A quantum mechanics/molecular mechanics study of the steric influence of the PR₃ spectator ligands on the energetics of ethylene insertion into the Rh–H bond of HRh(PR₃)₂(CO)(η²-CH₂[double bond, length half m-dash]CH₂)

Abstract

Details of a quantum mechanics/molecular mechanics (QM/MM) study aimed at determining how the substituents of the spectator phosphine ligands influence the energetics of the key step in olefin hydroformylation, the insertion of an olefin into the Rh–H bond of HRh(PR₃)₂(CO)(η²-olefin), are discussed. For ethylene there are a total of three insertion pathways originating from the two η²-ethylene isomers, with either a bis-equatorial arrangement (ee) or a mixed equatorial, axial arrangement (ea) of the two PR₃ ligands. The energetics, kinetic and thermodynamic, of these three pathways were computed for a variety of phosphine substituents (PR₃; R = Me, ^tBu, Ph, meta-PhSO₃⁻, and para-PhSO₃⁻) using the ONIOM QM/MM approach. These calculations predict that two reaction channels, one originating from the more stable ea η²-ethlyene adduct and the other from the less stable ee η²-ethylene adduct, will be operative for the ethylene insertion reaction with the PMe₃ ligand system, although the latter will be preferred thermodynamically over the former. In the case of the aryl phosphine ligands, a clear energetic preference, kinetically and thermodynamically, was found for ethylene insertion to proceed from the least stable ee ethylene adduct versus the paths originating from the more stable ea ethylene adduct.

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The hydroformylation of olefins (i.e., the conversion of an olefin, CO, and H₂ to the corresponding aldehyde) is one of the largest, most important industrial catalytic processes, producing millions of tons of aldehydes annually. As such it has garnered considerable attention from experimental and computational chemists. The widely accepted mechanism for olefin hydroformylation employing the HRh(PR₃)₂(CO) catalyst system was proposed over 30 years ago by Wilkinson et al.^1–5 and it is displayed in Scheme 1 for ethylene hydroformylation. The catalytic cycle is comprised of many of the fundamental reactions of organometallic catalysis: oxidative addition/reductive elimination, insertion/elimination, and ligand association/dissociation. Furthermore, the reaction coordinate involves changes in both formal oxidation state and coordination number, and is thus challenging to model. A variety of organometallic compounds have been employed as homogeneous catalysts for olefin hydroformylation, although the phosphine modified Rh carbonyl complexes of the type HRh(PR₃)_m(CO)_n (where m = 1 and n = 2 or m = 2 and n = 1) have emerged as the most popular catalysts.

Scheme 1 Wilkinson's catalytic cycle for the hydroformylation of ethylene.

The mechanism of olefin hydroformylation has been the focus of a number of computational studies, as illustrated in the recent review article by Torrent et al.⁶ Frenking and co-workers have explored the initial catalyst generation step for the HRh(PR₃)_m(CO)_n catalyst systems.⁷ Morokuma et al. have constructed the entire potential energy hypersurface for ethylene hydroformylation by a HRh(PH₃)(CO)₂ model catalyst.^8–12 More recently, our group has investigated the mechanism of ethylene hydroformylation by a HRh(PH₃)₂(CO) model catalyst.¹³ Interestingly, experimental evidence has been interpreted in favor of a rate-determining H₂ oxidative addition step,^2,3 while the theoretical studies by our group¹³ and Morokuma et al.¹² indicated that CO insertion is rate-determining.

