Mechanism, regioselectivity, and the kinetics of phosphine-catalyzed [3+2] cycloaddition reactions of allenoates and electron-deficient alkenes

Article abstract of DOI:10.1002/chem.200701725

With the aid of computations and experiments, the detailed mechanism of the phosphine-catalyzed [3+2] cycloaddition reactions of allenoates and electron-deficient alkenes has been investigated. It was found that this reaction includes four consecutive processes: 1) In situ generation of a 1,3dipole from allenoate and phosphine, 2) stepwise [3+2] cycloaddition, 3) a water-catalyzed [1,2]-hydrogen shift, and 4) elimination of the phosphine catalyst. In situ generation of the 1,3dipole is key to all nucleophilic phosphine-catalyzed reactions. Through a kinetic study we have shown that the generation of the 1,3-dipole is the rate-determining step of the phosphine-cat- alyzed [3 + 2] cycloaddition reaction of allenoates and electron-deficient alkenes. DFT calculations and FMO analysis revealed that an electron-with- drawing group is required in the allene to ensure the generation of the 1,3-dipole kinetically and thermodynamically. Atoms-in-molecules (AIM) theory was used to analyze the stability of the 1,3-dipole. The regioselectivity of the [3 + 2] cycloaddition can be rationalized very well by FMO and AIM theories. Isotopic labeling experiments combined with DFT calculations showed that the commonly accepted intramolecular [1,2]-proton shift should be corrected to a water-catalyzed [1,2]-proton shift. Additional isotopic labeling experiments of the hetero-[3+2] cycloaddition of allenoates and electron-deficient imines further support this finding. This investigation has also been extended to the study of the phosphine-catalyzed [3+2] cycloaddition reaction of alkynoates as the three-carbon synthon, which showed that the generation of the 1,3-dipole in this reaction also occurs by a water-catalyzed process.

Full text of DOI:10.1002/chem.200701725

FULL PAPER
DOI: 10.1002/chem.200701725
Mechanism, Regioselectivity, and the Kinetics of Phosphine-Catalyzed [3+2]
Cycloaddition Reactions of Allenoates and Electron-Deficient Alkenes
Yong Liang,[a] Song Liu,[a] Yuanzhi Xia,[a, b] Yahong Li,[b, c] and Zhi-Xiang Yu*[a]
Abstract: With the aid of computations
and experiments, the detailed mecha-
nism of the phosphine-catalyzed [3+2]
cycloaddition reactions of allenoates
and electron-deficient alkenes has been
investigated. It was found that this re-
action includes four consecutive pro-
cesses: 1) In situ generation of a 1,3-
dipole from allenoate and phosphine,
2) stepwise [3+2] cycloaddition, 3) a
water-catalyzed [1,2]-hydrogen shift,
and 4) elimination of the phosphine
catalyst. In situ generation of the 1,3-
dipole is key to all nucleophilic phos-
phine-catalyzed reactions. Through a
kinetic study we have shown that the
generation of the 1,3-dipole is the rate-
determining step of the phosphine-cat-
alyzed [3+2] cycloaddition reaction of
allenoates and electron-deficient al-
kenes. DFT calculations and FMO
analysis revealed that an electron-with-
drawing group is required in the allene
to ensure the generation of the 1,3-
dipole kinetically and thermodynami-
theories. Isotopic labeling experiments
combined with DFT calculations
showed that the commonly accepted
intramolecular [1,2]-proton shift should
be corrected to a water-catalyzed [1,2]-
proton shift. Additional isotopic label-
ing experiments of the hetero-[3+2]
cycloaddition of allenoates and elec-
tron-deficient imines further support
this finding. This investigation has also
been extended to the study of the
phosphine-catalyzed [3+2] cycloaddi-
tion reaction of alkynoates as the
three-carbon synthon, which showed
that the generation of the 1,3-dipole in
this reaction also occurs by a water-cat-
alyzed process.
cally.
Atoms-in-molecules
(AIM)
theory was used to analyze the stability
of the 1,3-dipole. The regioselectivity
of the [3+2] cycloaddition can be ra-
tionalized very well by FMO and AIM
Keywords: allenes · density func-
tional calculations · kinetics · phos-
phine organocatalysis
mechanisms
· reaction
Introduction
construction of five-membered heterocycles.[1,2] Inspired by
the success of Huisgenꢀs chemistry and other cycloaddition
reactions such as the Diels–Alder reaction, which has been
widely employed in the synthesis of six-membered carbocy-
cles and heterocycles, synthetic chemists have been continu-
ously searching for analogous [3+2] cycloaddition reactions
to synthesize five-membered carbocycles and heterocycles,
which exist predominantly as the backbones of many natural
products and other compounds of pharmaceutical signifi-
cance. Endeavors in this line have led to the discoveries of
several elegant [3+2] cycloaddition reactions by Danheis-
er,[3] Trost,[4] Lu,[5] and others.[6] All these [3+2] cycloaddi-
tion reactions employ Lewis acids or transition metals as
catalysts with the exception of Luꢀs [3+2] cycloaddition re-
actions of allenoates and electron-deficient alkenes or
imines which occur by catalysis with tertiary phosphines
(Scheme 1). This reaction can also be executed by using al-
kynoates instead of allenoates as the three-carbon synthon
(Scheme 1). Because phosphines are organocatalysts, Luꢀs
[3+2] cycloaddition reaction can be regarded as one of the
recently widely pursued organocatalytic reactions.[7] Lu, Kri-
The Huisgen [3+2] cycloaddition reactions between 1,3-di-
poles and dipolarophiles have been widely applied in the
[a] Y. Liang, S. Liu, Y. Xia, Prof. Dr. Z.-X. Yu
Beijing National Laboratory for Molecular Sciences (BNLMS)
Key Laboratory of Bioorganic Chemistry and Molecular Engineering
of the Ministry of Education, College of Chemistry
Peking University
Beijing 100871 (China)
Fax : (+86)10-6275-1708
E-mail: yuzx@pku.edu.cn
[b] Y. Xia, Prof. Dr. Y. Li
Qinghai Institute of Salt Lakes, Chinese Academy of Sciences
Xining 810008 (China)
[c] Prof. Dr. Y. Li
Key Laboratory of Organic Synthesis of Jiangsu Province
Department of Chemistry and Chemical Engineering
Suzhou University
Suzhou 215006 (China)
Supporting Information for this article is available on the WWW
under http://www.chemeurj.org/ or from the author.
