Chemical and electrochemical oxidation of [Rh(β-diketonato)(CO) (P(OCH2)3CCH3)]: An experimental and DFT study

Article abstract of DOI:10.1039/c3dt50310k

An experimental and computational chemistry study of the reactivity of [Rh(β-diketonato)(CO)(P(OCH₂)₃CCH₃)] complexes towards chemical and electrochemical oxidation shows that more electron withdrawing groups on the β-diketonato ligand reduce electron density on the rhodium atom to a larger extent than electron donating groups. This leads to a slower second-order oxidative addition rate, k₁, and a higher electrochemical oxidation potential, E_pa(Rh), linearly related by ln k₁ = -11(1) E_pa(Rh) - 2.3(5). The reactivity of these complexes can be predicted by their DFT calculated HOMO energies: E_HOMO = -0.34(8)E_pa(Rh) - 5.04(4) = 0.032(5) ln k ₁ - 4.96(4). k₁ of [Rh(β-diketonato)(CO)(P(OCH ₂)₃CCH₃)] complexes is slower than that of related [Rh(β-diketonato)(CO)(PPh₃)] and [Rh(β-diketonato) (P(OPh)₃)₂] complexes due to the better π-acceptor ability of the CO-phosphite-rhodium combination than that of CO-PPh ₃-rhodium or di-phosphite-rhodium.

Full text of DOI:10.1039/c3dt50310k

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Chemical and electrochemical oxidation of
[Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]:
Cite this: Dalton Trans., 2013, 42, 8655
an experimental and DFT study
Johannes J. C. Erasmusa and Jeanet Conradie*a,b
An experimental and computational chemistry study of the reactivity of [Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)] complexes towards chemical and electrochemical oxidation shows that more electron
withdrawing groups on the β-diketonato ligand reduce electron density on the rhodium atom to a larger
extent than electron donating groups. This leads to a slower second-order oxidative addition rate, k1, and
a higher electrochemical oxidation potential, Epa(Rh), linearly related by ln k1 = −11(1) Epa(Rh) − 2.3(5).
The reactivity of these complexes can be predicted by their DFT calculated HOMO energies: EHOMO
=
Received 30th January 2013,
Accepted 5th April 2013
−0.34(8)Epa(Rh) − 5.04(4) = 0.032(5) ln k1 − 4.96(4). k1 of [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]
complexes is slower than that of related [Rh(β-diketonato)(CO)(PPh3)] and [Rh(β-diketonato)(P(OPh)3)2]
complexes due to the better π-acceptor ability of the CO–phosphite–rhodium combination than that of
CO–PPh3–rhodium or di-phosphite–rhodium.
DOI: 10.1039/c3dt50310k
www.rsc.org/dalton
[Rh(CH3COCHCOCF3)(CO)(P(OCH2)3CCH3)] leads to a slower
oxidative addition step, the strong electron donation of
Introduction
Monsanto initiated development of its rhodium- and iodide- P(OCH2)3CCH3 over CO still accelerates the oxidative addition
catalysed process for the carbonylation of methanol to acetic step by ca. 20 times (at 35°), compared to that of the Monsanto
acid in 1966.1 To date the Monsanto [Rh(CO)2(I)2]− complex is catalyst.11 For this purpose we report with this communication
one of the best known rhodium(I) catalysts.2–4 The methyl the synthesis, characterization and oxidative addition kinetics of
iodide oxidative addition reaction that forms the rhodium(III) three new [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] complexes
alkyl reaction intermediate [Rh(CO)2(I)3(CH3)]− is the rate- in order to extend the series of [Rh(β-diketonato)(CO)-
determining step of the catalytic cycle.5 Square planar (P(OCH2)3CCH3)] complexes ranging from complexes containing
rhodium(I) complexes containing a β-diketonato ligand have electron donating groups (CH3), to complexes containing elec-
been extensively studied as precursors and model compounds tron withdrawing groups (CF3) on the β-diketonato ligand. For
in catalysis.6 Another important class of catalysts is based on the first time, results are presented here on the electrochemical
rhodium(I) complexes containing more electron-donating oxidation of RhI to RhIII for this series of complexes. In addition,
ligands (than CO or I in the Monsanto complex), such as phos- relationships are established between experimental values
phine,7 biphosphine ligands2,8 or phosphite ligands.9 A previous (kinetic rate constants and oxidation potential, as measured by
kinetic study of the rhodium(I)–β-diketonato–phosphite complex cyclic voltammetry), electronic parameters of the β-diketonato
[Rh(CH3COCHCOCH3)(CO)(P(OCH2)3CCH3)]10 showed that the ligand (electronegativity of the groups,12 the Hammett meta sub-
oxidative addition reaction of CH3I to this complex is first order stituent σ constants,13–15 the Lever ligand parameters16 and the
in both the Rh(I) complex and CH3I. It further showed that, com- pKa of the free β-diketone (R′COCH2COR)) and density func-
pared to the oxidative addition of methyl iodide to the Monsanto tional theory (DFT) calculated energies. Establishing relation-
catalyst [Rh(CO)2I2]−, this complex accelerates the oxidative ships that can predict the reactivity of oxidative addition, for a
addition step by ca. 400 times (at 35°), but inhibits the CO inser- series of complexes, is of great importance in the design of new
tion step. It has also been shown that while inclusion of the elec- catalysts with a specific reactivity.
tron withdrawing CF3 group on the β-diketonato backbone in
Results and discussion
Synthesis and identification of complexes
aDepartment of Chemistry, PO Box 339, University of the Free State, 9300
Bloemfontein, Republic of South Africa
bCentre for Theoretical and Computational Chemistry, University of Tromsø,
N-9037 Tromsø, Norway. E-mail: conradj@ufs.ac.za; Fax: +27-51-4446384;
Tel: +27-51-4012194
The new [Rh(R′COCHCOR)(CO)(P(OCH2)3CCH3)] complexes
with substituents R and R′ = CH3, Ph (3), Ph, CF3 (5) and CF3,
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two steps that can be expressed as follows:
The first reaction step involves the oxidative addition step
of CH3I to the rhodium complex, which is [CH3I] dependent,
i.e. k1 is a second order rate constant obtained from the
observed rate constant kobs1 = k1[CH3I]. The second reaction
step involves the migratory insertion of the methyl group of
the RhIII-alkyl into the carbonyl group, which is [CH3I] inde-
pendent, i.e. kobs2 = k2 is a first order rate constant. It was
Scheme 1 Synthetic route for the synthesis of [Rh(β-diketonato)(CO)2] and
[Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] complexes (1)–(6) from RhCl3·3H2O.