The hydroformylation of terminal olefins produces both linear and branched aldehydes, although linear aldehydes are the more desirable industrial product. The rational design and synthesis of transition metal catalysts that provide strict control of aldehyde regiochemistry has become one of the most active areas of research in hydroformylation catalysis.^14,15 The olefin insertion step has been shown to be irreversible, hence this step ultimately determines the regiochemistry of the aldehyde.¹⁶ Not surprisingly, the complex factors governing regioselectivity in olefin hydroformylation have been the subject of a number of theoretical studies,^17–19 including a recent QM/MM study by our group focusing on the insertion of propene into the Rh–H bond of HRh(PPh₃)₂(CO)(η²-CH₂[double bond, length half m-dash]CHCH₃).²⁰

The current research, which may be considered a corollary to our previous work,²⁰ employed the ONIOM^21,22 hybrid QM/MM approach to examine how the steric effects of the phosphine substituents (PR₃; where R = Me, ^tBu, Ph, meta-PhSO₃⁻, and para-PhSO₃⁻) influence the energetics of the key olefin insertion step in ethylene hydroformylation. (It should be added that the inclusion of the final two substituents in this study arose from their utility as ligands for the water-soluble olefin hydroformylation process.) Employing ethylene as a model olefin permits a thorough investigation of all possible reaction pathways originating from the two families of isomers of the ethylene adducts [i.e., a bis-equatorial (ee) and a mixed equatorial, axial (ea) arrangement of the two PR₃ ligands] for the insertion of ethylene into the Rh–H bond of HRh(PR₃)₂(CO)(η²-CH₂[double bond, length half m-dash]CH₂). Clearly, the use of ethylene as an olefin prohibits the investigation of regioselectivity in these catalyst systems, however, we feel that the results presented here provide a nice complement to our previous study.

Computational methods

The gas phase potential energy hypersurface for the insertion of ethylene into the RhH bond of HRh(PR₃)₂(CO)(η²-CH₂[double bond, length half m-dash]CH₂), for R = Me, ^tBu, Ph, meta-PhSO₃⁻, and para-PhSO₃⁻, was determined using a combined quantum mechanics (QM) and molecular mechanics (MM) approach according to the ONIOM methodology.^21,22 The QM region contained that portion of the molecule at the center of the insertion reaction and was comprised of the rhodium center and its inner coordination sphere, including the entire ethylene unit, that is HRh(PH₃)₂(CO)(η²-CH₂[double bond, length half m-dash]CH₂). Density functional theory, employing the B3LYP hybrid density functional (comprised of Becke's hybrid gradient-corrected exchange functional²³ and the gradient-corrected correlation functional of Lee, Yang, and Parr²⁴) was employed to model the QM region. In these DFT calculations, the effective core potential (ECP) valence basis set of Stevens et al.^25–27 was employed for Rh and the main group atoms. The standard 4-31G contracted basis set was employed for all of the hydrogen atoms in the calculations.²⁸ This basis set will hereafter be denoted as SBK. The MM region was limited to the bulky R substituents of the two spectator phosphine ligands, and these were modeled with the Universal Force Field (UFF²⁹) in the ONIOM calculations. The ONIOM approach employed will hereafter be denoted as B3LYP/SBK:UFF.

Full details of the ONIOM methodology have been described elsewhere,^21,22 thus only a short account of the energy expressions will be given here. In a two-layer ONIOM calculation, such as the DFT:UFF approach employed here, three energies must be calculated: the MM energy of the model system, the QM energy of the model system, and the MM energy of the real system. These three energies are then combined as follows in order to obtain the ONIOM total energy (in this case, the QM energy of the Rh core + the MM energy of the bulky phosphine substituents):

Employing the ONIOM approach one can calculate not only the QM/MM combined energy for the real system of interest, but also the gradient of the energy and the Hessian of the energy, needed for the optimization of geometries and the characterization of the resultant stationary points.

The geometries of all species were fully optimized, without any symmetry constraints, using analytical gradient techniques at the B3LYP/SBK:UFF level of theory. For all species, a preliminary conformational search was conducted, keeping the QM Rh core fixed, using the SYBYL force field³⁰ within the Spartan³¹ program prior to submission of the lowest energy conformer to a full ONIOM geometry optimization. All of the resultant optimized stationary points for the η²-ethylene adducts and the Rh–ethyl insertion products were characterized as minima on their respective potential energy hypersurfaces via harmonic vibrational analysis at the B3LYP/SBK:UFF level, using either analytical energy second derivatives or numerical differentiation of the analytical energy first derivatives. Calculation of the harmonic vibrational frequencies for the transition state (TS) species revealed that each contained the single imaginary frequency required to classify it as a true TS. Animation of the normal mode corresponding to this lone imaginary frequency displayed the nuclear motions expected for the ethylene insertion reaction. The Gaussian98 program package³² was employed for all of the ONIOM calculations. The Opt = NoMicro option within Gaussian98 was employed to aid the convergence of the geometry optimizations.

