Semiquantitative FMO Analysis of Substituent Effect on the Reaction of Permanganate Ion with Unsymmetrical Alkenes

Article abstract of DOI:10.1021/jo972163k

The substituent effects on the reactions of permanganate ion with unsymmetrical alkenes are analyzed on the assumption of a concerted (3 + 2) cycloaddition model by using an equation obtained by approximation based on the FMO theory in which development and localization of the frontier molecular orbitals at the reaction sites with progress of the reaction are considered. The Hammett plots are successfully reproduced with the newly obtained rate data for the reactions of trans-chalcone and its derivatives and the data for methyl cinnamates, cinnamate ions, and alkyl vinyl ethers taken from the literature using FMO energies and orbital coefficients calculated by the PM3 method. It was indicated that a factor introduced to the basic equation in order to estimate the extent of localization of the molecular orbitals at the transition state is closely related to the position of the transition state along the reaction path.

Full text of DOI:10.1021/jo972163k

J . Org. Chem. 1998, 63, 2627-2633
2627
Sem iqu a n tita tive F MO An a lysis of Su bstitu en t Effect on th e
Rea ction of P er m a n ga n a te Ion w ith Un sym m etr ica l Alk en es
Toshio Ogino,* Toru Watanabe, Masato Matsuura, Chikara Watanabe, and Hidetoshi Ozaki
Department of Chemistry, Faculty of Education, Niigata University, Niigata 950-21, J apan
Received November 26, 1997
Abstract: The substituent effects on the reactions of permanganate ion with unsymmetrical alkenes
are analyzed on the assumption of a concerted (3 + 2) cycloaddition model by using an equation
obtained by approximation based on the FMO theory in which development and localization of the
frontier molecular orbitals at the reaction sites with progress of the reaction are considered. The
Hammett plots are successfully reproduced with the newly obtained rate data for the reactions of
trans-chalcone and its derivatives and the data for methyl cinnamates, cinnamate ions, and alkyl
vinyl ethers taken from the literature using FMO energies and orbital coefficients calculated by
the PM3 method. It was indicated that a factor introduced to the basic equation in order to estimate
the extent of localization of the molecular orbitals at the transition state is closely related to the
position of the transition state along the reaction path.
Sch em e 1
In tr od u ction
It has been widely accepted that permanganate ion
(MnO4-) reacts with alkenes in a cycloaddition to form
the transient cyclic manganese(V) ester intermediate 1,
which subsequently decomposes into a 1,2-diol or carbo-
nyl compounds depending on the reaction conditions
(Scheme 1).1,2 A remarkable feature of the permanganate
oxidation is that the reactions are accelerated not only
by electron-releasing groups but also, in certain cases,
by electron-withdrawing groups, while other oxidative
reagents such as osmium tetraoxide (OsO4) react to
alkenes only in an electrophilic manner.3-5
Sch em e 2
Two different pathways, both of which lead to the
manganese(V) intermediate 1, have been proposed.6 The
(3 + 2) pathway a in Scheme 2 involves concerted attack
of the oxygen atoms to the unsaturated carbons and
proceeds via a five-membered cyclic transition state 2.7,8
This mechanism was also suggested by theoretical specu-
lations based on the frontier molecular orbital (FMO)
theory9 and the Zimmerman treatment.10 The other
mechanism, pathway b,1e in which a four-membered
organometallic intermediate 3 is formed first via [2 + 2]
cycloaddition and then rearranges to 1, is based on the
general proposal by Sharpless and co-workers11 for the
reactions between alkenes and oxo transition-metal spe-
cies. Goddard and Rappe´12 gave theoretical support for
this mechanism in analogy with a study on the reaction
between ethylene and chromyl chloride.
(1) (a) Wagner, G. J . Russ. Phys. Chem. Soc. 1895, 27, 219. (b)
Wiberg, K. B.; Saegebarth, K. A. J . Am. Chem. Soc. 1957, 79, 2822. (c)
Stewart, R. In Oxidation in Organic Chemistry Part A; Wiberg, K. B.,
Ed.; Academic Press: New York, 1965; pp 1-68. (d) Lee, D. G. In
Oxidation in Organic Chemistry Part D; Trahanovsky, W. S., Ed.;
Academic Press: New York, 1982; pp 147-206. (e) Fatiadi, A. J .
Synthesis 1987, 2, 85.
(2) (a) Ogino, T.; Kikuiri, N. J . Am. Chem. Soc. 1989, 111, 6174.
(b) Ogino, T.; Hasegawa, K.; Hoshino, E. J . Org. Chem. 1990, 55, 2653.
(3) Lee, D. G.; Brown, K. C. J . Am. Chem. Soc. 1982, 104, 5076.
(4) Toyoshima, K.; Okuyama, T.; Fueno, T. J . Org. Chem. 1980, 45,
1600.
For the oxidation of alkenes by other oxo transition-
metal reagents, in particular for the dihydroxylation by
OsO4, a similar mechanistic question, namely, whether
the reaction proceeds by a (3 + 2) cycloaddition mecha-
nism or by a stepwise mechanism that involves [2 + 2]
cyclization, has been studied more extensively since
Sharpless’s proposal for the metallaoxetane intermediate.
