A theoretical study of the activity in Rh-catalyzed hydroformylation: the origin of the enhanced activity of the π-acceptor phosphinine ligand.

10.1039/b000000x The factors governing the activity in Rh-catalyzed hydroformylation were investigated using a set of computational tools. We performed DFT calculations on the phosphinine-modified Rh catalyst [HRh(CO) 3 (PC 5 H 2 R 3 )] and compared it to the phosphane-modified HRh(CO) 3 (PR 3 ) and HRh(CO) 2 (PR 3 ) 2 complexes. The  -acceptor phosphinine ligand coordinates preferentially at the equatorial site of 10 pentacoordinated Rh complex with the heterocycle perpendicular to the equatorial plane, although the ligand freely rotates around the Rh-P bond. The overall energy barrier can be divided into the following contributions: alkene complex formation, alkene rotation and alkene insertion. In the absence of steric effects (model systems), the overall barrier correlates with the computed barrier for alkene rotation. This proves that  -acceptor ligands reduce backdonation to the alkene, leading to a lower rotational barrier, 15 and consequently, to a higher activity. The Rh-P donor-acceptor interactions were quantified using a modified version of energy decomposition analysis (EDA). In Rh-phosphinine systems, the efficient directionality of the  -backdonation, rather than the overall acceptor ability, is responsible for the high catalytic activity. Introducing steric effects increases the energy required to coordinate the alkene, increasing the overall barrier. The factors governing the activity in Rh-monophosphane catalysts seem to 20 be related to those derived for Rh-diphosphane during the development of a QSAR model ( Catal. Sci. Technol. 2012¸ 2 , 1694). To investigate whether the findings for mono- can be extrapolated to diphosphane ligands, we re-examine our previous QSAR model using the Topological Maximum Cross Correlation (TMACC) method based on easy-to-interpret 2D-descriptors. The TMACC descriptors highlight heteroatoms close to phosphorus as activity-increasing atoms, whereas highly substituted carbon 25 atoms groups are


Introduction
The hydroformylation of alkenes is one of the largest applications of homogeneous catalysis in industry. 1 It consists of the addition of carbon monoxide and hydrogen to alkenes, catalyzed by 30 cobalt, rhodium or platinum catalysts, leading to the formation of aldehydes. For industrial production, the phosphane-modified rhodium catalysts are widely used because they can show high activity and regioselectivity towards the usually desired linear aldehyde.1 ,2 35 Scheme 1 shows the generally accepted mechanism for the hydroformylation of alkenes catalyzed by phosphane-modified rhodium catalysts. 3 Different reaction kinetics have been observed experimentally depending on ligand properties that, in general, fit into one of two extreme cases. For electron-poor 40 ligands such as bulky monophosphites and the unmodified rhodium-carbonyl catalysts, the hydrogenolysis of acyl species 6 controls the overall rate of hydroformylation. 4, 5 On the contrary, the kinetics for electron-rich ligands are consistent with a ratedetermining step early in the catalytic cycle. Recently, a 45 combination of isotope effects study and computational analysis have demonstrated that the overall process from the resting state species 1 to hydride migration (from complex 3 to complex 4) governs the overall activity in 1-octene hydroformylation catalyzed by the rhodium-xantphos complexes. 6 Independently, a 50 theoretical study by Jensen and co-workers led to the same conclusion for phosphane and moderately electron-withdrawing phosphite ligands; whereas for strongly electron-withdrawing ligands, calculations supported hydrogenolysis as the ratedetermining step. 7 55 Recent clarification of the rate determining step6 , 7 indicates that the ligands that promote CO dissociation, alkene coordination, or hydride migration might yield higher catalytic turnovers. Besides this, some systematic studies have attempted to establish correlations between ligand structure and catalytic 60 activity. 