CF3 (6) of this study are synthesized as described previously for
complexes CH3, CH3 (1),10 Ph, Ph (2)17 and CH3, CF3 (4).11 (See
Scheme 1 for complex numbering.) Heating a DMF solution of
RhCl3·xH2O leads to the formation of the salt [NH2(CH3)2]+[Rh-
(CO)2Cl2]−.18 Addition of the appropriate β-diketone to the
reaction mixture results in the precipitation of [Rh(β-diketo-
nato)(CO)2]. Adding a slight excess of the phosphite 4-methyl-
2,6,7-trioxa-1-phosphabicyclo[2.2.2]octane to an ethanol–
acetone solution of [Rh(β-diketonato)(CO)2] leads to the for-
mation of the [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] product
(see Scheme 1). For [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]
complexes (3), (4) and (5), containing an unsymmetrical β-di-
ketonato ligand RCOCHCOR′, with R ≠ R′, two isomers of
[Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] are possible: one with
the (P(OCH2)3CCH3) group trans to the Oβ-diketonato nearest to
the R′ group (isomer A) and the other with the (P(OCH2)3CCH3)
group cis to the Oβ-diketonato nearest to the R′ group (isomer B)
(see Scheme 1). The presence of both isomers for complexes
(3), (4) and (5) was observed by NMR at a ratio of isomer
A : isomer B (%) = 37 : 63 for (3), 47 : 53 for (4) and 46 : 54 for
(5). Two isomers for the related [Rh(β-diketonato)(CO)(PPh3)]
complexes containing an unsymmetrical β-diketonato ligand
were also observed by NMR19 and in some cases isolated in the
solid state and characterized by means of solid state X-ray
crystallography.20–23
found that k−1 ≈ 0 ≈ k−2
.
Infrared study
IR spectroscopy is ideal to identify the reactants and products
of rhodium complexes containing CO groups, since CO bonds
in RhI–monocarbonyl complexes resonate at ∼1980–2050 cm−1
and at ∼2050–2150 cm−1 for RhIII–alkyl complexes. CO bonds
in RhIII–acyl complexes resonate at ∼1700–1750 cm−1 24,25
.
A representative series of the spectra obtained by IR when
following the two reaction steps of the reaction between CH3I
and [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] are shown in Fig. 1
(a) for complex (3). For complex (3) the first, relatively fast reac-
tion step (t1/2 ≈ 370 s) shows that the rate of disappearance of the
RhI complex (disappearance of the RhI–CO signal at 2018 cm−1
,
kobs1 = 1.87(7) × 10−3 s−1) basically corresponds to the rate of for-
mation of the RhIII–alkyl complex (formation of the RhIII–CO
signal at 2110 cm−1, kobs1 = 2.00(6) × 10−3 s−1). The second much
slower reaction step (t1/2 ≈ 15 hours), as observed by the IR
spectra, is illustrated in Fig. 1(b). The formation of the RhIII–acyl
species (formation of the RhIII–COCH3 signal at 1714 cm−1, kobs2
= 13.3(3) × 10−6 −1) corresponds to the depletion of the RhIII–
s
alkyl (disappearance of the RhIII–CO signal at 2110 cm−1, kobs2
=
12.7(2) × 10−6 s−1). It was not possible to distinguish between the
two isomers of complexes (3), (4) and (5) by IR.
Kinetics
UV/vis study
The kinetic data obtained for the reaction between CH3I and UV/vis time scans of the first reaction step exhibit a single iso-
complexes (1)–(6) showed that the reaction proceeds through sbestic point, indicating the formation of a single product on
Fig. 1 Illustration of the oxidative addition reaction between CH3I and [Rh(PhCOCHCOCH3)(CO)(P(OCH2)3CCH3)])], (3), as monitored on the IR spectrophotometer
between 1650–2200 cm−1 in chloroform at 25 °C. (a) The first reaction step (left, measured at 90 s intervals for the first 15 scans) is indicated by the disappearance
of RhI (peak at 2018 cm−1) and the simultaneous appearance of RhIII–alkyl (peak at 2110 cm−1) at the same rate. (b) The second reaction step (only the final scan is
shown) is indicated by the simultaneous disappearance of RhIII–alkyl (peak at 2110 cm−1) and the formation of an RhIII–acyl (peak at 1714 cm−1) species. The insets
give the absorbance vs. time data of the indicated species. Initial concentrations are: [CH3I] = 0.1234 mol dm−3, and [Rh] = 2.7 × 10−3 mol dm−3
.
8656 | Dalton Trans., 2013, 42, 8655–8666
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Fig. 2 Left: selected repetitive UV/vis scans (at 25 minute intervals) for the first reaction step of the oxidative addition of CH3I to [Rh(PhCOCHCOCF3)(CO)-
(P(OCH2)3CCH3)], (5), measured in acetone at 25.0(1) °C. Inset: absorbance–time data collected at 397 nm. Initial concentrations are: [CH3I] = 0.3519 mol dm−3 and
[Rh] = 2.5 × 10−4 mol dm−3, and kobs1 = 0.000141(3) s−1. Right: temperature and methyl iodide concentration dependence for observed pseudo-first-order rate con-
stants kobs1 for the oxidative addition of methyl iodide to [Rh(PhCOCHCOCF3)(CO)(P(OCH2)3CCH3)], (5), in acetone at 397 nm; [Rh] = 2.5 × 10−4 mol dm−3. Inset:
Eyring plot according to eqn (2).