It was indicated by J ørgensen and Hoffmann that the
frontier orbitals of OsO4 have the right symmetry for
interactions with π and π* orbitals of alkenes.13 Houk
(5) Henbest, H. B.; J ackson, W. R.; Rob, B. C. G. J . Chem. Soc. B
1966, 803.
(6) Freeman, F.; Fuselier, C. O.; Armstead, C. R.; Dalton, C. E.;
Davidson, P. A.; Karchesfski, E. M.; Krochman, D. E.; J ohnson, M.
N.; J ones, N. K. J . Am. Chem. Soc. 1981, 103, 1154.
(7) Freeman, F. Chem. Rev. 1975, 75, 439 and references therein.
(8) Freeman, F. Rev. React. Species Chem. Rect. 1976, 1, 179.
(9) Fukui, K. Bull. Chem. Soc. J pn. 1966, 39, 498.
(11) Sharpless, K. B.; Teranishi, A. Y.; Ba¨ckvall, J .-E. J . Am. Chem.
Soc. 1977, 99, 3120.
(12) Rappe´, A. K.; Goodard, W. A., III. J . Am. Chem. Soc. 1982, 104,
448, 3287.
(13) J ørgensen, K. A.; Hoffmann, R. J . Am. Chem. Soc. 1986, 108,
1867.
(10) Littler, J . S. Tetrahedron 1971, 27, 81.
S0022-3263(97)02163-4 CCC: $15.00 © 1998 American Chemical Society
Published on Web 03/28/1998

2628 J . Org. Chem., Vol. 63, No. 8, 1998
Ogino et al.
The following trans-chalcones were prepared by condensa-
tion of acetophenone and a corresponding derivative of ben-
zaldehyde in the presence of NaOH in EtOH at room temper-
ature and purified by crystallization from EtOH; 4-methoxy-
trans-chalcone, mp 76-77 °C (lit.19 mp 77-78.5 °C), 4-methyl-
trans-chalcone, mp 96-98 °C (lit.20 mp 97-98 °C), 4-chloro-
trans-chalcone, mp 112-113 °C (lit.21 mp 112-114 °C), 4-bromo-
trans-chalcone, mp 125-126 °C (lit.19 mp 127-128 °C), 4-nitro-
trans-chalcone, mp 163.5-164 °C (lit.22 mp 157-159 °C).
trans-Chalcone was purchased from Tokyo Kasei Kogyo Co.,
Ltd, and crystallized from ethanol. trans-Chalcone-R-d was
prepared by condensation of benzaldehyde and acetophenone-
R-d3 (Nippon Sanso Corp.) in EtOD containing a catalytic
amount of EtONa. trans-Chalcone-â-d was obtained by the
reaction of benzaldehyde-R-d (Nippon Sanso Corp.) and ac-
etophenone in a similar manner. Similarly, 4-nitro-trans-
chalcone-R-d was prepared from 4-nitrobenzaldehyde and
acetophenone-R-d3 and 4-nitro-trans-chalcone-â-d from ac-
etophenone and 4-nitrobenzaldehyde-R-d, which was obtained
from 4-nitrobenzoyl chloride by the reduction with LiAlD(t-
BuO)3 in diglyme at -78 °C. All the deuterated compounds
were confirmed to give satisfactory 200 MHz 1H NMR spectra
(no proton signals at the position of replaced protons), respec-
tively.
Permanganate ion solutions were prepared as follows.
Powdered potassium permanganate (50 mg, 0.32 mmol) and
benzyltriethylammonium chloride (172 mg, 0.76 mmol) were
dissolved in 5 mL of dichloromethane, and the solution was
allowed to stand overnight in a refrigerator. After suitable
dilution of the supernatant solution, the accurate concentration
of permanganate ion was determined by a spectrophotometric
method immediately before use.
The reactions were performed by mixing a solution of
permanganate ion (2 mL) with a solution of chalcone (2 mL)
in a 10 mm cuvette, and the kinetics were determined by
monitoring the changes in absorbance at 526 nm (disappear-
ance of permanganate ion) on a J ASCO Ubest-35 spectropho-
tometer connected to a floppy disk drive for data storage. The
temperature was maintained at 25.0 °C with a refrigerated
and heated bath circulator. The data were transferred to an
Apple Macintosh computer, and a correction was made at each
moment by subtracting the background absorbance of the
manganese product estimated from the observed absorbance
at 420 nm. All the rate constants are the average of three or
more experiments. Activation parameters for the reactions
of trans-chalcone and 4-nitro-trans-chalcone were obtained
from the plots of ln k2/T vs 1/T using k2 values determined at
15, 20, 25, and 30 °C, respectively.
