RESEARCH ARTICLE

 

Carbonyl substitution in β-diketonatodicarbonyl-rhodium(I) by cyclo-octadiene: Relationships with experimental, electronic and calculated parameters

 

 

Jeanet Conradie^{I, II, *}

^IDepartment of Chemistry, University of the Free State, Bloemfontein, P.O. Box 339, 9300, South Africa
^IIDepartment of Chemistry and Centre for Theoretical and Computational Chemistry, University of Tromsø, N-9037 Tromsø, Norway

 

 

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ABSTRACT

The substitution rate constant of the reaction between [Rh(β-diketonato)(CO)₂] and cyclo-octadiene is related to various empirical parameters and density functional theory calculated energies and charges, β-diketonato = R'COCHCOR. Results indicate that especially the Hammett meta substituent constants (σ), the Lever electronic parameters (E_L) and the density functional theory calculated energies and charges predict the substitution rate constant to a high degree of accuracy, for example: ln k₂ = 8.48 (σ_r + σ_r,) - 2.24 (R² = 0.99) = 31.8 ΣE_l - 63.0 (R² = 0.99) = - 9.16 E_HOMO - 52.1 (R² = 0.97) = 101 ΣQ_Mulliken(Rh(CO)₂) - 49.9 (R² = 0.99).

Keywords: BETA-diketone, rhodium, substitution; dicarbonyl, cyclo-octadiene, DFT.

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1. Introduction

The first [Rh(β-diketonato)(CO)₂] complexes were reported by Bonati and Wilkinson in 1964.¹ They showed that the carbon monoxide groups in [Rh(p-diketonato)(CO)₂] can be completely substituted by olefins such as cyclo-octa-1,5-diene (cod) (Scheme 1). The reverse reaction, i.e. treatment of [Rh(β-diketonato)(cod)] with CO resulted in better yields of [Rh(β-diketonato)(CO)₂] than the conventional synthetic pathway by treating [Rh(Cl)(CO)₂]₂ with the β-diketone in certain cases.² Reactions of [Rh(β-diketonato)(CO)₂] involving triphenylphosphine (PPh₃) or triphenylarsine (AsPh₃) lead to substitution of only one of the carbonyl ligands.^1,3-6 Rhodium(I) complexes with bi-dentate β-diketonato ligands are well-known catalysts for hydroformylation of olefins.^7-9 We have recently shown that experimental second-order substitution rate constants of the [Rh(R'COCHCOR)(cod)] + phen → [Rh(phen)(cod)]⁺ + (R'COCHCOR)^- reaction relate to the density functional theory calculated energies of the highest occupied molecular orbital of thermodynamically stable reactant [Rh(R'COCHCOR)(cod)] (phen = 1,10-phenanthroline).¹⁰ We were interested to see if a similar relationship exists if [Rh(R'COCHCOR)(cod)] is the  product of a substitution reaction. An experimental study of the kinetics of the substitution reaction [Rh(R'COCHCOR)(CO)₂] + cod → [Rh(R'COCHCOR)(cod)] + 2(CO) (Scheme 1) showed that the order of the effect of the β-diketonato ligands (R'COCHCOR)^- on the reactivity of the [Rh(β-diketonato)(CO)₂] complexes was (CH₃COCHCOPh)^- < (PhCOCHCOPh)^- < (CF₃COCHCOCH₃)^- < (CF₃COCHCOPh)^- < (CF₃COCHCOCF₃)^-, i.e. more electronegative substituents R or R' of the β-diketone led to a faster substitution rate.¹¹

 

 

The aim of this study is to establish relationships and trends between density functional theory (DFT) calculated, empirical and experimental data in order to be able to predict the reactivity of β-diketonatodicarbonyl-rhodium(I)- systems from calculated descriptors.

 

2. Methods

Density functional theory (DFT) calculations were carried out using the ADF (Amsterdam Density Functional) 2012 programme^12-14 with the GGA (Generalized Gradient Approximation) functional PW91 (Perdew-Wang 1991).¹⁵ The TZ2P (Triple ζ polarized) basis set, with a fine mesh for numerical integration and tight convergence criteria, was used for minimum energy searches. Throughout, all calculations have been performed with no symmetry constraints (C₁) and all structures have been calculated as spin-restricted singlet states. All calculations have been done in the gas phase. Optimized geometries obtained were used to perform an NBO analysis by the NBO 3.1 module.¹⁶

 

3. Results and Discussion

3.1. Kinetic Rate Constant and Electronic Parameters

The experimentally measured second-order rate constant k₂for the substitution of cod for CO in [Rh(R'COCHCOR)(CO)₂]is tabulated in Table 1 (cod = 1,5-cyclooctadiene).¹¹ Empirical parameters that are related to the electron donating property of the R and R' groups on the β-diketonato ligand (R'COCHCOR)^-, the sum of the Gordy scale group electronegativities (χ_R + χ_R'),^17,18 the sum of the Hammett meta substituent constants, (σ_R + σ_R),^19,20 and the sum of the Lever electronic parameter ΣE_L^21-24 for the [Rh(R'COCHCOR)(CO)₂] complexes are also given in Table 1. Figure 1 visualizes the linear relationships between ln k₂and the electronic parameters.