Fig. 3 Temperature and methyl iodide concentration dependence for the observed pseudo-first-order rate constants kobs1 for the oxidative addition of methyl
iodide to [Rh(PhCOCHCOCF3)(CO)(P(OCH2)3CCH3)], (5), in chloroform at 392 nm; [Rh] = 2.6 × 10−4 mol dm−3. Inset and right: the determination of the activation
parameters (ΔH#, ΔS#) is illustrated by the different Eyring plots according to eqn (2)–(4) respectively (see calculations in the experimental details section).
this timescale: see Fig. 2 for selected UV/vis scans for the first and/or partial charge creation (electrostriction) during the for-
reaction step of the oxidative addition of CH3I to [Rh(PhCOCH- mation of the transition state. A high pressure kinetic study of
COCF3)(CO)(P(OCH2)3CCH3)], complex (5), in acetone at the oxidative addition of CH3I to [Rh(CH3COCHCOCH3)(CO)-
25.0(1) °C. The inset in Fig. 2 shows the change in absorbance (P(OCH2)3CCH3)] (1) yields an experimental volume of acti-
at 397 nm for this reaction. Fig. 2 (right) and Fig. 3 (left) show the vation, ΔV# of −28(1) cm3 mol−1 in the relatively polar solvent
plots obtained by measuring kobs1 for a different initial [CH3I] acetone.10 This result might allow for a charge creation in the
and at different temperatures, for the first reaction step of the transition state, favouring the formation of an ion-pair inter-
oxidative addition reaction in acetone and chloroform as sol- mediate, which would suggest that the oxidative addition of
vents respectively. Values for k1, obtained from the slopes of methyl iodide to [Rh(CH3COCHCOCH3)(CO)(P(OCH2)3CCH3)],
the plots of the kobs1 vs. [CH3I], for complexes (1)–(6) are sum- (1), most probably proceeds via a linear transition state. An
marized in Table 1. The second reaction step for the CO inser- intimate two-step SN2 mechanism, similar to that presented by
tion (with rate kobs2 = k2) was not followed on UV/vis due to the Swaddle and co-workers,26 for the oxidative addition of methyl
long half-life of this reaction step, namely t1/2 > 11 hours.
iodide to β-diketonatobis(triphenylphosphite) complexes of
The determination of the activation parameters (ΔH#, ΔS#) rhodium(I), is therefore proposed for the oxidative addition
of the [Rh(PhCOCHCOCF3)(CO)(P(OCH2)3CCH3)] + CH3I oxi- step (first reaction step) of methyl iodide to all [Rh(β-diketo-
dative addition reaction, in acetone and chloroform as nato)(CO)(P(OCH2)3CCH3)] complexes (1)–(6):
solvent, is illustrated by the different Eyring plots in Fig. 2 and
3 respectively. The experimentally determined activation para-
meters of complexes (1)–(6) are given in Table 1. The relatively
small ΔH# values, accompanied by large negative ΔS# values,
indicate an associative mechanism including bond formation
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Dalton Trans., 2013, 42, 8655–8666 | 8657

Table 1 Kinetic rate constants and activation parameters for the oxidative addition of methyl iodide to the indicated [Rh((β-diketonato)(CO)(P(OCH2)3CCH3)] complexes (1)–(6), in various solvents, as monitored by
IR and UV/vis spectrophotometry at the indicated temperatures. k1 (second order) and k2 (first order) are the rate constants associated with the first and second stages of the reaction between CH3I and [Rh(β-diketo-
nato)(CO)(P(OCH2)3CCH3)]. The DFT calculated activation parameters are also given in selected solvents
Oxidative addition reaction
103 k1 (dm3 mol−1 s−1
)
ΔH#
ΔS#
ΔG#
ΔV#/cm3 Ea
CO insertion
k2 (s−1
Method
Solvent
TS/ε
15 °C
25 °C
35 °C
(kJ mol−1
)
(J K−1 mol−1
)
(kJ mol−1
)
mol−1
(kJ mol−1
)
)
Ref.
10
[Rh(CH3COCHCOCH3)(CO)-
(P(OCH2)3CCH3)] (1)
IR
UV/vis
Chloroform 4.8
Benzene 2.3
Chloroform 4.8
—
17.5(3)
0.45(2)
17.34(4)
5.54(7)
36.0(5)
—
—
—
—
—
—
—
−28(1)
—
—
—
—
—
—
—
—
0.0000127(8)
—
0.0000119(1)
—
—
0.28(1)
9.44(5)
3.36(3)
17.9(3)
0.89(4)
29.93(8)
10.18(9)
—
42(4)
40.5(8)
43(3)
64(3)
26
−168(15)
−143(3)
−145(9)
−56(11)
−160
92
83
86
81
73
192
Acetone
Methanol
Methanol
20.7
32.6
DFT
Linear
Bent
25
139
−177
[Rh(PhCOCHCOPh)(CO)-
17
(P(OCH2)3CCH3)] (2)
IR
UV/vis
Chloroform 4.8
Chloroform 4.8
10.12(2)
10.57(9)
4.81(9)
—
—
—
—
—
—
—
—
—
—
—
—
0.0000152(8)
5.85(5)
2.70(7)
18.07(10) 39.0(1.5)
10.00(9)
−152.0(4.9)
−138(12)
−192
84
86
82
80
82
196
Acetone
Acetone
20.7
20.7
44.8(5.3)
24
29
24
139
DFT
26
29
26
Chloroform 4.8
−170
Methanol
Linear
Bent
−194
−192
146
[Rh(CH3COCHCOPh)(CO)-
This study
(P(OCH2)3CCH3)] (3)
IR
UV/vis
Chloroform
Chloroform
Acetone
—
6.98(8)
3.08(6)
15.4(5)
13.4(2)
5.63(6)
—
23.53(8)
10.26(6)
—
—
—
90
86
81
88
—
—
—
—
—
0.0000133(2)
42.4(1)
41.9(8)
31
−158(4)
−147(3)
−167
−196
DFT
Methanol
Linear A
Linear B
31
31
29
[Rh(CH3COCHCOCF3)(CO)-
11
(P(OCH2)3CCH3)] (4)
IR
UV/vis
Chloroform
Chloroform
Acetone
—
0.46(1)
—
—
—
—
—
—
—
0.87(3)
0.78(1)
0.48(1)
—
—
—
—
—
—
—
—
1.30(7)
—
—
—
—
—
—
—
—
37.5(1.2)
—
27
28
105
140
30
32
24
—
—
91
—
—
—
—
—
—
—
—
—
—
—
—
0.00004(1)
−177.7(4.1)
—
—
—
—
—
—
—
—
—
—
—
DFT
Methanol
Linear B
Linear A
Front
−192
−195
−170
−188
−196
−195
−189
−165
84
82
156
196
89
90
80
76
29
30
111
147
32
34
26
Bent
Chloroform Linear B
Linear A
Acetone
Linear B
Linear A
—
—
—
—
—
27
27

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Density functional theory results previously obtained for
complexes (1), (2) and (4), as well as results obtained by calcu-
lation for complexes (3), (5) and (6) of this study, show
trans addition of methyl iodide to [Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)] via a linear transition state (see following
section). The resulting trans-RhIII-alkyl reaction product of the
first reaction step, can easily undergo an acyl formation reac-
tion (since CH3 and CO are located cis to each other). The