Sch em e 3
and co-workers showed that MM2 calculations based on
a symmetrical five-membered transition model reproduce
the stereoselectivities observed with several chiral di-
amine ligands.14 Furthermore, Corey and Noe proposed
a (3 + 2) model for the origin of the high enantioselectivty
of the dihydroxylation attained by an amine-OsO4
complex.15 Although the [2 + 2] mechanism for the
reaction of OsO4 can also rationalize the stereoselectivi-
ties caused by chiral ligands,16 and the rearrangement
of the metallaoxetane to a five-membered diolate was also
supported by theoretical considerations,12,17 many of
recent theoretical and experimental studies that ap-
peared during the course of this study support the (3 +
2) cycloaddition mechanism.18
In connection with the ambiphilic reactivity of per-
manganate ion, Lee and Brown3 gave an explanation by
assuming the occurrence of two different ionic transition
states in the [2 + 2] cycloaddition pathway depending
on the electronic nature of the substituent on alkenes
(Scheme 3).
In this paper, we present the semiquantitative frontier
molecular orbital analysis of the substituent effects on
permanganate oxidation of aryl-substituted alkenes. We
have assumed the concerted (3 + 2) cycloaddition model
and used newly introduced rate equations derived from
the general perturbation equation by approximations
based on the FMO theory. The results obtained by PM3
calculations well reproduced Hammett plots theoretically
for all the reactions examined and strongly support the
(3 + 2) cycloaddition mechanism.
Molecular orbital calculations were carried out by the PM3
method23 in MOPAC as implemented in the MacSpartan Plus,
Chem3D Pro, or CAChe Work System ver. 3.7 on an Apple
Macintosh computer. Calculations for the optimization of the
transition structure for the reaction between permanganate
ion and ethylenethe and graphical modeling for the orbitals
were accomplished by use of the PM3(tm) method24 in the
MacSpartan Plus.
Exp er im en ta l Section
The solvent (dichloromethane) used in the kinetic experi-
ments was purified before use by refluxing with potassium
permanganate and benzyltriethylammonium chloride followed
by distillation from the solution.
Resu lts a n d Discu ssion
Ap p r oxim a tion of Ba sic Equ a tion . On the basis
of the general perturbation method,25,26 the second-order
energy change caused by the FMO interactions between
two molecules (R and S) reacting in a cycloaddition is
(14) Wu, Y.-D.; Wang, Y.; Houk, K. N. J . Org. Chem. 1992, 57, 1362.
(15) Corey, E. J .; Noe, M. C. J . Am. Chem. Soc. 1993, 115, 12579.
(16) Hentges, S. G.; Sharpless, K. B. J . Am. Chem. Soc. 1980, 102,
4263.
(17) Bender, B. R.; Ramage, D. L.; Norton, J . R.; Wiser, D. C.; Rappe´,
A. K. J . Am. Chem. Soc. 1997, 119, 5628.
(19) Black, W. B.; Lutz, R. E. J . Am. Chem. Soc. 1955, 77, 5134.
(20) Noyce, D. S.; J orgenson, M. J . J . Am. Chem. Soc. 1962, 84, 4312.
(21) Frank, R. L.; Seven, R. P. J . Am. Chem. Soc. 1949, 71, 2629.
(22) Le Fevre, C. G.; Le Fevre, R. J . W. J . Chem. Soc. 1932, 2894.
(23) Stewart, J . J . P. J . Comput. Chem. 1989, 10, 221.
(24) Yu, J .; Adei, E.; Hehre, W. J . Manuscript in preparation.
(25) Dewar, M. J . S. J . Am. Chem. Soc. 1952, 74, 3341.
(26) Klopman, G. J . Am. Chem. Soc. 1968, 90, 223; In Chemical
Reactivity and Reaction Paths; Klopman, G., Ed.; Wiley: New York,
1974; Chapter 4.
(18) (a) Dapprich, S.; Ujaque, G.; Maseras, F.; Lledo´s, A.; Musaev,
D. G.; Morokuma, K. J . Am. Chem. Soc. 1996, 118, 11660. (b) Pidun,
U.; Boehme, C.; Frenking, G. Angew. Chem., Int. Ed. Engl. 1996, 35,
2817. (c) Corey, E. J .; Noe, M. C. J . Am. Chem. Soc. 1996, 118, 11038.
(d) Corey, E. J .; Noe, M. C.; Grogan, M. J . Tetrahedron Lett. 1996, 28,
4899. (e) Haller, J .; Strassner, T.; Houk, K. N. J . Am. Chem. Soc. 1997,
119, 8031. (f) DelMonte, A. J .; Haller, J .; Houk, K. N.; Sharpless, K.
B.; Singleton, D. A.; Strassner, T.; Thomas, A. A. J . Am. Chem. Soc.
1997, 119, 9907.

Reaction of Permanganate Ion with Unsymmetrical Alkenes
J . Org. Chem., Vol. 63, No. 8, 1998 2629
2
2â2
RT
(CRH1CSL1 + CRH2CSL2
)
ln k ) C +
ln k ) C +
(3)
(4)
[
]
]
|ERH - ESL
|
2
2â2
RT
(CRL1CSH1 + CRL2CSH2
)
[
|ESH - ERL|
theory,29 which states that the more closely lying HOMO-
LUMO pair plays the most important role at the transi-
tion state and dominates the reaction.