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4361

ionic intermediate A was formed by a [1,3]-proton shift in
zwitterionic intermediate E generated from the alkynoate
and phosphine (Scheme 2).[5a]
Despite the widespread application of phosphine-cata-
lyzed [3+2] cycloaddition reactions and the continuing de-
velopment of phosphine-catalyzed organocatalysis[10,11] and
allene chemistry,[12] the detailed mechanism of phosphine-
catalyzed [3+2] cycloaddition reactions has not been inves-
tigated experimentally or theoretically. To the best of our
knowledge only a few studies have been conducted to ra-
tionalize the regioselectivity of these reactions by scrutiniz-
ing the [3+2] cycloaddition transition-state structures locat-
ed by theoretical calculations.[13] The originally proposed
[1,2]-proton shift had not been investigated experimentally
or computationally until we published our preliminary re-
sults.[14] Furthermore, no detailed studies of the overall pro-
cess of phosphine-catalyzed [3+2] cycloaddition reactions
have been documented. Kinetic information on the [3+2]
cycloaddition reaction has not been obtained either. In addi-
tion, it is still unclear how 1,3-dipoles are generated from al-
kynoates and phosphine.
Herein we disclose the detailed mechanism of the phos-
phine-catalyzed [3+2] cycloaddition reaction through joint
computational and experimental studies with an emphasis
on how the 1,3-dipoles are generated, the geometric features
of the 1,3-dipoles, and how water and other protic solvents
catalyze this reaction. We have also carried out kinetic stud-
ies to quantitatively analyze the phosphine-catalyzed [3+2]
cycloaddition reaction of allenoates and electron-deficient
alkenes. These mechanistic studies give an insight into the
chemistry of nucleophilic phosphine organocatalysis and re-
lated reactions in general.[10] In addition, these mechanistic
insights will act as a guide in the future design of new reac-
tions and new chiral organocatalysts. Furthermore, the re-
sults of this study will prompt chemists to rethink the role of
a trace amount of water in “anhydrous” organic reactions
that involve [1,n]-hydrogen shifts.[10]
Scheme 1. The phosphine-catalyzed [3+2] cycloaddition reaction (only
the major product is given; E=electron-withdrawing group).
sche, and Pyne and their co-workers have used this [3+2]
cycloaddition reaction as a key step in the total synthesis of
natural products.[5c,8] As a result of studies by Zhang, Fu,
and Miller and their co-workers, asymmetric versions of
phosphine-catalyzed [3+2] cycloaddition reactions have
also been developed.[9] Since the discovery of the phos-
phine-catalyzed [3+2] cycloaddition reaction in 1995,[5a] fur-
ther elegant developments and extensions of the chemistry
based on nucleophilic phosphine catalysis have been widely
pursued by many other groups[10] and this chemistry is en-
riching the arsenal of chemical reactions.[11]
The commonly accepted mechanism for the phosphine-
catalyzed [3+2] cycloaddition reaction of allenoates and ac-
tivated alkenes is given in Scheme 2.[5a,11a] The catalytic cycle
Computational Methods
All of the DFT calculations were performed with the Gaussian 03 soft-
ware package.[15] Geometry optimization of all the minima and transition
states involved was carried out at the B3LYP level of theory[16] with the
6-31+G(d) basis set.[17] A diffuse function in the basis set is important to
describe zwitterionic species.[18] The vibrational frequencies were comput-
ed at the same level of theory to check whether each optimized structure
is an energy minimum or a transition state and to evaluate its zero-point
vibrational energy (ZPVE). IRC calculations[19] were used to confirm
that the transition states connect the corresponding reactants and prod-
ucts. Solvent effects were computed using the CPCM model[20] at the
B3LYP/6-31+G(d) level of theory using the gas-phase-optimized struc-
tures. The natural bond orbital (NBO) technique[21] was applied to calcu-
late the Wiberg bond indices to analyze the bonding. Topological analysis
of the electron densities at bond critical points was performed with the
AIM 2000 program.[22]
Scheme 2. The mechanisms originally proposed for the phosphine-cata-
lyzed [3+2] cycloaddition reactions (only the major product is given;
E=electron-withdrawing group).
starts with the formation of a zwitterionic intermediate A,
generated from allenoate and phosphine, which acts as a
1,3-dipole, reacting with an electron-deficient alkene to give
five-membered phosphorus ylide B. Then a [1,2]-proton shift
converts B into another zwitterionic intermediate C, which
gives rise to the final product D by elimination of the phos-
phine catalyst. The phosphine-catalyzed [3+2] cycloaddition
reaction between alkynoates and dipolarophiles also has to
occur via zwitterionic intermediate A to enter into the [3+
2] catalytic cycle. In this case, it was proposed that zwitter-
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Cycloaddition of Allenoates and Alkenes
FULL PAPER
Results and Discussion
vation free energy is 26.2 kcalmolꢀ1 in benzene (this value is
overestimated as a result of an overestimation of the entro-
py in calculations, see later discussions on the reaction kinet-
ics).