second reaction step is therefore:
CV study
The cyclic voltammograms of complexes (1)–(6) all exhibited
one irreversible oxidation peak on the forward scan and one
small reduction peak separated more than 700 mV from the
oxidation peak on the backward scan. Fig. 4 shows the cyclic
voltammogram of [Rh(PhCOCHCOPh)(CO)(P(OCH2)3CCH3)]
complex (2), as a representative example, and the data are
tabulated in Table 2. The oxidation peak is assigned to the oxi-
dation of Rh(I) to Rh(III). The irreversible two electron electro-
chemical oxidation of rhodium(I) in the [Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)] complexes of this study is followed by a fast
chemical reaction which is proposed to be the coordination of
two solvent molecules (see Scheme 2) similar to that which
was found for a series of [Rh(β-diketonato)(CO)(PPh3)],27,28
[Rh(β-diketonato)(CO)2],29 [Rh(β-diketonato)(cod)] (cod = 1,5-
cyclooctadiene)30 and [Rh(β-diketonato)(P(OPh)3)2] com-
plexes.31 It was not possible to distinguish between the oxi-
dation potential of the two isomers of complexes (3), (4) and
(5) with CV.
Inclusion of the strong electron withdrawing CF3 group
(group electronegativity on the Gordy scale χCH = 2.34 and χCF
3
3
= 3.0132) on the β-diketonato ligand in [Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)] in moving from [Rh(CH3COCHCOCH3)-
(CO)(P(OCH2)3CCH3)] (1, Epa = 317 mV vs. Fc/Fc+) to [Rh-
Fig. 4 Cyclic voltammetric response of [Rh(PhCOCHCOPh)(CO)(P(OCH2)3CCH3)]
in 0.1 mol dm−3 TBAPF6/CH3CN on a glassy carbon working electrode at ν =
100 mV s−1, T = 25.0(1) °C. Scan initiated in the positive direction as shown by
the arrow.
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Scheme 2 The proposed mechanism for the electrochemical oxidation of [Rh-
(β-diketonato)(CO)(P(OCH2)3CCH3)] complexes. S = solvent molecule = CH3CN.
(CF3COCHCOCH3)(CO)(P(OCH2)3CCH3)] (4, Epa = 482 mV vs.
Fc/Fc+) and to [Rh(CF3COCHCOCF3)(CO)(P(OCH2)3CCH3)] (6,
Epa = 938 mV vs. Fc/Fc+) results in a progressively more positive
peak anodic potential, Epa(Rh). With a strong electron with-
drawing CF3 side group on the β-diketonato ligand, the
Rh(I)
centre
in
[Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]
becomes more positive and it accordingly becomes more
difficult to be oxidized. The relationship between the electro-
chemical oxidation Epa and the experimental chemical oxi-
dation of RhI to RhIII as measured by k1 is linear:
ln k1 ¼ ꢀ11ð1Þ EpaðRhÞ ꢀ 2:3ð5Þ ðR2 ¼ 0:97Þ
Computational study
Density functional theory (DFT) calculations have been per-
formed to gain more insight into the geometry, transition state
and products of the [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] +
CH3I reaction for complexes (1)–(6). Two rhodium(I) isomers
are possible for complexes (3), (4) and (5); see Scheme 1.
Experimentally it was only possible to distinguish between the
isomers on NMR. Using computational chemistry, however, it
is possible to determine the geometry of each rhodium(I)
isomer, as well as the different transition states of CH3I oxi-
dative addition to each isomer and the different rhodium(III)
reaction products. In Tables 1 and 2 the DFT results of both
isomers of complexes (3), (4) and (5) are given with the isomer
and complex numbering according to Scheme 1. The calcu-
lated population of complexes (3), (4) and (5) is also given.
There is good agreement between the experimental isomer dis-
tribution of complexes (3), (4) and (5) as measured in chloro-
form on 1H NMR and the calculated isomer distribution.
When comparing experimental and calculated data of com-
plexes (3), (4) and (5), an effective calculated energy was deter-
mined by using the ratio of the relative population of the two
isomers as determined by the Boltzmann equation.
DFT calculations on complexes (1)–(6) indicated that the
oxidative addition reaction between [Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)] and CH3I involves a two-step SN2 mechanism
with (i) the nucleophilic attack of the metal on the methyl
carbon to displace iodide to form a metal–carbon bond and
(ii) coordination of iodide to the five-coordinated intermediate
to give a six-coordinated trans alkyl complex; see Fig. 5 for
complex (6) as an example. During the nucleophilic attack of
the metal on the methyl carbon, electron density is donated
from the HOMO of [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]
(mainly dz2 character) to the empty pz orbital on CCH -I to be
3
oxidized to Rh(III). Calculated activation parameters for the oxi-
dative addition step are summarized in Table 1 together with
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Fig. 7 Visualization of (a) the LUMO (lowest unoccupied molecular orbital) of
CH3I, (b) the HOMO (highest occupied molecular orbital) of [Rh(PhCOCHCOPh)-
(CO)(P(OCH2)3CCH3)] and (c) the HOMO of the linear transition state of [Rh-
(PhCOCHCOPh)(CO)(P(OCH2)3CCH3)] + CH3I. Note the dz2-orbital at the rhodium
centre of the HOMO diagrams and the pz-orbital at the methyl group of the LUMO
diagram. The colour code (online version) of the atoms is as indicated in Fig. 5.
kinetic parameter ln k1:
Fig. 5 The DFT calculated optimized structure of (a) reactants, (b) linear tran-
sition state (c) intermediate and (d) product of the [Rh(CF3COCHCOCF3)(CO)(P-
(OCH2)3CCH3)] + CH3I reaction. In (b) the displacement vector (blue arrow) indi-
Eact ðeVÞ ¼ ꢀ0:018ð5Þ ln k1 þ 0:19ð4Þ
+
cates the movement of the CH3 group at the imaginary frequency
(−230.3 cm−1 with a calculated intensity of −399.5). Distances (Å, black), angles
(°) and colour code (online version) of the atoms are as indicated.
