest temperatures. The observed binding energy is about 0.8 kcal/mol-much weaker even than adding the fifth and sixth H2 ligands. This result is reasonable. Given the strong H2-H2 steric interaction, the seventh H2 cannot be placed at the same distance from Co+ as the first six. Placing

58 The Journal of Physical Chemistry, Vol. 97, No. 1, 1993

the seventh Hz outside the octahedral sphere prevents any significant u- or ?r-bond interaction with the Co+, leaving only the weaker charge-induced dipole and charge-quadrupole in- teractions. A very large reduction in binding energy is thus expected.

At low temperatures, this results in a preponderance of Co+- (H2)6 in the equilibrium. (All previous clustering steps have large, negative AGO'S.) This observation is consistent with Lessen and Brucat's observation that Co+.Ar6 appeared far more abundant than smaller or larger clusters.35 They interpreted their results to imply a covalent interaction occurring in the octahedral cluster (leading to an enhanced stability) was at least partly responsible for the strongly enhanced Co+.Ar6 intensity. However, given the large difference in IPS between Co and Ar (7.86 and 15.76 eV) this seems unlikely. The work presented here indicates that such a cluster sizedistribution is expected, since the Co+.Ar6 (and Co+.(H2)6) lie a t the end of a series of very favorable equilibria, while the next step is unfavored due to its very low binding energy. The sixth Ar is probably not more strongly bound than the first five, but it i s much more strongly bound than the seventh.

Kemper et al.

( 5 ) Lessen, D.; Brucat, P. J. Chem.Phys. Lett. 1988,152,473;J. Chem.

(6) Lessen, D.; Asher, R. L.; Brucat, P. J. Int. J . MassSpectrom. Ion

(7) Kemper, P. R.; Bowers, M. T.J. Phys. Chem. 1991,95,5134;J.Am.

( 8 ) von Helden, G.; Kemper, P. R.; Hsu, M.-T.; Bowers, M. T. J . Chem.

(9) Wu, C. H. J . Chem. Phys. 1979, 71, 783.

Phys. 1989, 90, 6296; J . Chem. Phys. 1989, 91, 4522.

Proc. 1990, 102, 331; Chem. Phys. Lett. 1991, 177, 380.

Chem. Soc. 1990, 112, 3231.

Phys. 1992, 96, 6591.

(IO) Elkind, J. L.; Armentrout, P. B. J . Phys. Chem. 1987,91, 2037 and references therein. See also: Armentrout, P. B. In Gas Phase Inorganic Chemistry; Russell, D. H., Ed.; Plenum Press: New York, 1989; pp 1-42.

( I 1) Morse, M. D.; Geusic, M. E.; Heath, J . R.; Smalley, R. E. J . Chem. Phys. 1985, 83, 2293. Zakin, M. R.; Cox, D. M.; Whetten, R. L.; Trevor, D. J.; Kaldor, A. Chem. Phys. Lett. 1987, 135, 223. Whetten, R. L.; Zakin, M. R.; Cox, D. M.; Trevor, D. J.; Kaldor, A. J . Chem. Phys. 1986,85, 1697.

(12) Liu, K.; Parkes, E. K.; Richtsmeier, S. C.; Pobo, L. G.; Riley, S . J. J . Chem. Phys. 1985, 83, 2882. Richtsmeier, S . C.; Parkes, E. K.; Liu, K.; Pobo, L. G.; Riley, S . J. Ibid. 1985,82, 3659. Parks, E. K.; Nieman, G. C.; Pobo, L. G.; Riley, S. J. J . Phys. Chem. 1987, 91, 2671.

(13) Alford, J. M.; Weiss, F.D.;Laaksonen,R.T.;Smalley,R.E.J.Phys. Chem. 1986,90,4480. Elkind, J. L.; Weiss, F. D.; Alford, J. M., Laaksonen, R. T.; Smalley, R. E. J . Chem. Phys. 1988, 88, 5215.

(14) Kubas,G. J.; Ryan, R. R.;Vergamini, P. J.; Wasserman, H. J. J.Am. Chem. SOC. 1984, 106, 451. Wasserman, H. J.; Kubas, G. J.; Ryan, R. R. Ibid. 1986,108, 2294. Kubas, G. J.; Ryan, R. R.; Wrableski, D. Ibid. 1986, 108, 1239. Kubas, G. J . ; Unkefer. C. J., Swanson, B. I.; Fukushima, E. Ibid. 1986, 108, 7000.

(15) Crabtree, R. H.; Hamilton, D. G. Adu. Organomet. Chem. 1988,28, 299.