Results and discussion

The steric influence of the phosphine substituents on the energetics of the olefin insertion step in olefin hydroformylation was investigated in the present work. Employing ethylene as a model substrate, the energetics of the insertion reaction proceeding from the η²-ethylene adducts, HRh(PR₃)₂(CO)(η²-CH₂[double bond, length half m-dash]CH₂), through the various transition states (TSs) and on to the Rh–ethyl products, Rh(PR₃)₂(CO)(CH₂CH₃), were calculated for a variety of phosphine substituents (R) using the ONIOM hybrid QM/MM methodology. The results of these calculations are presented in the following sections.

Previous theoretical studies of the trigonal bipyramidal HRh(PH₃)_m(CO)_n(η²-CH₂[double bond, length half m-dash]CH₂) (m = 1 and n = 2 or m = 2 and n = 1) models found a strong energetic preference for ethylene to ligate in an equatorial coordination site, with the C[double bond, length half m-dash]C bond in the equatorial plane.^8,13 Although the increased steric demands of the PR₃ ligands appear to disfavor this parallel coordination mode for ethylene, all of the optimized structures obtained from the current ONIOM calculations revealed that the R groups are directed away from the ethylene ligand. Hence, it appears that the steric destabilization effect will be relatively small and will not override the strong electronic preference for the parallel coordination mode found previously. Given these findings, only structures with this parallel ethylene coordination mode were investigated in the present study. Within this structural motif there are two families of isomers for the η²-ethylene adducts: one in which the two PR₃ ligands are coordinated in the equatorial position, denoted as ee, and another containing an axial PR₃ and an equatorial PR₃ ligand, denoted as ea, as shown in Fig. 1.

Fig. 1 Schematic representation of the η²-ethylene adduct isomers, along with the notation adopted in the current paper.

Proceeding along the reaction coordinate towards the TS, the ethylene ligand rotates out of the equatorial plane and shifts upwards to align the incoming methylene unit with the axial hydride ligand. Interestingly, in the predicted TS structures the ethylene ligand does not complete the rotation to adopt a perpendicular arrangement but rather orients itself intermediate between a perpendicular and parallel alignment. The ethylene insertion reaction originating from the ee ethylene adduct goes through a single TS, denoted ee^‡, due to the C_s pseudo-symmetry of the ee isomer. On the other hand, there are two possible TSs for the ethylene insertion reaction originating from the ea adduct, denoted ea₁^‡ and ea₂^‡, depending on which direction the ethylene ligand rotates out of the equatorial plane (i.e., with the incoming CH₂ unit directed towards the equatorial PR₃ ligand or towards the equatorial CO ligand). Continuing along the reaction coordinate to the square planar Rh–ethyl insertion products the two PR₃ ligands can be either cis or trans to one another. These three reaction channels are displayed schematically in Fig. 2. The reaction channels displayed in Fig. 2 were verified previously by our group through the calculated intrinsic reaction coordinates (IRCs) for the analogous ethylene insertion in the PH₃ model catalyst system.¹³ Rocha and de Almeida¹⁷ have also corroborated this connectivity via IRC calculations for the related propene insertion reaction. Using this scheme as a guideline, the energetics, both kinetic and thermodynamic, for the three possible ethylene insertion reactions were computed for a variety of phosphine co-ligands of varying size (PR₃, where R = Me, ^tBu, Ph, meta-PhSO₃⁻, and para-PhSO₃⁻), the results of which are discussed in the following sections.