Generation of the 1,3-dipole from allenoate: The first step
in the phosphine-catalyzed [3+2] cycloaddition of an alle-
noate and alkene is the nucleophilic attack of the phosphine
catalyst on the allenoate to generate in situ a zwitterionic in-
termediate, which serves as a 1,3-dipole. This step is key to
all reactions involving allenes and nucleophilic phosphine
catalysts.[10] The kinetic and thermodynamic parameters of
this process have been computed. Figure 1 shows the energy
ꢀ
The forming C P bond length in the addition transition-
state structure TS1 is 2.393 Š and the P-C2-C1-C dihedral
angle is 57.98 (the atom numbering is given in Figure 2). To
better understand this nucleophilic attack, we carried out a
frontier molecular orbital (FMO) analysis[24] (Figure 3). The
Figure 1. DFT-computed energy surfaces for the reactions between 1/1’
and 2.
Figure 3. FMO diagram for the reactions between 1/1’ and 2. Orbital co-
efficients are given in italics.[25]
surfaces computed for the addition of trimethylphosphine
(2) to methyl 2,3-butadienoate (1) and the parent allene
(1’). The addition of phosphine to 1’ was studied in order to
understand substituent effects in allenes. The optimized
structures are shown in Figure 2.
energy gap of HOMO2–LUMO1 is much smaller than that
of HOMO1–LUMO2 (11.92 versus 15.98 eV), which indi-
cates that the major interaction in the transition state TS1 is
that between the phosphineꢀs lone pair and the p* orbital of
the C1=C2 double bond in 1.
This is the reason why phos-
phine attacks the C1=C2
double bond in a near perpen-
dicular fashion in TS1.
The phosphine-catalyzed [3+
2] cycloaddition reactions of al-
lenes and alkenes are usually
limited to allenes activated with
strong
electron-withdrawing
groups. This can be easily ap-
preciated by comparing the ad-
dition of phosphine to 1’. The
activation enthalpy and free
energy in the gas phase for the
addition of phosphine to 1’ are
29.5 and 41.4 kcalmolꢀ1, respec-
Figure 2. DFT-optimized structures of 1, 2, transition state TS1, and 1,3-dipole 3. Distances are in Š.
tively.
Both
are
about
15 kcalmolꢀ1 higher than their
Calculations indicate that, in the gas phase, the formation
of the zwitterionic 1,3-dipole is exothermic by
counterparts in the addition of phosphine to 1, which con-
firms that without an electron-withdrawing group on the
allene, formation of the 1,3-dipole is kinetically disfavored.
The lower reactivity of 1’ compared with 1 can be easily ra-
tionalized by FMO theory: The LUMO of 1’ is higher than
that of 1 by 1.83 eV (the difference in energy between the
HOMOs of 1 and 1’ is just 0.45 eV). Moreover, the forma-
3
1.4 kcalmolꢀ1 in terms of enthalpy, but is endergonic by
9.7 kcalmolꢀ1 owing to entropy loss. The activation enthalpy
for this nucleophilic addition is 14.8 kcalmolꢀ1 and its activa-
tion free energy is 26.6 kcalmolꢀ1 in the gas phase.[23] After
taking solvent effects into consideration, the computed acti-
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Z.-X. Yu et al.
Table 1. Electron density topological properties of selected (3,ꢀ1) critical
tion of the 1,3-dipole 3’ is thermodynamically disfavored in
terms of enthalpy as a result of an endothermicity of
22.1 kcalmolꢀ1. The above results show that the installation
of an electron-withdrawing group in allene stabilizes both
the transition state of phosphine addition and the 1,3-dipole
formed.
Very recently, Kwon and co-workers obtained the crystal
structures of stable tetravalent phosphonium enolate zwit-
terions.[26] The 1,3-dipole 3 can be regarded as a relatively
less stable tetravalent phosphonium enolate zwitterion.
Therefore, it is worth discussing the structure of the 1,3-
dipole 3 shown in Figure 2. In theory, there are four possible
structures for the 1,3-dipole generated from allenoate and
phosphine (Figure 4). It was found that the most stable
points in 3 and 3b.
2
Interaction Distance [Š]
1
5 1
l1
l2
l3
P···O (3)
P···O (3b)
H1···O (3b) 2.281
H2···O (3b) 2.255
2.514
2.961
0.0330 0.0626 ꢀ0.0252 ꢀ0.0216 0.1094
0.0123 0.0040 ꢀ0.0065 ꢀ0.0038 0.0503
0.0161 0.0544 ꢀ0.0174 ꢀ0.0140 0.0858
0.0165 0.0569 ꢀ0.0180 ꢀ0.0145 0.0894
which indicates the absence of bifurcated hydrogen bonding
in this intermediate. However, such an interaction was
found in its isomer 3b in which the methoxy group is orien-
tated towards the phosphorus atom. The H1···O and H2···O
interactions[27] in 3b have electron density values of 0.0161
and 0.0165 a.u. and Laplacian values of 0.0544 and
0.0569 a.u., respectively, which are within the range of a
normal hydrogen bond.[28] As confirmed by the electron
density topological analysis, the P···O interaction in 3 is
much stronger than that in 3b because the electron density
value of the former is much larger than that of the latter
(0.0330 versus 0.0123 a.u.). Despite the bifurcated hydrogen
bonding in 3b, the P···O interaction is the dominant stabiliz-
ing effect in the 1,3-dipole, making 3 lower in Gibbs free
energy than 3b by 8.2 kcalmolꢀ1 in the gas phase.
Figure 4. DFT-computed relative enthalpies and free energies of four
possible structures of the 1,3-dipole generated from PMe3 and allenoate.
