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Density functional theory calculations of Rh-β-diketonato complexes† J. Conradie Density functional theory (DFT) results on the geometry, energies and charges of selected Rh-β-diketonato reactants, products and transition states are discussed. Various DFT techniques are used to increase our understanding of the orientation of ligands coordinated to Rh, to identify the lowest energy geometry

Received 25th July 2014, Accepted 20th November 2014

of possible geometrical isomers and to get a molecular orbital understanding of ground and transition states. Trends and relationships obtained between DFT calculated energies and charges, experimentally

DOI: 10.1039/c4dt02268h

measured values and electronic parameters describing the electron donating power of groups and

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ligands, enable the design of ligands and complexes of specific reactivity.

1.

Introduction

Among the first Rh(I)-β-diketonato complexes to be reported, were [Rh(β-diketonato)(cod)] (cod = 1,5-cyclo-octadiene), by Chatt and Venanzi in 19571 and [Rh(β-diketonato)(CO)2] by Bonati and Wilkinson in 1964.2 These rhodium complexes are widely applied as catalysts, for example: [Rh(acac)(CO)2] (acac = acetylacetonato = (CH3COCHCOCH3)−) is used as a hydrogenation catalyst,3 [Rh(acac)(CO)2] in the presence of tertiary phosphines or phosphites (PX3) is used for hydrogenation, hydroformylation and isomerization reactions of olefins,4–6 [Rh(acac)(P(OPh3))2] is used for the hydrogenation of arenes and the hydroformylation of olefins, hex-1-ene and propylene,

Department of Chemistry, University of the Free State, 9300 Bloemfontein, Republic of South Africa. E-mail: [email protected] † Electronic supplementary information (ESI) available: DFT methods, Tables S1–S6 and Fig. S1–S6 as referred to in the text. See DOI: 10.1039/c4dt02268h

J. Conradie

Jeanet Conradie obtained her PhD. in Chemistry in 2000, from the University of the Free State, South Africa, where she now is a Professor in Physical Chemistry. Her research interests involve the synthesis, computational chemistry, electrochemistry and kinetics of novel transition metal complexes and their intermediates. She applies computational methods to predict or shed light on experimental observation.

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as well as the activation of diatomic molecules such as H2 and CO,5,7 and catalyst [Rh(acac)(CO)(PPh3)] is used for the hydroformylation of hex-1-ene.8 In the present paper, density functional theory (DFT) calculations on selected series of Rh(I) (Fig. 1) and related Rh(III) complexes, coordinated to a β-diketonato ligand (Fig. 2), will be reviewed. The influence on the reactivity of these rhodium complexes, due to the varying electron-donating properties of the different ligands attached to rhodium, will also be dealt with.

2. Discussion Coordination of the enolated anion (Fig. 2) of a β-diketone to rhodium, produces a stable metal complex. The β-diketonato ligand (RCOCHCOR′)− forms a pseudo-aromatic core with rhodium, and the electronic effect of the R and R′ groups through the conjugation on the rhodium is observed experimentally, by the reactivity of the Rh(I)-β-diketonato complexes

Fig. 1

Selected rhodium-β-diketonato complexes.

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Fig. 2

Keto–enol equilibrium for β-diketones.

towards oxidation (both chemically and electrochemically) and substitution reactions. The calculations were generally carried out with the ADF9 programme, using the PW9110 functional and the STO-TZ2P basis set, including scalar relativistic effects with the ZORA11 formalism. For transition states involving charged species, solvent effects were taken into account, using the COSMO12 model of solvation. Selected calculations with the Gaussian 0913 programme package, using the B3LYP14 functional and the GTO-LANL2DZ15 basis set for rhodium and GTO-6-311G(d,p) on all other atoms, yielded comparable results. Specific details on the computational methods used for each section, are provided in the ESI† (where STO = Slater type orbitals and GTO = Gaussian type orbitals, as implemented in the ADF and Gaussian programme). 2.1.

β-Diketonato ligands

β-Diketones exist in solution in three tautomeric forms, as shown in Fig. 2.16 In solution, β-diketones enolize predominantly to the cis-enolic form which is stabilized by intramolecular hydrogen bonding.17 Different empirical parameters are used to quantify the electron donating property of the R and R′ groups, such as Gordy scale group electronegativities, χR,18,19 Hammett meta substituent constants, σR,20,21 and the Lever electronic parameter, EL.22–25 Since there are two substituents on the β-diketonato chelate ring, the sum of the values for the two groups present are used: (χR + χR′) or (σR + σR′). The Lever parameter (EL) applies to the complete β-diketonato ligand. The pKa of the free β-diketone, describing the acidic strength of the ligand, can also be used to describe the influence of the β-diketonato ligand on the rhodium metal which it is coordinated to. Tables S1–S4† give a summary of (χR + χR′), (σR + σR′), EL and the pKa values, for different β-diketones. 2.2.

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[Rh(β-diketonato)(CO)2] complexes

[Rh(β-diketonato)(CO)2] complexes are generally obtained from either the [Rh(CO)2Cl]2 dimer2 or from RhCl3·nH2O.4,26 Since these square planar 16-electron d8 rhodium(I) complexes are electron deficient and coordinatively unsaturated, they tend to stack in dimeric units by formation of metal–metal bonds27 and chains,28 with weak metal–metal interactions between the rhodium atoms of 3.18–3.54 Å.29 Both CO groups are substituted by olefins such as cod or strong π-acceptor tertiary phosphines or phosphite groups (PX3) such as P(OPh)3 (Ph = phenyl), while a weak π-acceptor PX3 group, e.g. PPh3, leads only to a monosubstituted [Rh(β-diketonato)(CO)(PX3)] complex.30,31 Density Functional Theory calculations (DFT) on the substitution of PPh3 for CO in square-planar [Rh(β-diketonato)(CO)2] complexes, showed that the reaction occurs in two inter-

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Fig. 3 The two-step DFT calculated reaction mechanism for CO substitution in β-diketonato Rh(I) complexes, containing a bulky β-diketonato substituent, R’ > R. An equatorial position of group R’ during the second transition state (TS) leads to less steric interaction with PPh3.32b The reactant, intermediate and product are all square-planar, while both transition states are trigonal bipyramidal.32

changeable steps, involving the formation of a square-planar intermediate, as illustrated in Fig. 3.32 The course of the reaction is understood by the order of the trans influence of the ligands involved: PPh3 > CO > Oβ-diketonato.33 The trans influence is a purely thermodynamic effect of a coordinated ligand, that leads to the weakening of the metal–ligand bond trans to it.34 Since PPh3 has the largest and Oβ-diketonato the smallest trans influence, nucleophilic attack of PPh3 on [Rh(β-diketonato)(CO)2] results in the dissociation of a rhodium– Oβ-diketonato bond. The first step thus involves the nucleophilic attack by PPh3, with the formation of a trigonal bipyramidal (TBP) transition state. The angle between the entering PPh3 group and each of the two Oβ-diketonato atoms is ca. 90°. The Oβ-diketonato in the TBP plane trans to CO thus dissociates under the trans influence of CO > Oβ-diketonato, with the formation of a square-planar intermediate. This Oβ-diketonato group now acts as an entering group at the second transition state, with an equatorial angle between PPh3 and the attacking Oβ-diketonato of ∼135°. The leaving CO group is now positioned trans to PPh3 and dissociates under the trans influence of PPh3 > CO.32,33 2.3.