To understand the role of the HOMO (highest occupied
molecular orbital) in the TS, the HOMO of [Rh(PhCOCHCOPh)-
(CO)(P(OCH2)3CCH3)] (2) and the HOMO of the linear TS of
the [Rh(PhCOCHCOPh)(CO)(P(OCH2)3CCH3)] + CH3I reaction
are presented in Fig. 7 together with the LUMO of CH3I. Rh(I)
the experimentally measured values. The agreement between
experiment and theory for the individual components ΔH#
and ΔS# to ΔG# = H# − TΔS# is not as good as for ΔG# itself.
Large compensating variations ΔH# and ΔS# with a modest
change in ΔG# were also found by Ziegler.5 Fig. 6(a) displays
the relative energy of the linear transition state and the most
stable alkyl reaction product of complexes (1)–(6).
2
2
2
2
is a dxz dyz dxy dz2 dx2−y20 complex of which the HOMO exhi-
bits mainly a dz2 character (Fig. 7(b)). In the TS the bond
between Rh and C
forms as the bond between C
and I
CH3
CH3
breaks to form the five-coordinated cationic intermediate. The
main contribution to the Rh–C bond in the TS comes from
CH3
the overlap of the filled dz2 HOMO of the rhodium atom
with the empty pz LUMO (lowest unoccupied molecular
orbital) of the methyl carbon of CH3I. Table 2 gives the calcu-
lated HOMO (EHOMO) energies of the [Rh(PhCOCHCOPh)(CO)-
(P(OCH2)3CCH3)] complexes.
The experimentally measured second order rate constant k1
of the oxidative addition of methyl iodide to [Rh(β-diketonato)-
(CO)(P(OCH2)3CCH3)] is related to the activation energy Eact by
the Arrhenius equation:
The kinetic characteristics of the [Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)] + CH3I reaction can therefore be assessed by
considering frontier molecular orbital (FMO) interactions,
Ea
RT
ln k1 ¼ ꢀ
þ ln A
where R = gas constant, T = temperature and A = pre-exponen- since these are likely to be the major initial interactions as
tial factor. Fig. 6(b) shows the relationships between the DFT reactants approach each other. The FMO theory simplifies
calculated quantity Eact and the experimentally measured reactivity to interactions between the HOMO of one species
Fig. 6 (a) The DFT calculated energies of [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] + CH3I (left), the activation energy of the linear transition state and the energy of
the trans [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]-alkyl reaction product for complexes (1)–(6), indicated by coloured bars. The energy of the reactants is taken as
zero. (b) Linear relationship between ln k1, the second-order rate constant for the oxidative addition of CH3I to [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] and the calcu-
lated activation energy of the [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] + CH3I reaction. Data are shown in Table 2. Complex and isomer numbering is according to
Scheme 1.
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Fig. 8 (a) Linear relationship between ln k1, the second-order rate constant for the oxidative addition of CH3I to [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] and the
calculated HOMO energy of [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]. (b) Linear dependence of the experimental quantity Epa(Rh) on the calculated HOMO energy of
[Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]. Data are shown in Table 2.
and the LUMO of the other.33 The reactivity of an [Rh(β-diketo- are determined as below:
nato)(CO)(P(OCH2)3CCH3)] complex is therefore related to the
energy of its HOMO. An excellent relationship between the
EpaðRhÞ ¼ 0:40ð7Þ ðχR þ χR′Þ ꢀ 1:6ð3Þ ðR2 ¼ 0:90Þ
energy of the HOMO, EHOMO (in eV) of [Rh(β-diketonato)(CO)-
EpaðRhÞ ¼ 0:6ð2Þ ðσR þ σR′Þ þ 0:28ð7Þ ðR2 ¼ 0:78Þ
EpaðRhÞ ¼ 2:6ð5Þ ΣEL þ 0:42ð4Þ ðR2 ¼ 0:87Þ
EpaðRhÞ ¼ ꢀ0:12ð3Þ pKa þ 1:3ð2Þ ðR2 ¼ 0:79Þ
(P(OCH2)3CCH3)] and the rate constant k1 (in dm3 mol−1 s−1
)
is obtained, see Fig. 8(a), data are shown in Table 2.
EHOMO ¼ 0:032ð5Þ ln k1 ꢀ 4:96ð4Þ ðR2 ¼ 0:92Þ
Electro-oxidation of a complex corresponds to the removal
of electrons from the highest occupied molecular orbital, i.e.
the HOMO of the complex. A relationship between the HOMO
energy EHOMO of [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] and
the anodic peak potential Epa(Rh) of the electrochemical oxi-
dation of the Rh(I) nucleus is therefore expected,34 see Fig. 8(b),
data are shown in Table 2.
