331
Journal of Molecular Catalysis, 19 (1983) 331 - 343
METAL CATALYSIS IN OXIDATION BY PEROXIDES PART 18”. ON THE MECHANISM OF THE ELECTROPHILIC EPOXIDATION BY MOLYBDENUM(VI)-PEROXO COMPLEX
OLGA BORTOLINI,
VALERIA
OLEFIN
CONTE, FULVIO DI FURIA and GIORGIO MODENA
Centro CNR di Studio di Meccanismi di Reazioni Organiche, Zstituto di Chimica Organica, Universitci di Padova, Via Marzolo 1, 35131 Padua (Italy) (Received October 18, 1982)
Summary A kinetic analysis of two oxidizing systems, MoOz(acac),-H202 in EtOH and MoO,HMPT in DCE in the epoxidation of two alkenes, l-methylcyclohexene and cyclohexene, and an allylic alcohol, geraniol, has been carried out. The oxidation has been studied both in the absence and in the presence of HMPT (hexamethylphosphorotriamide), a strong complexing agent of molybdenum(V1) peroxo complexes. The kinetic behaviour observed and, in particular, the effect on the oxidation rates of added HMPT, leads to the conclusion that the oxidative process is carried out in solution by different Mo(VI)-peroxo complexes, carrying solvent molecules, substrate and HMPT in the coordination sphere, all acting as electrophilic oxidants toward an uncomplexed olefin molecule.
Introduction The chemistry of transition metal peroxo compounds has been the subject of a large number of synthetic and mechanistic investigations [ 11. These studies have demonstrated that such species are highly versatile reagents acting as oxidants of different compounds - alkenes, ketones, organic sulphides, amines etc. In each one of these reactions, a peroxide oxygen is transferred from the metal peroxo complexes to the substrate. Two alternative mechanistic pathways, as shown in the Scheme below, have been suggested for the oxygen transfer process:
*Part 17, preceding paper. 0304-5102/83/$3.00
@ Elsevier Sequoia/Printed in The Netherlands
332
Path A
-
M=O
+ S=O
(1)
-
(2)
0
M “OR+S-
MOR + S=O
Path B
MC]+s
+
y=p s
M
/O\
+
M’O\,
O
-
M=O
y’ S
S = substrate
molecule
(3)
A--’ S
0
OR + S 4
+ S=O
‘OR
+
ylh
-
MOR + S=O
(4)
9 k
Scheme 1.
Path A amounts to an electrophilic oxygen transfer to a nucleophilic substrate fully similar to the mechanism suggested for the oxidation by peroxo acids and hydroperoxides or hydrogen peroxide under acid catalysis
121. Path B implies an insertion of the substrate into the metal-oxygen bond, causing the inversion of the electronic properties of the substrate itself, which becomes electrophilic, whereas the peroxide oxygen acquires a nucleophilic character. This resembles, as far as the role of the peroxo compound is concerned, the mechanism suggested for the Baeyer-Villiger oxidation of ketones and similar reactions [2]. Evidence of a nucleophilic oxygen transfer, through the intermediacy of a peroxometallocycle (eqn. (3)) or a pseudoperoxometallocycle (eqn. (4)), has been provided in the oxidation of l,l-dicyanoisobutene to acetone by Pt and Pd peroxo compounds [ 31 as well as in the oxidation of terminal olefins, e.g. 1-octene, to methyl ketones by Rh and Pd peroxo compounds [ 4, 51. A similar mechanism is very likely to hold in the oxidation of ketones by Pt-peroxo complexes [6] or by Mo-dipicolinato peroxo complexes [7]. On the other hand, there are severe doubts that olefin epoxidation adopts this ‘intramolecular’ mechanism, as recently suggested [4], rather than the one generally accepted [2] involving electrophilic oxygen transfer. Indeed, our recent results of a kinetic investigation of sulphide oxidation by
333
MO-peroxo complexes provided strong evidence on the electrophilic character of the oxygen transfer process [ 81. Because of the crucial importance of defining the nature of the oxygen transfer process, not only from a mechanistic point of view but also for the implications in the stereochemistry of the reaction, we have undertaken a detailed kinetic study of the epoxidation of typical olefins (cyclohexene and 1-methylcyclohexene) and an allylic alcohol (geraniol) either in ethanol solvent, under catalytic conditions, or in dichloroethane (DCE) under stoichiometric ones, aiming to obtain further evidence on these systems. The results, particularly those obtained in the presence of a strong complexing agent of Mo(VI), hexamethylphosphorotriamide (HMPT), have confirmed the electrophilic character of the oxygen transfer process as is reported and discussed herein.