[Rh(β-diketonato)(cod)] complexes

In experimental [Rh(β-diketonato)(cod)] complexes, the two CvC bonds of the cod ligand are nearly parallel when coordinated to rhodium: for example [Rh(CH3COCHCOCH3)(cod)] has a dihedral angle between the two CvC bonds of 4.7°.35 The dihedral angle is 1.25° for the complex [Rh(CF3COCHCOPh)(cod)]36 and 1.2(5)° and 2.6(4)° for two [Rh(CF3COCHCOCF3)(cod)] molecules37); see Fig. 4(a). This is contrary to the relative orientation of the two CvC bonds in free cod, which has a dihedral angle ranging from 25.3(3)38 to 28.9(3)°,39 implying that the two bonds are markedly nonparallel; see Fig. 4(c). This trend that the two CvC bonds become increasingly parallel upon coordination with metals, is attributed to the preference for the –CH2CH2– backbone of cod to adopt a staggered conformation;40 see Fig. 4(b) for

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2.4.

Fig. 4 Experimental35 (red) and DFT PW91/STO-TZ2P optimized (black) geometries of [Rh(CH3COCHCOCH3)(cod)]. (a) Overlay (RMS = 0.12 Å) showing the near parallel orientation of the two CvC bonds. (b) DFT geometry showing the staggered formation of the two –CH2CH2– moieties of cod. (c) Free cod containing two CvC non-parallel bonds.39 H atoms are omitted for clarity in (a) and (b).

[Rh(CH3COCHCOCH3)(cod)]. The distorting energy involved in this distortion of the cod ligand from its preferred conformation, to the conformation found in metal complexes, is compensated by the back donation from the metal to the two π* orbitals on cod40 of [Rh(β-diketonato)(cod)]. Two metal dπ orbitals are involved in back donation from the rhodium to the two CvC bonds of cod, which are shown in Fig. 5 for [Rh(CF3COCHCOCF3)(cod)]. The bond between rhodium and the CvC double bond also has another main component, namely the donation of the π electron density of the double bond of CvC, to the vacant d acceptor orbital on the metal atom, to form a σ-type bond; see Fig. 5. The σ bond is complemented by π-backbonding.41 The cod ligand (a σ-donor π-acceptor) can therefore also be substituted by any other σ-donor π-acceptor ligand, such as CO26 or a phosphite group.42,43 On the other hand, it was found that the β-diketonato ligand (σ-donor) in [Rh(β-diketonato)(cod)] complexes can be substituted by 1,10-phenanthroline ( phen) or 2,2′-dipyridyl44 or another β-diketonato ligand45 (σ-donors) under certain conditions. The relationship between the substitution rate constants and DFT calculated energies will be discussed in Section 2.6 below.

Fig. 5 Selected Kohn–Sham frontier orbitals of the DFT PW91/ STO-TZ2P optimized geometry of [Rh(CF3COCHCOCF3)(cod)], with electron occupation dxy2dxz2dyz2dz22dx2−y20, illustrating the rhodium d → π*(CvC) back donation, and the (CvC)π → Rhx2−y2 σ donation. The MO plots use a contour of 45 e nm−3.

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[Rh(β-diketonato)(P(OPh3))2] complexes

Oxidative addition is a key step in many homogeneous catalytic processes. The Monsanto process is a well-known example, where the first step for the manufacture of acetic acid by catalytic carbonylation of methanol, involves the oxidative addition of methyl iodide to the rhodium catalyst cis[Rh(CO)2I2]−.46 The kinetic behaviour and structural details of potential rhodium catalytic systems are thus of importance. The oxidative addition reaction of CH3I to a series of [Rh(β-diketonato)(P(OPh)3)2] complexes was studied both experimentally43,47 and theoretically.43,48 The experimental studies of these reactions proposed a twostep SN2 mechanism for the oxidative addition step to the square planar [Rh(β-diketonato)(P(OPh3))2] complex, leading to a trans alkyl Rh(III) product, with the ligands octahedrally arranged around rhodium. In principle, seven potential Rh(III) alkyl oxidative addition product isomers of the formula [Rh(β-diketonato)(P(OPh)3)2(CH3)(I)] are possible; see Fig. 6. The first isomer in Fig. 6 results from trans addition, with the CH3I entering either at the top or bottom side of the square planar plane, which is formed by the two Oβ-diketonato atoms and the two P(OPh)3 atoms; while the other six isomers result from cis addition. DFT calculations on the relative energies of the possible alkyl products showed, in agreement with experimental observation by 1H NMR, that the trans product is the most stable.43,48 The three types of transition state (TS) structures which have been reported for the oxidative addition of methyl iodide to square planar rhodium(I) complexes,49 are illustrated in Fig. 7 for the reaction of [Rh(β-diketonato)(P(OPh)3)2] + CH3I. The linear TS structure (the first shown in Fig. 7, also called back TS) typically has a linear Rh–CCH3–I arrangement and all three Rh–CCH3–H angles close to 90°. The three H atoms of CH3I are located in the equatorial plane of the five-coordinated C atom at the moment of the TS, resulting in a TBP arrangement around C. The imaginary frequency of the linear transition state corresponds to a CH3I stretching vibrational mode, in which the Rh–CCH3 bond forms and the I–CCH3 bond breaks.43,48 On the other hand, the bent TS structure (the second shown in Fig. 7) corresponds to a side-on approach of the I–CCH3 bond to rhodium. The transition state displacement vectors of the bent TS can be described as a Rh–CCH3–I bending, in which the CH3+ group is making a rocking move-

Fig. 6 The geometry of the seven possible [Rh(RCOCHCOR’)(P(OPh)3)2(CH3)(I)]-alkyl oxidative addition reaction products of the reaction [Rh(RCOCHCOR’)(P(OPh)3)2] + CH3I: (a) one trans and (b) six cis isomers. Only four isomers are possible when R = R’; namely one trans and three cis isomers.

