J. Phys. Chem. 1993,97, 5890-5896
5890
Computational Study of the Transition State for H2 Addition to Vaska-Type Complexes (frsn~-Ir(L)2(CO)X): Substituent Effects on the Energy Barrier and the Origin of the Small H2/D2 Kinetic Isotope Effect Faraj Abu-Hasanayn, Alan S. Goldman,’ and Karsten Krogh-Jespersen’ Department of Chemistry, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08903 Received: January 19, 1993
Ab initio molecular orbital methods have been used to study transition state properties for the concerted addition reaction of H2 to Vaska-type complexes, trans-Ir(L)z(CO)X, 1 (L = PH3 and X = F, C1, Br, I, CN, or H; L = NH3 and X = C1). Stationary points on the reaction path retaining the trans-12 arrangement were located at the Hartree-Fock level using relativistic effective core potentials and valence basis sets of double-b quality. The identities of the stationary points were confirmed by normal mode analysis. Activation energy barriers were calculated with electron correlation effects included via Moller-Plesset perturbation theory carried fully through fourth order, MP4(SDTQ). The more reactive complexes feature structurally earlier transition states and larger reaction exothermicities, in accord with the Hammond postulate. The experimentally observed increase in reactivity of Ir(PPh&(CO)X complexes toward H2 addition upon going from X = F to X = I is reproduced well by the calculations and is interpreted to be a consequence of diminished halide-to-Ir ?r-donation by the heavier halogens. Computed activation barriers (L = PH3) range from 6.1 kcal/mol (X = H ) to 21.4 kcal/mol (X = F). Replacing PH3 by NH3 when X = C1 increases the barrier from 14.1 to 19.9 kcal/mol. Using conventional transition state theory, the kinetic isotope effects for H2/D2 addition are computed to lie between 1.1 and 1.7 with largervalues corresponding to earlier transition states. Judging from the computational data presented here, tunneling appears to be unimportant for H2 addition to these iridium complexes.
Introduction The addition of H2 to transition metal complexes is a fundamental elementary step in many catalytic systems.’ Factors influencing the energetics of Hz activation by a metal complex may exert considerableinfluenceon the catalytic activity of such systems, and such factors may also be of direct relevance to processes involvingthe activationof C-H, Si-H, or other nonpolar bonds. Crucial to any rational catalysis design is the a priori knowledge of substituent effects on the energetics of the elementary reactions that constitute a catalytic cycle. A significant step toward computer-assistedcatalysis design would be realized if this information could be obtained accurately from well-founded theoretical models. Recent developmentsin computationalquantum chemistry have made it possible to apply ab initio molecular orbital theory to investigate properties of transition metal compounds with chemical relevance.2 For example, the systematic use of effective core potentials (ECPs) to eliminate the explicit treatment of the numerous corelike electrons makes high-quality calculations feasible for large molecules at moderate computational expense^.^ These potentials also take into account some of the relativistic effects that become important in the heavier atoms.4 In the present work, ab initio molecular orbital theory employing relativistic ECPs has been used to elucidate the transition state properties for the concerted additionreaction of H2 to Vaska-typecomplexes, tran~-1r(L)~(CO)X, 1 (L = PH,; X = F, C1, Br, I, CN, or H). The effect of varying the substituent L has also been investigated by replacing PH3 with NH3 when X = C1. Experimental data on the thermodynamics and kinetics of this reaction system are available, which can be used to gauge the accuracyof the employed methods. Such evaluations may furthermore provide guidance concerningthe reliability of future results obtained by analogous computational methods on reactions where experimental data are not available. The literature describing theoretical studies on H2 activation by various transition metal ions and complexes is sub~tantial.~-~ Previous theoretical studies on H2 activation by d8 square planar
complexes have focused primarily on the general mechanism of the activation process.6 Hall et al. using ab initio methods have recently discussed the stereospecificity of H2 addition to 1 and other related Ir systems.’ Our intent here is to use ab initio electronic structure calculations to (a) fully characterize the transition state for H2 addition to 1 and obtain quantitative estimates of substituent effects on the activation barrier, (b) provide a qualitative interpretation of the reactivity trend, and (c) investigate the origin of the small observed H2/D2 kinetic isotope effect. Substituent effects on the thermodynamicsof this addition reaction have been briefly discussed elsewhere.*