8,9,10,11 Early experimental studies on monodentate Pdonor ligands showed that a relationship exists between ligand basicity and catalyst activity; thus the least basic phosphanes enhance the activity.8 In addition, van Leeuwen and coworkers showed that phenoxophosphane (phosphacyclic) moieties are less 65 basic than diphenylphosphino moieties and exhibit an increase in the rate. 9 In general, for the ligands enclosing a phosphorus atom inside a cycle, an increase of the activity was observed and was attributed to a lower basicity. 12 The differences in catalytic activity have also been related to the steric features of the ligands. For a series of phosphinine ligands, the variation in catalytic performance was attributed to the steric properties of the ligand. 13 According to the authors, the bulky phosphinine ligands favour the formation of a monoligand 10 rhodium species, which should have a larger accessible space compared with diligand rhodium species. Similarly, in industrial conditions excess of phosphane ligand is used because the selectivity towards linear aldehyde is improved; however the activity is reduced because the phosphane dissociation 15 equilibrium shifts from the monophosphane [HRh(CO) 3 (PR 3 )] towards the less active HRh(CO)(PPh 3 ) 2 species. On the other hand for a series of diphosphane xantphos-type ligands, 14 the rate increases with increasing the bite angle; 15 while we showed that increasing the bite angle increases the steric hindrance around the 20 metal center. 16 During the development of a quantitative structure-activity relationship (QSAR) model for the hydroformylation catalyzed by Rh-diphosphane complexes, we discovered that complex relationships underlie the origin of the activity; and that both the shape and the electronic properties of 25 the catalyst need to be considered. 17 Here, we focus on the study of phosphinine-modified rhodium catalyst [HRh(CO) 3 30 [HRh(CO) 2 (PR 3 ) 2 ] (Scheme 2). The Rh-phosphinine system showed a much higher activity than classical PPh 3 -based catalysts 13,19 and followed an analogous kinetics. 13 Our aim is to understand at molecular level the factors governing the activity, evaluating them and their interplay. In addition, we investigate 35 whether the findings for monophosphane ligands can be extrapolated to diphosphane, re-examining a previous QSAR Previous high pressure NMR studies on the analogous and more stable iridium(I) system had indicated that only one phosphinine ligand is coordinated to the transition metal center 60 under hydroformylation conditions. 13 These experiments also suggested an equatorial position for the phosphinine, presumably as two rotamers. The DFT calculated relative energies support the experimental proposal. For [HRh(CO) 3 (PC 5 H 5 )] model complex, the most stable isomer is 1e1 H followed by 1e2 H and 1a H (+1.1 65 and +1.4 kcal.mol -1 higher in energy, respectively). The preference for equatorial coordination with the phosphinine cycle perpendicular can be explained from electronic arguments based on frontier molecular orbitals (FMO). The in-plane d xy orbital of the metal fragment is high in energy and hybridized away from 70 the other equatorial ligands favouring the -back donation to the phosphorus p orbital perpendicular to the ligand plane. 23  [HRh(CO) 3 (2,4,6-PC 5 H 2 Ph 3 )] complexes did not change the order in relative energies (0.0, +0.5 and +3.3 kcal.mol -1 for 1e1, 1e2 and 1a). Nevertheless, the energy difference between the two equatorial rotamers diminishes, while between equatorial and apical coordination it increases. Both trends can be attributed to the steric effects. The ideal P-Rh-CO angle in 1e1 and 1a is 90º, whereas in 1e2 it is 120º (see Figure 1). Thus, the two former, 1e1 and 1a, with a smaller angle are slightly destabilized respect to 1e2 by the steric interactions between phosphinine substituents 5 and the auxiliary ligands.  In order to analyze the rotation around the Rh-P bond in 15 e compounds, we performed a relaxed energy scan of the H-Rh-P-C ortho dihedral angle. The calculations did not show any barrier connecting the rotational isomers 1e1 H and 1e2 H . This along with the small energy difference between the rotamers, even for the 2,4,6-triphenylphosphinine system, strongly indicates that the Rh-20 P bond rotates freely. This might hamper the application of axially chiral monodentate phosphinines in the asymmetric hydroformylation of prochiral substrates. 