DALTON FULL PAPER J. Chem. Soc., Dalton Trans., 1998, Pages 291–300 291 A theoretical study of [M(PH3)4] (M 5 Ru or Fe), models for the highly reactive d8 intermediates [M(dmpe)2] (dmpe 5 Me2PCH2- CH2PMe2). Zero activation energies for addition of CO and oxidative addition of H2 ‡ Stuart A. Macgregor,*,†,a Odile Eisenstein,a Michael K. Whittlesey b and Robin N. Perutz b a Laboratoire de Chimie Théorique, Bâtiment 490, Université de Paris-Sud, 91405 Orsay, France b Department of Chemistry, University of York, York, UK YO1 5DD Density functional calculations have been carried out on [M(PH3)4] species as models for transient [M(dmpe)2] formed from the photolysis of [M(dmpe)2H2] (M = Ru or Fe, dmpe = Me2PCH2CH2PMe2).Calculations have also been performed on [Rh(PH3)4]1 as a model for the relatively inert [Rh(dmpe)2]1. The singlet electron configurations of [Ru(PH3)4] and [Rh(PH3)4]1 were found to have D2d geometries with trans P]M]P angles of 159 (M = Ru) and 1728 (M = Rh1).Singlet [Fe(PH3)4] was computed to have a C2v structure with trans P]M]P angles of 137 and 1608 at Fe. The triplet configurations of [Fe(PH3)4] and [Ru(PH3)4] were predicted to adopt C2v geometries with angles of ca. 155 and 958 for both species. Singlet [Ru(PH3)4] is calculated to be 11.7 kcal mol21 more stable than the triplet, but the triplet form of [Fe(PH3)4] is the more stable by 8.0 kcal mol21. The addition of CO and oxidative addition of H2 to [M(PH3)4] (M = Ru or Fe) were calculated to be highly exothermic.In contrast, the reaction between [Rh(PH3)4]1 and H2 is less thermodynamically favoured, consistent with the lower reactivity of experimental Rh1 analogues. Both the oxidative addition of H2 and addition of CO were calculated to proceed without activation energy for [Ru(PH3)4], but only once the ‘end-on’ approach of H2 and an angled approach of CO at long ruthenium–substrate separations are considered. The calculations on [Ru(PH3)4] also reproduced the UV/VIS spectrum and geometry of [Ru(dmpe)2] satisfactorily.The reaction of singlet [Fe(PH3)4] with CO was calculated to be barrierless, while the oxidative addition of H2 required a very small activation energy (ª1 kcal mol21) at long Fe]H2 distances. The reaction of [Rh(PH3)4]1 with H2 has a somewhat larger activation barrier (ª3 kcal mol21) and is predicted to pass through a product-like C2v transition state. The problem of the geometry and reactivity of d8 ML4 complexes is longstanding and complex.Geometries close to tetrahedral with triplet spin states are found for first-row transition metals of Groups 9 and 10, while square-planar geometries with singlet spin states are common for second- and third-row metals of the same groups. The ML4 complexes of Group 8 metals are highly reactive molecules which have only a transient existence under conventional conditions. The importance of such molecules lies in their ability to undergo a large number of reactions, including co-ordination of an additional ligand, oxidative addition with reagents such as dihydrogen, and formation of metal–metal bonds.The isolobal analogy between d8 ML4 and carbenes1 highlights the problem of spin state and geometry as well as the high reactivity of these molecules. The first such molecule to be studied in detail was [Fe(CO)4].2 Matrix infrared and gas-phase time-resolved infrared (TRIR) experiments showed that this molecule adopts a C2v structure with C]Fe]C angles of 147 and 1208 and two unpaired electrons.As a result of a triplet ground state, the rate constants for its reaction with CO and H2 in the gas phase are 2–3 orders of magnitude lower than for the corresponding reactions of [Cr(CO)5].3 When xenon or methane matrices are used in place of argon, triplet [Fe(CO)4] is replaced by a species identified as [Fe(CO)4S] (S = Xe or CH4) which has a trigonal-bipyramidal structure with S in the equatorial plane.The C]Fe]C angles are now 174 and 1258; it is thought that the electrons are spin- † Present Address: Department of Chemistry, Heriot-Watt University, Riccarton, Edinburgh, UK EH14 4AS. ‡ Supplementary data available: calculated coordinates and energies. For direct electronic access see http://www.rsc.org/suppdata/dt/1998/ 291/, otherwise available from BLDSC (No. SUP 57317, 12 pp.) or the RSC Library. See Instructions for Authors, 1998, Issue 1 (http.//www.rsc.org/dalton). Non-SI unit employed: cal = 4.184 J.paired.2 Far less is known about the nature of [Fe(CO)4] as a transient species in solution. A recent summary of experimental results, collated by Grevels,4 indicates that the first species to be observed after laser flash photolysis of [Fe(CO)5] in cyclohexane is [Fe(CO)4(C6H12)], i.e. the analogue of [Fe(CO)4S], which is formed within the instrumental risetime of 3 ms. Any triplet [Fe(CO)4] must have a much shorter lifetime in solution.Thus the results indicate that three ML4 species need to be considered: a triplet, a singlet and a solvent adduct, ML4S. The structures of the triplet and singlet may both be far from the tetrahedral and square-planar limits. The ruthenium analogue, [Ru(CO)4], has been studied by TRIR in the gas phase, but the spectral data do not permit the structure to be determined. However, the high rate constant for reaction with CO indicates that [Ru(CO)4] has a singlet ground state.5 The combination of matrix isolation and time-resolved absorption spectroscopy in solution has recently been applied with considerable success to ML4-type complexes with chelating phosphine ligands, [M(dmpe)2] (M = Fe or Ru, dmpe = Me2PCH2CH2PMe2).6,7 These complexes are usually generated by photolysis of the corresponding dihydrides, [M(dmpe)2H2].The ruthenium complex, [Ru(dmpe)2], shows a three-band UV/ VIS spectrum and reacts with both H2 and CO at rates close to the diffusion limit (>1 × 109 dm3 mol21 s21).The spectrum suggests that it adopts a geometry very close to square planar. The large rate constants indicate that there is no barrier to reaction created by spin-state interconversion, and hence that [Ru(dmpe)2] has a singlet ground state. The NMR evidence demonstrates that [Ru(dmpe)2] undergoes oxidative-addition reactions with benzene, but not with alkanes.8 Recently, [Ru(CO)2L2] (L = PBut 2Me) was isolated in a singlet ground state and shown by X-ray crystallography to have a C2v structure with C]Ru]C 133.38 and P]Ru]P 165.68.292 J.Chem. Soc., Dalton