In k₂ = 4.25 (χ_R + χ_R') - 20.9                   (R² = 0.91)

In k₂ = 8.48 (σ_R + σ_R') - 2.24                   (R² = 0.99)

In k₂ = 31.8 ΣΕ_L - 63.0                           (R² = 0.99)

 

 

 

A lower (more acidic) pK_a value of the free β-diketone generally resulted in a faster substitution rate (see data in Table 1), but did not give a good linear fit. The Hammett constants and Lever parameters originate from substitution rate constants and electrochemical potentials respectively. The Hammett constants σ_R are empirical constants that relate the logs of rate or equilibrium constants for reactions of the substituted (k_R, R = substituent) and the unsubstituted (k_H, no substituent) benzoic acid derivatives to the reaction rate ρ: log (k_R/k_H) = (σ_R)ρ. σ_R depends solely on the nature and position of the substituent R.²⁵ In as much as the substituents on the β-diketonato chelate ring are meta with respect to rhodium, the σ values used are those for meta position substitution.²⁶ Since the β-diketonato ligand in [Rh(R'COCHCOR)(cod)] has two meta substituents relative to rhodium, the σ value is taken as the sum of the values for the two groups present. The Lever parameter is a redox potential parameterization approach,²¹ involving an empirical relationship between the oxidation potential (in volts vs. SHE) of the redox couple M(q)/M(q+1) of a complex and the Lever electrochemical parameters determined by the ligands and the metal centre, Ε_redox (vs.SHE) =S_M ΣΕ_L + I_M. ΣΕ_L is the sum of the values of the Lever ligand ΕL parameters for all the ligands (additive effects) in the complex and S_M and I_M represent the slope and intercept (dependent on the metal, redox couple, spin state and stereochemistry). We observe that both the Hammett constants and the Lever parameters give excellent descriptions of reactivity patterns of the [Rh(R'COCHCOR)(CO)₂] complexes containing different R and R' substituents as experimentally measured by the substitution rate constant k₂.

3.2. Kinetic Rate Constant, Electronic Parameters and DFT Calculated Energies

The reactivity of the rhodium complexes is in many respects due to the nature of ligand surroundings²⁷ and determined largely by the relative frontier orbital energies.^28-30 The Frontier Molecular Orbital Theory (FMO Theory) simplifies reactivity to interactions between the HOMO of one species and the LUMO of the other³¹ The reactivity of the [Rh(R'COCHCOR)(CO)₂] complex is therefore related to the energy of its HOMO. The high correlation found between the DFT calculated energy of the HOMO (highest occupied molecular orbital) of the [Rh(R'COCHCOR)(CO)₂] complexes 2-6, Ε_homo and the substitution rate constant (Figure 2 (a)) shows that the substitution reaction is frontier controlled:

ln k₂= -9.16 Ε_homo- 52.1           (R² = 0.97)

 

 

Table 2

 

The d-occupation of the [Rh(R'COCHCOR)(CO)₂] complexes 1-6 is d_xz² d_yz² d_xy² d_z2² d_x2-y2⁰ with the HOMO mainly d_z2 on rhodium, see Fig. 3. The calculated HOMO energy is largely influenced by the electronic effect of the substituent groups R and R' on rhodium. Figure 2 (b) displays the relationships between the various empirical parameters describing the electron-donating/withdrawing power of the R and R' groups and the energy of the HOMO of complexes 1-6:

Εhomo = -0.502 (χ_R + χ_R') - 3.20      (R² = 0.95)

Εhomo = -0.835 (σ_r + σR_') - 5.49       (R² = 0.96)

Εhomo = -3.34 ΣΕl + 0.928               (R² = 0.99)

 

 

The above relationships all show that more electron withdrawing R and R' substituent groups lead to a more negative Ε_HOMO, i.e. a more stable HOMO.

Experimental rate constants k₂ relate to the activation energy Ε_a by the Arrhenius equation:

where, R = gas constant, T = temperature and A = pre-expo-nential factor. We have previously shown that the relationship between the DFT calculated activation energy and the experimentally measured kinetic parameter ln k2 of the oxidative addition reaction [Rh(β-diketonato)(P(OPh)₃)₂] + CH₃l is less accurate than the relationship between EHOMO and ln k_2.³²Therefore we do not consider relationships involving transition states in this study.