ln k1 ¼ ꢀ4:6ð6Þ ðχR þ χR′Þ þ 16ð3Þ ðR2 ¼ 0:93Þ
ln k1 ¼ ꢀ8ð1Þ ðσR þ σR′Þ ꢀ 5:2ð5Þ ðR2 ¼ 0:91Þ
ln k1 ¼ ꢀ31ð3Þ ΣEL ꢀ 7:0ð3Þ
ln k1 ¼ 1:4ð3Þ pKa ꢀ 18 ð2Þ ðR2 ¼ 0:86Þ
EHOMO ¼ ꢀ0:34ð8Þ EpaðRhÞ ꢀ 5:04ð4Þ ðR2 ¼ 0:80Þ
EHOMO ¼ ꢀ0:15ð3Þ ðχR þ χR′Þ ꢀ 4:4ð2Þ ðR2 ¼ 0:83Þ
EHOMO ¼ ꢀ0:266ð9Þ ðσR þ σR′Þ ꢀ 5:116ð4Þ ðR2 ¼ 1:00Þ
EHOMO ¼ ꢀ1:05ð6Þ ΣEL ꢀ 5:178ð5Þ ðR2 ¼ 0:99Þ
EHOMO ¼ 0:05ð1Þ pKa ꢀ 5:55ð7Þ ðR2 ¼ 0:86Þ
The relationship obtained between EHOMO and Epa(Rh) of [Rh-
(β-diketonato)(CO)(P(OCH2)3CCH3)] is in agreement with the
DFT-Koopmans’s theorem stating that the first (vertical)
ionization energy of a system is related to the negative of the
corresponding Kohn–Sham HOMO energy.34–36
Reactivity correlations
On evaluating the relationships between the calculated
Effect of the β-diketonato ligand. Parameters that are energy (EHOMO), electronic parameters of the β-diketonato
related to the electronic effect of the R and R′ groups (of the ligand (R′COCHCOR)− ((χR + χR′), pKa, (σR + σR′) and ΣEL) and
β-diketonato ligand) on rhodium in [Rh(β-diketonato)(CO)- experimental data (Epa(Rh) and ln k1), we observe that the
(P(OCH2)3CCH3)] are group electronegativities (χR
+ χR′), linear correlations with the pKa and the Gordy scale group
Hammett meta substituent constants (σR + σR′), Lever electronic electronegativities are generally less accurate. Regarding
parameters ΣEL and the pKa of the free β-diketone. These para- relationships between experimental data and calculated par-
meters are tabulated in Table 2. The relationships between ameters, relationships involving ln k1 are 3% to 13% more
these electronic parameters and the electrochemical oxidation accurate than relationships with Epa(Rh).
potential Epa(Rh) (in eV), the chemical oxidation potential ln
Effect of the phosphite group. On comparing the second
k1 (k1 in dm3 mol−1 s−1), and the HOMO energy EHOMO (in V) order oxidative addition rate constant k1 of the oxidative
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Table 3 Second order kinetic rate constants, k1 in dm3 mol−1 s−1, for the oxidative addition step of CH3I to the indicated rhodium–β-diketonato complexes (1)–(6),
in acetone as a solvent, where β-diketonato = (R’COCHCOR)−
[Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)]
[Rh(β-diketonato)-
(CO)(PPh3)]
[Rh(β-diketonato)-
(P(OPh)3)2]
R
R′
Reference
Reference
Reference
1
2
3
4
5
6
CH3
C6H5
C6H5
CF3
C6H5
CF3
CH3
C6H5
CH3
CH3
CF3
0.00554(7)
0.00481(9)
0.00563(6)
0.00048(1)
0.00041(2)
0.0000029(9)
10
17
0.024(3)a
0.00961
0.00930
0.00146
0.00112
0.00013(1)b
41
42
42
42
42
43
0.096(2)
26
26
26
26
26
26
0.0149(3)
0.0342(5)
0.0056(1)
0.00263(5)
0.00024(3)
This study
11
This study
This study
CF3
a Value in 1,2-dichloroethane. b Value in chloroform.
addition step of the complexes (1)–(6) of the current study with slower oxidative addition found for the [Rh(β-diketonato)(CO)-
the k1 of related rhodium-β-diketonato complexes (Table 3), we (P(OCH2)3CCH3)] complexes relative to the [Rh(β-diketonato)-
observe that k1 of [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] < k1 (P(OPh)3)2] complexes is in agreement with this.
of [Rh(β-diketonato)(CO)(PPh3)]
< k1 of [Rh(β-diketonato)-
(P(OPh)3)2] by a factor 3 and 10 respectively. This result is in
agreement with the π-acceptor ability order, as will be dis-
cussed below:
Conclusion
The rates of oxidative addition of CH3I to [Rh(β-diketonato)(X)-
(Y)] complexes (X and Y = CO, PPh3, P(OPh)3 or P(OCH2)3-
CCH3) are determined by the electronic properties of the
β-diketonato ligand, as well as groups X and Y. More electron
withdrawing groups on the β-diketonato ligand coordinated to
[Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] reduce electron density
on the central metal atom to a larger extent compared to elec-
tron donating groups, thus leading to a slower oxidative
addition rate. The second-order oxidative addition rate (k1) of
[Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] complexes is slower
than that of related [Rh(β-diketonato)(CO)(PPh3)] and [Rh-
(β-diketonato)(P(OPh)3)2] complexes, due to the better π-accep-
tor ability of the CO–phosphite–rhodium combination than
that of the CO–PPh3–rhodium or di-phosphite–rhodium com-
binations. The reactivity of the [Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)] complexes towards CH3I oxidative addition
or electrochemical oxidation can be predicted by the DFT
calculated HOMO energy of the [Rh(β-diketonato)(CO)-
(P(OCH2)3CCH3)] complex: EHOMO = −0.34(8) Epa(Rh) − 5.04(4)
= 0.032(5) ln k1 − 4.96(4).
ðbest π-donatingÞ PPh3 < PðOPhÞ3 ꢁ PðOCH2Þ3CCH3
< CO ðbest π-acceptorÞ:
The Tolman’s electronic parameter37 is often used to rank
phosphine and phosphite π donor abilities. The higher the
Tolman’s electronic parameter, the lesser the π-donating (best
π-acceptor) ability of the phosphine/phosphite. Accordingly,
the P(OCH2)3CCH3 ligand of this study with a Tolman’s elec-
tronic parameter of ν(CO) = 2087.3 cm−1 is less π-donating
(better π-acceptor) than PPh3 with ν(CO) = 2068.9.38 Conse-
quently in a metal–phosphine complex, the better π-back
donation to the phosphite ligand P(OCH2)3CCH3 tends to
reduce electron density on the central metal atom to a larger
extent than with ligand PPh3. The strong delocalization of elec-
tron density away from the metal center in the phosphite
complex is expected to have a marked influence on the reactiv-
ity of the (rhodium) metal towards, for example, oxidative
addition, where the metal acts as a Lewis base. A progressively
slower oxidative addition rate (k1) is therefore expected when
moving from [Rh(β-diketonato)(CO)(PPh3)] to [Rh(β-diketonato)-
(CO)(P(OCH2)3CCH3)]. Experimentally, the oxidative addition
rate of [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] is found to be 2
to 4 times slower than that of [Rh(β-diketonato)(CO)(PPh3)], in
agreement with the larger Tolman’s electronic parameter of
P(OCH2)3CCH3.