Trans., 1998, Pages 291–300 Like the other d8 RuL4 complexes, it reacts very rapidly with several molecules.9 The analogue with L = PMe3 has been studied in low-temperature matrices and shown to have C]Ru]C larger than 1308 and to form adducts of the type [Ru(CO)2(PMe3)2S] (S = Xe or CH4).10 Ab initio second-order Møller-Plesset perturbation (MP2) calculations on [Ru(CO)2- (PH3)2] have revealed a C2v structure, indicating that the C]Ru]C bond angle is not constrained either by steric effects or the presence of S.9 The iron complex [Fe(dmpe)2],6 exhibits very different characteristics from its ruthenium analogue.The lowest-energy absorption is in the near-UV region at ca. 28 000 cm21, the rate constant for reaction with H2 is a factor of 7500 smaller than for [Ru(dmpe)2], whereas the rate constant for reaction with CO is only a factor of two slower.Oxidative-addition reactions with arenes and with alkanes compete effectively with the back reaction with H2. The NMR investigations provide decisive evidence that even methane reacts with [Fe(dmpe)2].11 Thus [Fe(dmpe)2] is substantially less reactive than [Ru(dmpe)2] towards H2, but more reactive towards hydrocarbons. The differences in spectra and reactivity between [Fe(dmpe)2] and [Ru(dmpe)2] suggest that [Fe(dmpe)2] is not square planar. Although the high rate constant for reaction with CO makes a singlet ground state for [Fe(dmpe)2] likely, it is not close enough to the diffusion limit to be decisive.The experimental data show that any effect of specific complexation by the solvent on the kinetics of reaction of [Fe(dmpe)2] is very slight. The structures of d8 ML4 species have also been investigated extensively by theoretical methods. Burdett 12 predicted on the basis of extended Hückel calculations that high-spin d8 [M(CO)4] complexes should adopt a C2v structure with angles of 110 and 1358.He noted that the square-planar geometry was preferred for low-spin d8, but that a D2d distortion was preferred over a C3v distortion. The conclusions from Burdett’s angular overlap analysis paralleled those from the extended Hückel calculations. 13 Since the angular overlap arguments were based solely on s interactions, they should be applicable (in a first approximation) to metal phosphine as well as metal carbonyl complexes.Elian and Hoffmann,14 who included the metal– ligand dp/pp interactions in their calculations, predicted a D2d geometry (angle ca. 1508) for a d8 low-spin [M(CO)4] molecule, but a square-planar geometry for the corresponding MCl4 complex. They did not consider the high-spin case. Ziegler and co-workers 15 returned to these problems with density functional calculations. This work predicts that [Fe(CO)4] and [Ru(CO)4] would have C2v structures both in their singlet and in their triplet states, that the angles in the singlet states should be ca. 175 and 1308, and that the angles in the triplet states should be ca. 155 and 958. The singlet state was strongly favoured for [Ru(CO)4], but the two states were almost equienergetic for [Fe(CO)4]. Ziegler et al.15a also examined the pathways for reaction of [Ru(CO)4] with H2 and CH4. Notable features were: (i) formation of s complexes as reaction intermediates albeit with very shallow potential wells, (ii) oxidative addition of H2 with an activation energy of ca. 2.6 kcal mol21 and (iii) oxidative addition of methane with a barrier of 19 kcal mol21. Wang and Weitz 16a have re-examined both singlet and triplet [Fe(CO)4] and published a critique of the various estimates of the singlet– triplet energy separation. Many other theoretical studies of the addition of small molecules to unsaturated transition-metal species have been performed at various levels of theory.17–27 These calculations have repeatedly demonstrated the existence of potential minima for s complexes of H2 and CH4 prior to full oxidative addition. The importance of s complexes is supported by a large body of experimental evidence.28 We report a theoretical study designed to reveal the molecular structure and ground electronic configuration of [Fe(dmpe)2] and [Ru(dmpe)2] and to examine the pathways for co-ordination of CO and oxidative addition of H2 to these molecules.We have employed [M(PH3)4] (M = Ru or Fe) as model compounds and used density functional methods29 which have proved to be particularly effective in reproducing the molecular geometries, dissociation energies and reactivity trends of transition-metal systems.30 The present study also includes a number of calculations on the isoelectronic model system [Rh(PH3)4]1. Many tetrakis- (phosphine)rhodium(I) species are known experimentally and several have been characterised crystallographically, including [Rh(dmpe)2]1.31,32 In the absence of structural information on the ruthenium and iron systems, this provides us with an experimental standard against which we can compare our computed results.In addition, whereas [Fe(dmpe)2] and [Ru(dmpe)2] are both extremely reactive species, their rhodium(I) analogue is relatively unreactive. We should therefore expect our computed results to reflect this large difference in reactivity before we can tackle the subtler distinctions between the ruthenium and iron systems with confidence.Jones et al.32 reported that [Rh(PMe3)4]1 undergoes oxidative addition with H2. The reactivity of [Rh(PR2R9)4]1 with H2 has been studied by Schrock and Osborn.33 They found when R = Me and R9 = Ph that oxidative addition occurred with the formation of [Rh(PMe2Ph)4H2]1. However, when R = Ph and R9 = Me or R = OMe and R9 = Ph no reaction was observed. Clearly the reactivity of these rhodium(I) systems is very sensitive to the steric and electronic properties of the phosphine.In the following we use the oxidative addition of H2 to [M(PH3)4] (M = Ru, Fe or Rh1) as a test of our computational approach. Computational Details All calculations used the Amsterdam Density Functional program (ADF, version 2.0.1) developed by Baerends et al.34 and employed the numerical integration scheme of te Velde and Baerends.35 For Ru, Fe and Rh a triple-z-STO (Slater type orbital) basis set was employed. For P, O, C and PH3 hydrogen atoms a double-z-STO basis set extended by a polarisation function was used.All hydrogen atoms directly involved in bonding to a metal were described using a triple-z-STO basis set extended with two polarisation functions. An auxiliary