For Diels-Alder reactions where R ) diene and S )
dienophile, for example, eq 3 dominates the reactions
with normal electron demand, while eq 4 dominates the
reactions with inverse electron demand.30 If â and the
numerators in parentheses of eqs 3 and 4 could be
assumed constant for the reactions between a diene and
a series of dienophiles, one can expect a linear correlation
between ln k and 1/|ERH - ESL|, or ln k and 1/|ESH - ERL|.
However, few examples for which such a linear relation-
ship is established have been known.28,30b
In order to apply eqs 3 and 4 more quantitatively to
permanganate oxidations of alkenes (R ) MnO4-, S )
alkene) it is necessary to consider the changes in frontier
orbital coefficients at the transition state, and hence, we
have further modified these equations in the following
manner. First, it was assumed that frontier orbital
coefficients at the reaction sites of the symmetrical
F igu r e 1. FMO interactions when two molecules (R and S)
react in a cycloaddition.
given by eq 1.27,28 In this equation, ∆E is the interaction
-
component, MnO4 in this case, are equal and constant
for the transition states of the reactions with similar
alkenes (CRH1 ) CRH2 ) CRH, CRL1 ) CRL2 ) CRL). Thus,
eqs 3 and 4 are reduced to simpler forms as eqs 5 and 6,
respectively, where CRH and CRL are constant. Second,
2
(CRH1CSL1 + CRH2CSL2
ERH - ESL
)
∆E ) 2â2
+
[
2
(CRL1CSH1 + CRL2CSH2
ESH - ERL
)
(1)
]
2â2CR2 H (|CSL1| + |CSL2|)2
ln k ) C +
ln k ) C +
(5)
(6)
[
[
]
]
RT
|ERH - ESL|
energy; â is the resonance integral for the two interacting
MO pairs; C and E refer, respectively, to eigenvector
coefficients and eigenvalues specified by the subscripts;
subscripts R and S refer, respectively, to the reacting
molecules R and S; subscripts 1 and 2 refer, respectively,
to the reaction sites 1 and 2; and subscripts H and L
refer, respectively, to HOMO and LUMO (Figure 1).
For a series of reactions where one component of the
reactant differs from one another only in electronic effects
of the substituents, the relative reaction rate would be
expressed by eq 2, which has been given by Mok and Nye
2â2CR2 L (|CSH1| + |CSH2|)2
RT
|ESH - ERL|
in order to indicate to what extent the frontier orbital
coefficients of the unsymmetrical component have devel-
oped and localized at the reaction sites when the transi-
tion state is reached, we introduced a factor, d, and
obtained eqs 7 and 8 as the final equations.
2â2C2RH (1 - d)(|CSL1| + |CSL2|)2 + 2d
2
2â2
RT
(CRH1CSL1 + CRH2CSL2
)
(7)
(8)
ln k ) C +
ln k ) C +
ln k ) C +
+
[
]
RT
|ERH - ESL|
[
|ERH - ESL
|
2
(CRL1CSH1 + CRL2CSH2
)
2â2C2RL (1 - d)(|CSH1| + |CSH2|)2 + 2d
(2)
]
|ESH - ERL
|
[
]
RT
|ESH - ERL|
through connecting eq 1 with the Eyring equation for rate
constant (k) and activation energy (∆Eq).28 This equation
is based on the assumption that the stabilization energy
at the transition state is proportional to that given by
eq 1.
Eq 2 would be simplified to eq 3 if |ERH - ESL| is
smaller than |ESH - ERL| or to eq 4 if |ESH - ERL| is
smaller than |ERH - ESL|. As pointed out by Mok and
Nye,28 this simplification is rationalized by the FMO
The value of d varies from 0 to 1 with the position of
the transition state along the reaction path. The nu-
merator in the parentheses of the equations linearly
changes from the minimum value [(|CSL1| + |CSL2|)2 or
(|CSH1| + |CSH2|)2] to the theoretical maximum value of
(29) Fukui, K. Kagakuhannou to Denshi no Kidou, Maruzen, Tokyo,
1976; Theory of Orientation and Stereoselection; Springer-Verlag:
Heidelberg, 1970.
(27) Sustman, R. Pure Appl. Chem. 1974, 40, 569.
(28) Mok, K.-L.; Nye, M. J . J . Chem. Soc., Perkin Trans. 1 1975,
1810.
(30) (a) Sauer, J .; Wiest, H. Angew. Chem., Int. Ed. Engl. 1962, 1,
269. (b) Sauer, J .; Sustmann, R. Angew. Chem., Int. Ed. Engl. 1980,
19, 779.

2630 J . Org. Chem., Vol. 63, No. 8, 1998
Ogino et al.
F igu r e 2. Changes in (1 - d)(|CSL1| + |CSL2|)2 + 2d against d
for the case of trans-chalcone.
F igu r e 3. Surface drawings of the PM3(tm)-calculated fron-
-
tier molecular orbitals for MnO4
.