Computational Methods Ab initio electronic structure calculations9were carried out with the GAUSSIAN 90 packageloon the Cray-YMP computer at the Pittsburgh Supercomputer Center and on a local Convex C220 minisupercomputer. Stationary points on the potential energy surfaces were located at the single determinant restricted Hartree-Fock (HF) level using energy gradient methods.” All geometrical parameters were optimized within appropriate symmetry constraints (C2, for reactants; C, for transition states and products). Normal mode analysis was carried out to verify the identity of the located stationary points. The vibrational frequencies were also used to obtain zero-point energies (ZPE) and in the computation of kinetic isotope effects. Relativistic effective core potentials (ECPs) generated by Ermler, Christiansen, and co-workers12were used on all nonhydrogen atoms. In previous work, we and other researchers have found these potentials accurate and reliable in describing the electronic and structural properties pertaining to a variety of complexes.I3 Two types of ECPs are available for atoms with more than 18 electrons. One type, ECP- 1, has a larger number of core electrons than the other, ECP-2. The iridium ECP-1 has 68 electrons in the core, leaving only thevalence 5d and 6s electrons for explicit treatment, while the Ir ECP-2 has 60electrons in the core, thus adding the penultimate shell of 5s25p6electrons for explicit description with basis functions. It has been argued
0022-365419312097-5890%04.00/0 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 22, 1993 5891
TS for H2 Addition to Vaska-Type Complexes recentlyI4that calculations using ECP-1 type potentials tend to overestimate the correlation energy due to the absence of nodes in the valence orbitals, and the use of ECP-2 potentials has been recommended. Our comparison of the Ermler-Christiansen ECPs in studies of H2 addition to 1(X = C1 or I) has shown that ECP-2 is more repulsive in character than ECP- 1, leading to longer bonds and lower reaction energiesthan measured experimentally.* However, reaction energies obtained from either ECP compare reasonably well with experimental data provided that certain additive corrections are included. More importantly, the comparison has shown that the experimental substituent effects on the reaction energies are accurately reproduced by either ECP. We conclude that, in the present system and for the purpose of elucidating substituent effects, the use of ECP-2 does not exhibit any obvious advantages relative to ECP- 1. Accordingly, in the present study the more economical ECP-1 potential was used on all Ir, Br, and I atoms. The Gaussian basis sets provided with the ECPs were employed for the description of the valence electrons. In geometry optimizations,the iridium basis set12dwas contracted as (3s,3p,4d) (1,1,1/2,1/3,1) and the basis sets on all other non-hydrogen atoms (C, N, 0,F, P, C1, Br, and I) were split todouble-{quality by liberating the outermost primitive into a separate function: (4s,4p) (3,1/3,1) for C ,N, 0,F, and Pl2a (3s,3p) (2,1/2,1) for Brl2b and I.lZc Hydrogen atoms in the H2 molecule or bonded directly to the metal were described by the 31 1G basis set,lSa while hydrogens bonded to phosphorus or nitrogen carried the minimal STO-3G set.Isb Electronic correlation energy contributions were estimated via Moller-Plesset perturbation theory applied fully through fourth order, MP4(SDTQ),16 at the optimized RHF geometries. In these calculations, which are intended to provide improved activation and reaction energies, the double-{ or better quality basis sets described above were augmented by an additional diffuse set of d functions on iridium (exponent = 0.038) and diffuse sets of sp functions1Scon the formally anionic substituents (X) and the hydrogens from H2.
-
-
-
Results and Mscwion Transition State Struchves and Activation Energy Barriers. The addition of H2to Vaska-type complexes is commonlyaccepted to occur via a concerted reaction mechanismI7 where H2 approachesthe metal center latitudinally, as illustrated in 2. This geometrical approach has also been proposed for H2 addition to other systems18and has received experimental support from the isolation and characterizationof molecular hydrogen complexe~.'~ The ci~,frans-(H)2Ir(L)~(CO)X isomer (3a) is produced when H2 adds to 1 parallel to the X-Ir-CO axis (2a).
TABLE I: Computed Transition State (4a) Geometrid Parameters for H2 Additioa to b.a4b(PH3)2(CO)Xa x Ir-Ha Ha-Hb HbIrX HJrC XkC 0.858 82 108 1.829 142 F 1.736 CI Br
I H CN Clb
1.914 1.988 2.066 2.152 1.972 1.953
2.001 2.092 2.175 2.247 2.075 2.050
H
I
C
I
0
2.
L1
\
3 .
H
75 74 75 73 78 74
113 112 112 102 102 117
150 152 153 164 157 146
a Bond lengths in angstroms; bond angles in degrees. PH3 replaced by NH3.
TABLE Ik Computed (L = PH3) and ExperiWntrl (L = PW3) Activation and Reactioa Energies (kd/mol) for H2 Addition to Ir(L)2(CO)Xa x AE& M$,, AH$p4 AHHt;, AE;; AEK4 m K 4 me:; F C1 Br
I CN
H Clf
21.9 13.9 12.0 11.6 14.0 7.8 16.7
20.4 13.3 11.2 9.2 7.6 6.0 18.7
21.4 14.1 11.9 9.8 7.4 6.1 19.9
-25.8 12) 11' -34.2 lZe -36.2 6' -39.3 -38.3 -45.4 -28.9
-13.6 -22.0 -24.1 -27.3 -28.3 -38.8 -12.8
-10.4 -18.4 -20.1 -23.3 -24.9 -35.3 -9.6
-14d -17d -19d -18'
a 'HF" and 'MP4" refer to Hartree-Fock and MPYSDTQ) values, respectively;enthalpies ( m M p 4 ) were obtained by adding corrections for zero-point energies and thermal excitations (298 K) to u M p 4 values. b Measured in ~ h l o r o b c n z e n e . ~ Measured ~~ in Reference 17b. e Reference 8. fPH3 replaced by NH3.
the cis,cis-(H)2Ir(L)2(CO)X isomer (3b) that arises from H2 addition perpendicular to the X-Ir-CO axis (2b). Only the parallel approach (2a) leading to the cis,trans isomer (3a) is included in this study. Consideration of this path avoids possible complications from electronic and steric factors affecting the perpendicular path, effects that would not be properly accounted for when PH3 is used as the computational model for the bulkier phosphines used experimentally. Transition states (4) were located for H2 addition to 1 (L = PH3 and X = F,C1, Br, I, H, or CN; L = NH3 and X = Cl), and normal mode analyses confirmed that each stationary point possessed just one imaginary frequency.22
L 1.