set of s, p, d, f and g STO basis functions centred on all nuclei was used in order to fit the molecular density and describe accurately the Coulomb and exchange potentials in each SCF (selfconsistent field) cycle.36 Core electrons (up to and including 3d for Ru and Rh, 2p for Fe and P and 1s for C and O) were treated using the frozen-core approximation.34 The calculations incorporated the quasi-relativistic corrections of Ziegler et al.37 Geometry optimisation was carried out using the local density approximation (LDA) employing the parameterisation of Vosko et al.38 and made use of the optimisation procedure developed by Versluis and Ziegler.39 Geometries were fully optimised under the appropriate symmetry constraints.Test calculations on the C2v geometries of singlet and triplet [M(PH3)4] species (M = Fe or Ru) in which symmetry constraints were relaxed first to Cs and then C1 symmetry gave very similar results. Energies of all optimised structures were recalculated with the BP86 functional, including the non-local (NL) corrections of Becke 40 (exchange) and Perdew41 (correlation). Electronic transition energies and ionisation potentials were calculated using the DSCF method.Total computed energies (at both local and non-local levels of calculation) and cartesian coordinates for all optimised structures are available as supplementary information (SUP 57317). Results Structures of M(PH3)4 species Singlet electronic configuration (M 5 Ru, Fe or Rh1). The geometries of [M(PH3)4] (M = Ru, Fe or Rh1) were optimisedJ. Chem. Soc., Dalton Trans., 1998, Pages 291–300 293 for a singlet electronic configuration under the C2v symmetry constraint, corresponding to a staggered arrangement of the PH3 ligands.The optimised structures of all three species exhibit distortions away from a square-planar geometry (see Fig. 1). For [Ru(PH3)4] and [Rh(PH3)4]1 the MP4 cores are close to overall D2d symmetry with the M]P bonds being displaced away from a square-planar geometry by an average of 10.7 (M = Ru) and 3.98 (M = Rh1). For [Fe(PH3)4] we calculate a C2v structure with angles of 137.0 and 159.78 at the metal.The calculated average M]P bond length for [Rh(PH3)4]1 is 2.239 Å. This is somewhat shorter than the distance found experimentally in the crystal structure of [Rh(dmpe)2]1 (Rh-P 2.282 Å) in which the geometry at the metal is very close to square planar.31 In the crystal structure of [Rh(PMe3)4]1 the trans P]Rh]P angles average 1508; this larger distortion is probably due to steric crowding of the phosphine ligands.32 The Rh]P distances in this species average 2.297 Å.Comparison of the two experimental structures suggests that one effect of the chelating phosphine may be to force the geometry nearer to square planar. Thus, in the case of [Ru(PH3)4] the deviation away from square-planar geometry may be a consequence of the inability of PH3 to model fully the dmpe ligand, especially its steric bulk and the consequences of its bidentate binding mode. The calculated average Ru]P distance in this species (2.239 Å) is again shorter than those found experimentally in related species, for example [Ru- (dmpe)2(CO)], in which the Ru]P distances average 2.297 Å.42 The underestimation of metal–ligand bond lengths is usually found when the LDA (local density approximation) level of theory is employed.30 § Optimising [Ru(PH3)4] in C2v symmetry but constraining the RuP4 core to a square-planar geometry yielded an average Ru]P bond distance of 2.246 Å and a calculated energy only 2 kcal mol21 higher than the global D2d minimum.As has been suggested previously,14 the deformation of the d8 MP4 core appears relatively facile. The calculated C2v structure of [Fe(PH3)4] has Fe]P bonds of 2.103 (axial) and 2.088 Å (equatorial). These calculated distances are somewhat shorter than expected, even given the usual underestimation of metal–ligand bonds with the LDA. A review of structures contained in the Cambridge Structural Database gave Fe]PR3 distances of 2.246 (R = Me, average of 20 systems) and 2.237 Å (R = Ph, average of 31 systems).43 The Fig. 1 Geometries (distances in Å, angles in 8) of singlet [M(PH3)4] species (M = Fe, Ru or Rh1) § Reoptimisation of [Ru(PH3)4] including non-local gradient corrections yielded an equivalent (to within 0.58) D2d structure with an average Ru]P bond length of 2.268 Å. short calculated Fe]P distances may arise from the lack of steric crowding around the small iron metal centre in our model compounds. Triplet electronic configuration (M 5 Ru or Fe).Optimisations for the triplet structures of [M(PH3)4] species (M = Ru or Fe) were based upon a bent C2v structure. The deformation of square-planar d8 ML4 species towards such a structure is known to lead to a reduction in the HOMO–LUMO (highest occupied–lowest unoccupied molecular orbital) gap.44 A formally nonbonding (neglecting p effects) metal-based d orbital is strongly destabilised while, at the same time, an unoccupied metal p orbital is stabilised (see Fig. 2). Geometries for the triplet electronic configuration were therefore optimised for single occupation of the appropriate b2 and a1 orbitals (Fig. 2, right-hand side) under the C2v symmetry constraint. The geometries obtained (see Fig. 3) are similar to those of the triplet forms of [M(CO)4] (M = Fe or Ru) calculated by Ziegler and co-workers 3 and that obtained more recently by Wang and Weitz 16a for [Fe(CO)4]. Using an equivalent method to that used here, both sets of authors calculated triplet [Fe(CO)4] to be slightly more stable (< 2 kcal mol21) than the singlet,¶ in accord with the experimental evidence that ‘naked’ [Fe(CO)4] exists as a triplet.2,3 The singlet form of [Ru(CO)4] was calculated to be significantly more stable than Fig. 2 Schematic representation of ML4 valence orbital changes upon C4v to C2v distortion Fig. 3 Geometries of triplet [M(PH3)4] species (M = Fe or Ru) ¶ It has been pointed out that calculated singlet–triplet separations can be dependent on the density functional employed and that the B3LYP functional exhibits a greater preference for the higher spin-state species than does the BP86 functional used here.16a Recently, Ruiz et al.16b have found the B3LYP functional to be especially effective at reproducing the singlet–triplet energy difference in hydroxy- and alkoxo-bridged copper(II) binuclear complexes.294 J.Chem. Soc., Dalton Trans., 