Experimental Materials 1-methylcyclohexene, cyclohexene and geraniol were commercially available reagent grade materials carefully distilled before use. Commercial bis(acetylacetonato)dioxomolybdenum(VI), MoO,(acac),, was purified by crystallisation. Molybdenum(V1) oxodiperoxo complex, MoO(O~)~HMPT, was prepared and purified according to the original procedure by Mimoun et al. [9]. Commercial Hz02 (36% v/v) was used as obtained; HMPT (hexamethylphosphoric acid triamide) was reagent grade material distilled before use. Anhydrous ethanol and dichloroethane (DCE) were obtained by standard procedures from highly pure commercial samples. Product analyses and kinetic measurements The stoichiometry of the epoxidation of l-methylcyclohexene by Mo0,(acac)2-HzOz in EtOH and of cyclohexene by MoOsHMPT in DCE have been established previously; in both cases the corresponding epoxide is formed (yield > 90%) [9, lo]. Epoxidation of geraniol either by MoO,(acac),-HzOz or by MoOsHMPT gives the 2,3-epoxygeraniol in quantitative yield. Kinetic data were obtained according to a general procedure described elsewhere [8, 91 by titration of the residual oxidant by standard iodometric procedures. A BASIC version of the Nelder-Mead algorithm was used in the calculations of equilibrium and rate constants [ 111. ‘H NMR experiments ‘H NMR spectra of MoOsHMPT were recorded on a Bruker WP-200 instrument at 200 MHz with TMS as internal standard both in methanol-d, and in CDCl,, at 20.0 “C. The chemical shifts were read to kO.3 Hz. In the methyl proton resonance region the ‘H NMR spectrum of a 5 X lo-* M solution of MoOsHMPT dissolved in methanol-d4 exhibits a doublet (2.80 ppm) 3Jp_H 9.9 Hz. Upon dilution new signals appear: 2.65 ppm (d,jJr_n 9.4 Hz).
334
By comparison with the ‘H NMR spectrum of HMPT in the same solvent, the signals centered at 2.65 ppm are attributed to the CH3 resonance of the free ligand. On the basis of the relative intensities of the two doublets in the range of MoOsHMPT concentration 1 X low2 - 5 X low3 M, a value of 200 M-i may be estimated for the coordination equilibrium constant of HMPT to MOO,. Similar experiments carried out in CDCl, indicate that in the MoosHMPT concentration range 1 X lop2 M - 1 X low3 M only one doublet is observed (2.80 ppm) 3JP_H 9.9 Hz and accordingly, no signals attributable to the free ligand appear even at the lowest concentrations.
Results and discussion Catalytic epoxidation
by Mo-peroxo
complexes
The epoxidation of 1-methylcyclohexene, 1, and geraniol, 2, by H202 in the presence of Mo02(acac)2, has been studied in ethanol at 50.0 “C and 40.0 “C respectively. The general features of the oxidizing system and the general techniques employed have been reported previously [ 81. The oxidant has been shown to be an oxodiperoxomolybdenum(V1) complex, M00(0~)~(MOO,), likely involving ethanol molecules in the coordination sphere, formed through an irreversible displacement of the acacH ligands by Hz02. This leads to a zero-order kinetic dependence of rates on [H202]. Table 1 collects the initial rate (R) values for the epoxidation of 1. It may be seen that the rates increase linearly with increasing concentration of 1 over a wide concentration interval, i.e. the kinetic order in 1 is clearly one. Upon addition to the reaction mixture of increasing amounts of hexamethylphosphorotriamide, HMPT, a strong ligand of MoOS [8,9], the R values decrease. However, at [ HMPT] /[Moo,] ratios > 200 the rates become independent of [HMPT]. The order in 1, in the presence of HMPT 1.0 M is still one. Similar results are obtained in the epoxidation of 2, as indicated by the data reported in Table 2. Worth noting is that the rates become independent of [HMPT] at [HMPT]/[MoO,] > 100. If the hypothesis of an association olefin-Moo, leading to the peroxometallocycle is taken into account [9, 121, then the data in Tables 1 and 2, and particularly the first-order dependence of rates on substrate concentration, indicate that such an equilibrium process*, eqn. (5), should be largely shifted to the left, i.e. that K,,, in the alcoholic solvent is very small. In fact, Moos + 01 =
MoOsOl, KAss
(5)
by combining eqn. (5) with eqn. (6), which is the product-forming step, one obtains the calculated rate law as a function of the initial and stoichiometric concentrations: *For the sake of simplicity, sphere of Moos and the consequent
the ethanol displacement
molecules involved in the coordination by the substrate are not considered.