H -H
0.777 0.766 0.759 0.757 0.772 0.771
4b
The vector components of this mode are dominated by a relative translation of the H2 molecule with respect to the Ir fragment (Sa), but the mode also contains small contributions from the bending of the CO-Ir-X moiety. A closely related transition state has been reported by Morokuma et al. for H2 addition to F?(pH3)2.23 H-H
c-H-H
I
L 2b
3b
This isomer is in all reported cases the experimentally observed thermodynamic product. When X = halogen and L = PMej20a, PPh3,20borphosphite,2h3a is also the kinetically favored product. On the other hand, in the case of X = H, L = PPhs21aand when X = Me21bor Ph20a and L = PMe3, then the kinetic product is
Table I includes the important geometrical parameters for the transition states (4) optimized at the H F level. Table I1 provides pertinent activation and reaction energies obtained at both H F and MP4(SDTQ) levels with and without corrections for zeropoint energy differences and thermal excitations (298 K). The
5892 The Journal of Physical Chemistry, Vol. 97,No. 22, 195'3
transition states occur early along the reaction path and typically possess Ir-H distances of ca. 2 A and Ha-Hb bond lengths only about 5% larger than that computed in free H2 (0.732 A). In the product, 3a, the Ir-H Bond length is 1.6A and the nonbonded Ha-& distance is 2.1 A. The average Ir-H bond length in 4 is comparableto the 1.9-Avalueobservedfor the W-H bond length in the molecular H2 complex W(C0)3(P1Pr3)2(H2).19a If the H2 reactant is regarded as a single ligand, then the transition state geometry may be described as bipyramidal with an angle near 90' between H2 and substituent X; this view is emphasized in 4b. Crabtree et alO2Oa have presented a closely related viewpoint in their discussion of the stereospecificity of Hz addition to 1 by invoking a trigonal-bipyramidalH2intermediate. A direct search for a molecular H2 precursor complex when X = C1 proved negative, however. It is notable that if the axis connecting the Ir atom with the midpoint of the *H2ligand" is taken as a reference, then the CO group in the transition state (4a) may be viewed as "more bent" from theoriginal X-Ir-CO axis than the substituent X. In 4a, the H&X angle is near 75' and remains close to 90' throughout the addition process, whereas the HaIrC angle is near 110' and Ha appears to be synchronously following the bending motion of the CO group to the product geometry. Structural trends are readily extracted from the data obtained on 4 in the halogen series (X = F, C1, Br, and I; Table I), and they are seen to conform well with expectations based on the Hammond postulate.24 With increasing reaction exothermicity (Table 11), the transition states are located earlier along the reaction path and are more reactantlike in geometrical structure. For example, H2 addition to the iodo complex is the most exothermic reaction within the halogen series (mgp4 = -23.3 kcal/mol) and has a transition state structure characterized by Ha-& = 0.759 A, Ir-Ha = 2.066 A, and Ir-Hb = 2.175 A. The computed exothermicity decreases by ca. 3 kcal/mol when Br is substituted for I and by about 2 kcal/mol upon going from Br to C1. Accordingly, in 4 small increases in the H,-Hb distance (0.766 A, X = Br; 0.777 A, X = C1) are computed and the Ir-H distance decreases slightly, Ir-Ha = 1.988 A when X = Br and h-Ha = 1.914 A for X = C1. The exothermicity is significantly less for addition to the fluoro complex, H4np4= -10.4 kcal/mol, which has the latest transition state in the halogen series characterized by a noticeable lengthening of the H2 bond (HaHb = 0.858 A) and shorter distances to the Ir metal (Ir-Ha = 1.736 A; Ir-Hb = 1.829 A). In the transition state, the H-H stretching mode from the free H2 molecule (v = 4580 cm-I) develops into an in-plane HMH bending mode (5b). As the transition state becomes late and the H-H bond increasingly cleaved, the frequency of this mode decreases; for example, the values are 4090 and 2910 cm-I for X = I and X = F, respectively. The relative position of the transition state, early vs late, is also uniformly reflected in the XIrC angle, which is computed to be near 150' for X = I, Br, and C1 but near 140' for X = F; this angle approaches 95' in the products. The contribution of COIr-X angle bending to the imaginary mode characterizing the reaction path (Sa) also grows as the lateness of the transition state increases (X = I F). The complex with X = H has the most exothermic reaction in the entire series and has an early transition state with markedly long M-H bonds (2.1 52 and 2.247 A) and a barely stretched H2 moiety (H-H = 0.757 A). The reported activation barrier for H2 addition to trans-Ir(PPh3)2(CO)X is near 11 kcal/mol when X = C1 or Br.I7 At the HF level, the computed barriers (L = PH3) for these two substituents, MA,, are 13.9 and 12.0 kcallmol, respectively, and remarkably close to the experimental values. Neither correlation nor ZPE corrections have any significant influence on the activation barriers for this reaction, in marked contrast to calculations on the overall thermodynamics. The reaction exothermicities are diminished by ca. 10 kcal/mol when correlation is included and by an additional 4 kcal/mol from ZPE
-
Abu-Hasanayn et al. corrections.8 A substantial part of the insensitivity in the computed activation energies can be attributed to the early character of the transition state and the complex still resembling the separate reacting fragments. The computed activation energies, AHhp4,for the series of halide complexes decrease as the substituent is changed from C1 (14.1 kcal/mol) to Br (1 1.9 kcal/mol) to I(9.8 kcal/mol). This is in good agreement with the known experimental trend, where the rate constant values are reported to be 0.93 (Cl), 14.3 (Br), and >IO0 (I) M-l s-l (T = 303 K, 1 atm of H2 in b e n ~ e n e ) . l ' ~ , ~ ~ The fluoro complex is computed to possess a much higher barrier (21.4 kcal/mol). This is consistent with the fact that there are no reports of HJr(PR&(CO)F complexes, although their nonexistence is more likely due to unfavorable thermodynamics (rather than kinetics) of H2 addition to the fluoride (see above). The low barrier computed for X = H (6.1 kcal/mol) is in accord with the very high reactivity reported for the corresponding hydrido ~omp1ex.l~~ The activation barrier when X = CN (7.4 kcal/mol) is computed to be close to that for X = I (9.8 kcal/ mol). Qualitative observations (L = PPh3) show that the cyano complex reacts much faster than the chloro complex, but a direct comparison with the iodo complex has not been made since both complexes add H2 rapidly.* Amine complexes analogous to the phosphine complexes are unknown. The model computationspredict such complexesshould be much less reactive toward H2 addition, the barrier for Ir(NH3)2(CO)C1being1 9 . 