1998, Pages 291–300 the triplet.15 For [Ru(PH3)4] the singlet is more stable by 11.7 kcal mol21, but for [Fe(PH3)4] the triplet was more stable than the singlet by 8.0 kcal mol21.The singlet–triplet energy gap is therefore significantly larger for [Fe(PH3)4] than for [Fe(CO)4]. UV/VIS spectra. The experimental evidence for the structure of [Ru(dmpe)2] is based mainly on its UV/VIS spectrum which exhibits three low-energy absorption bands and is consistent with a square-planar geometry. The lowest-energy band is assigned as a dz2 > pz transition on the basis of its absorption coefficient and occurs experimentally at 13 800 cm21 in pentane solution. The equivalent transition occurs at 25 600 cm21 for square-planar [Rh(dmpe)2]1 in methanol.7 The calculated energies of these transitions in the [M(PH3)4] model species are 13 900 and 26 200 cm21 for M = Ru and Rh1 respectively. Thus, we find remarkably good reproduction of the experimental trend.For [Fe(dmpe)2] in pentane solution a single band has been observed at 28 200 cm21.6 The dz2 > pz transition in singlet [Fe(PH3)4] is calculated to occur at 2530 cm21, and so the lowest-energy excitation would be expected to occur in the IR region of the spectrum.However, as we have seen, the dmpe ligand appears to favour a planar structure. Recalculation of this transition energy for square-planar [Fe(PH3)4] [optimised under C2v symmetry, Fe-P (average) = 2.107 Å] gives a value of 6600 cm21. This suggests a low-lying band would be seen in the visible/near-IR spectrum of square-planar singlet [Fe(dmpe)2].Following this prediction, we measured the spectrum of [Fe(dmpe)2] in an argon matrix from 4000 to 12 500 cm21, a region which has not been examined previously. No absorptions were detected. In summary, our calculations on [Ru(PH3)4] support the experimental evidence that [Ru(dmpe)2] has a singlet electronic configuration in the ground state and a structure close to square planar.For [Fe(PH3)4] the calculations favour the triplet structure. The experimental data on [Fe(dmpe)2] do not provide direct evidence for or against a triplet state, nor do they preclude a spin-state equilibrium. Reactivity of [M(PH3)4] species with H2 and CO The reactivity of [M(dmpe)2] species was modelled by computing the reaction profiles for the approach of the substrate molecules towards the [M(PH3)4] model species in the singlet electronic configuration. The energy of each point on the reaction profile was then plotted relative to that of the reactants in their optimum singlet-state geometries.We do not include any correction for zero-point energies. The difference in zero-point energy between products and reactants for the oxidative addition of H2 is estimated to be about 2.2 kcal mol21 based on two M]H stretching frequencies at 1770 cm21 and four deformations modes at 600 cm21. Oxidative addition of H2 to [M(PH3)4] (M 5 Ru, Fe or Rh1). The geometries of the octahedral products of oxidative addition of H2 to [M(PH3)4] are shown in Fig. 4 along with the calculated energies of formation (DEform) for the products. As expected, the two (equatorial) phosphine ligands in the plane of addition bend away from the hydride ligands while the other two (axial) phosphines incline slightly towards the H ? ? ?H midpoint. The optimised M]H bond lengths compare well with available neutron diffraction data: in [Fe(dppe)2H(H2)]1 the Fe]H bond is 1.535 Å 45 and the Fe]H distance averages 1.526 Å in [Fe(PEtPh2)3H2(H2)] 46 compared with a computed value of 1.511 Å.The Rh]H distance in [Rh(h5-C5Me5)H2(SiEt3)2] 47 average 1.581 Å compared with the calculated Rh]H value of 1.598 Å, while the computed Ru]H distance of 1.643 Å compares to experimental values of 1.630 Å in [Ru(h5-C5H5)- (PMe3)2H] and 1.602 Å (average) in [Ru(h5-C5H5)(PMe3)2H2]1.48 In all three structures the trans influence of the hydride ligand causes the equatorial M]P bonds to be slightly longer than both the M-P axial bonds and the M]P distances calculated for the four-co-ordinate singlet reactants.Little elongation of the axial M]P bonds is seen. The large negative values obtained for DEform with singlet [Fe(PH3)4] and [Ru(PH3)4] (242.6 and 237.6 kcal mol21 respectively) suggest a strong thermodynamic drive for the addition of H2. With triplet [Fe(PH3)4] DEform is calculated to be 234.4 kcal mol21. For [Rh(PH3)4]1 the thermodynamic driving force is much smaller (DEform = 215.6 kcal mol21).The calculated values of DEform are therefore consistent with the high reactivity of the experimental ruthenium and iron analogues and with the relatively lower reactivity of Rh1 experimental analogues towards oxidative addition of H2. In order to understand the origin of the high reactivity of the neutral [M(PH3)4] systems toward H2, we have computed reaction profiles for the oxidative-addition process.Previous studies have found that an ‘end-on’ (or h1) approach of H2 is energetically favoured over a ‘side-on’ (or h2) approach at long M](H2) separations.18–20 Two reaction profiles corresponding to these two different orientations of the H2 moiety relative to the [M(PH3)4] reactant were therefore considered. Both were computed within C2v symmetry and defined by the M]x distance, x being the H ? ? ? H midpoint (Scheme 1). All other variables were optimised. Profiles for the reaction of [Ru(PH3)4] 1 H2 (Fig. 5) compare the h1 and h2 approaches calculated both at the LDA level and with the inclusion of non-local corrections, LDA 1 NL. At the LDA level the h1 approach is indeed favoured at long Ru]x distances (>2.4 Å) and, within C2v symmetry, a [Ru(PH3)4- (h1-H2)] adduct is formed with Ru]x 2.25 Å. This species is calculated to be 9.0 kcal mol21 more stable than the isolated reactants. At shorter Ru]x distances the h1 approach is rapidly destabilised.When the geometry of the C2v adduct is reoptimised in Cs symmetry the H2 moiety moves off the local C2 axis Fig. 4 Geometries of singlet [M(PH3)4H2] species (M = Fe, Ru or Rh1) Scheme 1 M H x H M x H H h1 approach h2 approachJ. Chem. Soc., Dalton Trans., 1998, Pages 291–300 295 and the optimised structure of the final [Ru(PH3)4H2] species is obtained. The addition of H2 to [Ru(PH3)4] via an h2 approach is calculated to proceed without any activation barrier at the LDA level.Similar trends are seen in the reaction profiles calculated at the LDA 1 NL level [Fig. 5(b)]. The h1 approach