231 with increasing d (Figure 2). If one can determine
the right value of d for a series of related cycloadditions,
a linear relationship can be expected between ln k and
[(1 - d)(|CSL1| + |CSL2|)2 + 2d]/|ERH - ESL| or [(1 -
d)(|CSH1| + |CSH2|)2 + 2d]/|ESH - ERL|. A relatively small
value of d implies that the reaction rate is dependent not
only on the HOMO-LUMO energy difference but also
to some extent on the frontier orbital coefficients, while
a relatively large value of d implies that the reaction rate
is dependent primarily on the HOMO-LUMO energy
difference. Furthermore, for the reaction of alkenes
whose frontier orbital coefficients are significantly un-
symmetrical, a value of d close to zero indicates an early,
unsymmetrical transition state, while a value of d close
to 1 indicates a symmetrical, product-like transition
F igu r e 4. Drawings of the first and second highest filled
obitals of the transition state optimized by the PM3 (tm)
-
method for the reaction between MnO4 and ethylene.
and its theoretical analysis that the 2e orbitals (Figure
3) are in the lowest unfilled level,34 and one of these
orbitals fulfills the symmetry requirement for the FMO
interaction with the HOMO of an alkene. It is notewor-
thy that the transition state optimized by PM3 (tm)24
calculations for the reaction between MnO4- and ethylene
exhibits surface drawings of the first and second highest
filled orbitals, which are just made up of the combination
of π orbital of ethylene and one of 2e orbitals and of the
combination of the π* orbital of ethylene and one of the
1t1 orbitals, respectively (Figure 4).
state.
-
Molecu la r Or bita ls of Mn O4
. In spite of many
papers on semiempirical32 and ab initio MO calculations33
for MnO4-, it seems to be difficult to find the proper FMO
-
energies of MnO4 from the currently available data,
since there remains considerable disagreement in the
orbital energies and even in the order of energy levels.
It is still worthwhile, however, to presume a roughly
estimated value for the FMO energy since the purpose
here is to approximate the relative energies of the
transition state for a series of closely related reactions.
The 1t1 orbitals (Figure 3) have been placed on the
highest level of filled orbitals by many calculations, and
one of these orbitals meets the symmetry requirement
for the FMO interaction with the LUMO of an alkene in
the same manner as suggested for the reaction of osmium
tetraoxide.13 Despite the disagreement among the MO
calculations as to the order of the first unfilled orbitals,
In this paper, we tentatively take the orbital energies
-
for HOMO and LUMO of MnO4 as -8.5 and -0.5 eV,
respectively. The satisfactory results of this work are
little affected by changing these values in the range of
(3 eV or somewhat more, since the ambiguity introduced
in eqs 7 and 8 is weakened by changing d value as
described below in the practical discussions. Therefore,
the d value determined for a series of reactions has no
absolute meaning at present so long as the reliable MO
2-
it has been supported by ESR measurements of MnO4
-
energies of MnO4 are unknown.
-
Rea ction of Mn O4 w ith tr a n s-Ch a lcon es. The
(31) At this point, the frontier orbital coefficients at the reaction
sites of the alkene are completely grown up and equalized to 1/x2,
respectively.
(32) (a) Wolfsberg, M.; Helmholz, L. J . Chem. Phys. 1952, 20, 837.
(b) Ballhausen, C. J .; Gray, H. B. Molecular Orbital Theory; Ben-
jamin: New York, 1964; p 107. (c) Oleari, L.; de Michelis, G.; Di Sipio,
L. Mol. Phys. 1966, 10, 111. (d) Brown, R. D.; J ames, B. H.; McQuade,
T. J . V.; O’Dwyer, M. F. Theor. Chim. Acta (Berlin) 1970, 17, 279. (e)
Brown, R. D.; J ames, B. H.; O’Dwyer, M. F. Theor. Chim. Acta (Berlin)
1970, 17, 362.
(33) (a) Hillier, I. H.; Saunders, V. R. Proc. R. Soc. London A 1970,
320, 161. (b) Dacre, P. D.; Elder, M. Chem. Phys. Lett. 1971, 11, 377.
(c) J ohansen, H. Chem. Phys. Lett. 1972, 17, 569. (d) Mortola, A. P.;
Basch, H.; Moskowitz, J . W. Intern. J . Quantum Chem. 1973, 7, 725.
(e) Wood, M. H. Theor. Chim. Acta (Berlin) 1975, 36, 309. (f) Hsu, H.;
Petterson, C.; Pitzer, R. M. J . Chem. Phys. 1976, 64, 791.
second-order rate constants obtained for the reactions of
permanganate ion with a series of 4-substituted trans-
chalcones in CH2Cl2 are listed in Table 1 together with
the MO data calculated by the PM3 method. A good
linear Hammett plot with a positive slope (F ) 1.28) was
obtained (Figure 5). These results indicate that the
reactions are nucleophilic, and hence, the kinetic data
could be analyzed on the basis of eq 7 as the normal
(34) (a) Carrington, A.; Ingram, D. J . E.; Lott, K. A. K.; Schonland,
D. S.; Symons, M. C. R. Proc. R. Soc. London A 1959, 254, 101. (b)
Schonland, D. S. Proc. R. Soc. London A 1959, 254, 111.