24 As matter of fact, the preferred equatorial coordination would place the chiral centers far away from the apical region, in which the key ligand-substrate 25 interactions should take place . 25,26,17 For example, ligands based on axial chirality such as Binaphos, which shows excellent performance in Rh-catalyzed asymmetric hydroformylation, 27 induce enantioselectivity via interactions between the substrate and the axially chiral groups of the apical ligand moiety. 26 30 Moreover, the very low barrier computed for ligand rotation would allow easy ligand reorganization upon interaction with the incoming substrate, leading to low enantiodiscrimination. Next, we analyzed the coordination preferences of the phosphinine ligand in the rate-determining step, in which the transition state for alkene insertion into the Rh-H bond is 40 involved ( Figure 2). Using ethene as a model substrate, the computed equatorial path for the model system, TSe1 H , is lower in energy than the apical, TSa H , by 2.0 kcal.mol -1 , increasing somewhat the preference found in the resting-state (1.4 kcal.mol -1 ). For equatorial coordination, the attempts to locate a transition 45 state with the phosphinine parallel to the equatorial plane ended in the corresponding TS for path e1. The perpendicular disposition of the ligand favours back-donation from the Rh, and in turn, reduces back-donation to the alkene, which then can easily rotate to reach the TS for insertion. If we recall the low 50 rotational barrier for the Rh-P bond, it reasonable to think that in case that the alkene complex 3e2 is formed, the system would tend to switch to the lower-energy easily-accessible e1 reaction channel. Thus, calculations indicate that most of the reaction will occur through a channel with the phosphinine in an equatorial 55 position and perpendicular to the equatorial plane.

Analysis of the overall energy barrier for Rh-phosphinine and phosphane systems.
The overall energy barrier can be computed as the energy difference between the transition state for alkene insertion (TS) 60 and the rhodium hydride-carbonyl resting-state of the catalyst 1.6 , 7 To identify the individual factors governing the activity, we decomposed the overall barrier into the energetic cost of several steps: the formation of the alkene complex (E alkene ) and the energy barriers for alkene rotation (E ≠ rot ) and insertion (E ≠ inser ). The overall energy barriers reproduce the experimental observations, 13,19 providing a clear picture about the activity differences. The phosphinine system shows a lower value (19.0 kcal.mol -1 ) than the monophosphane complex (22.4 kcal.mol -1 ), while the bis(phosphane)-based complex shows a higher value 10 (25.9 kcal.mol -1 ); see Table 1. For monocoordinated phosphinine and phosphane complexes, the overall barrier follows the same trend as the alkene insertion and rotation barrier, the energy increasing by ~3 kcal.mol -1 on going from phosphinine to phosphane. This indicates that the alkene rotation process 15 governs the overall barrier, and it is responsible for the observed higher activity in Rh-phosphinine system. Furthermore, it proves previous statements suggesting that for electron-withdrawing ligands the amount of back-donation is small, leading to facile rotation of the alkene moiety and therefore a low barrier for 20 alkene insertion.7 , 21 Following the previous arguments, for electron-donor bis(phosphane) systems one would expect higher rotational barriers, and consequently higher overall barriers. This is observed for the model system, in which both barriers increase by 25 ~1 kcal.mol -1 with respect to the monophosphane system (Table  1, values in parenthesis). On the other hand, for bulky PPh 3 phosphanes the alkene rotation barrier decreases upon bicoordination, whereas the overall barrier is still higher. Introducing the bulky groups increases the steric repulsion 30 between the alkene substrate and the equatorial PR 