335 TABLE Rates added
1 of epoxidation of I-methylcyclohexene with hydrogen peroxide, catalyzed MoOz(acac), at 50.00 -+ 0.05 “C in ethanol-O.5 M Hz0 under nitrogena
[ 1-Methylcyclohexene] WI
Rb (M s-l x 10’)
[ HMPT] W
0.2 0.3 0.5 0.8 1.0 1.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.77 1.0 2.0
by
3.3 5.1 7.7 12.1 17.7 29.7 4.1 3.6 2.0 1.8 1.6 1.5 1.1 1.1 1.1 1.74 2.56 4.81
0.01 0.02 0.04 0.08 0.1 0.5 1.0 1.8 3.0 1.0 1.0 1.0
aIn all experiments [HzOzlo = 0.01 M, [MoOz(acac)2]& = 0.001 M. b Slopes of plots of [ H202] us. time, linear to up 80% reaction.
TABLE
2
Rates of epoxidation of geraniol with (acac), at 40.00 + 0.05 “C in ethanol-O.5
hydrogen peroxide, catalyzed M Hz0 under nitrogena
by added
Mo02-
[ Geraniol] UW
[HMPT] U’4
Rb (M s-l x 10’)
0.1 0.2 0.4 1.0 0.2 0.2 0.2 0.2 0.2 0.2
-
5.1 11.2 23.0 60.2 5.9 3.9 3.9 3.8 3.8 3.6
0.01 0.04 0.06 0.08 0.1 0.5
a In all experiments [ H20&, bAs note b, Table 1.
M00501+
Products,
Fzi
= 0.01 M, [MoOz(acac)z]d
= 0.001 M.
(6)
(7) The rate, as expressed by eqn. (7), agrees with the experimental only if l> KAss [Ol],. When HMPT is added to the reacting system, it is expected [8, an additional equilibrium process takes place. Thus, the strong ligand may displace the olefin from the coordination sphere of Mo(VI), as (8). MoOSHMPT + 01, KS
MoOsOl + HMPT =
The process envisaged in eqn. (8) might explain the inhibitory added HMPT. In fact, in the presence of the ligand, the calculated is:
R=
hiK,ss[O1l,[Mo(VI)I, 1+ K,,,[011 o + K,s,KsWMPTl,,
Equation R =
(9) is simplified
results 91 that HMPT in eqn. (8)
effect of rate law
(9)
to eqn. (lo),
kK~ss[Ollo [Mo(VI)lst 1 + KA~sKJHMPTI,~
(10)
since, also in the presence of HMPT, the kinetic order in [Ol] is one. However, eqn. (10) predicts that the rates drop continuously with increasing [HMPT] , the limiting value of eqn. (10) being zero for [HMPT] -j 00, whereas the data reported clearly indicate the reaching of a limiting non-zero value. On the other hand, the alternative electrophilic mechanism [8] agrees rather satisfactorily with the experimental results, as it simply requires that MOO, reacts with an external olefin molecule (the complication arising from the theoretically possible coordination of the olefin to MOO, may be ignored under the experimental conditions adopted because of the large excess of basic solvent molecules) as shown in eqn. (11): MOO, + 01~
Products,
h2
(11)
An overall second-order rate law, first-order both in the substrate and the catalyst and zero-order in H202, is expected and experimentally found: R = k2[01][Mo(VI)]
(12)
On the other hand, the remarkable affinity of MoOS for HMPT suggests that, in the presence of the ligand, HMPT-complexed peroxomolybdenum species may occur in solution, as shown in eqn. (13): Moo5 + HMPT =
MoOsHMPT,
K,
(13)
As a consequence, two peroxo complexes, Moos and MoO,HMPT, exist in solution. Under the hypothesis that both are capable of epoxidizing the substrate, a two-term rate-law should be considered:
337
R = h2[Mo0J[01] In terms comes:
+ h,‘[MoO,HMPT][Ol] of initial
R = ~,[Oll,DW’I)l,t
and stoichiometric
(14) concentrations,
+- k,‘~,[O1l,[Mo(VI)I,,[HMPTl,, 1 + K,[HMPT],,
1 + &[HMPT],,
eqn.