Fig. 2 A schematic representation of the three possible ethylene insertion reaction pathways. The adducts and TSs are viewed along the Rh–C[double bond, length half m-dash]C_centroid bond for illustrative purposes.

Phosphine substituent effects on alkene adduct stability

The relative energies of the ee and ea isomers of HRh(PR₃)₂(CO)(η²-CH₂[double bond, length half m-dash]CH₂) for the different phosphine substituents are organized in Table 1. Also included in Table 1 is a decomposition of each ONIOM energy into its quantum mechanics (QM) and molecular mechanics (MM) components. The results indicate an energetic preference of 1–2 kcal mol⁻¹ for the ea isomer over the ee isomer for all of the PR₃ ligands studied. It is interesting to note that the relative ONIOM energies of the ee and ea isomers are roughly constant for the alkyl/aryl groups investigated. A decomposition of the ONIOM energy reveals that the stability of the ea isomer arises from a lower electronic (QM) energy. Interestingly, the energy difference between ea and ee is very similar for R = Ph and R = para-PhSO₃⁻, indicating that the two substituents possess very similar steric profiles, while the ea–ee energy difference is slightly larger for R = Me and R = meta-PhSO₃⁻. Also included in Table 1 are the results obtained previously for PH₃ co-ligands.¹³ At the B3LYP/SBK(d) level of theory the ee and ea isomers were predicted to be degenerate. However, a refinement of the energies at the CCSD(T)/SBK(d)//B3LYP/SBK(d) level of theory predicted the ea isomer to be more stable than the ee isomer by 1.2 kcal mol⁻¹. Hence, it appears that the electronic preference for ea overrides the larger steric crowding between the two PR₃ ligands. The geometry optimizations of the ee and ea isomers of HRh(P^tBu₃)₂(CO)(η²-CH₂[double bond, length half m-dash]CH₂) led to the dissociation of one of the P^tBu₃ ligands. Although this prevents us from comparing the results for R = ^tBu, these results do suggest that for extremely bulky phosphine substituents the mono-phosphine, bis-carbonyl catalyst system [HRh(PR₃)(CO)₂] is likely the active catalyst species.

Table 1 Summary of the relative energies^a of the ethylene adducts and decomposition of the ONIOM energy into the QM and MM components

R	E(ee)^b	E QM(ee)^c	E MM(ee)^d	E(ea)^b	E QM(ea)^c	E MM(ea)^d
a All energies are in units of kcal mol^−1 and are taken relative to the lowest energy isomer. b Relative energies computed based on the total ONIOM energies for the real system. They include the zero-point energy corrections and are taken relative to the lowest energy isomer. c Relative energies computed based on the energies of the QM region of the molecule [i.e., EQM(model)] and are taken relative to the lowest energy isomer. d Relative energies computed based on the energies of the MM region of the molecule [i.e., EMM(real) − EMM(model)] and are taken relative to the lowest energy isomer. e Relative energies taken from a previous theoretical study by our group with the model PH3 ligand taken relative to the lowest energy isomer.^13 The first set of values were computed at the B3LYP/SBK(d) level of theory while those in parentheses correspond to the values computed at the CCSD(T)/SBK(d)//B3LYP/SBK(d) level of theory.
Me	2.0	1.8	0.2	0.0	0.0	0.0
Ph	1.5	1.5	0.0	0.0	0.0	0.0
m-PhSO3^−	2.4	1.0	1.4	0.0	0.0	0.0
p-PhSO3^−	1.4	1.3	0.1	0.0	0.0	0.0
H^e	0.0			0.0
	(1.2)			(0.0)

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Phosphine substituent effects on transition state stability