Regioselectivity of the [3+2] cycloaddition process: When
an unsymmetrical alkene is used as a dipolarophile in the
phosphine-catalyzed [3+2] cycloaddition reaction of alle-
noates, two cycloadducts can be obtained as regioisomers.
The origin of the regioselectivity of this reaction was ex-
plored by computing the energy surface of the [3+2] cyclo-
addition process (Figure 6, the transition-state structures in-
volved are given in Figure 7). Previous work revealed that
the [3+2] cycloaddition reaction occurs by a stepwise pro-
cess.[13,14,29] In the a-addition mode, the first transition state
a-TS2 requires an activation free energy of only 18.2 kcal
molꢀ1 in benzene. The subsequent ring-closure transition
state a-TS3 is slightly higher in energy than a-TS2 by
0.4 kcalmolꢀ1. In the g-addition mode, the two terminal
ꢀ
structure for the 1,3-dipole is 3. The formed P C2 bond dis-
tance in 3 is 1.836 Š (Figure 2). More importantly, there is a
ꢀ
short P O distance (2.514 Š) between the phosphorus and
carbonyl oxygen atoms. The Wiberg bond index shows the
bond order between these two atoms is 0.10, which indicates
that a significant intramolecular P···O interaction stabilizes
this intermediate.[21] To better understand the energetic pref-
erence of 3 over 3b, which also has a P···O interaction, we
carried out an atoms-in-molecules (AIM) analysis of these
two species (Figure 5 and Table 1).
Table 1 summarizes the computed electron density values
2
(1), the corresponding Laplacian values (5 1), and the ei-
2
genvalues (l1 <l2 <l3, 5 1=l1 +l2 +l3) for selected bond
ꢀ
critical points. As shown in Figure 5, no bond critical point
carbon atoms form a C C single bond via g-TS2 with an
can be found between the oxygen and hydrogen atoms in 3,
energy barrier of 19.4 kcalmolꢀ1 in benzene. The subsequent
ring-closure transition state g-
TS3 is lower in energy than g-
TS2 by 3.5 kcalmolꢀ1. Based on
the energy difference (18.6 kcal
molꢀ1 for the a-addition mode
versus 19.4 kcalmolꢀ1 for the g-
addition mode), our B3LYP/6-
31+G(d) calculations predict a
79:21 product ratio for a-
versus g-cycloaddition, close to
the experimental ratio of
85:15.[5a]
As a-TS2 and a-TS3 are very
similar in energy, the above a-
versus g-cycloaddition regiose-
lectivity can be analyzed by
Figure 5. The bond critical points in the 1,3-dipole 3 and its isomer 3b.
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Cycloaddition of Allenoates and Alkenes
FULL PAPER
than that in the 1,3-dipole 3
(Table 1) as their electron den-
sities are much lower than that
of
3
(0.0129 a.u. in a-TS2,
0.0145 a.u. in g-TS2, 0.0330 a.u.
in 3). However, there are sever-
al hydrogen-bonding interac-
tions in both a-TS2 and g-TS2
(Figure 9). Compared with g-
TS2, a-TS2 has one more hy-
drogen
bond
(H4···O2,
Figure 9), although the other
H···O and P···O interactions in
it are all slightly weaker than
those in g-TS2 (Table 2). This
Figure 6. DFT-computed energy surfaces for the [3+2] cycloaddition of 3 and 4.
comparing the relative energies of the Michael addition
transition states a-TS2 and g-TS2. FMO theory[24,30] can be
easily applied to explain why a-TS2 is more favored than g-
TS2 (Figure 8). The energy gap of the HOMO3–LUMO4 is
much smaller than that of HOMO4–LUMO3 (9.15 versus
14.44 eV), which indicates that the most favored orbital in-
teraction in the transition state is between the allylic anion
fragment of the 1,3-dipole 3 and the p* orbital of the C=C
bond in the acrylate 4. The HOMO coefficient of C1 (the
atom numbering is given in Figure 7 and Figure 8) in the
1,3-dipole 3 is larger than that of C3 (0.69 versus 0.55),
which suggests that C1 rather than C3 is a better match with
C4 (with a LUMO coefficient of 0.68, Figure 8) in 4, accord-
ing to FMO theory. Therefore, the [3+2] cycloaddition
from C1 (the a position) of the 1,3-dipole 3 is more favored
than that from C3 (the g position).
Figure 8. FMO diagram of the reaction between 3 and 4. Orbital coeffi-
cients are given in italics.[25]
In addition to the satisfactory explanation of the above
regioselectivity by FMO theory, analysis of the structures of
a-TS2 and g-TS2 can also explain their relative stability.[31]
Here we present our understanding of the structures of a-
TS2 and g-TS2 with the aid of AIM analysis. AIM analysis
indicates that there is no P···O interaction between the phos-
phorus and the carbonyl oxygen atom of the alkenoate
moiety (O2 in Figure 9) in either a-TS2 or g-TS2. The
P···O1 interactions in a-TS2 and g-TS2 (Table 2) are weaker
shows that a-TS2 is lower in enthalpy and Gibbs free energy
in benzene than g-TS2 by 1.5 and 1.2 kcalmolꢀ1, respective-
ly.
Water-catalyzed [1,2]-proton shift: The formation of the cy-
cloadduct a-6 from reactants 1 and 4 and catalyst 2 is ender-
gonic by about 11 kcalmolꢀ1 in terms of free energy in ben-
zene, which suggests that this transformation is not thermo-
dynamically favorable. Therefore, the stepwise [3+2] cyclo-
Figure 7. DFT-optimized structures of the transition states in the [3+2] cycloaddition of 3 and 4. Distances are in Š. For clarity, each methyl group is
represented by a carbon atom.