9 ~ 14.1 s kcal/molfor thePH3complex. For all substituents, the entropy of activation is computed to be around -25 eu, a value typical for bimolecular reactions. Electronic Structureof the Transition States and Rationalization of the Reactivity Trend. The general bonding scheme between the hydrogen molecule and a transition metal complex has been discussed in many places.6 Briefly, the scheme involves a-type bonding between the doubly occupied u(H.2) MO and an empty metal orbital as well as n-type bonding between a doubly occupied metal d orbital and the empty u*(H2) M0.26 Both interactions contribute to H2 bond cleavage. The activation barrier in the addition reaction to ds square-planar complexes arises primarily from the repulsive interaction between the a(H2) and a doubly occupied metal d orbital. The rather small increase in the H2 bond length computed for 4 implies that electron transfer to and from the H2 molecule is negligible, a result supportedby electronic chargedistribution analyses using the natural bond orbital (NBO) s ~ h e m e . This ~ ~ .method ~ ~ assigns overall charge neutrality to the H2 unit (net charge for all transition states around -0.02 except when X = F (-0.09) or L = NH3 (-0.04)) with localized a(H2) and a*(H2) orbital occupancies very close to two and zero electrons, respectively. The small variations observed in orbital occupanciesstill exhibit a regular trend consistent with the location of the transition state (early vs late). For example, in the series X = I, Br, C1, and F, the a(H2) occupancies are 1.96, 1.95, 1.94, and 1.88 electrons, whereas the a*(H2) occupancies are 0.04, 0.05, 0.06, and 0.18, respectively, with small occupancies of Rydberg-type orbitals making the final net charge on the H2 unit slightly negative for X = C1, Br, and I. Thus, in the transition state the Ir metal atom still has four doubly occupied 5d orbitals. A pictorial description of bonding in such a situation is not obvious and is complicated further by the low symmetry of the complex (C,) and the high degree of orbital mixing on the metal. For example, the d,2, d , ~ ~ 2and , d, orbitals are all of a' symmetry, and it is impossible to designate any one of them as the unique empty metal orbital. In order to elucidate some qualitative features of bonding in the transition state, it is helpful to regard the structure as a severely distorted trigonal bipyramid with an empty metal d,z orbital and the PH3 ligands along the x-axis (4b). Such a geometry allows one of the two filled equatorial metal 5d orbitals (roughly a d,, dX2~y2 hybrid with antibonding character) to be polarized toward
TS for H2 Addition to Vaska-Type Complexes the CO group, thus enhancing Ir back-donation to CO and reducing the electron repulsion in the plane of H2 addition. Polarization of equatorial orbitals in five-coordinate bipyramidal complexes has been invoked to rationalize the structures and relative stabilities of isomeric five-coordinatec~mplexes.~~ When X = C1, a decrease in the carbonyl stretching frequency occurs from the reactant (2047cm-I) to the transition state (2026cm-I), and the total negative charge on the CO group increases from -0.21 to -0.30,Table 111. Both changes support the idea of enhanced back-donation to CO occurring in the transition state relativetothereactant. Intheproduct,3a(X = Cl), theseentities change in the opposite direction (qco = -0.04, vco = 21 51 cm-I), consistent with the oxidative nature of the addition reaction. Details of the charge distribution in the MOs localized on the carbonyl indicate that a donation from CO to the metal is slightly reduced in the activated complex, a factor that can further reduce electron repulsion in the plane of addition. The electron redistribution in 4 relative to the reactants also involves an increase in electron donation from PH3 to Ir, which can be interpreted as a ligand response to the increased positive charge on Ir induced by the increased back-donation to CO. Thechargeon the chloride ligand changes only slightly from 1 to 4. The important role played by the CO ligand in reducing the electron repulsion encountered in a five-coordinate transition state has been recognized by Eisenberg and co-workers in their work on the stereochemistry of H2 addition to (dppe)Ir(CO)X (dppe = 1,2-bis(diphenylphosphino)ethane,a cis-bidentateligand). For X = halide, H, and CN, the addition is observed to be more facile along the P-Ir-CO rather than the P-Ir-X axis,30and calculations on models of Eisenberg's system support this r e ~ u l t .In ~ these reports, the transition state was presented in a way similar to 4a, and the d,2 orbital was retained as pointing toward the approaching H2species. The T * MOs of the CO bent away from CO-Ir-X collinearity were then proposed to interact with the metal dZ2 orbital in a bonding fashion, lowering the activation barrier. In this picture, back-donation from d,, to u*(H2) was also proposed to be stabilizing and enhanced by the bent orientation of the CO moiety. Though this pictorial scheme can explain why CO bends back easier than a halide when both are trans to a phosphine, the alternative representation, 4b, appears more appropriate because it allows hybridization in the equatorial plane and produces a polarized filled MO of correct directionality to engage in extensive back-donation to the CO ligand. 4b also avoids pointing a filled metal orbital (d,2 in 4a) directly toward H2. Our study of the thermodynamics for H2 addition to 1indicated that increased *-donation from the substituent X distinctly disfavors H2additiox8 Similarly, increased *-donation from X seems to strongly contribute to the kinetic barrier to Hz addition. Among the halides, n-donation decreases in strength down the group. As pointed out by Doherty and Hoffman,)I this electronic substituent effect receives strong support in observed UV-vis absorption maxima and carbonyl stretching frequency shifts, since the magnitudes of both A,, and vco in 1 increase upon descent in the halogen group.32 This ordering of the halide *-donating properties is also evident in other metal systems.33 The extent of substituent r-donation may affect the magnitude of the activation barrier in two related ways. First, 4e/3 orbital interactions exist involving filled halide p orbitals, filled metal d orbitals, and empty CO(**) orbitals. These are strongly directional and most favorable when the n-donating halide is trans to the *-accepting CO group. Since this effect is most important in the presence of strong *-donors, increased *-donation from X may increase the barrier to addition by resisting the necessary bending of the X-IR-CO moiety of the reactant. Second, the LUMO in the four-coordinate square-planar complex is an Ir(p,) orbital with some admixture of CO(?r*) and halide .rr character.32~34Increased A halide to metal donation raises the energy of this virtual orbital and thereby enlarges the HOMO-
The Journal of Physical Chemistry, Vol. 97, No. 22, 1993 5893
TABLE Ilk Computed Carbonyl Stretching Frequencies, YCO (cm-I), and Net NBO Atomic Charges, q, for 1,4, and 3a (X = Cl)' complex
L
YCO
q1r
qci
qco
qL
1 4 1
NH3
4 3a
NH3
2047 2026 2151 2046 2021 2143
+0.58 +0.64
3a
PH3 PH3 PH3
-0.76 -0.79 -0.75 -0.82 -0.84 -0.79
-0.21 -0.30 -0.06 -0.24 -0.40 -0.07
+0.19 +0.24 +0.30 +0.15 +0.15 +0.19
NH3
+0.83 +0.76 +0.96 +1.24
qH.' 0.00 -0.02 -0.61 0.00 -0.04 -0.76
Computed with the basis set used in geometry optimization; see computational methods. Total net charge on the two hydrogen atoms.