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Fig. 7 Schematic illustration of possible transition states during the nucleophilic attack of a square planar rhodium(I) complex on methyl iodide: a linear TS (also called back TS), bent TS and front TS (also called concerted cis TS). The arrows indicate the displacement vectors of the imaginary frequencies. The solid and dotted arrows correspond to bond formation and bond cleavage respectively, while the curved dashed arrow shows the movement of the P(OPh)3 group.

ment between Rh and I.43,48 Both the bent and linear TS structures result in a cationic five-coordinated rhodium complex plus a free I− ion as intermediate product.49 Coordination of the I− ion to the cationic intermediate product, proceeds with a barrierless energy to form the trans alkyl product (the first isomer shown in Fig. 6). Both the mechanisms of the linear and the bent TS structures can therefore be described as SN2 processes. In comparison, the front TS structure (the last shown in Fig. 7, also called concerted cis TS), which also has a side-on approach of the I–CCH3 bond to rhodium, leads to a concerted three-centre TS, in which the Rh–I and Rh–CCH3 bonds form simultaneously, while the I–CCH3 bond is breaking. The front TS therefore leads to cis addition of CH3I to rhodium. The imaginary frequency of the front TS has two contributions, namely a Rh–CCH3–I bending and an I–Rh– Oβ-diketonato bending. The latter bending mode leads to the movement of the Oβ-diketonato away from the original square plane (consisting of the two Oβ-diketonato and the two P atoms) to a new square plane (formed by the two Oβ-diketonato, one P atom and I), thereby shifting the CH3 and one P(OPh)3 group into the axial positions.43,48,50 DFT calculations of a series of [Rh(β-diketonato)(P(OPh)3)2] complexes, showed that the linear transition state, leading to a trans [Rh(β-diketonato)(P(OPh)3)2(CH3)(I)]-alkyl product, is favoured by a large margin of energy. DFT calculations further showed that the trans [Rh(β-diketonato)(P(OPh)3)2(CH3)(I)]alkyl product is the most stable of the possible products shown in Fig. 6.43,48,50 Fig. 8 presents the frontier molecular orbitals (MOs) of the reactants and TS of the [Rh(acac)(P(OPh)3)2] + CH3I reaction, as representative example of the [Rh(β-diketonato)(P(OPh)3)2] + CH3I reactions. The HOMO (highest occupied molecular orbital) of the Rh(I) reactant exhibits mainly a dz2 character (Fig. 8). In the TS, the bond between Rh and CCH3 is formed, while the bond between CCH3 and I is breaking, to result in a five-coordinated cationic intermediate. In order to form a bond between Rh and CCH3, electron density has to be donated from the filled HOMO on Rh, to the empty LUMO (lowest unoccupied molecular orbital) of CCH3. The main contribution to the Rh–CCH3 bond in the TS therefore comes from the overlap of the filled dz2 HOMO of the rhodium atom, with

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Fig. 8 PW91/STO-TZP optimized geometry and selected Kohn–Sham frontier orbitals of the reactant complexes, as well as the linear TS, of the [Rh-(CH3COCHCOCH3)(P(OPh)3)2] + CH3I oxidative addition of the reaction. The MO plots use a contour of 40 e nm−3. H atoms are omitted for clarity, except for CH3I.

the empty pz LUMO of the methyl carbon of CH3I. It is important to note that the more electron-rich the Rh(I) metal centre is, the more easily electron-density will be donated to the CCH3. DFT calculations indeed confirmed that [Rh(β-diketonato)(P(OPh)3)2] complexes with more electron-rich R and R′ groups on the β-diketonato ligand (RCOCHCOR′)−, generally exhibit a lower DFT calculated activation energy, i.e. they are more reactive;50 see Fig. 9 as example. 2.5. [Rh(β-diketonato)(CO)(PX3)] complexes, where PX3 = PPh3, (P(OCH2)3CCH3) or other tertiary phosphines Substitution of one CO group in [Rh(β-diketonato)(CO)2] complexes, affords the mono substituted square-planar [Rh(β-diketonato)(CO)(PX3)] complex. Two isomeric monocarbonyl complexes are possible for those [Rh(β-diketonato)(CO)(PX3)] complexes containing an unsymmetrical β-diketonato ligand (RCOCHCOR′)−: one where the PX3 group is trans to the oxygen

Fig. 9 Relationship between the sum of the Gordy scale group electronegativities (χR + χR’) of the R and R’ groups of the β-diketonato in [Rh(RCOCHCOR’)(P(OH)3)2] and the PW91/STO-TZP calculated activation energy of the [Rh(RCOCHCOR’)(P(OH)3)2] + CH3I reaction. Complex (5) did not fit the trend. Complex numbering is according to Fig. 1. Data is obtained from ref. 50.

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nearest to R and one where the PX3 group is trans to the oxygen nearest to R′ (Fig. 10). The isomer expected to be predominant due to the larger trans-influence, is the isomer where the PX3 group is trans to the oxygen nearest to an electron donating β-diketonato side group R. Generally, both isomers are observed on NMR,30,51 but X-ray crystallographic studies on different [Rh(β-diketonato)(CO)(PX3)] complexes, indicated that in most instances, only one specific isomer crystallizes from solution.52 Steric factors, temperature and solvent polarities also seem to play a role in determining which isomer in the mixture actually crystallizes from solution.53 In two cases, both the isomers crystallized as independent units in the same unit cell, namely for the two complexes [Rh(PhCOCHCOCH3)(CO)(PPh3)]54 and [Rh(PhCOCHCO(CH2CH3))(CO)(PPh3)],32a while only once both isomers of [Rh(PhCOCHCO(CH2)3CH3)(CO)(PPh3)] crystallized in the same space in the unit cell.55 DFT calculations on the relative energies of the two isomers of various [Rh(β-diketonato)(CO)(PX3)] complexes, confirmed the existence of both isomers (Fig. 10).51,56 DFT calculations of the geometry of selected [Rh(β-diketonato)(CO)(PPh3)] complexes, comparing the geometrical bonds and angles of experimental crystal structures with DFT results, using different functionals and basis sets, indicated that DFT PW91/STO-TZP calculations generally gave the best agreement with experiment.51,56 On the other hand, COSMO (PW91/ STO-TZP) calculations in methanol or chloroform as solvent, yielded geometry parameters that are for all practical purposes the same as those obtained by gas phase DFT PW91/STO-TZP calculations.51 “Often the most bulky part of the molecule determines the shape of the complex, its reactivity and the manner in which it is packed into the unit cell upon crystallization. In the case of PPh3-containing complexes, the conformations of the rings often determine the bulkiness of the complex. Knowledge of the conformational preferences of PPh3-containing complexes should provide a contribution to the development of improved reagents and catalysts and can be used to predict the outcome of stereoselective reactions.”57 A DFT study (PW91/STO-TZP calculations) of the orientation of PPh3 in a series of [Rh(β-diketonato)(CO)(PPh3)] complexes, showed that the minimum energy orientation can be described in terms of the plane of nadir energy. This plane, defined by Costello as the plane incorporating all points of minimum steric compression of a specific complex,58 will be perpendicular to the square plane57 of [Rh(β-diketonato)(CO)(PPh3)] complexes, as illustrated in Fig. 11(a). The DFT study showed that the minimum energy orientation of PPh3 in [Rh(β-diketonato)(CO)(PPh3)]

Fig. 10 Structural isomers of [Rh(RCOCHCOR’)(CO)(PX3)], where PX3 = PPh3, (P(OCH2)3CCH3) or other tertiary phosphines.