Experimental
Materials and apparatus
Solid reagents used in preparations (Merck, Aldrich and Fluka)
were used without further purification. Liquid reactants and sol-
vents were distilled prior to use; water was doubly distilled.
Organic solvents were dried according to published methods.44
CO is a better π-acceptor than all phosphines and phos-
phites, therefore
a metal–CO–phosphite complex (better
π-acceptor) will reduce electron density on the central metal
atom more than a metal–di-phosphite complex (for the same
phosphite group). This predicts a slower oxidative addition
rate to the metal–CO–phosphite than to the metal–di-phos-
Synthesis
phite complex. Since the Tolman electronic parameter of The general procedure to synthesize the [Rh(β-diketonato)-
P(OCH2)3CCH3 (2087.3 cm−1) is similar to that of P(OPh)3 (CO)2)] and [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)] complexes
(2085.3 cm−1), it can be predicted that
a
metal–CO–P- is as described previously.10,11,17 [Rh(CO)2Cl2]− 45 was prepared
(OCH2)3CCH3 complex will have a slower oxidative addition in situ by refluxing RhCl3·3H2O (0.2 g, 0.76 mmol) in
rate than metal–di-P(OPh)3. The experimentally 3 to 18 times DMF (3 ml) until the colour changed from red to yellow
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(ca. 30 minutes).46 The solution was allowed to cool on ice and chemical shifts were reported relative to SiMe4 (0.00 ppm).
an equivalent amount of solid β-diketone (0.76 mmol) was Positive values indicate a downfield shift. Infrared spectra were
slowly added while stirring. After 30 min of stirring at room recorded on a Hitachi 270-50 infrared spectrometer either in a
temperature, the crude [Rh(β-diketonato)(CO)2], complex was KBr matrix or in chloroform solutions. UV measurements were
precipitated with an excess of water and filtered, dried in air recorded on a GBC-916 UV/VIS spectrophotometer equipped
and recrystallised from hexane. The [Rh(β-diketonato)(CO)2)] with a multi-cell thermostated cell holder ( 0.1 °C).
complex (0.200 mmol) was redissolved in 5 ml of an 8 : 2 (v/v)
mixture of ethanol and acetone and a slight excess of
solid resublimed 4-methyl-2,6,7-trioxa-1-phosphabicyclo[2.2.2]-
octane47 (0.242 mmol) was added. The bright yellow precipi-
tate, which separated after a few minutes, was redissolved by
heating the stirred solution to ca 50 °C. Hot filtration through
a short Celite column yielded a dark-yellow concentrated solu-
tion. Brightly yellow prismatic crystals separated upon cooling
down the concentrated solution in a covered container.
Characterization data are as given below.
Kinetic measurements
Oxidative addition reactions were monitored on the IR (by
monitoring the formation and disappearance of the carbonyl
peaks in chloroform) and on the UV/vis (by monitoring the
change in absorbance at the indicated wavelength and solvent)
spectrophotometers. All kinetic measurements were monitored
under pseudo-first-order conditions with [CH3I] in a 50 to
2000 times access over the concentration of the [Rh(β-diketo-
nato)(CO)(P(OCH2)3CCH3)] complex. The concentration of [Rh-
(β-diketonato)(CO)(P(OCH2)3CCH3)] ≅ 0.0002 mol dm−3 for UV/vis
measurements and ≅0.003 mol dm−3 for IR measurements.
Kinetic measurements, under pseudo-first-order conditions for
different concentrations of [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]
at a constant [CH3I], confirmed that the concentration of [Rh-
(β-diketonato)(CO)(P(OCH2)3CCH3)] did not influence the
observed kinetic rate constant. The observed first-order rate
constants were obtained from least-squares fits of absorbance
vs. time data.48 The [Rh(β-diketonato)(CO)(P(OCH2)3CCH3)]
complexes were tested for stability in solution by means of an
overlay of IR and UV/vis spectra for at least 24 hours.
[Rh(CH3COCHCOCH3)(CO)(P(OCH2)3CCH3)]
1 IR (KBr):
ν/cm−1: 1998 (CvO). 1H NMR (δ/ppm, CDCl3): 0.78 (s, 3H,
phosphite-CH3); 1.95 (s, 3H, chelate ring-CH3); 2.01 (s, 3H,
chelate ring-CH3); 4.23 (d, 6H, 3× OCH2); 5.45 (s, 1H, CH).
1
31P NMR ((δ/ppm, CDCl3): 113.282 (d, 1P, phosphite-P, JRh-P
=
285.04 Hz).
[Rh(PhCOCHCOPh)(CO)(P(OCH2)3CCH3)]
2
IR (KBr):
ν/cm−1: 1992 (CvO). 1H NMR (δ/ppm, acetone-d): 0.935 (s, 3H,
phosphite-CH3); 4.47 (d, 6H, 3× OCH2); 7.105 (s, 1H, CH),
7.43–7.57 and 8.07–8.14 (2× m, 10 H, phenyl). 31P NMR
1
((δ/ppm, acetone-d): 114.513 (d, 1P, phosphite-P, JRh-P
=
282.029 Hz).
[Rh(CH3COCHCOPh)(CO)(P(OCH2)3CCH3)] 3 IR (KBr): ν/cm−1
:
1998 (CvO). 1H NMR (δ/ppm, acetone-d6): 0.90/0.915 (s, 3H,
phosphite-CH3), 2.08/2.18 (s, 3H, chelate ring-CH3), 4.40/4.435 (d,
6H, 3× OCH2), 6.355/6.39 (s, 1H, CH), 7.37–7.53 and 7.93–7.98
(2× m, 2× 3H/2× 2H, aromatic protons of both isomers undistin-
guishable). 31P NMR ((δ/ppm, acetone-d6): 114.704/114.297 (d, 1P,
phosphite-P, 1JRh-P = 280.765/283.642 Hz).