The relative energies of the three TS species (ee^‡, ea₁^‡, and ea₂^‡) for each phosphine substituent studied are displayed in Table 2, along with the QM and MM components of the ONIOM energy. As seen in Table 2, ea₁^‡ is predicted to be the least stable of the three TSs for all of the phosphine substituents studied here, due primarily to its substantially higher electronic energy. This TS isomer was also found to have the highest energy for R = H, supporting the inference that the instability of ea₁^‡ arises primarily from unfavorable electronic interactions.¹³ For R = Me, ea₂^‡ is predicted to be slightly more stable than ee^‡ by 0.7 kcal mol⁻¹ due primarily to a lower MM energy. For all of the aryl substituents, the ee^‡ TS isomer was predicted to be the most stable TS species, lower than ea₂^‡ by 1.3 (Ph), 0.2 (meta-PhSO₃⁻), and 1.7 (para-PhSO₃⁻) kcal mol⁻¹ and lower than ea₁^‡ by 3.7 (Ph), 0.7 (meta-PhSO₃⁻), and 4.3 (para-PhSO₃⁻) kcal mol⁻¹. Although, in all cases ea₂^‡ is favored electronically, the larger steric repulsion in ea₂^‡ raises its total energy versus the ee^‡ TS isomer.

Table 2 Summary of the relative energies^a of the ethylene insertion transition states and decomposition of the ONIOM energy into the QM and MM components

R	E(ee^‡)^b	E QM(ee^‡)^c	E MM(ee^‡)^d	E(ea1^‡)^b	E QM(ea1^‡)^c	E MM(ea1^‡)^d	E(ea2^‡)^b	E QM(ea2^‡)^c	E MM(ea2^‡)^d
a All energies are in units of kcal mol^−1 and are taken relative to the lowest energy isomer. b Relative energies computed based on the total ONIOM energies for the real system. They include the zero-point energy corrections and are taken relative to the lowest energy isomer. c Relative energies computed based on the energies of the QM region of the molecule [i.e., EQM(model)] and are taken relative to the lowest energy isomer. d Relative energies computed based on the energies of the MM region of the molecule [i.e., EMM(real) − EMM(model)] and are taken relative to the lowest energy isomer. e Relative energies taken from a previous theoretical study by our group with the model PH3 ligand taken relative to the lowest energy isomer.^13 The first set of values were computed at the B3LYP/SBK(d) level of theory while those in parentheses correspond to the values computed at the CCSD(T)/SBK(d)//B3LYP/SBK(d) level of theory.
Me	0.7	0.1	0.6	5.2	4.5	0.7	0.0	0.0	0.0
Ph	0.0	0.0	0.0	3.7	3.2	0.6	1.3	−1.0	2.3
m-PhSO3^−	0.0	0.0	0.0	0.7	4.1	−3.4	0.2	−0.9	1.1
p-PhSO3^−	0.0	0.0	0.0	4.3	3.1	1.2	1.7	−1.0	2.7
H^e	0.3			4.4			0.0
	(1.1)			(3.4)			(0.0)

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Phosphine substituent effects on product stability

The relative energies of the cis and trans Rh–ethyl insertion products are given in Table 3, along with the partitioning of the ONIOM energies into QM and MM components. From Table 3, the cis isomer is preferred energetically over the trans isomer by 0.9–5.8 kcal mol⁻¹, for all of the aryl substituents. In each case the trans isomer is preferred electronically, however, the overall stability is dictated by the lower steric energy of the cis isomer. From the optimized structures it appears that there is a π-stacking type interaction between the phenyl rings of the equatorial PR₃ ligand and the axial PR₃ ligand that acts to stabilize the cis isomer for these aryl phosphines, as shown in Fig. 3 for R = meta-PhSO₃⁻. The centroid⋯centroid distance of the two interacting rings in these cis products for the aryl phosphines is ≈3.6 Å, which agrees quite well with the available crystal structure data for Rh complexes containing two cis PPh₃ ligands, which is of the order of 3.5–3.8 Å.³³ Since the phosphine substituents are described in the MM region, this π-stacking is an MM component of the total energy. A UFF geometry optimization of 2 benzene molecules yields a centroid⋯centroid distance of 3.5 Å and a binding energy of 5 kcal mol⁻¹, which is more than ample to override the roughly 1–2 kcal mol⁻¹ electronic preference for the trans isomer. As seen in Table 3 for PMe₃, which has no possible π-stacking interaction, the trans isomer is predicted to be more stable than the cis isomer, by 1.3 kcal mol⁻¹. This stability arises from the lower QM energy of the trans isomer. The results for R = Me agree with those found previously for R = H, which predicted the trans isomer to be 1.9 kcal mol⁻¹ lower in energy than the cis isomer [2.3 kcal mol⁻¹ at the CCSD(T)/SBK(d)//B3LYP/SBK(d) level].