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Fig. 11 (a) The dotted red line shows the nadir energy plane associated with the square planar geometry of a [Rh(β-diketonato)(CO)(PPh3)] complex, (b) P (clockwise) and (c) M (anti-clockwise) orientation of PPh3, (d) and (e) the preferred PPh3 orientation (P helicities) in [Rh(β-diketonato)(CO)(PPh3)] complexes, as viewed along the P–Rh axis.

complexes (P helicity i.e. clockwise orientation of Ph rings, as viewed along the P–M axis), is “characterized by a near vertical PhA, tilted to the right (P helicity) and oriented as near as possible to the nadir plane perpendicular to the square plane through the metal, CO and the two Oβ-diketonato ligands, a tilted PhB in the quadrant below the square plane and to the right of the nadir plane and a near horizontally tilted PhC”;55,57,59 as illustrated in Fig. 11. This DFT calculated minimum energy orientation is similar to the preferred orientation of PPh3 in most experimental [Rh(β-diketonato)(CO)(PPh3)] crystal structures. The combined DFT and experimental crystallographic study also found that the “steric influence of Oβ-diketonato and CO is similar on the preferred orientation of the vertical phenyl ring A of PPh3 in [Rh(β-diketonato)(CO)(PPh3)] complexes. The size of the side groups R and R′ on the β-diketonato ligand (RCOCHCOR′)− does not influence the preferred conformation of coordinated PPh3 in [Rh(β-diketonato)(CO)(PPh3)].”55 Oxidative addition of CH3I to [Rh(β-diketonato)(P(OPh)3)2] leads to only one trans and six possible cis [Rh(β-diketonato)(P(OPh)3)2(CH3)(I)] alkyl oxidative addition product isomers (see Fig. 6). On the other hand, the alkyl complex [Rh(β-diketonato)(CO)(PPh3)(CH3)(I)] gives rise to a theoretical possibility of 12 different octahedral RhIII-alkyl isomers ( plus 12 enantiomers); see Fig. 12(a). Furthermore, CO insertion may also take place, leading further to 6 different RhIII-acyl isomers of the formula [Rh(β-diketonato)(COCH3)(PPh3)(I)] ( plus 6 enantiomers); see Fig. 12(b). Experimental studies of the CH3I oxidative addition to [Rh(β-diketonato)(CO)(PPh3)], showed that the oxidative addition of CH3I to any β-diketonato complex of the type [Rh(β-diketonato)(CO)(PPh3)], follows the following general reaction sequence, controlled by the values of the indicated equilibrium (Kci) and rate (ki) constants (i = ±1 to ±4), see Scheme 1.60–64 The notations 1 and 2 in RhIII-alkyl1, RhIIIacyl1, RhIII-alkyl2 and RhIII-acyl2 denote the firstly- or secondly-formed alkyl or acyl species during the reaction course. The two geometrical isomers of RhI, called RhI-A and RhI-B,

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Fig. 12 (a) The geometry of the twelve possible [Rh(RCOCHCOR’)(CO)(PX3)(CH3)(I)]-alkyl oxidative addition reaction products of [Rh(RCOCHCOR’)(CO)(PX3)] + CH3I. (b) Migratory CO insertion leads to six possible [Rh(RCOCHCOR’)(COCH3)(PX3)(I)] acyl products. Only six alkyl and three acyl isomers are possible when R = R’.

lead to two geometrical isomers of each of the RhIII species, indicated by A and B respectively in Scheme 1.60 While 1H NMR51,56,64,65 and IR51,56,64 shed light on the formulation of the products (alkyl or acyl), the specific stereochemistry of the reaction products in the reaction sequence above, could only in some cases be determined by crystal structure determination62,64 and an in situ 1H–1H NOESY NMR study.56,64,66 Computational chemistry studies on the relative energies of the different reaction products, in agreement with experimental observation, proposed the stereochemistry of the different reaction products, as given in Scheme 2.51,56,64 A combined experimental and “DFT study provided more information on the stereochemistry and the mechanism of the oxidative addition and methyl migration steps of the reaction [Rh(acac)(CO)(PPh3)] + CH3I, as summarized in Scheme 3. Methyl iodide is added trans to the square planar [Rh(acac)(CO)(PPh3)] complex. This oxidative addition corresponds to an SN2 nucleophilic attack by the rhodium metal centre on the methyl iodide. To summarize stereochemistry according to this study: • RhIII-alkyl1: Methyl iodide is oxidatively added to the square planar Rh(I) complex to form an octahedral RhIII-alkyl1 complex with the CH3 group in the apical position and the PPh3 group in the plane of the acac ligand. The relative positions of the iodide and the CO group can not be determined

Scheme 1 General reaction sequence for the oxidative addition reaction [Rh(β-diketonato)(CO)(PPh3)] + CH3I.60

Scheme 3 The proposed reaction mechanism of the multistep reaction [Rh(acac)(CO)(PPh3)] + CH3I from PW91/STO-TZP calculations in methanol as solvent. The movement of the relevant atoms in the transition states are indicated by the red arrows. Reproduced from ref. 66.

by 1D 1H NOESY spectroscopy, although a CO group trans to a PPh3 group is hardly possible. The DFT study showed trans addition of CH3I to [Rh(acac)(CO)(PPh3)], i.e. with the iodide and CH3 group in the apical position and the CO and PPh3 groups in the plane of the acac ligand. • RhIII-acyl1: The DFT study indicates that the migration of the CH3 group to the CO group results in a square pyramidal RhIII-acyl1 complex, with the COCH3 and PPh3 groups in the plane of the acac ligand and the iodide in the apical position. No reliable information on the stereochemistry of RhIII-acyl1 can be obtained by means of 1D 1H NOESY spectroscopy. • RhIII-alkyl2: The RhIII-alkyl2 complex has an octahedral arrangement around the rhodium centre, with the PPh3 group in the apical position. The relative positions of the iodide and the CO group can not be determined by 1D 1H NOESY spectroscopy. The DFT study indicates that the iodide and PPh3 group are in the apical position and that the CO and CH3 groups are in the plane of the acac ligand. • RhIII-acyl2: The final product observed on the NMR is a square pyramidal RhIII-acyl2 complex, with the PPh3 group in the plane of the acac ligand. DFT calculations indicate this complex is the most stable product of the reaction, with the COCH3 group in the apical position and the iodide and PPh3 group in the plane of the acac ligand.”66 2.6. DFT and chemical kinetics (for oxidative addition and substitution reactions)

Scheme 2 The proposed reaction scheme of the reaction of methyl iodide with [Rh(acac)(CO)(PPh3)], showing specific stereochemistry. Reproduced from ref. 66.