Reaction of Permanganate Ion with Unsymmetrical Alkenes
J . Org. Chem., Vol. 63, No. 8, 1998 2631
-
Ta ble 1. Secon d -Or d er Ra te Con sta n ts a n d MO Da ta for Rea ction s betw een Mn O4 a n d tr a n s-Ch a lcon es
(XP h CHdCHCOP h )
orbital energy (eV)
eigenvector
k2
X
(M-1 s-1
)
ESH
ESL
CSL1
CSL2
|ERH - ESL
|
|ESH - ERL|
a
b
p-OMe
p-Me
H
p-Cl
p-Br
p-NO2
12.3
18.3
25.4
59.0
71.3
265.0
-8.965 78
-9.187 04
-9.376 54
-9.225 87
-9.492 06
-10.158 01
-0.795 41
-0.829 05
-0.836 97
-0.987 36
-1.011 79
-1.711 16
-0.347 06
-0.355 46
-0.362 55
-0.374 17
-0.381 47
-0.360 58
0.412 31
0.410 50
0.413 63
0.398 61
0.400 28
0.292 67
7.704 59
7.670 95
7.663 03
7.512 64
7.488 21
6.788 84
8.465 78
8.687 04
8.876 54
8.725 87
8.992 06
9.658 01
a
b
ERH is taken as -8.5 eV. ERL is taken as -0.5 eV.
-
F igu r e 5. Hammet plot for the reactions of MnO4- with trans-
chalcones.
F igu r e 7. Hammet plot for the reactions of MnO4 with
methyl cinnamates (data from refs 3 and 35).
F igu r e 8. Plots of log k2 vs [(1 - d)(|CSL1| + |CSL2|)2 + 2d]/
|ERH - ESL| for the reactions of MnO4- with methyl cinnama-
tes, d ) 0.72 (rate data from refs 3 and 35).
F igu r e 6. Plots of log k2 vs [(1 - d)(|CSL1| + |CSL2|)2 + 2d]/
-
|ERH - ESL| for the reactions of MnO4 with trans-chalcones,
d ) 0.51.
the Hammett plot given by Lee and Brown for the
reactions of permanganate ion with a series of methyl
cinnamates in CH2Cl2.3,35 The Hammett plot is repro-
duced with good fidelity when log k2 is plotted against
[(1 - d)(|CSL1| + |CSL2|)2 + 2d]/|ERH - ESL| with the d
value taken as 0.72 (Figure 8). Although, as indicated
in Table 2, the magnitude of the eigenvector coefficients
at the reaction sites of methyl cinnamates (|CSL1|, |CSL2|)
appear roughly symmetrical and unchanged by the
substituent, the plot obtained by taking d as unity
exhibits more widely scattered points (Supporting Infor-
mation). These results indicate that even a slight dif-
ference in eigenvector coefficients between methyl cin-
electron-demand cycloaddition. When d is taken as 0.51,
the plot of log k2 vs [(1 - d)(|CSL1| + |CSL2|)2 + 2d]/|ERH
-
ESL| follows a straight line with the best correlation, and
this is remarkably similar to the Hammett plot (Figure
6). Very similar plots with nearly the same correlation
were also obtained even when ERH was taken as -10.5
or -6.5 eV but using alternate d values (Supporting
Information). However, when log k2 is plotted against
2/|ERH - ESL| on the assumption that CSL1 and CSL2 have
completely localized at the reaction sites when the
transition state is reached (d ) 1), the plot considerably
deviates from the straight line (Supporting Information).
-
Rea ction of Mn O4 w ith Meth yl Cin n a m a tes.
Further attempts to test eqs 7 and 8 have been made by
taking kinetic data from the literature. Figure 7 shows
(35) Lee, D. G.; Brown, K. C.; Karaman, H. Can. J . Chem. 1986,
64, 1054.

2632 J . Org. Chem., Vol. 63, No. 8, 1998
Ogino et al.
Ta ble 2. MO Da ta for Meth yl Cin n a m a tes
(XP h CHdCHCOOCH3) by P M3 Ca lcu la tion sa
orbital energy (eV)
eigenvector
X
ESH
ESL
|CSL1
|
|CSL2
|
p-OMe
p-Me
p-iPr
m-Me
H
m-MeO
p-Cl
m-F
-9.0357
-9.2741
-9.3282
-9.4127
-9.4777
-9.2404
-9.3050
-9.7104
-9.4939
-0.727 28
-0.775 52
-0.775 21
-0.759 04
-0.793 46
-0.813 59
-0.978 75
-1.023 25
-0.946 44
0.436 62
0.438 40
0.440 37
0.446 17
0.445 50
0.450 57
0.431 82
0.426 89
0.440 77
0.449 63
0.443 66
0.445 86
0.454 85
0.450 98
0.454 38
0.417 90
0.411 40
0.431 27
m-Cl
a
MPOAC 93 in MacSpartan Plus was used. For the m-fluoro
derivative, PM3 calculations in the other package programs gave
somewhat different values of the eigenvectors, and the point in
Figure 8 appreciably deviates from the straight line.