Table 3 Summary of the relative energies^a of the ethylene insertion products and decomposition of the ONIOM energy into the QM and MM components

R	E(cis)^b	E QM(cis)^c	E MM(cis)^d	E(trans)^b	E QM(trans)^c	E MM(trans)^d
a All energies are in units of kcal mol^−1 and are taken relative to the lowest energy isomer. b Relative energies computed based on the total ONIOM energies for the real system. They include the zero-point energy corrections and are taken relative to the lowest energy isomer. c Relative energies computed based on the energies of the QM region of the molecule [i.e., EQM(model)] and are taken relative to the lowest energy isomer. d Relative energies computed based on the energies of the MM region of the molecule [i.e., EMM(real) − EMM(model)] and are taken relative to the lowest energy isomer. e Relative energies taken from a previous theoretical study by our group with the model PH3 ligand taken relative to the lowest energy isomer.^13 The first set of values were computed at the B3LYP/SBK(d) level of theory while those in parentheses correspond to the values computed at the CCSD(T)/SBK(d)//B3LYP/SBK(d) level of theory.
Me	1.3	1.2	0.1	0.0	0.0	0.0
Ph	0.0	0.0	0.0	0.9	−1.3	2.2
m-PhSO3^−	0.0	0.0	0.0	5.8	−1.6	7.5
p-PhSO3^−	0.0	0.0	0.0	5.2	−2.4	7.6
H^e	1.9			0.0
	(2.3)			(0.0)

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Fig. 3 ONIOM optimized geometric structure of the cis isomer of the Rh–ethyl insertion product, HRh[P(meta-PhSO₃⁻)₃]₂(CO)(CH₂CH₃). Two views are given, one looking side-on at the two interacting phenyl rings and the other looking at the two rings from the top.

Phosphine substituent effects on reaction energetics

The calculated activation barriers (ΔE_a) and thermodynamic energies (ΔE) for the three ethylene insertion reaction channels: ee → ee^‡ → cis, ea → ea₁^‡ → trans, and ea → ea₂^‡ → trans (see Fig. 2) are summarized in Table 4 for the various phosphine substituents studied here. Also included in Table 4 are the ΔE_a and ΔE values for the three reaction channels calculated previously by our group for the model PH₃ ligand systems.¹³

Table 4 Summary of the calculated ethylene insertion activation barriers (ΔE_a) and thermodynamic energies (ΔE)^a

	Activation barrier ΔEa(i)^b			Thermodynamic energy ΔE(i)^c
R	ΔEa(1)	ΔEa(2)	ΔEa(3)	ΔE(1)	ΔE(2)
a All energies are in units of kcal mol^−1. They were computed based on the ONIOM energies of the various species involved and they include the zero-point energy correction. b Activation barriers were calculated based on the ONIOM energies of the adducts and the TS species and they include the zero-point energy correction. The index i refers to the numbering scheme of the ethylene insertion reaction pathways adopted in Fig. 2 (i.e., i = 1 for ee → ee^‡ → cis, i = 2 for ea → ea1^‡ → trans, and i = 3 for ea → ea2^‡ → trans). c Thermodynamic energies were calculated based on the ONIOM energies of the adducts and the Rh–ethyl insertion products and they include the zero-point energy correction. The index i refers to the numbering scheme of the ethylene insertion reaction pathways adopted in Fig. 2 (i.e., i = 1 for ee → cis and i = 2 for ea → trans). d Activation barriers and thermodynamic energies taken from a previous theoretical study in our group employing the model PH3 ligand.^13 The first set of values were computed at the B3LYP/SBK(d) level of theory while those in parentheses correspond to the values computed at the CCSD(T)/SBK(d)//B3LYP/SBK(d) level of theory.
Me	15.5	21.4	16.2	−3.1	−1.1
Ph	11.7	16.5	14.3	−3.8	−2.2
m-PhSO3^−	13.3	18.1	15.6	−6.6	0.8
p-PhSO3^−	11.6	16.6	14.2	−5.6	0.1
H^d	13.4	17.5	13.1	−4.8	−6.8
	(16.6)	(20.0)	(16.6)	(−0.6)	(−1.8)