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Z.-X. Yu et al.
47.3 kcalmolꢀ1
anion
is
(Scheme 3, R=H).[34] In the
phosphine-catalyzed [3+2] cy-
cloaddition reaction, intermedi-
ate a-6 is a zwitterionic species
and its C2 atom (the atom num-
bering is given in Figure 11) is
carbanionic, that is, it has more
negative charge than the other
carbon atoms. Thus, a [1,2]-hy-
drogen shift in a-6 can be re-
garded as a [1,2]-proton shift of
a carbanion and, consequently,
a high activation energy is re-
quired for this intramolecular
four-electron process.[35]
Figure 9. The bond critical points in the transition states a-TS2 and g-TS2.
To obtain more information
about the [1,2]-proton shift pro-
cess in the [3+2] cycloaddition
reaction, we conducted a PPh3-
catalyzed [3+2] cycloaddition
of deuterium-labeled 2,3-buta-
dienoate 7 (2-D incorporation
level is about 95%) and fuma-
rate 8 (reaction I, Scheme 4) in
benzene (refluxed with sodium
and freshly distilled prior to
use). The 4-D- and 4-H-substi-
Table 2. Electron density topological properties of selected (3,ꢀ1) critical points in the transition states a-TS2
and g-TS2.
2
Interaction
Distance [Š]
1
5 1
l1
l2
l3
P···O1 (a-TS2)
H1···O1 (a-TS2)
H2···O1 (a-TS2)
H3···O2 (a-TS2)
H4···O2 (a-TS2)
P···O1 (g-TS2)
H1···O1 (g-TS2)
H2···O1 (g-TS2)
H3···O2 (g-TS2)
2.996
2.361
2.287
2.204
2.507
2.935
2.365
2.237
2.127
0.0129
0.0129
0.0151
0.0164
0.0092
0.0145
0.0131
0.0165
0.0179
0.0374
0.0461
0.0538
0.0556
0.0322
0.0398
0.0470
0.0605
0.0622
ꢀ0.0068
ꢀ0.0130
ꢀ0.0157
ꢀ0.0178
ꢀ0.0088
ꢀ0.0085
ꢀ0.0133
ꢀ0.0175
ꢀ0.0205
ꢀ0.0051
ꢀ0.0093
ꢀ0.0117
ꢀ0.0163
ꢀ0.0070
ꢀ0.0062
ꢀ0.0089
ꢀ0.0127
ꢀ0.0190
0.0493
0.0684
0.0812
0.0897
0.0480
0.0545
0.0692
0.0907
0.1017
addition must be followed by an exergonic process to drive
the whole reaction to completion. Calculations show that
the subsequent [1,2]-proton transfer (conversion of B into
C, Scheme 2) is exergonic by about 8 kcalmolꢀ1, which im-
plies that the formation of C can drive the above stepwise
[3+2] cycloaddition. This step can further drive the reaction
to completion by generating the product and the catalyst.
DFT calculations indicate that the activation free energy of
a direct [1,2]-proton shift from a-6 to 18 via TS4 is 39.6 and
39.3 kcalmolꢀ1 in benzene and in the gas phase, respectively
(Figures 10 and 11). Because the phosphine-catalyzed [3+2]
cycloaddition reaction is usually conducted at room temper-
ature, this direct intramolecular [1,2]-proton shift pathway,
requiring such a high activation free energy, is impossible
from the viewpoint of kinetics.
The high activation energy for the [1,2]-proton shift can
be easily understood in terms of orbital interactions[32]
(Scheme 3). It is well known that the [1,2]-hydride shift for
the carbocation is very facile with activation barriers of
about 5 kcalmolꢀ1.[33] This process is a two-electron process
and its transition state has a two-electron–two-orbital stabi-
lizing interaction between the proton and the p orbital of
the alkene. In contrast, the [1,2]-proton shift for the carban-
ion is a four-electron process and is difficult as the corre-
sponding transition state involves a four-electron–two-orbi-
tal destabilizing interaction between the hydride and the p
orbital of the alkene. The B3LYP/6-31+G(d)-computed ac-
tivation free energy for the [1,2]-proton shift in the ethyl
Figure 10. DFT-computed energy surface for the [1,2]-proton shift (E1 =
E2 =CO2Me).
tuted products 9 and 10 were both obtained in a ratio of
75:25. This indicates that the [1,2]-proton transfer from a-6
to 18 is not an intramolecular process.[36] If the [1,2]-hydro-
gen shift were a simple intramolecular process, the ratio of
the 4-D- and 4-H-substituted products 9 and 10 would be
about 95:5, in accord with the 2-D incorporation level of the
allenoate 7. Where does the extra 4-H-substituted product
10 come from? We speculated that the formation of extra
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Cycloaddition of Allenoates and Alkenes
FULL PAPER
Figure 11. DFT-optimized structures of the transition states and intermediate 16 in the [1,2]-proton shift. Distances are in Š. For clarity, each methyl
group is represented by a carbon atom.
10 was due to the presence of a
trace amount of water in the re-
action system. To prove our hy-
pothesis, we added 1 equiv. of
H2O to the [3+2] cycloaddition
reaction between 7 and 8 (reac-
tion II, Scheme 4). As expected,
the ratio of the 4-H-substituted
product 10 increased remarka-
bly from 25 to 88%.[37,38] I n a
previous communication, we re-
ported that control experiments
showed that deuterium and hy-
drogen exchange occurred nei-
ther between water and the al-
lenoate 7 nor between water
and the [3+2] product 9.[14]
This has been further rational-
ized by DFT calculations which
show that deuterium and hydro-
gen exchange between water
and allenoate is disfavored
compared with the [3+2] cyclo-
Scheme 3. Orbital interaction diagrams for the concerted [1,2]-hydrogen shifts in the carbanion and carbocat-
ion.
addition reaction. Discussions
relating to this are presented in
the Supporting Information.