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In this section, the influence of the different groups R and R′ attached to the β-diketonato ligand (RCOCHCOR′)−, on the reactivity of the rhodium complexes towards chemical substitution and oxidative addition reactions, will be discussed and related to DFT calculated energies and charges.

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From a computational chemistry point of view, the reactivity of complexes is largely determined by the frontier orbital energies of the reactants.67–69 The Frontier molecular orbital theory (FMO Theory) simplifies the reactivity between complexes to merely the interaction between the HOMO of one complex and the LUMO of the other,70 since during the TS, the greatest orbital overlap is between FMO’s.71 The interaction between the Rh-dz2 orbital of the HOMO of [Rh(acac)(P(OPh)3)2] and the pz orbital on CCH3 of the LUMO of CH3I (as discussed in Section 2.4 and illustrated in Fig. 8) for the [Rh(acac)(P(OPh)3)2] + CH3I oxidative addition reaction, serves as example of the application of the FMO theory. Fig. 13 illustrates the linear relationship obtained between the DFT PW91/ STO-TZP calculated energy of the HOMO, EHOMO, of a series of [Rh(β-diketonato)(P(OPh)3)2] complexes and the second order rate constant, k2, of the oxidative addition of CH3I to [Rh(β-diketonato)(P(OPh)3)2]. The consistent linear relationship obtained, shows that DFT calculated HOMO energies can indeed be used as an indication of the reactivity of a complex, as expressed by the reaction rate constant (ln k2). DFT calculations also showed that the TS of both the oxidative addition reaction [Rh(β-diketonato)(CO)(PPh3)] + CH3I discussed in Section 2.5, as well as the TS of the [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] + CH3I reaction, is similar to the TS of the oxidative addition reaction illustrated in Fig. 8, which involved the overlap of the filled dz2 HOMO of the rhodium atom with the empty pz LUMO of the methyl carbon of CH3I.66,72 The kinetic characteristics of these complexes can therefore be assessed in a similar way (as in Fig. 13), by considering FMO interactions as expressed by the EHOMO − ln k2 relationship, as visualized in Fig. 14. The two curves in Fig. 14 (one for the phosphine and the other for phosphite [Rh(β-diketonato)(CO)(PR3)] complexes) have similar slopes, indicating that the reactivity is largely determined by the overlap of the FMOs. The relative energy of a specific [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] complex is on average 0.14 eV lower than that of the related [Rh(β-diketonato)(CO)(PPh3)] complex, due

Fig. 13 Linear relationship between the DFT PW91/STO-TZ2P calculated EHOMO of [Rh(β-diketonato)(P(OPh3)3)2] and the experimental kinetic rate constant, ln k2 (k2 in dm3 mol−1 s−1), of the [Rh(β-diketonato)(P(OPh)3)2] + CH3I reaction. Complex numbering is according to Fig. 1. Data was compiled for this study, see Table S5.† Fig. S1† gives the B3LYP/GTO-TZP (DZ on Rh) relationship.

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Fig. 14 Linear relationship between the DFT PW91/STO-TZ2P calculated EHOMO and the experimental kinetic rate constant k2 (in dm3 mol−1 s−1) of the CH3I oxidative addition, to both [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] (grey triangles) and [Rh(β-diketonato)(CO)(PPh3)] (black dots). Note k2 in this graph corresponds to k1 in Scheme 2. Complex numbering is according to Fig. 1 (for complexes 1–14), and further R, R’ = Ph, CH2CH3 (15); Ph, (CH2)2CH3 (16); Ph, (CH2)3CH3 (17). Data was compiled for this study, see Tables S6 and S7.†

to the stabilization effect of the better π-acceptor ability of P to Rh of the phosphite, in comparison with that of the phosphine group. Comparing the relationship obtained between the oxidative addition kinetic rate constants for [Rh(β-diketonato)(P(OPh)3)2] and EHOMO (Fig. 13), and for [Rh(β-diketonato)(CO)(PPh3)] and EHOMO (Fig. 14), with that obtained from DFT calculations, using the B3LYP functional and the LANL2DZ basis set for Rh, and 6-311G(d,p) on other atoms (Fig. S173 and S2†), we observe that both DFT methods give similar results: [Rh(β-diketonato)(P(OPh)3)2] + CH3I: EHOMO ðeV; PW91=STO-TZ2PÞ ¼ 0:067 ln k2  4:21

ðR 2 ¼ 0:97Þ

EHOMO ðeV; B3LYP=GTO-TZPÞ ¼ 0:062 ln k2  5:21

ðR 2 ¼ 0:92Þ

[Rh(β-diketonato)(CO)(PPh3)] + CH3I: EHOMO ðeV; PW91=STO-TZ2PÞ ¼ 0:094 ln k2  4:12

ðR 2 ¼ 0:91Þ

EHOMO ðeV; B3LYP=GTO-TZPÞ ¼ 0:086 ln k2  5:01

ðR 2 ¼ 0:87Þ

In all three these oxidative addition reactions (for the three complexes shown in Fig. 13 and 14), Rh acts as a nucleophile, donating electron density to the pz LUMO of the methyl carbon of CH3I, to form a bond between Rh and CCH3. More electron-rich R and R′ groups on the β-diketonato ligand (RCOCHCOR′)−, which donate electron density via conjugation through the β-diketonato backbone to Rh, causing the Rh to be relatively more electron-rich, thereby enhancing the rate of oxidative addition, lead to a larger rate constant (k2) and a lower activation energy barrier (Ea) during the TS (see also Fig. 9). Fig. 15 illustrates how the oxidative addition rate of the [Rh(β-diketonato)(CO)(PPh3)] + CH3I reaction increases, as the R and R′ groups become increasingly electron-rich; as

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described by the Gordy scale group electronegativities, Hammett meta substituent constants, Lever electronic parameters or the pKa of the free β-diketonato ligand (see ESI Fig. S3 and S4† for the other two reactions). However, during the two substitution reactions given below, involving [Rh(β-diketonato)(cod)], rhodium acts in the opposite way, namely as the electrophile, while the incoming ligand (Hphen or P(OPh)3) acts as the nucleophile. This implies that more electron-rich R and R′ groups on the β-diketonato ligand (RCOCHCOR′)−, will lead to a slower (smaller) substitution rate, i.e. the graph of EHOMO versus ln k2 (substitution) will have a negative slope (see Fig. 16 74 and Fig. 17 75), which is contrary to the positive slope of the EHOMO versus ln k2 (oxidative addition) graph (see Fig. 13 and 14). Fig. 15 Linear dependence of the empirical quantities (χR + χR’), (σR + σR’), pKa and ΣEL on the oxidative addition rate constant k2 (in dm3 mol−1 s−1), of the [Rh(β-diketonato)(CO)(PPh3)] + CH3I reaction. Note k2 in this graph corresponds to k1 in Scheme 2. Data was compiled for this study, see Table S5.†