LUMO gap.35 Part of the electron redistribution and Ir-H2 interaction in the transition state is expected to involvethis orbital, which will be less accessible when X is a strong ?r donor. In general, an increased HOMO-LUMO gap in a molecule implies a reduced tendency to engage in chemical reactions. Density functional theory, for instance, regards the HOMO-LUMO separations in chemical species as indices of their chemical reactivity.36 For the above reasons, we propose that the magnitude of *-donation is the major factor determining the effect of X on the barrier to H2 addition. This explanation is consistent with the decreased reactivity of complexes of the lighter halides as well as the high reactivity of the cyano and hydrido complexes. We note that a more conventional interpretation based primarily on ligand electronegativities or a-donation cannot be definitively ruledout at present. However, inour study of the thermodynamics of H2 addition, which involved a wider range of ligands X,8 enthalpy values (which correlate well with the activation barriers calculated in this work) were consistent with an interpretation based predominantly on r-donation but not with one based on a-donation. When the PH3 ligands in 1 are replaced by NH3 (X = Cl), the activation barrier is computed to increase by about 5 kcal/mol. The NH3 group may be considered a stronger 7~ donor than PH3. Though the position of these ligands is not in the plane of addition, their ?T properties may still have an influence similar to that discussed for X. Increased *-donation from L, for example, raises the energy of the empty pz orbital of the reactant, which can cause an increase in the activation barrier as mentioned above. An effect due to differences in u properties between PH3 and NH3 may be significant in this case, however. The charges on the atoms and ligands given in Table I11 show that the phosphine ligands increase their electron donation to the metal in the transition state, while the amines do not. The latter case results in accumulation of positive charge on the metal, which may produce a higher energy of the system. In other words, the PH3 ligands respond to electronic changes taking place on the metal in an energetically less costly manner than NH3 (PH3 is a softer ligand than NH3).36c We do not propose a similar dominating role for a-donation in the halide series, because the net charges on the halides vary only slightly between reactants and transition states and the small computed differences are virtually constant for all the complexes (net charges become more negative by about 0.03 e, Table 111). In conclusion, the proposal of a strong deactivating influence induced by increased *-donation from the substituents on 1 provides a simple interpretation (and may be a guide for prediction) of the substituent effect on the activation barrier of H2 addition to Vaska-type complexes. H2/DZKinetic Isotope Effects. Kinetic isotope effects (KIEs) are among the very limited observable parameters which afford insight into the detailed nature of transition ~tates.3~ The KIE for H2/D2addition to Ir(PPh3)2(CO)C1is reported to be 1.09 in toluene38 and 1.22in benzene.17b Considering the high dissociation energy of the H2bond, this weak KIE value has often been used to advocate an early transition state for the H2 addition reaction.39
5894
The Journal of Physical Chemistry, Vol. 97,No. 22, 1993
Abu-Hasanayn et al.
TABLE I V Jhetic Isotope Effect for HJDz Addition to tnsos-Ir(PHs)z(CO)X X
F CI Br I CN
H CY
EXC 0.70 0.57 0.56 0.54 0.53 0.49 0.63
AZPE:; 2.57 2.41 2.32 2.27 2.20 2.12 2.47
EXP WE) 0.28 0.38 0.43 0.47 0.53 0.61 0.34
Via
309 245 343 404 348 444 334
Vi/":,
1.16 1.19 1.28 1.32 1.27 1.34 1.25
kH/kDc
(kH/kohd
Q,",,/Q:,'
1.13 1.21 1.35 1.44 1.61 1.69 1.21
1.08 1.16 1.30 1.38 1.49 1.57 1.14
1.02 1.01 1.04 1.06 1.04 1.08 1.03
a Transition-state imaginary frequency in cm-I (unscaled). Ratio of the protium transition-state imaginary frequency to the isotopic one; used in evaluating eq 5. Isotope effect computed from eq 3 with scaled frequencies (0.92) at 300 K, tunneling correction factor not included. d Values in = Bell's tunneling correction factor. parentheses are obtained using the simplified expression, eq 5, tunneling correction factor not included. e f PH, replaced by NH3.