Besides, a further experiment indicated that water also cata-
lyzes the [1,2]-proton shift in the phosphine-catalyzed
hetero-[3+2] cycloaddition reaction between the allenoate
and an electron-deficient imine (reaction IV, Scheme 4).
Computational studies were also conducted to reveal how
a trace amount of water catalyzes the [1,2]-proton shift. The
computed energy surface is depicted in Figure 10 and the
optimized geometries of the transition states and one key in-
termediate 16 are shown in Figure 11. In the water-catalyzed
[1,2]-proton shift process, a-6 first reacts with water to form
complex 15 with a reaction enthalpy of ꢀ8.0 kcalmolꢀ1 and
a reaction free energy of 4.0 kcalmolꢀ1 in benzene. Proton
transfer from water to C2 (the atom numbering is given in
Figure 11) via TS5 requires only 0.3 kcalmolꢀ1 of activation
free energy in benzene. A hydroxide anion is generated
Scheme 4. Isotopic labeling experiments (E1 =CO2Me, E2 =CO2Et).
from water after donating a proton. Calculations indicate
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4367

Z.-X. Yu et al.
that the generated hydroxide is not free in the reaction
ments, calculations, and discussions are given in the Support-
ing Information.
ꢀ
system. Instead, it forms a P O bond with the phosphorus
ꢀ
atom, as demonstrated by the P O distance of 1.877 Š and
the bond order of 0.43. The phosphorus-bound hydroxy
group then acts as a base to deprotonate the hydrogen atom
at C1. The deprotonation step to generate intermediate 17
via TS6 is also facile and has an activation free energy of
7.7 kcalmolꢀ1 in benzene. Dissociation of water from 17
leads to the formation of 18 which is exergonic by about
10 kcalmolꢀ1 in terms of free energy in benzene.
The last step in the phosphine-catalyzed [3+2] cycloaddi-
tion reaction is to transform intermediate 18 into the final
[3+2] product and to regenerate the phosphine catalyst
(Figure 12). This process requires only 0.9 kcalmolꢀ1 activa-
tion free energy and is exergonic by 33 kcalmolꢀ1.
Through the joint forces of computation and experiment,
the catalytic role of a trace amount of water in the [1,2]-
proton shift process has been discovered.[39–42] Further stud-
ies show that other protic sources, such as methanol, can
catalyze the [1,2]-proton shift as well (reactions III and V,
Scheme 4). Details of these experiments and calculations
are given in the Supporting Information. In addition, about
8% 5-H-substituted products 9 and 10 were obtained in re-
action III (Scheme 4), whereas no 5-D-substituted products
13 and 14 were found in reaction V (Scheme 4). This indi-
cates that deuterium and hydrogen exchange occurred to
some extent between deuterium-labeled allenoate 7 and the
added methanol when fumarate was employed as the trap-
per. Through further calculations and experiments, we at-
tributed these experimental results to a competition be-
tween H/D exchange and [3+2] cycloaddition. The extent
of this competition depends on the concentration of the ad-
ditives in benzene solution and the trappers used in the [3+
2] cycloaddition reactions. Details of the relevant experi-
Kinetic studies: The DFT-computed energy surface for the
complete catalytic cycle of the phosphine-catalyzed cycload-
dition of allenoate 1 and alkene 4 is summarized in
Figure 12 and reveals that the rate-determining step of the
reaction is the [3+2] cycloaddition step and the activation
free energy of the whole reaction is about 28 kcalmolꢀ1.
However, the phosphine-catalyzed [3+2] cycloaddition re-
action is usually completed at room temperature in a few
hours, which indicates that the actual activation free energy
is lower than the DFT-computed one. The overestimation of
the computed activation barrier here can be easily under-
stood considering that the [3+2] cycloaddition reaction is a
multimolecular process and the computed DGsol values are
somewhat overestimated (owing to the overestimation of
the entropic contributions in solution for a bi- or trimolecu-
lar process).[43] To obtain a more quantitative description of
the mechanism, kinetic studies of the above [3+2] cycload-
dition reaction are demanded. Such a study will also serve
to test whether the DFT method used here is suitable or not
for the study of this and other phosphine-catalyzed organo-
catalytic reactions. The information obtained from kinetic
studies, such as rate constants and activation parameters,
will greatly benefit the understanding of other related reac-
tions and the design of novel phosphine-catalyzed reactions.
According to the computational results of the phosphine-
catalyzed [3+2] cycloaddition reaction (Figure 12), the for-
mation of the 1,3-dipole and the stepwise cycloaddition are
difficult steps in the catalytic cycle. Therefore, in the simpli-
fied kinetic model for the [3+2] cycloaddition reaction
(Scheme 5, k1, kꢀ1, ka, and kg are the corresponding rate
constants), we assume that the formation of the 1,3-dipole is
Figure 12. DFT-computed energy surface for the phosphine-catalyzed [3+2] cycloaddition reaction between 1 and 4 (E1 =E2 =CO2Me, R=Me).
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Cycloaddition of Allenoates and Alkenes
FULL PAPER
Scheme 5. The simplified kinetic model for phosphine-catalyzed [3+2]
cycloaddition reaction.
reversible, but that the cycloaddition of the 1,3-dipole to the
trapper by the a- or g-addition mode is irreversible. These
two assumptions are reasonable and consistent with the
computed results shown in Figure 12. Based on our pro-
posed kinetic model (Scheme 5), the rate constants and
other kinetic parameters can be measured by kinetic studies
[Eqs. (1)–(4)].