½Rhðβ-diketonatoÞðcodÞ þ Hphen ! ½RhðphenÞðcodÞþ þ ðβ-diketonatoÞ ½Rhðβ-diketonatoÞðcodÞ þ 2 PðOPhÞ3 ! ½Rhðβ-diketonatoÞðPðOPhÞ3 Þ2  þ cod

Fig. 16 Linear dependence of the substitution rate constant k2 on the DFT PW91/STO-TZ2P calculated HOMO energy for the [Rh(β-diketonato)(cod)] + Hphen → [Rh( phen)(cod)]+ + (β-diketonato)− reaction. Complex numbering is according to Fig. 1. Data is obtained from ref. 74.

We observe from Fig. 16 and 17 that the energy of the HOMO of “[Rh(β-diketonato)(cod)], relates to the experimental second order substitution rate constant ln k2, for a series of [Rh(β-diketonato)(cod)] complexes, irrespective whether the β-diketonato ligand or cod is substituted. Linear equations thus obtained, may be used for theoretical estimation of substitution rates of similar complexes.”75 The experimental kinetic rate of the substitution of cod for CO in [Rh(β-diketonato)(CO)2], leading to [Rh(β-diketonato)(cod)], also showed that more electronegative substituents R or R′ on the β-diketone lead to a faster substitution rate.76 DFT calculations77 showed that the kinetic substitution rate relates to the DFT calculated EHOMO of [Rh(β-diketonato)(CO)2], to a high degree of accuracy (see Fig. 18).

Fig. 17 Linear dependence of the substitution rate constant k2 on the DFT PW91/STO-TZ2P calculated HOMO energy for the [Rh(β-diketonato)(cod)] + 2P(OPh)3 → [Rh(β-diketonato)(P(OPh)3)2] + cod reaction. Complex numbering is according to Fig. 1. Data was obtained from ref. 75.

Fig. 18 Linear dependence of the substitution rate constant k2 on the DFT PW91/STO-TZ2P calculated HOMO energy for the [Rh(βdiketonato)(CO)2] + cod → [Rh(β-diketonato)(cod)] + 2CO reaction. Complex numbering is according to Fig. 1. Data was obtained from ref. 77.

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2.7.

Perspective

DFT and electrochemical oxidation

Since electrochemical oxidation of a complex corresponds to the removal of electrons from the HOMO of the complex, there should be a relationship between the HOMO energy, EHOMO, of the complex and the electrochemical oxidation potential: the higher the energy of the HOMO, the easier it should be to remove an electron. The relationship obtained between EHOMO and the electrochemical oxidation of the Rh(I) nucleus to Rh(III), in a series of [Rh(β-diketonato)(P(OPh)3)2] complexes, is illustrated in Fig. 19.73 The relationship obtained here between EHOMO and Epa(Rh) agrees with the DFT-Koopmans’s theorem, which states that the first (vertical) ionization energy of a system is related to the negative of the corresponding Kohn– Sham HOMO energy.78–80 The electrochemical oxidation potential of Rh(I) to Rh(III), Epa(Rh), should also be related to the chemical oxidation of Rh(I) to Rh(III), as measured by the oxidative addition rate constant and the empirical parameters determining or describing the electron density on the rhodium in [Rh(β-diketonato)(P(OPh3)3)2]. The following relationships were obtained: Epa ðRhÞ ¼ 0:098 ln k2  0:029 ðR 2 ¼ 0:90Þ73 Epa ðRhÞ ¼ 0:31 ðχ R þ χ R′ Þ  1:1

ðR 2 ¼ 0:90Þ73

Epa ðRhÞ ¼ 0:56 ðσ R þ σ R′ Þ þ 0:28

ðR 2 ¼ 0:87Þ73

Epa ðRhÞ ¼ 1:1

X

EL  0:85

ðR 2 ¼ 0:96Þ73

“The quantum chemical approach makes it possible to compute explicitly the electron density distribution in a complex, for example Mulliken charges. Although atomic charge is not physically observable, it has been proven to be useful to briefly describe and analyse the electron density distribution in a molecule. The determination of atomic charges is based on different approaches and methods,81 such as the population analysis of wave functions (e.g. Mulliken population analysis82 and Natural charges83), partitioning of elec-

Fig. 19 Linear relationship between the DFT B3LYP/GTO-TZP (DZ on Rh) calculated EHOMO of [Rh(β-diketonato)(P(OPh3)3)2] and the experimental oxidation potential Epa(Rh). Complex numbering is according to Fig. 1. Data was obtained from ref. 73.

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tron density distributions (e.g. Bader charges obtained from an atoms in molecules analysis84 and Hirshfeld charges), charges derived from density-dependent properties (e.g. MDC, Multipole derived atomic charges85), charges derived from electrostatic potential and charges derived from experimental data (e.g. electronegativity-based charges or from spectroscopic or other physicochemical data, such as reaction rate constants).”73 The relationships obtained between these charges and Epa(Rh) are: X Epa ðRhÞ ¼ 4:6 QMulliken  2:6 ðR 2 ¼ 0:93Þ73 Epa ðRhÞ ¼ 21