(14) be-
(15)
The agreement of eqn. (15) with the data reported in Tables 1 and 2 have been checked by means of a computer program which sets the best izz, kz’ and K, values to fit the experimentally observed dependence of R on [HMPT] . The results shown in Fig. 1 for 1-methylcyclohexene epoxidation may be considered rather satisfactory. The values of the constants obtained are: 1, at 50.0 “C!, k2 = 1.5 X 10e3 M-i s-l; h,’ = 2.2 X 10e4 M-’ s-l; K, = 100 M-*; 2, at 40.0 ‘C, hz = 6.1 X 10m3 M-i s-i; k,’ = 1.7 X10p4 M-i s-‘; Kc = 240 M-‘. Independent experiments, carried out by a NMR technique, (see Experimental), have provided for K,, in MeOH at 20.0 “C a value of 200 M-l. Thus, a reasonably good agreement of these values obtained by different techniques is observed. It is worth pointing out that, for both substrates, it is found that k, > hz’ as is expected on the basis of the higher electrophilic character of the uncomplexed molybdenum compound as compared with that of the HMPTcomplexed species [ 81.
OE 0
20
IO IO
30
[HMPT-J
Fig. 1. Calculated (see text) R values (epoxidation of 1-methylcyclohexene by MoOz(acac)2-H202 in ethanol at 50.0 “C) as a function of added HMPT, at constant alkene, hydrogen peroxide and catalyst concentrations (circles are experimental points, see Table 1).
338 Stoichiometric
epoxidation
by MoO,HMPT
The rates of oxidation of cyclohexene, 3, by MoOsHMPT have been measured in DCE at 25.0 “C using a tenfold excess of the substrate over the oxidant. Under such conditions, the observed rate law is: R = -d[O].,,/dt
= h(obs)[OIAct
(16)
. Thus, the pseudo-firstwhere h(obs) = h[Cy]” and [O].,_, = 2 [MoOsHMPT] order rate constants, k(obs), are obtained as slope of plots of log[OIAct us. time. Table 3 collects the k(obs) values obtained both in the presence and in the absence of added HMPT. The comparison with the results reported in the preceding paragraph immediately reveals some important differences. It may be observed that in the absence of added HMPT, the k(obs) values do not increase linearly with increasing concentration of the substrate, i.e. x < 1, thus confirming the previous results obtained in identical, or very similar, systems [ 9, 121. Furthermore, the addition of HMPT causes a continuous decrease of k(obs) so that the rate becomes eventually comparable with that of the slow self-decomposition of the oxidant. The most striking feature disclosed by the kinetic data of Table 3 is the apparent order in cyclohexene, larger than one, observed in the presence of HMPT 0.11 M. It is very difficult to reconcile this experimental finding with a mechanistic pathway involving the oxidation of a coordinated molecule of olefin. By consequence, the most likely alternative is again an electrophilic external oxidation. As to the nature of the peroxo species involved in such a process, the possibility exists that in a non-coordinating solvent such as DCE, and in the presence of a large excess of alkene, this may enter the coordination sphere of MoOsHMPT, which has a vacant coordination site [ 71. Therefore, if such an equilibrium process takes place: MoOsHMPT
+ Cy =
MoOsHMPTCy,
KAss
two molybdenum peroxo compounds acting as electrophilic oxidants. The predicted rate-law will be:
exist
R = -d[
0] Act/dt = k, [ Cy ] [ MoOsHMPT]
Equation becomes: R =
(18),
in terms
k2[CYlo[Ol*ct
2(1+
+
KASSICYIO)
(17) in solution,
both
capable
+ k,‘[ Cy] [ MoOsHMPTCy ]
of initial and stoichiometric
(13)
concentrations,
WbsCCylo2Wltict 20
of
(19)
+ KASS[CYlO)
By combining eqn. (19) with eqn. (16), the dependence substrate initial concentration is given by eqn. (20):
of k(obs)
on
+ k2’KAs.s WY102 (20) 2 1 + KASS]CY]O Thus, by means of a computer program, it is possible to calculate the k(obs) values as a function of [Cylo obtaining the best k2, k,’ and KAss
k(obs)
= 5
2
[CY],
1 + ~ASS[CylO
339
TABLE 3 Rates of epoxidation
of cyclohexene
by MoOsHMPT at 25.00 f 0.05 “C in DCEa
[ Cyclohexene] (M)
[ HMPT ] (M)
0.16 0.49 1.48 2.14 2.96 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 0.49 0.71 0.98 1.15 1.97 2.46 2.63 2.96
-
1.1 3.2 7.4 11.4 14.6 3.2 2.4 1.9 1.4 0.57 0.32 0.24 0.1 0.05 o.15c 0.24’ o.30c o.43c o.94c 1.25’ 1.51C 1.8gc
0.01 0.03 0.048 0.076 0.11 0.19 0.3 0.57 0.95 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11
a In all experiments [ MoOsHMPT]e = 0.025 M ([ 01~~ = 0.05 M). bMeasured as alope of plots of ln[OIAct us. time. CIn the presence of cyclohexane; [cyclohexene] + [cyclohexanelAdd
= 3 M.