3 ligands in 3Pee (see Figure 3). This was reflected in longer Rh-alkene carbon distances for 3Pee than for 3Pe (2.287 vs. 2.272 Å on average); and in smaller alkene interaction energies (-24 and -30 kcal.mol -1 ); and therefore, the more loosely bound alkene in 3Pee 35 can rotate more easily. On the other hand, the formation of the alkene complex 3Pee is energetically more costly than the formation of 3Pe (15.1 vs. 11.5 kcal.mol -1 ). The latter effect dominates, explaining the higher overall barrier. Thus, the increase of the overall barrier upon coordination of a second 40 phosphane is not a direct consequence of the electronic properties of the ligands but of their steric properties. This is in line with our previous findings which indicated that the activity of Rhcatalyzed hydroformylation depends on both the basicity and the shape of the ligand; 17 and with the proposed rate-controlling 45 factors by Jensen and co-workers.7 Thus, we can propose for the design of new active ligands that reducing their steric hindrance and increasing their -acidity will favour alkene coordination and rotation to reach the insertion TS, causing a reduction of the overall energy barrier and higher catalytic activities. To evaluate the electronic properties of the P-ligands, we can use the IR stretching frequencies of the CO ligand ( CO ) in trans-L 2 Rh(CO)Cl complex. They follow the order: P(OPh) 3 > P(OMe) 3 > 2,4,6-triphenylphosphinine > PPh 3 > PEt 3 . 28 A large 60  CO value indicates -acceptor properties due to a reduced backdonation from the metal center to the CO ligand, while a small value is indicative of strong -donation. Thus, these values show that phosphinines are poorer electron donors than phosphanes but richer than phosphites. Besides the overall 65 electronic donating ability of the ligand, it is interesting to consider the decomposition into the individual contributions; donation and -backdonation, as done within the classical Dewar-Chatt-Duncanson model. To evaluate these contributions we used a modified version of energy decomposition analysis (EDA) 70 based on an orbital deletion procedure, which allows the bonding to be broken into physically meaningful components (see ESI and Figure S1 for details). 29 Figure 4 schematically describes the orbital interactions in the analysis of the Rh-P bonding. We focused on the model systems because steric effects are put aside.    3 ) eq ] complex 30 obtained at the same computational level in a previous work. 26 For the P-ligands 15 we observed that the interaction energies (E int ) follow the same trend of the CO stretching frequencies: P(OH) 3 > PC 5 H 5 > PH 3 (-29.6, -24.8 and -20.8 kcal.mol -1 , respectively). The values of  donation [E  (L→Rh)] are very similar for all the ligands (~13 kcal.mol -1 ). On the other hand, the  backdonation energy 20 decreases within the series (-10.3, -8.5, and -6.9 kcal.mol -1 for P(OH) 3 , PC 5 H 5 and PH 3 ), explaining the higher overall charge donation from the ligand to the metal. The analysis of the Rhalkene bond nicely correlates with rotational barriers and with the donor/acceptor properties on going from phosphinine to mono- 25 phosphane and to bis(phosphane). Thus, this analysis quantifies the electronic factors and proves that -acceptor property enhances the activity in Rh-catalyzed hydroformylation.
Interestingly, for phosphinine -backdonation occurs preferentially in the equatorial plane of the complex to the out-of- 30 plane p  -type orbitals of phosphorus (E  (a'') in Table 2). This directionality would lead to a more effective competition for metal electron density with the alkene, resulting in activities close to those of electron-poorer ligands such as phosphites. Accordingly, the computed overall barriers for 35 HRh(CO) 3 (PC 5 H 5 ) and HRh(CO) 3 (P(OH) 3 ) systems are similar, 19.3 and 20.6 kcal.mol -1 respectively. Thus, although the overall -acceptor property in phosphinines is somewhat reduced respect to phosphites, 13 the efficient directionality of -backdonation in phosphinines leads to a very active catalysts.

40
Factors governing the catalytic activity. Correlation with QSAR models for diphosphane ligands.