Calculations
Pseudo-first-order rate constants, kobs, were calculated by
fitting48 kinetic data to the first-order equation49
At ꢀ A ¼ ðA0 ꢀ A ÞeðꢀkobsꢂtÞ
1
1
[Rh(CH3COCHCOCF3)(CO)(P(OCH2)3CCH3)]
4
IR (KBr):
ν/cm−1: 2000 (CvO). 1H NMR (δ/ppm, acetone-d6): 0.905 (s,
2× 3H, 2× phosphite-CH3), 2.18/2.26 (s, 3H, chelate ring-CH3),
4.42 (broad d, 2× 6H, 2× (3× OCH2)), 6.06 (s, 2× 1H, 2× CH).
31P NMR ((δ/ppm, acetone-d6): 113.880/113.287 (d, 1P, phos-
phite-P, 1JRh-P = 282.998/282.329 Hz).
with At, A∞ and A0 = the absorbance of the indicated species at
time t, infinity and 0 respectively. The experimentally deter-
mined pseudo-first-order rate constants were converted to
second order rate constants, k1, by determining the slope of
the linear plots of kobs against the concentration of the incom-
ing methyl iodide ligand. Non-zero intercepts implied that
[Rh(PhCOCHCOCF3)(CO)(P(OCH2)3CCH3)]
5
IR (KBr):
ν/cm−1: 2000 (CvO). 1H NMR (δ/ppm, acetone-d6): δ 0.935
(broad s, 2× 3H, 2× phosphite-CH3), 4.42–4.53 (broad d, 2× 6H,
2× (3× OCH2)), 6.77–6.80 (broad s, 2× 1H, 2× CH), 7.48–7.68
and 8.07–8.12 (2× m, 2× 3H/2× 2H, aromatic protons of both
isomers undistinguishable). 31P NMR (acetone): δ 113.507 (d,
kobs = k1[CH3I] + k−1
.
All kinetic and other mathematical fits were done utilizing
the fitting program MINSQ.48 The error of all the data is indi-
cated according to crystallographic conventions, for example
kobs = 0.0236(1) s−1 implies kobs = (0.0236 0.0001) s−1
.
1
2× 1P, 2× phosphite-P, JRh-P = 283.158 Hz). Isomers not dis-
The activation parameters were determined by a least
squares fit to the Eyring equation49
tinguishable on 31P NMR.
[Rh(CF3COCHCOCF3)(CO)(P(OCH2)3CCH3)]
6
IR (KBr):
ꢀ
ꢁ
TkB
h
ΔH#
RT
ΔS#
R
ν/cm−1: 2008 (CvO). 1H NMR (δ/ppm, acetone-d6): δ 0.93 (s,
k ¼
exp ꢀ
þ
ð2Þ
3H, phosphite-CH3), 4.49 (d, 6H, 3× OCH2), 6.44 (s, 1H, CH).
as well as from two linear forms of the equation50
Spectroscopy and spectrophotometry
k
T
ΔH#
RT
ΔS#
R
kB
h
NMR measurements at 298 K were recorded on a Bruker
Avance DPX 300 NMR spectrometer (1H 300.130 MHz). The
ln ¼ ꢀ
þ
þ ln
ð3Þ
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and
constant, T is the temperature and S is the entropy. The
entropy (S) was calculated from the temperature dependent
partition function in ADF at 298.15 K. The computed results
assume an ideal gas.
ꢀ
ꢁ
k
T
kB ΔS#
ΔH#
R
Tln ¼ T ln
þ
ꢀ
ð4Þ
h
R
with ΔH# = activation enthalpy, ΔS# = activation entropy, k =
second order rate constant, kB = Boltzmann’s constant, T = temp-
erature, h = Planck’s constant, R = universal gas constant. Values
determined for ΔH# and ΔS# using eqn (2)–(4) were the same
(see Fig. 3 for [Rh(PhCOCHCOCF3)(CO)(P(OCH2)3CCH3)]). The
calculated standard errors obtained from ΔH# and ΔS# relate to
the average experimental temperature51 within 8 K:
Solvent effects were taken into account for all calculations
reported here. The COSMO (Conductor like Screening Model)
model of solvation58–60 was used as implemented61 in ADF. The
COSMO model is a dielectric model in which the solute mole-
cule is embedded in a molecule-shaped cavity surrounded by a
dielectric medium with a given dielectric constant (ε0). The type
of cavity used is Esurf62 and the solvent used is methanol (ε0 =
32.6). Selected activation parameters were also calculated in
chloroform (ε0 = 4.8) and acetone (ε0 = 20.7) as solvents.
σðΔH#Þ
¼ Tav
ð5Þ
σðΔS#Þ
The activation Gibbs energy was calculated from equation49
Acknowledgements
ΔG ¼ ΔH ꢀ TΔS
Computational chemistry
ð6Þ
Financial assistance by the South African National Research
Foundation and the Central Research Fund of the University of
the Free State is gratefully acknowledged. This work has received
support from the Norwegian Supercomputing Program (NOTUR)
through a grant of computer time (Grant No. NN4654K).
Density functional theory (DFT) calculations were carried out
using the ADF (Amsterdam Density Functional) 2012
programme52–54 with the GGA (Generalized Gradient Approxi-
mation) functional PW91 (Perdew–Wang, 1991).55 The TZP
(Triple ζ polarised) basis set with a fine mesh for numerical
integration, a spin-restricted formalism and full geometry
optimization with tight convergence criteria was used for
minimum energy and transition state (TS) searches. Approxi-
mate structures of the TS have been determined with linear
transit (LT) scans, with a constrained optimization along a
chosen reaction coordinate, to sketch an approximate path
over the TS between reactants and products. Numerical fre-
quency analyses,56,57 where the frequencies are computed
numerically by differentiation of energy gradients in slightly
displaced geometries, have been performed to verify the TS
geometries. Finally, the TS was allowed to relax after displacing
the atoms according to the reaction coordinate as determined
by the eigenvectors. This gave the reactants (relax from
minimum stretch of frequency gave a rhodium(I) complex and
CH3I) and the products (relax from maximum stretch of fre-
quency gave a cationic five coordinated complex and I−)
respectively. Throughout, all calculations have been performed
with no symmetry constraint (C1) and all structures have been
calculated as singlet states.
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