values to fit the experimental points. The results of such a calculation are graphically reported in Fig. 2, indicating a very good agreement of the rate law calculated on the basis of an electrophilic oxygen transfer from MOO,HMPT and MoOsHMPTCy, with that experimentally observed. The values of 12*, k?’ and K,,, thus obtained are respectively: 1.3 X 10e3 M-’ s-l, 0.86 X 10m3 M-i s-‘, 0.81 M-‘. It is confirmed that uncomplexed Mo-peroxo compounds are more reactive than the olefin-complexed ones. Also, a relatively small association constant for the coordination of cyclohexene to MOO, is found, as expected. An independent check of the validity of the mechanism of external oxygen transfer is provided by the rate data collected in the presence of HMPT. Under such conditions, an additional equilibrium, i.e. the coordination of a second molecule of the ligand to Mo05HMPT, should be considered. This process may be written as in eqn. (21): MoOsHMPTCy
+ HMPT Z
MoOJHMPT)~
+ Cy, KS
(21)
20
10
IO
30
40
~yclohrxenc],M
Fig. 2. Dependence of the calculated (see text) k(obs) values (epoxidation of cyclohexene by MoOsHMPT in DCE at 25.0 “C) on substrate initial concentration at constant oxidant concentration (circles are experimental points, see Table 3).
Thus, assuming that MoOJIMPT, MoOsHMPTCy and MoOS(HMPT)2 are all oxidizing species, a three term equation is obtained: k(obs)
KY]0
k2
= -
2 +
l+&sECY]o+
+
[CYlo2
karK~ss
2
1 + K~sdCYlo
k2IrKASSKs 2
+
KASF,&[H~T~
+
+ KASSKS[HMPT~S~
KJYlol-HMPTlst 1+ K~ss[CYlo
+ bsKs~HMP%
(22)
Figures 3 and 4 show the excellent agreement of the k(obs) calculated on the basis of eqn. (22) with the experimental ones either as a function of added [HMPTISt or of initial substrate concentration. In particular, it may be noticed that at [HMPT] = 0.11 M an apparent kinetic order in Cy > 1 is predicted and experimentally found. The values of k2, kz’, kz”, KAs and KS are respectively: 1,3 X 10e3 M-l s-i, 0.86 X 10e3 M-i s-l, 2.7 X 10e7 M-i s-l, 0,81 M-l and 275. These data confirm that HMPT is by far a better ligand to
341 I
0
2
4 IO
6
[HMPT],M
I)
IO
0
IO
20 IO
30
40
50
[Gyc!ohexe"e],M
Fig. 3. Calculated (see text) h(obs) values (epoxidation of cyclohexene by MoOsHMPT in DCE at 25.0 “C!) as a function of added HMPT, at constant alkene and oxidant concentrations (circles are experimental points, see Table 3). Fig. 4. Dependence of the calculated (see text) k(obs) values (epoxidation of cyclohexene by MoOeHMPT in DCE at 25.0 “C) on substrate initial concentration, at constant oxidant concentration, in the presence of HMPT 0.11 M (circles are experimental points, see Table 3).