In this section, we analyzed whether the findings for monophosphanes can be extrapolated to diphosphane ligands. As stated in the introduction, we had discussed the factors governing 45 the activity for Rh-diphosphane catalysts during the development of a 3D-QSAR model. 17 We had observed the correlation between high activity and low basicity for a given subset of structurally related complexes, while when comparing ligands of similar basicity the shape of the catalyst seems to determine the 50 activity differences. 17 Nevertheless, the use of alignmentindependent 3D-descriptors made the chemical interpretation of the mathematical model difficult. 31 Thus, here we re-examined the previous QSAR model using the Topological Maximum Cross Correlation (TMACC) method based on easy-to-interpret 55 alignment-independent 2D-descriptors. 20 During recent years, QSAR approaches have emerged as an alternative in the theoretical study of catalysis, 32 including those based on alignment-independent descriptors. 17 The dataset defined from the experimental work in ref. 34 consist of 19 diphosphane ligands (set 1: L1 -L19, see Figure 5) and uses the percentage of conversion (%conv) as the response 65 variable. Unfortunately, we could not expand the model including monophosphane ligands because there are no suitable data available that allows one to compare conversion values. We considered four atomic properties: Gasteiger partial charges 35 to represent electrostatics, Crippen-Wildman molar refractivity 36 to 70 represent steric properties; and in addition, Crippen-Wildman logP parameters 36 representing lipophilicity, and logS parameter 37 representing solubility. Table 3 collects the statistical parameters of 10-fold cross-validation. All the defined individual descriptors yielded models that are close to the limit of prediction ability 75 (0.55 < q 2 < 0.65), a model with q 2 < 0.5 being considered nonpredictive. When we combined the four properties, an acceptable model was obtained, q 2 = 0.71. Closer inspection to the data revealed that ligand L13 has the largest difference between experimental and predicted conversion values, 61 %, and consequently it could be classified as an outlier. The analysis of the chemical space showed that all ligands with medium or high 5 activities have heteroatoms in their structures except L13. This means that the features of this type of structures are probably not well represented in the training data. When we set aside ligand L13 (set 2), the statistical parameters improved significantly (q 2 = 0.89 and r 2 = 0.92). These findings indicate that the structure-10 activity relationship requires sophisticated descriptors that include electronic and steric factors.  Besides, the TMACC descriptors provide a method for interpreting the results when combined with a linear regression method such as PLS. The predicted activity of the ligand can be 25 partitioned among its constituent atoms. Figure 6 shows the representation of the interpretation for the diphosphite ligands L1 and L11, the phosphane-phosphite L5, and the diazophospholane L7 that have the highest activities (%conv > 80) of the dataset. TMACC method displays the atoms that most contribute 30 positively to activity in blue and those that decrease the activity the most in red (yellow and orange colors represent intermediate positive and negative contributions). The oxygen atoms of the phosphite moieties and the hydrazine groups of the diazophospholane ligand are coloured blue (Figure 6), and hence 35 have been identified as activity-increasing groups. On the other hand, disubstituted sp 2 carbons involving terminal alkyl groups and some other highly substituted carbons are colored in red ( Figure 6), indicating activity-decreasing groups. These substituted carbons may be related with ligand bulkiness, which 40 in turns is related with the reduction of catalyst activity. Figure 7 displays the interpretation the electrostatic to the steric-property models for ligand L5. The change in coloring for these properties indicates that the electrostatics has a more dramatic effect on activity of the ligand: the heteroatoms change from blue in the 45 electrostatic-based model to uncolored in the steric-based model. A similar pattern was observed for ligands L1, L7 and L11, indicating that for them the high activity is also dominated by the electrostatic properties induced by the heteroatoms. To sum up, the interpretation of the QSAR model for diphosphane ligands 50 can be related to our findings for monophosphane, indicating that similar rules govern the activity for both types of ligands. We divided the overall energy barrier into several steps and/or contributions (alkene complex formation, alkene rotation and alkene insertion) and evaluated them. In the absence of steric effects (model systems), the overall barrier correlates with the 70 barrier for alkene rotation. This proves that for -acceptor ligands the amount of backdonation to the alkene is small, leading to its facile rotation, and consequently, to a higher activity. We also quantified the donor/acceptor interactions of the Rh-P bonds using a modified version of EDA analysis. Although the overall 75 -acceptor ability of phosphinines is lower than that of other ligands such as phosphites, the efficient directionality of their inplane -backdonation leads to very active catalysts. Introducing the steric effects of the ligands causes an increase of the energy required to form the alkene complex, and consequently an 80 increase of the overall barrier. The factors governing the activity in Rh-monophosphane catalysts are closely related to those of Rh-diphosphane catalysts. This was confirmed by re-examining a previous QSAR model using the easy-to-interpret TMACC descriptors. 85 Thus, the design of active ligands in rhodium-catalyzed alkene hydroformylation should increase their -acidity and reduce their steric hindrance. Nevertheless, one should be aware that bulky monodentate ligands could favor the formation of [HRh(CO) 3 L] complexes which are more active than the [HRh(CO) 2 L 2 ] ones.