X

Epa ðRhÞ ¼ 4:8 Epa ðRhÞ ¼ 5:2 Epa ðRhÞ ¼ 5:8

QHirshfeld þ 2:4

X X

ðR 2 ¼ 0:92Þ73

QMDC  2:8 ðR 2 ¼ 0:89Þ73 QBader  3:2 ðR 2 ¼ 0:84Þ73

X

QNPA  2:7 ðR 2 ¼ 0:70Þ73

“Although in some cases quite different values are obtained when calculating the charges by the different methods, good consistent relationships between the calculated charges and the experimental oxidation potential exist. These relationships can serve as a tool to predict the oxidation potential of related [Rh(β-diketonato)(P(OPh)3)2] complexes.”73 The cyclic voltammograms of [Rh(β-diketonato)(cod)] complexes (1), (2), (3), (6) and (8), containing a β-diketonato ligand (FcCOCHCOR′)− with at least one ferrocene group, exhibit two oxidation peaks in the region 0–0.6 V vs. Fc/Fc+ (three peaks for complex (1)). The first irreversible anodic oxidation peak is assigned to the oxidation of Rh(I) to Rh(III), and the second reversible couple is assigned to the one-electron transfer process of the ferrocenyl group of the (FcCOCHCOCF3)− ligand, coordinated to rhodium.86 This experimental assignment of the observed oxidation peaks, agrees with the character of the DFT calculated Kohn–Sham HOMO and HOMO−1 of the [Rh(FcCOCHCOR′)(cod)] complexes: the HOMO is mainly of rhodium dz2 character and the HOMO−1 is mainly Febased;74,87 (see Fig. 20). The oxidation of [RhI(FcCOCHCOR)(cod)] therefore firstly involves the removal of 2 e− from the HOMO, to form [RhIII(FcCOCHCOR)(cod)], followed by the 1 e− oxidation of the FeII of ferrocene to the FeIII of ferrocenyl, which involves an electron in the HOMO−1 of the neutral complex.87 Further support for this interpretation is obtained, by the good linear relationship obtained between the electrochemical anodic oxidation potential of Rh(I) to Rh(III), Epa(Rh), and the energy of the HOMO, EHOMO, as well as a linear relationship between the formal oxidation potential of the ferrocenyl group, E°′(Fc), and the energy of the HOMO−1, EHOMO−1; see Fig. 21. The linear relationships obtained between Epa(Rh)88 and EHOMO for the [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]72 and [Rh(β-diketonato)(CO)(PPh3)]89 complexes, is visualized in the ESI Fig. S5 and S6.†

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various series of related complexes. All these relationships serve as methods to predict the reactivity of complexes towards chemical oxidative addition or substitution kinetics, and also reactivity in terms of electrochemical oxidation and reduction potentials.

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Acknowledgements Fig. 20 PW91/STO-TZ2P Kohn–Sham HOMO and HOMO−1 orbitals of [Rh(FcCOCHCOCF3)(cod)]. The HOMO is 79% rhodium based and the HOMO−1 is 88% iron based, confirming the location of both the first (RhI→III) and second (FeII→III) experimentally observed oxidations. The MO plots use a contour of 45 e nm−3.

Financial assistance by the South African National Research Foundation and the Central Research Fund of the University of the Free State, is gratefully acknowledged. A grant of computer time from the Norwegian supercomputing program NOTUR (grant no. NN4654 K) is gratefully acknowledged.

Notes and references

Fig. 21 Linear relationship between EHOMO of [Rh(β-diketonato)(cod)] and the experimental oxidation potential Epa(Rh) (graph with black dots), as well as between EHOMO−1 and E°’(Fc) (graph with red dots). Complex numbering is according to Fig. 1. Data is obtained from ref. 74 (by PW91/ STO-TZ2P calculations).

3. Conclusions This contribution focuses on Rh-β-diketonato complexes, but we have found that Ir-β-diketonato complexes similarly exhibit consistent linear relationships between HOMO energies and kinetic substitution rate constants.90 Therefore the FMO theory, which simplifies reactivity between complexes to merely the interaction between the HOMO of one complex and the LUMO of another, can thus be applied on both the Rhand Ir-β-diketonato complexes. We have also found that the reduction of the uncoordinated β-diketonato ligand of these complexes, which involves the removal of an electron from the LUMO of the ligand, exhibits a linear trend with the LUMO energy.19 On the other hand, the electrochemical oxidation of ferrocene in a series of para-substituted ferrocene-containing chalcone derivatives, correlates well with the HOMO energies.91 Further, the electrochemical oxidation of Cr92 and W93 in Fischer carbene complexes, exhibits good linear trends with the HOMO energies, while the reduction of the carbene ligand of the same complexes again exhibits good linear trends with the LUMO energies. These results show that the Koopmans’s theorem, which relates ionization energy of a system to the negative of the corresponding Kohn–Sham HOMO energy, can be applied to the electrochemical oxidation (and reduction) of

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one atom but a group of atoms like R = CF3 or CH3 to attract electrons including those in a covalent bond, as a function of the number of valence electrons n and the covalent radius r in Å, of groups as discussed in: (a) P. R. Wells, in Progress in Physical Organic Chemistry, John Wiley & Sons Inc., New York, 1968, vol. 6, pp. 111–145; (b) R. E. Kagarise, J. Am. Chem. Soc., 1955, 77, 1377–1379. A. Kuhn, K. G. von Eschwege and J. Conradie, Electrochemical and DFT-modeled reduction of Enolized 1,3-Diketones, Electrochim. Acta, 2011, 56, 6211–6218. L. P. Hammett, Chem. Rev., 1935, 17, 125–136. C. Hansch, A. Leo and R. W. Taft, Chem. Rev., 1991, 91, 165–195. A. B. P. Lever, Inorg. Chem., 1990, 29, 1271–1285. M. F. C. Guedes da Silva, A. M. Trzeciak, J. J. Ziółkowski and A. J. L. Pombeiro, J. Organomet. Chem., 2001, 620, 174– 181. A. M. Trzeciak, B. Borak, Z. Ciunik, J. J. Ziółkowski, M. F. C. Guedes da Silva and A. J. L. Pombeiro, Eur. J. Inorg. Chem., 2004, 1411–1419. I. Kovacik, O. Gevert, H. Werner, M. Schmittel and R. Söllner, Inorg. Chim. Acta, 1998, 435, 275–276. Selected examples: (a) J. Conradie, T. S. Cameron, M. A. S. Aquino, G. J. Lamprecht and J. C. Swarts, Inorg. Chim. Acta, 2005, 358, 2530–2542; (b) J. G. Leipoldt, S. S. Basson, J. J. J. Schlebush and E. C. Grobler, Inorg. Chim. Acta, 1982, 62, 113–115. Selected examples: (a) S.-S. Chern, G.-H. Lee and S.-M. Peng, J. Chem. Soc., Chem. Commun., 1994, 1645– 1646; (b) G. M. Finniss, E. Candall, C. Campana and K. R. Dunbar, Angew. Chem., Int. Ed. Engl., 1996, 35, 2772– 2774; (c) M. Mitsumi, H. Goto, S. Umebayashi, Y. Ozawa, M. Kobayashi, T. Yokoyama, H. Tanaka, S. Kuroda and K. Toriumi, Angew. Chem., Int. Ed., 2005, 44, 4164–4168. Selected examples: (a) M. Jakonen, L. Oresmaa and M. Haukka, Cryst. Growth Des., 2007, 7, 2620–2626; (b) J. S. Miller, Extended linear chain compounds, Plenum Press, New York, 1982, vol. 1–3; (c) J. K. Bera and K. R. Dunbar, Angew. Chem., Int. Ed., 2002, 23, 4453–4457. Selected examples: (a) M. J. Decker, D. O. K. Fjeldsted, S. R. Stobart and M. J. Zaworotko, J. Chem. Soc., Chem. Commun., 1983, 1525–1527; (b) C. Crotti, S. Cenini, B. Rindone, S. Tollari and F. Demartin, J. Chem. Soc., Chem. Commun., 1986, 784–786; (c) G. M. Villacorta and S. J. Lippard, Inorg. Chem., 1988, 27, 144–149; (d) G. Matsubayashi, K. Yokoyama and T. Tanaka, J. Chem. Soc., Dalton Trans., 1988, 253–256; (e) L. A. Oro, M. T. Pinillos, C. Tejel, M. C. Apreda, C. Foces-Foces and F. H. Cano, J. Chem. Soc., Dalton Trans., 1988, 1927–1933; (f ) J. Pursiainen, T. Teppana, S. Rossi and T. A. Pakkanen, Acta Chem. Scand., 1993, 47, 416–418; (g) F. Ragaini, M. Pizzotti, S. Cenini, A. Abbotto, G. A. Pagain and F. Demartin, J. Organomet. Chem., 1995, 489, 107–112; (h) A. Elduque, C. Finestra, J. A. Lopéz, F. J. Lahoz, F. Merchan, L. A. Oro and M. T. Pinillos, Inorg. Chem.,