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Thermodynamics. An examination of the calculated thermodynamics for the ethylene insertion reaction reveals a preference for ee → cis (reaction 1 in Fig. 2) over ea → trans (reactions 2 and 3 in Fig. 2) for all of the substituents studied here. For R = Me and R = Ph both of the reaction channels are predicted to be exothermic, with the ee → cis pathway predicted to be more exothermic, by 2.0 and 1.6 kcal mol⁻¹, respectively, than the ea → trans pathways. For the two PhSO₃⁻ substituents the ee → cis reaction channel is predicted to be exothermic (by 6.6 kcal mol⁻¹ for meta-PhSO₃⁻ and 5.6 kcal mol⁻¹ for para-PhSO₃⁻) while the ea → trans channel is predicted to be slightly endothermic (by 0.8 kcal mol⁻¹ for meta-PhSO₃⁻ and 0.1 kcal mol⁻¹ for para-PhSO₃⁻). Hence, the substitution of the phenyl rings with sulfonate groups is predicted by the ONIOM calculations to lead to a large thermodynamic preference for the cis product.

Kinetics. For the PMe₃ ligands, a slight energetic preference of 0.7 kcal mol⁻¹ was predicted for the ethylene insertion reaction to proceed along reaction channel 1 (cis product) as opposed to reaction channel 3 (trans product), while the barrier for reaction channel 2 was found to be substantially higher (by 5.9 kcal mol⁻¹). However, given the small difference between the energy barriers for these two preferred reaction pathways, it is likely that pathways 1 and 3 will be operative for the ethylene insertion reaction. Hence, for R = Me there does not appear to be a kinetic preference for the ethylene insertion reaction to proceed from either the ee or ea ethylene adduct. These results are similar to those found previously for the PH₃ model ligand system, which predicted the barriers for reaction paths 1 and 3 to be nearly equivalent, at 13.4 and 13.1 kcal mol⁻¹, respectively [16.6 kcal mol⁻¹ for both channels at the CCSD(T)/SBK(d)//B3LYP/SBK(d) level], and much lower than that predicted for pathway 2, at 17.5 kcal mol⁻¹ [20.0 kcal mol⁻¹ at the CCSD(T)/SBK(d)//B3LYP/SBK(d) level].¹³ However, the same cannot be said for the aryl substituents. For R = Ph, meta-PhSO₃⁻, and para-PhSO₃⁻ the energy barrier for ethylene insertion following reaction channel 1 was predicted to be significantly lower, by 2–3 kcal mol⁻¹, than the reaction following channel 3, while the barrier for reaction channel 2 was even larger, by 4–5 kcal mol⁻¹. Hence, the present calculations predict a clear energetic preference for the ethylene insertion reaction to proceed from the ee ethylene adduct (leading to the cis ethyl product) over the ea adduct (leading to the trans ethyl product) for the aryl phosphine ligands studied here.