3.3. Kinetic Rate Constant, Electronic Parameters and DFT Calculated Charges

A detailed quantum chemical examination of electron state variations of an active metal-containing centre versus different ligand characteristics may lead to a better understanding of the relationship between the activity and catalyst structure, as well as to ways of predicting catalytic activity. The wavefunction population analysis methods assign a partial charge to each atom. Although the absolute magnitudes of the atomic charges yielded by population analysis have little physical meaning,³³ the relative magnitude of the numbers can be interpreted and can yield useful information.^34,35 The Mulliken population analy-sis³⁶ is one of the oldest, simplest and most common population analysis methods. The calculated Mulliken charge on the Rh(CO)₂ fragment in the reactant [Rh(R'COCHCOR)(CO)₂] complexes 1-6 relates to the experimental and empirical parameters tabulated in Table 1 (average R² = 0.95, see Figs 4 and 5):

ln k₂ = 101 ΣQ_Mulliken(Rh(CO)₂) - 49.9               (R² = 0.99)

ΣQ_Mulliken(Rh(CO)₂) = 0.0470 (χ_r +χ_r') + 0.257      (R² = 0.84)

ΣQ_Mulliken(Rh(CO)₂) = 0.0851 (σ_r + σ_r') + 0.470     (R² = 1.00)

ΣQ_Mulliken(Rh(CO)₂) = 0.333 ΣEL - 0.170             (R² = 0.98)

 

 

 

 

The natural population analysis (NPA), another wavefunction population analysis method, yields natural charges. The natural charge on rhodium generally increased (became less negative) in going from complex 1 to 6 (fastest substitution rate, most reactive). The charge alteration of the rhodium-dicarbonyl fragment correlates with the different experimental and empirical parameters (see Figs 4 and 5, data are in Table 1):

ln k₂ = 94.7 ΣQ_NPA(Rh(CO)₂) - 35.2                     (R² = 0.98)

ΣQnpa(Rh(CO)₂) = 0.0493 (X_r +X_r')+ 0.127            (R² = 0.93)

ΣQnpa(Rh(CO)₂) = 0.0841 (σ_r + σ_r') + 0.351            (R² = 0.98)

ΣQ_NPA(Rh(CO)₂) = 0.334 ΣE_L + 0.290                   (R² = 0.99)

From the relationships obtained above, we note that the calculated charges are valuable indicators of chemical behaviour. Other computational methods³⁷ of atomic charge determination include the partitioning of electron density distributions (e.g. Bader charges obtained from an atoms in molecules analysis³⁸ and Hirshfeld³⁹ charges) and charges derived from density-dependent properties (e.g. MDC, Multipole derived atomic charges⁴⁰). See Figs 4 and 5 for a visualization of the good relationships obtained between the calculated charges and experimental and empirical parameters (data are in Table 1):

ln k₂ = 84.7 ΣQ_Bader(Rh(CO)₂) - 48.3                   (R² = 0.95)

ΣQ_Bader(Rh(CO)₂) = 0.0527 (Xr +Xr') + 0.309         (R² = 0.98)

ΣQ_Bader(Rh(CO)₂) = 0.0848 (σr + σr') + 0.551          (R² = 0.93)

ΣQ_Bader(Rh(CO)₂) = 0.341 ΣE_L + 0.104                  (R² = 0.96)

ln k₂= 72.6 ΣQ_Hirshfeld(Rh(CO)₂) - 13.1                    (R² = 0.97)

ΣQ_Hirshfeld(Rh(CO)₂) = 0.0633 (χ_R + χ_R') + 0.134        (R² = 0.95)

ΣQ_Hirshfeld(Rh(CO)₂) = 0.105 (σ_R + σ_R') + 0.156          (R² = 0.96)

ΣQ_Hirshfeld(Rh(CO)₂) = 0.421 ΣE_L + 0.653                  (R² = 0.99)

ln k₂ = 109 ΣQ_MDC(Rh(CO)₂) - 60.3                   (R² = 0.99)

ΣQ_MDC(Rh(CO)₂) = 0.0434 (χR +χ_R') + 0.334         (R² = 0.79)

ΣQ_MDC(Rh(CO)₂) = 0.0805 (σ_R + σ_R') + 0.530        (R² = 1.00)

ΣQ_MDC(Rh(CO)₂) = 0.313 ΣE_L + 0.0714               (R² = 0.97)

Voronoi deformation density (VDD) is a method based on the partitioning of space into non-overlapping atomic areas modelled as Voronoi cells and then computing the deformation density within those cells.⁴¹ The relationship between the calcu-lated Voronoi charges and the experimental substitution rate and empirical electronic parameters is illustrated in Figs 4 and 5 (data are in Table 1):

ln k₂ = 91.9 ΣQ_Voronoi(Rh(CO)₂) - 72.0                    (R² = 0.98)