Experimental section
Computational Details. DFT calculations 5 The DFT calculations were carried out using the Amsterdam density functional program (ADFv2008). 38 The electronic configurations were described by a triple- plus polarization Slater-type basis set, as included in ADF package. The 1s-3d electrons for Rh, the 1s electrons for C and O, and the 1s-2p electrons for P were treated as frozen cores. We applied 10 scalar relativistic corrections to them via the zeroth-order regular approximation (ZORA) with the core potentials generated using the DIRAC program. 38 We used the GGA functional BP86. 39, 40 Full geometry optimization without any symmetry constraints were performed, unless otherwise stated. The transition states were characterized by a single 15 imaginary frequency and the normal mode, which corresponds to the expected reaction path. In some structures, we found a residual imaginary frequency related with the loose torsion angles of bulky substituents. We are aware that most of the popular DFT methods such as BP86, B3LYP or PBEh are unable to describe noncovalent interactions in their attractive 20 regime. 41 In a recent study of Rh-catalyzed hydroformylation, 26 we tested the M06 class of functional recommended to study noncovalent interactions, 42 and B97D functional including explicit dispersion corrections. 43 Both functional types gave qualitatively the same results as BP86 one for these systems, in which, the ligand-substrate interactions 25 were dominated by repulsive interactions. 26 We expect the same results here. Indeed, the interaction between phenylphosphino moieties and aliphatic alkenes were proved to be repulsive in nature for alkene insertion into the Rh-H bond by means of QM/MM calculations. 22g To analyze the nature of Rh-phosphorus and -alkene bonds, we 30 employed the Energy Decomposition Analysis (EDA) method; 44 and a modified version based on orbital deletion that allows separating the  and the  interactions in a physically meaningful manner. 29 The details are provided in the Supporting Information.
QSAR TMACC-based modelling 35 These descriptors are generated using atomic properties (electrostatics, solubility, steric effect and lipophilicity) determined by molecular topology. The source code for computing TMACC descriptors is available for download from http://comp.chem.nottingham.ac.uk/download/TMACC. The electrostatic 40 properties are represented by the Gasteiger partial charge, 35 which is calculated using the method of partial equalization of orbital electronegativity. This procedure calculates atomic charges in σ-bonded and non-conjugated π-system using only the topology of the catalysts. The Crippen-Wildman molar refractivity (MR) is used as a measure of the 45 steric effects that it is determined through the classification of atoms based on neighbour atoms. 36 The Crippen-Wildman partition coefficients (logP) are assigned to each atom as a measure of atomic lipophilicity, determined in the same way as Crippen-Wildman molar refractivity (MR). 36 The solubility properties are described by logS parameters, 50 representing solubility and solvation phenomena. 37 We scaled each contribution by the largest absolute value, so that the positive and negative values took maximum values of +1 and -1.
The TMACC autocorrelation descriptor (xac) is where p is one of the properties and d is the topological distance between atoms i and j, normally the shortest number of bonds between atoms. The sum is over all atom pairs that are separated by distance d. We treat each atomic property that can take positive and negative values as separate properties. The molar refractivity is the exception that only takes 60 positive values. Like for GRIND descriptor, we keep only the maximum value calculated for any given distance. For the purposes of interpretation (see above), for each descriptor, we recorded which atoms contribute to the maximum product. In the event of more than one pair having the same value, we record all pairs. The maximum distance was as large as the 65 largest distance in the molecule. The minimum distance was zero, that is, we allowed i = j.
We employed the Partial Least Squares (PLS) Regression 45 as the multivariate regression technique. Ten-fold cross validation was used for model building and evaluation. Different statistical parameters facilitated 70 evaluation of the predictive ability of models during the fitting and test stages, namely; the Pearson correlation coefficient (r 2 ) and the crossvalidated correlation coefficient (q 2 ), see ESI. 46 The TMACC descriptor string for each molecule comprises several hundred elements. Clearly, it is not practicable to present the resultant QSAR equation, in which the 75 latent variables in the PLS regression are linear combinations of the descriptors. A more qualitative summary of the model is provided via the graphical interpretations in Figures 6 and 7, in which the PLS has effectively been reversed to ascribe contributions to activity to individual atoms.