Summary and conclusions

The current work employed the ONIOM QM/MM methodology to examine how the substituents of the spectator phosphine ligands (PR₃) influence the energetics of the key step in olefin hydroformylation, that is the olefin insertion step. Using ethylene as a model olefin, the energetics, both kinetic and thermodynamic, of the three possible ethylene insertion reaction pathways were computed for a variety of phosphine substituents (PR₃ where R = Me, ^tBu, Ph, meta-PhSO₃⁻, and para-PhSO₃⁻).

All geometry optimizations for R = ^tBu resulted in dissociation of one of the P^tBu₃ ligands, suggesting that the less sterically crowded HRh(P^tBu₃)(CO)₂ may be the active species in the olefin hydroformylation process, instead of the HRh(P^tBu₃)₂(CO) complex being investigated here.

The results of the current study indicated an energetic preference, of 1–2 kcal mol⁻¹, for the η²-ethylene adduct with a mixed equatorial, axial disposition of the two PR₃ ligands over the bis-equatorial isomer for the remaining phosphine substituents studied. A comparison of the energies of the two possible Rh–ethyl products, with PR₃ ligands either cis or trans, revealed an energetic preference for the trans arrangement when R = Me, due to a lower electronic energy, and an energetic preference for the cis arrangement when R was one of the aryl substituents, due to its lower MM energy. Although this latter results seems somewhat misleading, it can be rationalized by the existence of a stabilizing π-stacking interaction between the phenyl rings of the equatorial and axial phosphine ligands.

A comparison of the computed activation barriers for the three ethylene insertion reaction pathways reveals that the barrier for pathway 2 (ea → ea₁^‡ → trans) is significantly higher (by 2–5 kcal mol⁻¹) than that predicted for the two alternative reaction pathways (ee → ee^‡ → cis and ea → ea₂^‡ → trans) for all of the phosphine substituents studied, in agreement with the results obtained previously for the PH₃ model system. For R = Me the activation barrier for pathway 1 (ee → ee^‡ → cis) was predicted to be slightly smaller, by 0.7 kcal mol⁻¹, than that predicted for pathway 3 (ea → ea₂^‡ → trans). Furthermore, reaction 1 was predicted to be more exothermic (by 2 kcal mol⁻¹) than reaction channel 3 for the PMe₃ system. However, since the difference in activation barriers is quite small, in all likelihood both reaction channels will be operative for the ethylene insertion reaction in this catalyst system. These results are in line with those found previously for the PH₃ model system.¹³ For the arylphosphine ligands studied the activation barrier for reaction channel 1 (ee → ee^‡ → cis) was predicted to be significantly smaller, by 2–3 kcal mol⁻¹, than that found for reaction channel 3 (ea → ea₂^‡ → trans). A comparison of the computed thermodynamic energies for the ee → cis and ea → trans paths reveals that the former path is predicted to be more exothermic, by 2–7 kcal mol⁻¹, than the latter path for all of the arylphosphines studied. Hence, in the case of the arylphosphine co-ligands a clear energetic preference, both kinetic and thermodynamic, was found for ethylene insertion to proceed from the least stable ee ethylene adduct to the ee^‡ TS and then to the most stable cis Rh–ethyl insertion product.

Acknowledgements

The authors wish to acknowledge support of this research by the United States Department of Energy (grant no. DE-FG02-97ER14811). S. A. D. wishes to thank the Natural Sciences and Engineering Research Council of Canada for financial support through a Postdoctoral Fellowship. This research was performed in part using the Molecular Science Computing Facility (MSCF) in the William R. Wiley Environmental Molecular Sciences Laboratory at the Pacific Northwest National Laboratory. The MSCF is funded by the Office of Biological and Environmental Research in the U.S. Department of Energy. Pacific Northwest is operated by Battelle for the U.S. Department of Energy under contract DE-AC06-76RLO 1830. The authors would also like to acknowledge the National Center for Supercomputing Applications for a CPU allotment on the high performance computing facility at the University of Kentucky and the Department of Defense for an allotment of CPU time on the Maui High Performance Computing Center facility. The authors also acknowledge Prof. Feliu Maseras (UA Barcelona) for communicating the results of his research prior to publication.

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