ΣQ_Voronoi(Rh(CO)₂) = 0.0505 (χ_R + χ_R') + 0.531         (R² = 0.94)

ΣQ_Voronoi(Rh(CO)₂) = 0.08545 (σ_R + σ_R') + 0.762        (R² = 0.97)

ΣQ_Voronoi(Rh(CO)₂) = 0.341 ΣE_L + 0.107                  (R² = 0.99)

In all the above relationships that involved calculated partial charges, the sum of the charges on the Rh(CO)₂ fragment gave relationships with a better fit than the charge on Rh alone. The thermodynamic trans infiuence of the two O_{β-diketonato} atoms of the chelate ring trans to the carbonyl groups of [Rh(R'COCHCOR) (CO)₂] may contribute to this phenomenon. The trans influence of the O_{β-diketonatoo} is due to the electron withdrawing power of the R group nearest to it. The Rh-CO bonding (CO-to-M σ bond) and back-bonding (M-to-CO π bond) may also contribute to this phenomenon. Shor similarly found that for [Rh(R'COCHCOR) (CO)₂] complexes the NPA charge alteration of the metal-di-carbonyl fragment (and not on Rh alone) in [Rh(R'COCHCOR) (CO)₂] correlated with CO bond lengths and vibration frequencies of carbonyl group.

The above relationships show the same trend; stronger electron attracting R and R' substituent groups decrease the electron density on Rh(CO)₂ in going from complex 1 to 6, making the complex a stronger Lewis acid. The five-coordinate transition state⁴² of the substitution reaction [Rh(R'COCHCOR)(CO)₂]+ cod is therefore more stabilized as R and R' become more elec-tron attracting. This leads to an increase of the reactivity of the complex towards substitution reactions.

The relationships obtained from DFT charges make the estimate of k₂ for any [Rh(R'COCHCOR)(CO)₂] complex possible with an accuracy of >97 %.

 

4. Conclusions

The aim of this study was to establish relationships and trends between caicuiated, empiricai and experimentai data in order to predict the reactivity as experimentally measured by the chemical substitution rate (k₂) of cod for CO in [Rh(R'COCHCOR)(CO)₂]. From the DFT optimized structures of [Rh(R'COCHCOR)(CO)₂] complexes 1-6 we found that both the HOMO energy and the charges on Rh(CO)₂ are valuable indicators of chemical behaviour. Results show that k₂ can be predicted with a high degree of accuracy by the following equations:

ln k₂ = 4.25 (χ_R+ χ_R') - 20.9                    (R² = 0.91)

= 8.48 (σ_R + σ_R') - 2.24                           (R² = 0.99)

= 31.8 ΣE_L- 63.0                                    (R² = 0.99)

= - 9.16 Ε_HOMO- 52.1                             (R² = 0.97)

= 101 ΣQ_Mulliken(Rh(CO)₂) - 49.9              (R² = 0.99)

= 94.7 ΣQ_NPA(Rh(CO)₂) - 35.2                  (R² = 0.98)

= 84.7 ΣQ_Bader(Rh(CO)₂) - 48.3                (R² = 0.95)

= 72.6 ΣQ_Hirshfeld(Rh(CO)₂) - 13.1            (R² = 0.97)

= 109 ΣQ_MDC(Rh(CO)₂) - 60.3                   (R² = 0.99)

= 91.9 ΣQ_Voroni(Rh(CO)₂) - 72.0                (R² = 0.98)

A lower (more negative) Ε_HOMO, i.e. a more stable HOMO, therefore systematically resulted in a faster substitution rate. The complex is therefore more reactive, due to the stabilization of the five-coordinate transition state of the substitution reaction. The electronic influence of R and R' groups in [Rh(R'COCHCOR) (CO)₂] complexes is reflected in the stability of the HOMO of the complex. Higher group electronegativities (χ_R + χ_R'), higher Hammett meta substituent constants (σ_R + σ_R'), higher Lever electronic parameters ΣΕ_L and lower pΚ_a values of the free β-diketone result in a more stable HOMO with a lower (more negative) energy. Relationships between calculated and experimental parameters allow for the design of ligands that can enhance the substitution rate.

 

Acknowledgements

The South African National Research Foundation and the Central Research Fund of the University of the Free State, Bloemfontein for funding.

 

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Received 14 December 2012
Accepted 5 February 2013

 

 

* E-mail: conradj@ufs.ac.za

 

 

Submitted by invitation in support of the 2012 celebrations "100 years of SACI: The Past, The Present, The Future".