Q:,/QE,
All the vibrational frequencies pertaining to the activated complex were included in KIE calculations according to eqs 1 or 3. The computed frequencies for the reactant and product complexes are about 8%larger than the experimentalfrequencies, a typical result from harmonic frequency calculations employing ab initio electronic structure models.9 For example, in the dihydride product of the chloro complex the two Ir-H stretching frequencies are computed at 2379 and 2283 cm-I as compared with themeasuredvaluesof2190and2100cm-~.17a Consequently, all computed frequencies were scaled by a factor of 0.92 prior to their use according to standard practice,4°b,cbut experimental frequencies were used for H2 and D2 (4395 and 3118 cm-I, respectively) .44 The classical description of the H2/D2 translational and rotational partition function ratios in eq 1 produces values of 2.83 and 2.00, respectively. On the other hand, the metal complexes Kn do not contribute to the MMI term, as their masses are only Dt D2 D2)( * H *H 1") Qtr Qrot Qvib e - ( ~ ~ ~ slightly ~ ~ influenced / ~ by ~ isotopic substitution. Accordingly, the MMI Qtr QrotQvib (1) term has a value of 5.66.45 Both EXC and EXP(ZPE) terms 1 D l D *D Q:2Ql;',:Q% Qtr Qrot Qvib contribute in reversing the effect of the large MMI factor to where K is the transmission coefficient, Qtr = ( 2 u m k ~ T ) ~ / ~ / h ) , produce a computed KIE value of 1.21, in good agreement with value of 1.09-1.22.46 The origin of this result Qrot= 8u21kBT/uh2(linear molecules),Qrot= 8 ~ ~ ( 8 7 r ~ l ~ l $ ~ )the ~ / experimental ~lies in the number and magnitudes of the additional isotope( k ~ T ) I / ~ / (nonlinear uh~ molecules), Qvib = I&( 1-e-(hvi/kBT))-I, sensitive vibrational modes present in the activated complex. In AAZPE= AZPE:; - A Z P E ~AZPE? , = ZPEH~ - ZPEDZ,ZPE the reactants, there is only one vibration that is sensitive to isotope = Ci(hvi/2) (zeropoint energy), m is the molecular mass, h is the substitution, Le., the HZstretching vibration. Since the frequency Planck constant, k~ is the Boltzmann constant, Tis the absolute of this vibration is very high, it gives a large normal contribution temperature, l i s themoment of inertia, uis thesymmetry number, to EXP(ZPE) but no contribution to EXC. On the other hand, and vi is the (real) vibrational frequency with index "i" covering in the activated complex (4) there are formally five normal modes all normal modes of the molecule. that are directly sensitive to isotope substitution (in the product To a first approximation, the transmission coefficient ratio these five modes with the addition of the reaction coordinate cancels out and eq 1 can be reexpressed as the product of three vibration develop into the six M(H);! vibrations). For X = C1, terms: three of these modes have frequencies lower than 500 cm-I, one KIE = MMI*EXC*EXP(ZPE) has a frequency value around 1100 cm-1, and the last has a frequency around 3800 cm-I (5b).47 Upon deuteration, the where MMI is the mass-moment of inertia component, EXC is frequency of each of these vibrations decreases, an effect which the vibrational excitation component, and EXP (ZPE) is the when summed over all the vibrations leads to a AZPE:; value differential zeropoint energy component. The isotope effect may alternativelybe computed using the Bigeleisentreatment of isotope that is larger than AZPE? (2.41 vs 1.83 kcal/mol). The result (eq 3), which requires knowledge of only the vibrational is a positive AAZPE value (0.58 kcal/mol) that gives an inverse frequencies EXP (ZPE) effect (0.38). Thestrongly inverse EXC effect (0.57) has its major contribution from the low-frequency vibrations that produce significantly more occupied excited states at room (3) temperature in the DZactivated complex than in the HZcomplex. It is through the final combinationof the three contributing terms where v* refers to the imaginary frequency in either transition that the KIE becomes normal (Le., larger than unity) and weak. state: Consideration of the low-lying frequencies is crucial in this case for both the EXC and EXP(ZPE) components. When these frequencies are excluded from the calculations (X = C1, L = PH3), the EXC and EXP(ZPE) terms become 0.95 and 0.78, respectively, and the KIE becomes 4.20.48 Saunders et using the empirical bond-order method for Generally, we obtain similar results using either expression, but isotope calculated an inverse KIE (ca. 0.5) for a model the full expression has the advantage of being easier to interpret. of Vaska's complex and accordingly proposed the Occurrence of The computed KIE values from both expressions are given in Table IV. substantial hydrogen tunneling (Qi,/QE, 2.5) in order to Closer examination of the equations governing kinetic isotope effects reveals, however, that even if the transition state occurs extremely early, a strong kinetic isotope effect should actually be expected based solely on the large H2/D2 mass-moment of inertia contribution. We utilize here the computed vibrational frequencies to calculate the KIE and to determine its major contributingcomponents. While the use of computed frequencies is becoming common in studies of isotope effects in reactions involving small organic to our knowledge the only reported case where computed frequencies have been used to study isotope effects in an organometallic system is Morokuma's study of H2/D2 addition to P t ( p H j ) ~ . ~ ~ According to conventional transition-state theory:' the kinetic isotope effect expression for H2/D2 addition to 1 is
($)(
-
TS for HZAddition to Vaska-Type Complexes account for the observed normal KIE. At the computational level employed here, the semiclassical treatment of KIE, which does not include tunneling corrections, reproduces the ChelT'ed normal but weak isotope effect quite well, and there is no need to invoke tunneling corrections to obtain agreement. we have nevertheless calculated the ratio of the tunneling partition functions, Q,",,/QL,, using the approximate expression for estimating the tunneling correction factors43
where Y * is the transition state imaginary frequency. The correction factors obtained are indeed quite small and range from 1.01 to 1.08 with the larger values associated with the earlier transition states (larger imaginary frequencies). These results indicate that tunneling, though most likely present, is not a dominant factor in determining KIE in this system.50 An interesting and unexpected trend arises from the zeropoint energy component to the KIE. With increasing lateness of the transition state, the KIE for the reaction decreases. For example, among the studied complexes the computed KIE is weakest (1.13) for the fluoro complex, which exhibits a markedly late transition state. As the transition state becomes earlier as one m o w down the halidegroup, KIE becomes gradually stronger (1.44 when X = I). For X = H, where the transition state occurs early along the reaction path, the KIE is even larger (1.69). As the strong H2 bond becomes increasingly cleaved in a late transition state, the developing Ir-H bonds are strengthened, causing a net increase in AZPE:; and thus a smaller KIE. In the dihydride product, which represents the extreme in H2 bond cleavage, the M-H bonds formed are sufficiently strong to produce an inverse thermodynamic isotope effect (value around
Concluding Remarks The present computational study of H2 addition to Vaska-type complexes, trans-Ir(L)z(CO)X, demonstrates that ab initio molecular orbital calculations with effective core potentials and moderately sized valence basis sets can provide reliable information regarding structural and energetic substituent effects in transition metal complexes. For that purpose, full geometry optimization and normal mode characterization of reactants and products are essential. Our interpretation of the computedresults is that increased *-donation from the substituent X increases the energy barrier of Hz addition. The kinetic isotope effect for Hz/ D2 addition to 1 is calculated using computed frequencies and a semiclassicaltreatment of reaction rates. The result for X = C1 is in excellent agreement with the observed normal weak value, and detailed analysis shows that the small isotope effect does not result simply from the presence of an early transition state. On the contrary, the complexes which add Hz via later transition states are computed to have smaller isotope effects. Application of electronic structure techniques similar to the ones employed here should prove valuable in the interpretation of isotope effects for other organometallic reaction systems.