remains favoured at long Ru]x distances and, within C2v symmetry, a [Ru(PH3)4(h1-H2)] adduct is formed without any activation barrier. This species is only 1 kcal mol21 more stable than the isolated reactants. Significantly, at this level of calculation the h2 approach of H2 towards [Ru(PH3)4] is computed to have a small activation barrier (ª 2 kcal mol21).This result is inconsistent with the kinetic data for the oxidative addition of H2 to [Ru(dmpe)2] which indicate the absence of an activation barrier for this reaction. As we have only included non-local corrections as a perturbation on the LDA results and not selfconsistently in the computation of the reaction geometries, we cannot be certain that the [Ru(PH3)4(h1-H2)] adduct corresponds to a local minimum at the LDA 1 NL level. Likewise, true transition states involved in these processes have not been optimised (as no transition state is calculated in the LDA reaction profiles) and so we only provide estimates of the energies associated with these species from the shape of the LDA 1 NL reaction profiles.The reaction profiles calculated at the LDA level for the reactions of [Fe(PH3)4] and [Rh(PH3)4]1 with H2 are similar to those described above for [Ru(PH3)4]. For [Fe(PH3)4] at the LDA 1 NL level a small activation barrier (ª 1 kcal mol21) is associated with both the h1 and h2 approaches of H2 at Fe]x separations greater than 3 Å (Fig. 6).Within C2v symmetry we compute the presence of an h1 adduct with Fe]x 2.1 Å at this level. In contrast, for [Rh(PH3)4]1 1 H2 (Fig. 7) no h1 adduct is predicted: the LDA 1 NL curve for h1 approach is weakly repulsive at long Rh]x distances and is destabilised above the h2 approach at Rh]x ª 2.3 Å. An activation energy of approximately 3 kcal mol21 is required for the h2 approach of H2 in this case and the transition state occurs with an Rh]x distance of approximately 2.3 Å.Note that at the LDA level the h2 Fig. 5 Reaction profiles for the h1 and h2 approaches of H2 towards singlet [Ru(PH3)4] calculated at the LDA level (a) and including nonlocal corrections (LDA 1 NL) (b) approach of H2 towards [Rh(PH3)4]1 is calculated to proceed without any activation barrier. This result is inconsistent with the relatively low reactivity of experimental rhodium(I) analogues and stresses the need to include non-local corrections in the computation of reaction profiles.For all three systems therefore, the optimum reaction coordinate for addition of H2 may involve an h1 approach early in the reaction. As the M]x distance decreases further the H2 fragment must swing round into an h2 conformation. To investigate this process we have calculated a third reaction pro- file defined by the M]H]H angle, q. The h1 adducts described above have q = 1808, while at the other extreme the final octahedral oxidative-addition products have q ª 488.Fig. 8 shows this reaction profile for [Ru(PH3)4], computed at the LDA 1 NL level, as well as a schematic representation of the changes in r(H]H), r(Ru]H) and the Peq]Ru]Peq angle during the approach of H2 toward [Ru(PH3)4]. Most significantly, the h1/h2 swing proceeds without activation energy for the Ru(PH3)4 1 H2 reaction. This contrasts with the reaction pro- file computed for the oxidative addition of H2 to [Ru(CO)4] which displayed a distinct activation barrier.15a However, only the h2 approach of H2 was considered in that study, whereas the results presented here indicate that the orientation of the H2 moiety during the oxidative-addition reaction can be important in determining activation barriers.Fig. 8 shows that the steep fall in energy begins when r(Ru]H) ª 1.77 Å and q = 1408. At this stage Peq]Ru]Peq also starts to decline rapidly. However, the value of r(H]H) remains little changed until q = 1008 at which r(Ru]H) = 1.65 Å is close to its final value of 1.64 Å.Only then elongation of H]H occurs. Similar results were obtained with [Fe(PH3)4]. In contrast, for [Rh(PH3)4]1 the h1/h2 swing requires an activation energy of >4 kcal mol21. Addition of CO to [M(PH3)4] (M 5 Ru or Fe). The addition reaction with CO was studied with [Ru(PH3)4] and [Fe(PH3)4]. Fig. 6 Reaction profiles for the h1 and h2 approaches of H2 towards singlet [Fe(PH3)4] (LDA 1 NL) Fig. 7 Reaction profiles for the h1 and h2 approaches of H2 towards singlet [Rh(PH3)4]1 (LDA 1 NL)296 J. Chem. Soc., Dalton Trans., 1998, Pages 291–300 Since the experimental analogues of [Rh(PH3)4]1 undergo phosphine substitution with CO rather than forming an addition product,32 this system was not studied. The geometries of the five-co-ordinate product species optimised in C2v symmetry are shown in Fig. 9. As for the dihydride species, the equatorial M]P bonds are somewhat longer than the axial M]P bonds. The calculated Ru]C bond distance (1.870 Å) is comparable to that found experimentally for [Ru(dmpe)2(CO)] (1.850 Å).42 The calculated Fe]C bond length (1.714 Å) is shorter than those found in the structure of [Fe(dppm)(CO)3] (dppm = Ph2PCH2PPh2) in which the average Fe]C bond distance is 1.76 Å.49 The energy of formation for the two products (259.5 and 243.5 kcal mol21 for M = Fe and Ru Fig. 8 Reaction profile and schematic representation of geometrical changes for the h1/h2 swing of H2 with singlet [Ru(PH3)4] (LDA 1 NL).Energies are relative to the sum of the isolated reactants set to zero, as indicated at the extreme right of the profile Fig. 9 Geometries of [M(PH3)4(CO)] species (M = Fe or Ru) respectively) shows that addition of CO to the model species is a strongly thermodynamically favoured process. An ab initio study of addition of CO to Vaska’s compound has found a transition state featuring a non-linear Ir]C]O unit to be more stable than its linear equivalent.19a Reaction profiles for the addition of CO to [M(PH3)4] species, defined by the M]C distance, were therefore computed in both C2v and Cs symmetry, the latter allowing the CO moiety to move off the local C2 axis of the [M(PH3)4] fragment if it was energetically favourable to do so.The computed reaction profiles are shown in Fig. 10 for M = Ru. Similar results were obtained for M = Fe.The addition of CO to [M(PH3)4] species is computed to proceed without an activation barrier for both M = Fe and Ru once the non-linear approach of CO is taken into account. These results are consistent with the experimental rate constant obtained for the addition of CO to [M(dmpe)2] species which exceeded 109 dm3 mol21 s21 for both metals and, in the case of Ru, was near diffusion control (i.e. very little, if any, activation energy).6 At long M]C separations (>2.5 Å) we found that geometries with M]C]O angles of approximately 1078 were favoured for both metals.Imposing a linear approach of CO (C2v symmetry) resulted in a small activation barrier (ª2 kcal mol21) for both metals at long M]C separations (M]C > 3.5 Å). Discussion Structure and ground-state electronic configuration of [M(dmpe)2] species The UV/VIS spectrum of [Ru(dmpe)2] suggests that this species has a geometry which is square planar or close to it.7 The rate constants for reaction with CO and H2 are close to the diffusion limit suggesting that [Ru(dmpe)2] has a singlet electronic state.The calculations on [Ru(PH3)4] show that a near square-planar D2d geometry with a singlet-state configuration is 11 kcal mol21 more stable than the triplet configuration (C2v geometry). The calculated energy of the dz2 > pz transition is also consistent with the experimental results and the computed profiles for reaction with both H2 and CO do not feature any activation barrier.Thus both experiment and calculation are in agreement with a near square-planar, singlet ground state for [Ru(dmpe)2]. For the iron system neither experiments nor calculations are so clear. Experimentally, the lack of correspondence in spectra and the different rates of reaction relative to the ruthenium system point to a change in structure. The reaction with CO is extremely rapid, but not close enough to the diffusion limit to exclude a triplet configuration.The experimental evidence for the role of specific solvation is inconclusive. The calculations on [Fe(PH3)4] show that a C2v triplet is more stable than a C2v singlet structure by 8.0 kcal mol21. The dz2 æÆ pz transition of singlet [Fe(PH3)4] is predicted to occur in the visible/near-IR Fig. 10 Reaction profiles for the addition of CO to singlet [Ru(PH3)4] allowing for linear (C2v) and non-linear (Cs) approaches of CO (LDA 1 NL)J. Chem. Soc., Dalton Trans., 1998, Pages 291–300 297 region of the spectrum, but no absorptions are observed within this spectral range.The calculations predict a small barrier for the addition of H2 to singlet [Fe(PH3)4] but no barrier for addition of CO. Overall the reactivity of singlet [Fe(PH3)4] is predicted to be similar to that of singlet [Ru(PH3)4]. The experimental and theoretical evidence both argue therefore against a square-planar singlet ground state. Since the reaction may involve singlet [Fe(dmpe)2], triplet [Fe(dmpe)2] and the solvent adduct [Fe(dmpe)2S], calculations including this solvated species would therefore be necessary for a full understanding of the reactivity of the iron system.If one assumes a triplet structure for [Fe(dmpe)2] the activation energies for addition of CO and oxidative addition of H2 can be estimated from the difference in energy between the triplet and singlet states to increase by 8.0 kcal mol21. Influence of the L group on the singlet and triplet states of ML4 The energy patterns computed for singlet and triplet [M(PH3)4] are similar to those calculated previously for analogous [M(CO)4] species (M = Ru or Fe).15 The geometries calculated here for singlet [Fe(PH3)4] and triplet [M(PH3)4] are also similar to their carbonyl analogues.However, our calculations predict a D2d structure for singlet [Ru(PH3)4] with angles of about 1608 at Ru whereas singlet [Ru(CO)4] was computed to have a C2v geometry with angles of about 175 and 1308 at the metal.The mixed-ligand species [Ru(CO)2(PH3)2], appears to be closer to the tetracarbonyl complex since it adopts a singlet ground state with C]Ru]C and P]Ru]P angles of 133 and 1738 respectively (MP2 optimisation).9 These structural trends in the ruthenium systems are consistent with the conclusions of Elian and Hoffmann, 14 who showed that the tendency for d8 ML4 systems to deviate from square-planar geometry is associated with the presence of p-acceptor ligands and is consistent with the relatively weak p-acceptor capability of phosphine ligands.Distortion away from a square-planar geometry is also a reflection of the metal centre. The C2v structure of [Ru(CO)2- (PH3)2] is promoted by strong p-back donation from the highlying metal-based orbitals. In contrast, [Rh(CO)2(PH3)2]1, in which the metal-based orbitals are much lower in energy, adopts a square-planar geometry.9 The deviations from square planarity calculated for singlet [Fe(PH3)4] and [Ru(PH3)4] in the present study suggest that p-back donation from high-lying metal-based orbitals is important in these systems with lowoxidation- state metal centres as well.The near square-planar structure computed for [Rh(PH3)4]1 is consistent with these ideas. Reactivity of singlet [M(PH3)4] species Oxidative addition of H2. The oxidative addition of H2 to [M(PH3)4] species has been studied for three metal systems where M = Fe, Ru or Rh1. Experimental data demonstrate that the iron and ruthenium experimental analogues, [Fe(dmpe)2] and [Ru(dmpe)2], are highly reactive species.In contrast, [Rh(dmpe)2]1 is unreactive enough to be characterised crystallographically. Starting from a singlet geometry, product formation is calculated to be strongly favoured thermodynamically with the iron and ruthenium model complexes. In contrast, addition of H2 to [Rh(PH3)4]1 is much less exothermic. We attempt to account for the greater reactivity of the neutral [M(PH3)4] systems by employing an energy-decomposition scheme 50 to analyse the bonding between the [M(PH3)4] and {H ? ? ? H} fragments within [Rh(PH3)4H2]1 and [Ru(PH3)4H2].The major interactions between these two fragments are summarised in Fig. 11 in which the orbital numbering employed in the following discussion is also indicated. The decomposition approach allows the bonding energy between two closed-shell fragments to be split up into a stericrepulsion term (DEsteric) and an orbital-interaction term (DEoi); DEsteric is made up of the four-electron destabilising interactions between occupied orbitals (exchange repulsion) and the electrostatic interaction between the nuclear and electronic distributions of the two fragments.The orbital-interaction term can be further divided into contributions from each symmetry representation. We also consider the energy required to distort each of