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2196; (b) L. Cavallo and M. Sola, J. Am. Chem. Soc., 2001, 123, 12294–12302; (c) A. Haynes, P. M. Maitlis, G. E. Morris, G. J. Sunley, H. Adams, P. W. Badger, C. M. Bowers, D. B. Cook, P. I. P. Elliott, T. Ghaffer, H. Green, T. R. Griffin, M. Payne, J. M. Pearson, M. J. Taylor, P. W. Vickers and R. J. Watt, J. Am. Chem. Soc., 2004, 126, 2847–2861. Selected examples: (a) J. G. Leipoldt, E. C. Steynberg and R. van Eldik, J. Inorg. Chem., 1987, 26, 3068–3070; (b) G. J. van Zyl, G. J. Lamprecht, J. G. Leipoldt and T. W. Swaddle, Inorg. Chim. Acta, 1988, 143, 223–227; (c) G. J. van Zyl, G. J. Lamprecht and J. G. Leipoldt, Inorg. Chim. Acta, 1987, 129, 35–37. M. M. Conradie and J. Conradie, J. Organomet. Chem., 2010, 695, 2126–2133. (a) M. Feliz, Z. Freixa, P. W. N. M. van Leeuwen and C. Bo, Organometallics, 2005, 24, 5718–5723; (b) T. R. Griffin, D. B. Cook, A. Haynes, J. M. Pearson, D. Monti and G. E. Morris, J. Am. Chem. Soc., 1996, 118, 3029–3030. J. Conradie, Inorg. Chim. Acta, 2012, 392, 30–37. M. M. Conradie and J. Conradie, Inorg. Chim. Acta, 2009, 362, 519–530. Selected examples: (a) J. G. Leipoldt, S. S. Basson and J. T. Nel, Inorg. Chim. Acta, 1983, 74, 85–91; (b) J. G. Leipoldt, S. S. Basson and J. H. Potgieter, Inorg. Chim. Acta, 1986, 117, L3–L5; (c) G. J. Lamprecht, J. C. Swarts, J. Conradie and J. G. Leipoldt, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1993, 49, 82–84; (d) A. Roodt and G. J. J. Steyn, Recent Res. Dev. Inorg. Chem., 2000, 2, 1–23. Selected examples: (a) J. Conradie, G. J. Lamprecht, S. Otto and J. C. Swarts, Inorg. Chim. Acta, 2002, 328, 191–203; (b) M. M. Conradie and J. Conradie, Inorg. Chim. Acta, 2008, 361, 208–218. W. Purcell, S. S. Basson, J. G. Leipoldt, A. Roodt and H. Preston, Inorg. Chim. Acta, 1995, 234, 153–156. N. F. Stuurman, A. Muller and J. Conradie, Inorg. Chim. Acta, 2013, 395, 237–244. M. M. Conradie and J. Conradie, S. Afr. J. Chem., 2008, 61, 102–111. J. Conradie, Dalton Trans., 2012, 41, 10633–10642. J. F. Costello and S. G. Davies, J. Chem. Soc., Perkin Trans. 2, 1998, 1683–1690. N. F. Stuurman, A. Muller and J. Conradie, Transition Met. Chem., 2013, 38, 429–440. Reaction Scheme: Reprint from: M. M. Conradie and J. Conradie, Inorg. Chim. Acta, 2008, 361, 2285–2295; Copyright (2008), with permission from Elsevier. N. F. Stuurman and J. Conradie, J. Organomet. Chem., 2009, 694, 259–268. J. Conradie, G. J. Lamprecht, A. Roodt and J. C. Swarts, Polyhedron, 2007, 23, 5075–5087. J. Conradie and J. C. Swarts, Organometallics, 2009, 28, 1018–1026. M. M. Conradie and J. Conradie, Inorg. Chim. Acta, 2008, 361, 2285–2295.

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83 E. D. Glendening, J. K. Badenhoop, A. E. Reed, J. E. Carpenter, J. A. Bohmann, C. M. Morales and F. Weinhold, NBO 3.1, Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 2001. 84 R. Bader, Chem. Rev., 1991, 91, 893–928. 85 M. Swart, P. T. van Duijnen and J. G. Snijders, J. Comput. Chem., 2001, 22, 79–88. 86 J. Conradie and J. C. Swarts, Dalton Trans., 2011, 40, 5844– 5851. 87 K. G. von Eschwege and J. Conradie, S. Afr. J. Chem., 2011, 64, 203–209. 88 J. J. C. Erasmus and J. Conradie, Electrochim. Acta, 2011, 56, 9287–9294. 89 H. Ferreira, M. M. Conradie and J. Conradie, Electrochim. Acta, 2013, 113, 519–526. 90 J. Conradie, Polyhedron, 2013, 51, 164–167. 91 T. J. Muller, J. Conradie and E. Erasmus, Polyhedron, 2012, 33, 257–266. 92 Selected examples: (a) M. Landman, R. Lui, P. H. van Rooyen and J. Conradie, Electrochim. Acta, 2013, 114, 205– 214; (b) M. Landman, R. Liu, R. Fraser, P. H. van Rooyen and J. Conradie, J. Organomet. Chem., 2014, 752, 171–182. 93 Selected examples: (a) M. Landman, R. Pretorius, B. E. Buitendach, P. H. van Rooyen and J. Conradie, Organometallics, 2013, 32, 5491–5503; (b) M. Landman, R. Pretorius, R. Fraser, B. E. Buitendach, M. M. Conradie, P. H. van Rooyen and J. Conradie, Electrochim. Acta, 2014, 130, 104–118.

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