Acknowledgment. We gratefully acknowledge the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research of the U.S. Department of Energy, for financial support and the Pittsburgh Supercomputer Center for a grant of computer time. Supplementaq Material Available Tables containing total energies (HF, MPZ-MP4(SDTQ)) and NBO net atomic charges of reactants, transition states, and products for all the reactions studied here, and the Z-matrices, frequency values, and vector component of all the normal modes for the HZand Dz transition states with X = C l ( l 1 pages). Ordering information is given on any current masthead page.
The Journal of Physical Chemistry, Vol. 97, No.22, I993 5895
References and Notes (1) (a) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 5th ed.; Wiley: New York, 1988. (b) Crabtree, R. H. The Organometallic Chemistry of Transition Metals; Wiley: New York, 1988. (c) Collman, J. P.; Hegedus, L. S.; Norton, J. R.; Tinke, R. G. Principlesof Organotransition Metal Chemistry; University Science Books: Mill Valley, CA, 1987. (d) Parshall, G. W. Homogeneous Catalysis; Wiley: New York, NY, 1980. (2) For recent reviews: (a) Tsipis, C. A. Coord. Chem. Reu. 1991,108, 161. (b) Davidson, E. R. Chem. Reu. 1991, 91, 651. (c) The Challengeof d and f Electrons: Theorv and Comoutarion:Salahub. D. R.. Zerner. M. C.. Eds.; XCS Symposium Series; American Chemical Society: Washington, DC, 1989. (3) (a) Christiansen, P. A.; Ermler, W. C.; Pitzer, K. S.Annu. Reu. Phys. Chem. 1985,36,407. (b) Krauss, M.; Stevens, W. J. Annu. Rev. Phys. Chem. 1984, 35, 357. (4) (a) Pitzer, K. Acc. Chem.Res. 1979,8,271. (b) Pyykko, P.; Desclaux, J. P. Acc. Chem. 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L.; Hall, M. B. J. Comput. Chem. 1991,12,923. (15) (a) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J . Chem. Phys. 1980, 72,650. (b) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969,51,2657. (c) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J. Comput. Chem. 1983, 4, 294. (16) Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244. Moller, C.; Plesset, M. S.Phys. Reu. 1934, 46, 618. (17) (a) Chock, P. B.; Halpern, J. J . Am. Chem. SOC.1966,88,3511. (b) Vaska, L.; Werneke, F. Trans. N . Y. Acad. Sci. 1971, 33, 70. (c) Ugo, R.; Pasini, A,; Fusi, A.; Cenini, S.J . Am. Chem. SOC.1972,94,7364. (d) Shaw, L. B.; Hyde, M. E. J. Chem. Soc., Chem. Commun. 1975, 765. (e) Drouin, M.; Harrod, J. F. Inorg. Chem. 1983, 22, 999. (18) (a) Ziegler, T.; Tschinke, V.; Becke, A. J . Am. Chem.SOC.1989, 1 11 , 9177. (b) Rabaa, H.; Saillard, J.-Y.; Hoffmann, R. J . Am. Chem. SOC.1986, 108,4327. (19) (a) Kubas, G. J.; Ryan, R. R.; Swanson, B. I.; Vergamini, P. J.; Wasserman, H. J. J. Am. Chem. SOC.1984,106,451. (b) Kubas, G. J. Acc. Chem. Res. 1988, 21, 120. (20) (a) Burk, M. J.; McGrath, M. P.; Wheeler, R.; Crabtree, R. H. J . Am. Chem. SOC.1988, 110, 5034. (b) Vaska, L. Acc. Chem. Res. 1968, 1 , 335. (c) Luo,X.; Michos, D.; Crabtree, R. H.; Hall, M. B. Inorg. Chim. Acta 1992, 298 (200), 429. (21) (a) Harrod, J. F.;Hamer,G.;York, W.J. Am. Chem.Soc. 1979,101, 3987. Harrod. J. F.: York. W. Inora. - Chem. 1981, 20, 1156. (b) Milestein, D. Ace. Chem. Res. 1984, 17, 221. (22) The vibrational analysis produced two additional imaginary frequencies with small values corresponding to PHI or NH3 rotations for L = PHI and X = H or CN as well as L = NH3, X = CI.