the two isolated reactants to arrive at the geometries found in the optimised structure of the product (DEprep).The results of the energy decomposition analysis are given in Table 1. On comparing the ruthenium and Rh1 systems, we find DEprep to be 8.4 kcal mol21 higher for [Rh(PH3)4]1–{H ? ? ? H}, the majority of this difference resulting from the higher energy required to distort the [Rh(PH3)4]1 moiety away from a squareplanar geometry. Analysis of the DEsteric term indicates that the electrostatic interaction is more stabilising by 15 kcal mol21 for [Rh(PH3)4]1–{H ? ? ? H}, as would be expected for a cationic fragment.In contrast, the exchange repulsion term is less destabilising for [Ru(PH3)4]–{H ? ? ? H} by 34 kcal mol21. Finally the orbital interaction contribution is larger for [Rh(PH3)4]1–{H ? ? ? H} by 5 kcal mol21. The major difference in DEform therefore originates from DEsteric (19 kcal mol21) and can be traced to the much larger exchange repulsion seen in the Rh1 system.The origin of the larger exchange repulsion calculated in [Rh(PH3)4H2]1 compared with [Ru(PH3)4H2] must arise from Fig. 11 Schematic representation of major interactions between [M(PH3)4] and {H ? ? ? H} fragments. The 3a2 and 6b, metal-based valence orbitals which are non-bonding with respect to the {H ? ? ? H} fragment have been omitted for clarity Table 1 Energy decomposition data (kcal mol21) for [M(PH3)4H2] (M = Ru or Rh1) DEsteric Exchange repulsion Electrostatic Total DEoi a1 b2 Total Total bonding energy DEprep * DEform [Ru(PH3)4]– {H ? ? ? H} 206.3 2208.2 22.0 248.2 2119.4 2168.1 2170.1 14.2 1 115.0 237.6 [Rh(PH3)4]1– {H ? ? ? H} 240.2 2223.3 16.9 259.7 2113.1 2173.3 2156.4 25.3 1 112.5 215.6 * The two figures refer to DEprep terms for the [M(PH3)4] and {H ? ? ? H} fragments298 J.Chem. Soc., Dalton Trans., 1998, Pages 291–300 the interaction of the occupied sg orbital of {H ? ? ? H} with occupied metal fragment orbitals of a1 symmetry, in particular the metal-based 9a1 orbital.In general, one would expect the metal-based orbitals of a ruthenium(0) species to lie to much higher energy than those of an isoelectronic Rh1 cation.9 This should result in a larger energy gap between sg {H ? ? ? H} and the 9a1 orbital of the ruthenium fragment, leading to reduced exchange repulsion in that case. Although DEoi between the [M(PH3)4] and {H ? ? ? H} fragments in the final product molecules is rather similar for both ruthenium and Rh1 systems the contributions from the different symmetry representations depend on the nature of the metal centre.Thus for [Ru(PH3)4]–{H ? ? ? H} we find the a1 and b2 orbital interactions contribute 248 and 2119 kcal mol21 respectively. The corresponding figures for [Rh(PH3)4]1– {H ? ? ? H} are 260 and 2113 kcal mol21. These differences can again be understood in terms of the higher energy of the metalbased orbitals of the [Ru(PH3)4] fragment.The high energy of the 6b2 orbital of [Ru(PH3)4] should result in it acting as a better donor into su*{H ? ? ? H} than the equivalent low-lying 6b2 orbital of the [Rh(PH3)4]1 fragment. For similar reasons the acceptor capabilities of the 10a1 orbital will be relatively poor in [Ru(PH3)4] compared to [Rh(PH3)4]1. These conclusions are supported by the calculated orbital populations of the sg and su* orbitals of the {H ? ? ? H} fragment in the final [M(PH3)4H2] species (see Table 2).The stronger acceptor nature of [Rh(PH3)4]1 results in the more efficient depopulation of the sg orbital in this case while back donation into su* is greater for [Ru(PH3)4]. However, in terms of the overall orbital interaction these two effects approximately cancel out. A similar comparison between the iron and ruthenium systems is hampered by the different geometries of the species involved. This results in large changes in DEprep and DEsteric which may simply reflect these geometrical changes rather than any difference in the intrinsic electronic properties of the iron and ruthenium centres.We shall therefore not use this fragmentation approach for the comparison of the first- and second-row transition-metal species. Reaction with CO. The reactions of [M(PH3)4] with CO (M = Fe or Ru) are both computed to be highly exothermic, consistent with the high reactivity of their M(dmpe)2 experimental analogues. In this case DEform can be equated to a M]CO bond dissociation enthalpy, DH, and is computed to be slightly larger for the iron system.This conclusion, that DH3d > DH4d, is consistent with the results of previous theoretical 15,51 determinations of M]CO bond dissociation in related polycarbonyl systems, including a recent study employing highlevel ab initio calculations.52 However, an experimental study of the first M]CO bond-dissociation enthalpy in Group 6 M(CO)6 species gave the order DH5d > DH4d > DH3d.53 We shall not pursue this issue further in the present paper but note that DEform for the oxidative addition of H2 to [Fe(PH3)4] and [Ru(PH3)4] is again computed to be larger for the first-row metal.For reasons discussed in the previous section we do not attempt a more detailed comparison of the 3d and 4d M(PH3)4(CO) systems. Reaction profiles. The different reaction profiles computed for the oxidative-addition reaction of H2 to [M(PH3)4] species allow us to propose the likely course of these reactions.For [Ru(PH3)4] both the initial h1 approach of H2 and subsequent Table 2 Orbital populations (e) for the {H ? ? ? H} fragment in [M(PH3)4H2] species (M = Ru or Rh1) M sg su* Ru 1.34 1.03 Rh1 1.15 0.91 h1/h2 swing can occur without any activation barrier. For singlet [Fe(PH3)4] both the h1 and h2 approaches appear equally probable, both requiring small activation energies (ª1 kcal mol21) at long Fe]x separations (>3.0 Å). The h1/h2 swing is again barrierless in this case.For [Rh(PH3)4]1 the h1 approach is favoured at long Rh]x separations, but we estimate the activation energy required for the h1/h2 swing to be at least comparable and possibly slightly larger than that estimated for the h2 approach. The transition state in this case may well have a ‘product-like’ C2v geometry with Rh]x ª 2.3 Å. The different reaction profiles can be understood in terms of the fragmentation analysis performed above. For example, the absence of a barrier for the reaction between [Ru(PH3)4] and H2 is a result of the donor/acceptor characteristics of the metal species.The