(16) Unpublished data of Crabtree, R. H.; Hamilton, D. J., quoted in ref 15, p 312.

(17) Crabtree, R. H. Acct. Chem. Res. 1990, 23, 95. (18) Bauschlicher, C. W.; Partridge, H.; Langhoff, S. R. J . Phys. Chem.

1992, 96, 2475. (19) (a) Niu, J.; Rao, B. K.; Jena, P. Phys. Reu. Lett. 1992,68,2277. (b)

Perry, J.; Ohanissien, G.; Goddard, W. A. 1992, private communication. (20) Rappt, A. K.; Upton, T. H. J . Chem. Phys. 1986,85, 4400. (21) Kemper, P. R.; Bowers, M. T. J . Am. SOC. Mass Spectrosc. 1990,

(22) Part # TFD, Omega Engineering, Inc., Stamford, CT. (23) van Koppen, P. A. M.; Kemper, P. R.; Bowers, M. T. J . Am. Chem.

Soc., in press. (24) The Co+ excited 4s3d' states do not measurably deactivate in He

collisions. In Ne the rate is barely measurable, about 1 X cmg/s.g In both these cases, equilibria could be measured easily since the Co+ electronic state population remained essentially unchanged. In H2. however, the deactivation rate is too fast to be ignored and tooslow for efficient deactivation to ground state.

I , 197.

(25) Meot-ner, M. Private communication. (26) McQuarrie, D. A. Statistical Mechanics; Harper and Row: New

York, 1976. (27) (a) Moore, C. E. Atomic Energy Leuels; US. National Bureau of

Standards: Washington, DC, 1952; Circ. 467 ( U S . Nat. Bur. Stand.). (b) Sugar, J.; Corliss, C. J . Phys. Chem. ReJ Data 1981, I O , 1097.

(28) Bauschlicher, C . W.; Partridge, H.; Langhoff, S. R. Chem. Phys. Leu. 1990, 165, 272.

(29) Bauschlicher, C. W.; Langhoff, S. R. Int. Reo. Phys. Chem. 1990, 9, 149.

(30) Partridge, H., private communication, 1992. The frequencies were calculated by using a harmonic oscillator approximation fitted to a nine-point sample of the MCPF potentials discussed in ref 18.

(3 1 ) Herzberg, G. Molecular Spectra and Molecular Structure I . Spectra of Diatomic Molecules, van Nostrand: Princeton, NJ, 1950.

(32) Partridge, H., private communication, 1991. (33 ) Davidson, N.StatisticalMechanics; McGraw-Hill: New York, 1962;

p 196. (34) A first-order correction to the vibrational frequencies was calculated

according to w a (BE/p,)'12. This assumes the force constant is directly proportional to the binding energy.

(35) Lessen, D.; Brucat, P. J. Chem. Phys. Left . 1988, 149, 10.

V. Summary From temperature-dependent equilibrium measurements, bind-

ing energies have been determined for the addition of one through seven hydrogen molecules to Co+. The Co+ ion does not insert in the H-H bonds and the product ions are consequently relatively weakly bound Co+.(H2)" clusters. Assuming two electrons for each Hz ligand, the Co+.(H2)6 complex violates the 18-electron rule.

A statistical mechanical fitting of the AGO vs Tdata was used to analyse the data and accurately determine A@ (binding energy) and ASo. The results agree well with theoretical calculations on Co+.(H2)1,2,3 by Partridge and Bauschlicher.18

The experimental binding energies decrease in a pairwise fashion with cluster size: Co+.(H2)1,2 - 17.6 kcal/mol, Co+. (H2)3,4 -9.6 kcal/mol, Co+'(H2)5,6 -4.2 kcal/mol. Theseventh Hz was far more weakly bound, indicating the start of a new solvation sphere.

The majority of the binding energy reduction and the observed pattern can be explained by a simple model of H2-H2 steric interference, although changes in bonding and hybridization also probably contribute to a lesser extent.

Acknowledgment. Support of the National Science Foundation under Grant CHE91-19752 is gratefully acknowledged. We also thank Dr. Harry Partridge for communicating results prior to publication.

References and Notes ( I ) Kebarle, P. J . Am. Soc. Mass Spectrosc. 1992, 3, I . (2) Keesee, R. G.; Castleman, A. W., Jr. J . Phys. Chem. Ref. Data 1986,

(3 ) Kemper, P. R.; Hsu, M.-T.; Bowers, M. T. J . Phys. Chem. 1991,95, IS, 1011.

10600. (4) Partridge, H.; Bauschlicher, C. W.; Langhoff, S . R. J . Phys. Chem.

1992, 96, 5350.