5896 The Journal of Physical Chemistry, Vol. 97, No. 22, 1993 (23) (a) Kitaura, K.; Obara, S.; Morokuma, K. J. Am. Chem. Soc. 1981, 103, 2891. (b) Obara, S.; Kitaura, K.; Morokuma, K. J . Am. Chem. SOC. 1984,106,7482. (24) Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 334. (25) Although ref 17a measures a larger rate constant for the reaction when X = Br than when X = CI, the experimental data show some unusual behavior with AH* reported larger for X = Br (12 kcal/mol) than for X = CI (1 1 kcal/mol) along with a large difference in the entropies of activation for CI (-23 eu) and Br (-14 eu); no values are given in ref 17a for X = I. (26) This bonding scheme has been proposed first by Orchin: Orchin, M.; Rupilius, W. Catal. Rev. 1972, 6, 85. (27) Reed, A. E.; Weinhold, F. J . Chem. Phys. 1983,78,4066. Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735. (28) TheNBOcalculations werecarried out with thedefaults implemented by Weinhold et al. in GAUSSIAN 90. For an alternative procedure, see: Maseras, F.; Morokuma, K. Chem. Phys. Lett. 1992, 195, 500. (29) (a) Rossi, R. A.; Hoffmann, R. Inorg. Chem. 1975,2,365. (b) Riehl, J. F.; Jean, Y.; Eisenstein, 0.;Pelissier, M. Organometallics 1992, 11, 729. (30) Deutsch, P. P.; Eisenberg, R. Chem. Rev. 1988, 88, 1147. (31) Doherty, N. M.; Hoffman, N. W. Chem. Rev. 1991, 91, 553. (32) (a) Peone, J.; Vaska, L. J . Chem. Soc., Chem. Commun. 1971,418. (b) Brady, R.; Flynn, 9. R.; Geoffroy, G. L.; Gray, H. B.; Peone, J.; Vaska, L. Inorg. Chem. 1976, I S , 1485. (33) Poulton,T. J.; Folting, K.;Streib, W. E.; Caulton,G. K. Inorg. Chem. 1992, 31, 3190. (34) Abu-Hasanayn, F.; Krogh-Jespersen. K., unpublished results. (35) The HOMO-LUMO gap may be estimated either from the orbital energy difference between the HOMO and the LUMO or as a transition energy from single excitation configuration interaction calculations, In either case, the gap is computed to decrease as one moves down the halide group. (36) (a) Parr, R. G.; Yang. W. Density Funciional Theory of Atoms and Molecules; Oxford Press: New York, 1989. (b) Pearson, R. G. J . Mol.Strucr. (Theochem) 1992,255,261. (c) Pearson, R. G. Inorg. Chem. 1988,27,734. (37) For recent reviews of isotope effects in organometallics and homogeneouscatalytic processes,see: (a) Bulluck, M. In TransirionMetal Hydrides; Dedieu,A.,Ed.;VCHPublishers: New York, 1991;Chapter8. (b)Rosenberg, E. Polyhedron 1989, 8, 383. (38) Zhou, P.; Vitale, A.; San Filippo,J.; Saunders, W. J . Am. Chem. SOC. 1985,107,8054.
Abu-Hasanayn et al. (39) Collman, J. P.; Roper, W. R. Adu. Organomer. Chem. 1967, 7, 53. (40) (a) Hout, R. F.;Wolfsberg, M.; Hehre, W. J. J . Am. Chem. Soc. 1980. 102. 3296. (b) Houk. K. N.: Gustafson. S. M.: Black. K. A. J. Am. Chem. Soc. 1992, ilb, 8565: (c) Vijay, A.; Sathyanarayana, D N. J. Phys. Chem. 1992, 96, 10735. (41) Laidler, K. Chemical Kinetics, 3rded.; Harpexand Row: New York, 1987. (42) (a) Bigeleisen, J. J . Chem. Phys. 1949, 17, 675. (b) Bigeleisen, J.; Mayer, M. G. J. Chem. Phys. 1947, IS, 675. (43) Bell, R. P. The Tunnel Effect in Chemistry; Chapman and Hall: London, 1980. (44) Moelwyn-Hughes,E. A. Physical Chemisrry; Pergamon Press: New York, 1961; p 427. (45) Including quantum mechanical corrections in the H2/D2rotational partition function ratio results in an additional correction factor of 1.05 (see ref 42b). This factor is, for simplicity, ignored in the present calculations. (46) The computed KIEis sensitiveto the magnitude of the scaling factor. For the chloro complex, a scaling factor of 0.94 gives a KIE of 1.12 and a scaling factor of 0.90 gives a value of 1.31 . (47) Thesemodesareactually coupled withother modes, which makes the number of isotope-sensitivevibrations in the transition state larger than five. Inclusion of all the vibrational frequencies in the KIE calculations avoids this complication. (48) To account for coupling among the low-frequencymodes, this result was obtained by ignoring the lowest 13 real vibrational frequencies (all lower than 500 cm-I) from the KIE calculations. (49) Sims, L. B.; Lewis, D. E. In Isotopes in Organic Chemistry; Buncel, E., Lee, C. C., Eds.; Elsevier: Amsterdam, 1984; Vol. 6, pp 161-259. (50) We note that the computed differential zero-point energies indicate an inversetemperature dependenceof the KIE, oppositeto what was observed experimentally in ref 38. However, earlier experimental work (Werneke, M. F. Ph.D. Thesis, Clarkson College of Technology, 1971) found an inverse temperature dependence. The measured and computed effects are small, and, considering the difficulties in describing the complex temperature dependence of reaction rates:' we find neither the experimental nor the computational data conclusive on this issue. (51) Abu-Hasanayn, F.; Krogh-Jespersen, K.;Goldman, A. S., submitted for publication.