linear approach of H2 is stabilised by good donation from the high-lying 9a1 into su*(H2) while any 9a1/sg destabilisation is relatively small due to the large energy mismatch between these orbitals. This reduced destabilisation coupled with the strong p-donor power of the metal 6b2 orbital, which is further enhanced by the distortion of the [Ru(PH3)4] moiety,18–20 allows the reorientation and cleavage of the H2 moiety to proceed without any activation barrier.The similar form of the reaction profile calculated between [Fe(PH3)4] and H2 suggests a comparable series of orbital interactions with decreasing Fe]x distances, although in this case we calculate a small activation barrier for the h1 approach at Fe]x ª 3.5Å. This may simply be due to reduced overlap arising from the more contracted Fe-based orbitals in this case.The small activation barrier calculated for the reaction between singlet [Fe(PH3)4] and H2 may contribute to the slower reaction rate observed with [Fe(dmpe)2] compared to [Ru(dmpe)2]. However, as the precise nature of the transient species formed in the case of the iron complex is not known, the role played by this activation barrier in determining the overall reaction rate is not clear. As for [Fe(CO)4] 1 H2,45 the triplet ground state of [Fe(PH3)4] complicates any analysis of reaction profiles. For the reaction of [Rh(PH3)4]1 with H2 the linear approach is again preferred at long Rh]x separations.However, reorientation of the H2 moiety entails a significant activation barrier due to the low energy of the metal 9a1 orbital (greater 9a1/sg destabilisation) and the lower p-donor ability of the metal 6b2 orbital in this case. Overall an h2 approach may be favoured in this case as this maximises the donation from sg (H2) into the low-lying 10a1 acceptor orbital of the [Rh(PH3)4]1 fragment.Similar considerations apply to the addition of CO to [M(PH3)4] species (M = Fe or Ru). In this case the four-electron destabilisation occurs between the lone pair of CO and the 9a1 metal-based orbital. However, as has been described previously for the addition of CO to trans-[Ir(PH3)2(CO)Cl],19a this destabilisation can be reduced by a non-linear approach of CO towards the metal fragment. The early stages of this reaction have been described as a nucleophilic attack of the metalbased a1 HOMO on the p* acceptor orbital of CO.For the addition of CO to [M(PH3)4] species the computed reaction curves indicate that the non-linear approach of CO can completely override the effect of any four-electron destabilisation early in the reaction profile. The subsequent reaction then proceeds without any activation barrier. This is in contrast to the above study of the reactivity of Vaska9s complex where an activation barrier of 4.6 kcal mol21 was calculated.This difference is again probably a reflection of the high energy of the metal-based orbital in our systems which results in better MÆCO p donation and reduced four-electron destabilisation compared to the equivalent interactions involving trans- [Ir(PH3)2(CO)Cl]. Conclusion Density functional calculations have been carried out onJ. Chem. Soc., Dalton Trans., 1998, Pages 291–300 299 [M(PH3)4] as models for transient [M(dmpe)2] species which are formed from the photolysis of [M(dmpe)2H2] (M = Fe or Ru).Calculations have also been performed on [Rh(PH3)4]1 as a model for the relatively inert [Rh(dmpe)2]1. The singlet electron configurations of [Ru(PH3)4] and [Rh(PH3)4]1 were found to have D2d geometries with trans] P]M]P angles of 159 and 1728 respectively. Singlet [Fe(PH3)4] was computed to have a C2v structure with angles of 137 and 1608 at Fe. The structure of [Ru(PH3)4] differs, therefore, from the isoelectronic [Ru(CO)4] and [Ru(CO)2L2] species while the computed structure of singlet [Fe(PH3)4] is similar to that calculated for singlet [Fe(CO)4].The triplet configurations of [Fe(PH3)4] and [Ru(PH3)4] were predicted to adopt C2v geometries with P]M]P angles ca. 155 and 958 and thus resemble analogous [M(CO)4] triplet species (M = Fe or Ru). For [Ru(PH3)4] the singlet structure is calculated to be 11 kcal mol21 more stable than the triplet, while the triplet form of [Fe(PH3)4] is 8 kcal mol21 more stable in this case.The singlet/triplet energetic preferences have therefore now been calculated for the two known pairs of homoleptic ML4 species (M = Fe or Ru, L = CO or PH3). The calculations on [Ru(PH3)4] and [Rh(PH3)4]1 reproduce the UV/VIS spectra, geometries and relative reactivities of these species towards H2 satisfactorily. For [Ru(PH3)4] the reaction with H2 is calculated to be highly exothermic and to proceed without an activation barrier.For [Rh(PH3)4]1 the reaction with H2 is much less thermodynamically favoured and proceeds with an activation barrier of approximately 3 kcal mol21. The reaction between H2 and singlet [Fe(PH3)4] is also highly exothermic and proceeds with a small activation barrier at long Fe]H2 separations. An h1 approach of H2 to [M(PH3)4] (M = Fe or Ru) is preferred at large M ? ? ?H2 separations, but H2 is predicted to tilt to an h2 orientation in the later stages of reaction.Elongation of the H ? ? ? H distance occurs very late in the reaction profile. Although the h1 approach is computed to be more stable at long Rh1 ? ? ?H2 separations, the transition state formed with [Rh(PH3)4]1 is likely to have an h2-H2 geometry. The addition of CO to [M(PH3)4] (M = Fe or Ru) is calculated to be highly exothermic. With an angled approach of CO, the activation energy for reaction with both species is zero. The zero {or, in the case of singlet [Fe(PH3)4] 1 H2, minimal} activation energies computed for the reactions of [M(PH3)4] species (M = Fe or Ru) with H2 and CO reflect the high energies of the metal-based valence orbitals of these systems.This allows the metal centre to act as a strong electron donor and reduces the four-electron destabilisation that occurs upon approach of the substrate molecule. The high energy of the metal-based valence orbitals results in these species being relatively poor acceptors of electron density.However, any acceptor capabilities will be enhanced by a small HOMO– LUMO gap and will further promote low activation barriers. Acknowledgements We thank the EPSRC for a Western European NATO Fellowship (S. A. M.) and support (R. N. P., M. K. W.). 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