F igu r e 10. Plots of log k2 vs [(1 - d)(|CSL1| + |CSL2|)2 + 2d]/
|ERH - ESL| for the reactions of MnO4- with cinnamate ions; d
) 0.93 (rate data from ref 36).
Ta ble 3. MO Da ta for Cin n a m a te Ion s
(XP h CHdCHCOO-) in Aqu eou s Solu tion by th e P M3
Meth od a
orbital energy (eV)
eigenvector
X
ESH
ESL
|CSL1
|
|CSL2
|
p-CH3
H
m-MeO
p-Cl
-9.268 16
-9.453 19
-9.399 19
-9.281 21
-9.465 21
-9.555 07
-9.621 74
-9.626 20
-9.814 93
-0.528 87
-0.612 97
-0.681 79
-0.681 46
-0.621 96
-0.781 21
-0.717 15
-1.103 24
-1.422 40
0.453 50
0.454 01
0.449 23
0.431 59
0.445 64
0.435 10
0.395 08
0.166 55
0.332 60
0.332 68
0.383 25
0.372 39
0.297 81
0.313 08
0.372 67
0.269 89
0.106 89
0.216 16
m-Cl
m-Br
m-CF3
m-NO2
p-NO2
-
F igu r e 9. Hammet plot for the reactions of MnO4 with
cinnamate ions in alkaline solution (from ref 36).
a
The solvent (water) was specified by the COSMO option in
CACheMOPAC version 94.
namates significantly influences their reactivity, and the
semiempirical MO calculation is precise enough to detect
such differences.
Ta ble 4. Com p a r ison of d Va lu e w ith Activa tion
En tr op y a n d kH/kD
-
kH/kD
Rea ction of Mn O4 w ith Cin n a m a te Ion s in Al-
compd
t-chalconea
d
∆Sq (eu)
R-d
â-d
k a lin e Solu tion . We next applied eq 7 to the rate data
for the reaction of permanganate ion with cinnamate ions
in aqueous alkaline solution as elaborated by Lee and
Nagarajan.36 The reaction is also nucleophilic since the
Hammett plot follows a straight line of positive slope
(Figure 9). A very similar straight line was obtained with
the best correlation for the plot of log k2 against [(1 -
d)(|CSL1| + |CSL2|)2 + 2d]/|ERH - ESL| when d is taken as
0.93 (Figure 10). The fairly large value of d indicates
that the lobes of the LUMO of cinnamate ions develop
and localize to a considerable extent at the reaction sites
when the transition state is reached, and the structure
of the transition state is more symmetrical and product-
like than those for the reactions of chalcones and methyl
cinnamates. It should be noted, however, that differences
in size of the LUMO coefficient between the reaction sites
of cinnamate ions (|CSL1| and |CSL2|) are more significant
than those of methyl cinnamates (Table 3).
-31.1 0.96 ( 0.02 0.93 ( 0.02
-30.0 0.94 ( 0.02 0.96 ( 0.02
-38
0.51
0.72
0.93 (-29)
}
4-NO2-t-chalconea
methyl cinnamateb
cinnamate ionc
1.0
0.91
0.89
0.87
a
b
This work, in CH2Cl2. From ref 3, in CH2Cl2. c From ref 36,
in 0.5 M NaOH.
also supported by comparing the d values with the
activation entropies and secondary deuterium isotope
effects as shown in Table 4. The relatively small negative
value of activation entropies and relatively insignificant
inverse secondary isotope effects observed for the reaction
of chalcone derivatives indicate a loosely bonded and sp2-
dominant early transition state in accord with the small
value of d. On the other hand, the relatively significant
inverse secondary isotope effects observed for the reaction
of cinnamate ion36 suggest a sp3-dominant later transition
state in accord with the relatively large value of d. In
addition, this sp3 dominant transition state also explains
the small F value for the reaction of cinnamate ions since
the electronic effects from the substituents may be
blocked by an sp3-like carbon more significantly than by
an sp2-like carbon.
It has been observed that there are distinct differences
in magnitude of d among the three reactions above
discussed. According to the definition of d, the degree
of bond formation at the transition state should be in the
order of the magnitude of d, namely, cinnamate ions,
methyl cinnamates, and chalcones. This conclusion is
Rea ction of P er m a n ga n a te Ion w ith Electr on -
Relea sin g Alk en es. The rate data reported by Okuya-
(36) Lee, D. G.; Nagarajan, K. Can. J . Chem. 1985, 63, 1018.

Reaction of Permanganate Ion with Unsymmetrical Alkenes
J . Org. Chem., Vol. 63, No. 8, 1998 2633
-
F igu r e 11. Taft plot for the reactions of MnO4 with alkyl
vinyl ethers in aqueous dioxane (from refs 3 and 4).
F igu r e 12. Plots of log k2 - 0.33ES vs -[(1 - d)(|CSH1| +
|CSH2|)2 + 2d]/|ESH - ERL| for the reactions of MnO4- with alkyl
vinyl ethers; d ) 0.91 (rate data from ref 4).