Figure 13. The relationship between X and Y at different temperatures.
½a-productŠ ka
¼
ð1Þ
phile (for details, see the Supporting Information). The ki-
netic results are summarized in Table 3.
kg
½g-productŠ
The experimentally measured activation free energies, en-
thalpies, and entropies are summarized in Figure 14 and
d½a-productŠ kakl½allenoateŠ½phosphineŠ½trapperŠ
ninitial
¼
¼
dt
kꢀ1 þ ðka þ kgÞ½trapperŠ
ð2Þ
ð3Þ
Table 3. Experimentally measured values of ka/kg, k1, ka/kꢀ1, and kg/kꢀ1
at different temperatures.
ka þ kg
½allenoateŠ½phosphineŠ
kꢀ1
k k
a
1
¼
þ
kakl
k1 [10ꢀ3 Lmolꢀ1 sꢀ1
]
ka/kꢀ1
kg/kꢀ1
ninitial
½trapperŠ
l
T [K]
ka/kg
284
290
297
304
3.09
2.88
2.56
2.52
1.36ꢁ0.02
2.14ꢁ0.06
4.19ꢁ0.04
8.03ꢁ0.55
18.0ꢁ2.6
10.9ꢁ1.4
6.06ꢁ0.15
4.06ꢁ0.53
5.83ꢁ0.83
3.78ꢁ0.48
2.37ꢁ0.06
1.61ꢁ0.21
ka þ kg
kꢀ1
kakl
ð4Þ
Y ¼
X þ
kakl
The kinetic studies were conducted for the reaction between
ethyl allenoate and methyl acrylate in the presence of tri-
phenylphosphine as catalyst. From the kinetic model [the
detailed derivation of Equations (1) and (2) and the experi-
mental details are given in the Supporting Information], the
ratio of ka/kg is equal to the ratio of the [3+2] cycloadducts
generated from the two cycloaddition pathways [Eq. (1)].
This ratio can be measured by gas phase chromatography
(GC), which can also be used to determine the initial reac-
tion rate [the rate of a-product formation, Eq. (2)] at a low
conversion of allenoate. Equation (2) can be rearranged to
Equation (3) to give an important linear relationship. The
value of the [allenoate][phosphine]/ninitial ratio [denoted as Y
in Eq. (4)] only depends on the reciprocal of the trapperꢀs
Table 4. For comparison, the DFT-computed values are also
given in Table 4. The data show that the rate-determining
step of the phosphine-catalyzed [3+2] cycloaddition reac-
tion of allenoate 1 and alkene 4 is the generation of the 1,3-
dipole with a measured activation free energy of 20.6 kcal
molꢀ1 in benzene. The transition states of the [3+2] cyclo-
addition processes from the a- and g-position (19.6 and
20.1 kcalmolꢀ1, with respect to the reactants) have Gibbs
free energies very close to that of the transition state TS-1.
These data indicate that the formation of the 1,3-dipole is
more difficult than the stepwise [3+2] cycloaddition pro-
cess. However, the [3+2] cycloaddition step might also
become rate-determining if the phosphine catalyst or the
trapper is changed. No matter which step is rate-determin-
ing, it is evident that the first two steps of the [3+2] cyclo-
addition reaction, the generation of the 1,3-dipole and its
subsequent cycloaddition to a dipolarophile, are crucial to
understand the whole reaction process. Besides, the experi-
mentally determined activation enthalpies for both the 1,3-
dipole formation and the [3+2] cycloaddition are quite
close to the DFT-computed ones (Table 4). The computed
activation entropies are higher than the experimental ones
(Table 4), further confirming the overestimation of entropy
in computing bi- or trimolecular processes. The overestimat-
ed activation free energies in solution are indeed a result of
the overestimation of the entropic contributions in solu-
concentration [1/[trapper], denoted as X in Eq. (4)] at a
A
given temperature. Thus, a series of values for the [alle-
noate][phosphine]/ninitial ratio were determined at different
concentrations of the trapper at the same temperature.
Through a simple linear regression, both intercept and slope
can be obtained. Based on the values of the ka/kg ratio and
intercept, the rate constant for the formation of the 1,3-
dipole (k1) can be calculated. Then the value of the ka/kꢀ1
or kg/kꢀ1 ratio can be obtained according to the slope. We
conducted our kinetic studies at four different temperatures
(Figure 13) and derived the activation parameters from the
Eyring equation for the first two steps of the phosphine-cat-
alyzed [3+2] cycloaddition reaction, the generation of the
1,3-dipole and its subsequent cycloaddition to the dipolaro-
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4369

Z.-X. Yu et al.
the geometry optimization of TS8 shows that the length of
ꢀ
the forming P C2 bond is 2.147 Š (the atom numbering is
given in Figure 16). However, the formation of the 1,3-
dipole 21 is a highly endergonic process (by 23.2 kcalmolꢀ1
in terms of free energy and 14.2 kcalmolꢀ1 in terms of en-
thalpy). Consequently, the formation of 21 must be followed
by an exergonic process to drive this reaction forward. Con-
version of 21 into 3 is the process of choice, which is exer-
gonic by 16.3 kcalmolꢀ1 in free energy and 19.7 kcalmolꢀ1 in
enthalpy. At this stage, it is necessary to discuss the mecha-
nistic details of the conversion of 21 into 3.
The most obvious pathway connecting these two 1,3-di-
poles is a concerted [1,3]-proton shift process. Geometry op-
timization of TS9 shows that the lengths of the forming and
ꢀ
breaking C H bonds are 1.414 and 1.541 Š, respectively.