Moos than the substrate. It may also be noticed that MoO~(HMPT)~ has little, if any, oxidizing ability. The data referring to the epoxidation of geraniol to give the 2,3epoxide are collected in Table 4. It may be seen that, from a qualitative point of view, the kinetic behaviour of the allylic alcohol is similar to that of cyclohexene discussed above. Thus, in the absence of HMPT, the rates drop quite rapidly with increasing substrate concentration. Furthermore, added HMPT inhibits the oxidation; in the presence of HMPT 0.57 M, the apparent order in the substrate is larger than one. Indeed, in such conditions an apparent order > 2 could be calculated. Therefore, it appears that .the kinetic effects observed in geraniol epoxidation are somewhat magnified as compared with those discussed in the case of cyclohexene. This is likely connected with the presence of the hydroxo group on geraniol. Accordingly, as the data of Table 5 indicate, the addition of a protic species, such as EtOH, to DCE in the absence of added HMPT has a remarkable inhibitory effect on epoxidation rates, whereas in the presence of HMPT 0.57 M added EtOH and CF$H,OH enhance the
342 TABLE 4 Rates of epoxidation
of geraniol by MoOsHMPT at 15.00 + 0.05 “C in DCE under air
[ Geraniol] (M)
[ HMPT] (M)
k(obs)a*b (s-i x 103)
0.126 0.175 0.25 0.50 1.00 0.25 0.25 0.25 0.25 0.25 0.125 0.500 0.75 1.00
-
5.1 6.1 7.3 8.0 9.4 5.6 2.4 0.52 0.04 0.013 0.011 0.24 0.88 1.20
0.01 0.06 0.20 0.57 0.95 0.57 0.57 0.57 0.57
a In all experiments [MoOsHMPT]e bAs b. Table 3.
= 0.025 M ( [O]A~~= 0.05 M).
TABLE 5 Effect of added alcohols upon the epoxidation rates of geraniol by MoOsHMPT at 15.00 + 0.05 “C in DCE under air
[ HMPTIadd (Ml
[ CH3CH20H] (M)
[ CF3CH20H] (M)
k(obs)a (s-l x 103)
-
-
-
0.57
0.25 0.50 0.75 -
0.57 0.57 0.57 0.57 0.57
0.25 0.50 0.75 -
0.28 0.93
7.3 2.5 1.5 1.5 0.039 0.11 0.22 0.28 0.065 0.39
a In all experiments [MoOsHMPT] bAs b, Table 3.
= 0.025 M ([ 0] k=
0.05 M); [geraniol] = 0.25 M.
rates. The rate enhancement could be easily explained considering that the alcohol may hydrogen bond with the phosphoramide as, for instance, in RO-*-H-**OP(NR2)3. This should decrease the donor ability of the oxygen in the P=O group of HMPT, thus reducing the concentration of ineffective MoO~(HMPT)~ species and hence enhancing the overall oxidizing power of the system.
343
The detailed kinetic analysis reported above seems to establish that in both protic and aprotic solvents, Mo(VI)-peroxo species have no tendency to form peroxometallocyclic intermediates with olefins. Therefore, an external electrophilic oxygen transfer from the peroxide to the nucleophilic substrate appears to be the most likely mechanism of the oxidations by such species, and indeed the kinetic behaviour observed is fully consistent with such a process.
Acknowledgements This research was sponsored by the Italian National Finalizzato (CNR, Rome) in the frame of the Progetto Secondaria’.
Research Council ‘Chimica Fine e
References
7 8 9 10 11 12
R. A. Sheldon and J. K. Kochi, Metal-Catalyzed Oxidations of Organic Compounds, Academic Press, New York, 1981 and references therein. R. Curci and J. 0. Edwards, in D. Swern (ed.), Organic Peroxides, Wiley-Interscience, New York, 1970, ch. 4. R. A. Sheldon and J. A. van Doorn, J. Organometal. Chem., 94 (1975) 115. H. Mimoun, M. M. Perez Machirant and I. Seree de Roth, J. Am. Chem. Sot., 100 (1978) 5437. H. Mimoun, R. Charpentier, A. Mitschier, J. Fischer and R. Weiss, J. Am. Chem. Sot., 102 (1980) 1047. (a) R. Ugo, F. Conti, S. Cenini, R. Mason and G. B. Robertson, J. Chem. Sot., Chem. Commun., (1968) 1498; (b) R. Ugo, G. M. Zanderighi, A. Fusi and D. Carreri, J. Am. Chem. SOL, 102 (1980) 3745. S. E. Jacobson, R. Tang and F. Mares, J. Chem. Sot., Chem. Commun., (1978) 888. 0. Bortoiini, F. Di Furia and G. Modena, J. Mol. Catal., 14 (1982) 53. H. Mimoun, I. S. de Roth and L. Sajus, Tetrahedron, 26 (1970) 37. 0. Bortolini, F. Di Furia, G. Modena, C. Scardellato and P. Scrimin, J. Mol. Catal., 1 I (1981) 107. J. C. Nash, Compact Numerical Methods for Computers, Adam Hilger Ltd., Bristol, 1979, p. 141. H. Mimoun, J. Mol. Catal., 7 (1980) 1 and references therein.