Ta ble 5. MO Da ta for Alk yl Vin yl Eth er s (CH2dCHOR)a
orbital energy (eV)
eigenvector
found that this method not only reproduces simple
Hammett plots but also reproduces extended Hammett
plots and other linear free-energy relationship for Diels-
Alder reactions (Supporting Information). The detailed
comparative studies of permanganate ion oxidations and
Diels-Alder reactions of the same sets of alkenes will
appear elsewhere.
R
ESH
ESL
|CSH1
|
|CSH2
|
CH3
C2H5
i-C3H7
t-C4H9
n-C4H9
i-C4H9
-9.515 08
-9.458 51
-9.442 51
-9.427 08
-9.465 34
-9.452 22
1.301 70
1.329 90
1.365 74
1.390 78
1.322 40
1.326 04
0.495 30
0.488 14
0.499 09
0.503 56
0.487 96
0.485 77
0.670 89
0.669 52
0.680 18
0.682 36
0.669 08
0.668 26
a
Calculated by PM3 in CACheMOPAC ver. 94.
Con clu sion
ma and co-workers for the reaction of permanganate ion
with alkyl vinyl ethers in aqueous dioxane indicate that
the reaction is electrophilic.4 It was shown later by Lee
and Brown3 that the rate data conform to a Taft equation
with a steric parameter of 0.33ES and F* value of -1.837
(Figure 11). The PM3 calculation disclosed that LUMO
energies of the alkyl vinyl ethers are 2 eV or somewhat
more higher than those of electron-withdrawing alkenes
such as chalcone and cinnamate derivatives (Table 5).
This fact will make it likely that the FMO interaction
between HOMO of an alkyl vinyl ether and LUMO of
The substituent effects on the reactions of permanga-
nate ion with unsymmetrical alkenes were analyzed with
the newly proposed rate equations, eq 7 or 8, on the
assumption of concerted (3 + 2) cycloaddition mechanism.
The linear free-energy relationships obtained as the
results are remarkably similar to those obtained from
Hammett equation or its correction forms, supporting the
(3 + 2) mechanism for the formation of cyclic manga-
nese(V) diesters. Equations 7 and 8 are generally ap-
plicable to other concerted cycloadditions such as Diels-
Alder reactions without any corrections. The factor d,
which was introduced to the equations to estimate the
extent of localization of the frontier orbitals at the
reaction sites of the transition state, agrees with other
parameters that are closely related to the position of the
transition state such as activation entropy or secondary
deuterium isotope effect.
-
MnO4 is more favorable than that between the HOMO
-
of MnO4 and the LUMO of an alkyl vinyl ether, and
hence, the reactions will be analyzed by eq 8 as inverse-
electron-demand reactions. The straight line of the Taft
plot is well reproduced when log k2 - 0.33ES is plotted
against -[(1 - d)(|CSH1| + |CSH2|)2 + 2d]/|ESH - ERL|,
taking the d factor as 0.91 on the basis of the presumed
LUMO energy of -0.5 eV for MnO4- (Figure 12). When
the LUMO energy was taken as +1.5 and -2.5 eV, very
similar plots with nearly the same correlation were also
obtained using alternate d values, 0.93 and 0.89, respec-
tively (Supporting Information).
Test of Eqs 7 a n d 8 w ith Oth er Con cer ted Cy-
cloa d d ition Rea ction s. Since eqs 7 and 8 cannot
inherently apply to the (2 + 2) cycloaddition reaction
model of permanganate ion oxidation (Scheme 2b), our
results cannot definitely exclude this mechanism. How-
ever, these equations can apply in general to other
concerted cycloadditions such as Diels-Alder reactions
if one component of the reactants has a symmetrical
structure. We have analyzed some rate data of Diels-
Alder reactions in the literature on the basis of eq 7 or 8
using MO data obtained by PM3 calculations. It was
Su p p or tin g In for m a tion Ava ila ble: Figures of the plots
of log k2 vs [(1 - d)(|CSL1| + |CSL2|)2 + 2d]/|ERH - ESL| for the
reactions of chalcone derivatives plotted with alternate ERH
and d values, a figure of the plot of log k2 vs [(1 - d)(|CSL1| +
|CSL2|)2 + 2d]/|ERH - ESL| for the reactions of methyl cinnamate
derivatives plotted with d ) 1, figures of the plots of log k2 -
0.33ES vs - [(1 - d)(|CSH1| + |CSH2|)2 + 2d]/|ESH - ERL| for the
reactions of alkyl vinyl ethers plotted with alternate ERL
values, and the results of the analysis for the Diels-Alder
reactions between 9,10-dimethylanthracene and a set of seven
directly substituted trans-dienophiles and between maleic
anhydride and six anthracene derivatives (5 pages). This
material is contained in libraries on microfiche, immediately
follows this article in the microfilm vesion of the journal, and
can be ordered from the ACS; see any current masthead page
for ordering information.
(37) The F* value of -0.6 in ref 3 may be incorrect.
J O972163K