Unfortunately, this concerted step is extremely energy-de-
manding with an activation free energy of 52.8 kcalmolꢀ1 in
benzene and an activation enthalpy of 51.1 kcalmolꢀ1. As a
result, this concerted [1,3]-proton shift cannot be achieved
under mild reaction conditions (usually room temperature is
used for phosphine-catalyzed
Figure 14. Experimentally measured activation free energies and enthal-
pies for the 1,3-dipole generation and the [3+2] cycloaddition.
[3+2] cycloaddition reactions
with alkynoates as the three-
Table 4. Activation parameters determined from calculations and experiments.
TS-1
a-TS
g-TS
carbon synthon). In view of the
mechanism of the [3+2] cyclo-
addition reaction discussed
above, we proposed that a trace
amount of water present in the
so-called “anhydrous” reaction
DH computed in the gas phase [kcalmolꢀ1
DH measured in benzene [kcalmolꢀ1
DS computed in the gas phase [calKꢀ1 molꢀ1
DS measured in benzene [calKꢀ1 molꢀ1
]
14.8
2.2
4.0
]
14.8ꢁ0.7
1.9ꢁ0.6
3.7ꢁ0.3
]
ꢀ39.6
ꢀ97.7
ꢀ91.3
]
ꢀ19.6ꢁ1.7
ꢀ59.6ꢁ2.2
ꢀ55.2ꢁ1.0
tion.[23,43] The computed entropic contribution in the gas
phase should be taken as an upper limit in solution; the
actual value in such systems is 50–60% of the computed gas
phase value.
mixture could also play a catalytic role in the [1,3]-proton
shift process.[45]
Computational results show that the water-catalyzed [1,3]-
proton transfer is very facile. First, a water–dipole complex
22 is formed between 21 and water with a reaction enthalpy
Alkynoate as the precursor of the 1,3-dipole and a water-
catalyzed [1,3]-hydrogen shift: In addition to the method of
in situ generation of the 1,3-dipole from allenoate and phos-
phine, alkynoates can also be used as an alternative three-
carbon synthon to give the 1,3-dipole when phosphine is
used as a catalyst. This provides another important approach
to nucleophilic phosphine catal-
of ꢀ7.4 kcalmolꢀ1 and
a
reaction free energy of
3.6 kcalmolꢀ1 in benzene. Then the olefinic anion moiety of
21 is quickly protonated by water via TS10 with a very low
energy barrier.[46] Conversion of 22 into 23 is exergonic by
12.6 kcalmolꢀ1 in terms of free energy. In intermediate 23
the in situ generated hydroxide anion is coordinated to the
ysis. In our model reaction we
computed this process by using
methyl 2-butynoate (20) and
trimethylphosphine (2) as the
starting materials. The comput-
ed energy surface is given in
Figure 15, and the optimized
geometries are shown in
Figure 16.
As shown in Figure 15, the
nucleophilic attack of phos-
phine 2 on alkynoate 20 re-
quires an activation free energy
of 29.2 kcalmolꢀ1 in benzene
and an activation enthalpy of
17.6 kcalmolꢀ1.[44] In addition, Figure 15. DFT-computed energy surface for the formation of the 1,3-dipole 3 from PMe3 and alkynoate.
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Cycloaddition of Allenoates and Alkenes
FULL PAPER
Figure 16. DFT-optimized geometries of the transition states and intermediate 23 in the formation of the 1,3-dipole 3 from PMe3 and alkynoate. Distan-
ces are in Š.
phosphorus atom. From 23, deprotonation of the g-hydrogen
atom is very facile, requiring an activation free energy of
12.5 kcalmolꢀ1. Geometry optimization of TS11 shows that
of the 1,3-dipoles and their energies has been analyzed and
the results indicate that the interaction between the phos-
phorus and carbonyl oxygen atoms is very important for the
stabilization.
The stepwise [3+2] cycloaddition between the in situ gen-
erated 1,3-dipole and an unsymmetrical alkene can lead to
regioisomeric cycloadducts. This regioselectivity can be
easily rationalized by FMO theory and AIM analysis. Hy-
drogen bonding in the stepwise [3+2] process is also critical
to the relative stabilities of the a- and g-addition transition
states.
ꢀ
ꢀ
the O H and H C3 distances are 1.476 and 1.232 Š, respec-
tively. Once this energy barrier to deprotonation has been
overcome, the reaction process goes downhill to give the
1,3-dipole 3. An isotopic labeling experiment (Scheme 6)
Another important and interesting phenomenon in the
[3+2] cycloaddition reaction is the [1,2]- or [1,3]-hydrogen
shift (when the 1,3-dipole is generated from alkynoate and
phosphine). Calculations indicate that the commonly accept-
ed intramolecular [1,2]- and [1,3]-hydrogen shifts are impos-
sible owing to very high activation barriers. Further isotopic
labeling experiments and computations corroborate with
each other and demonstrate that water or other protic sour-
ces can catalyze [1,2]- and [1,3]-proton shifts with very low
activation free energies. The discovery of the catalytic role
of a trace amount of water in phosphine-catalyzed [3+2] cy-
cloaddition reactions will help chemists understand some
other “anhydrous” reactions in which a [1,n]-hydrogen shift
is implicated.
Scheme 6. Isotopic labeling experiment (E=CO2Et).
also supported the involvement of water in the [3+2] cyclo-
addition reaction involving alkynoate.[47] Further computa-
tional studies indicate that other protic sources (e.g., metha-
nol) can catalyze such a [1,3]-proton shift as well (see the
Supporting Information). These results also explain why the
phosphine-catalyzed isomerization of alkynoates to the cor-
responding dienoates works better in the presence of some
protic sources such as acetic acid or ethanol.[48]
Kinetic studies of the phosphine-catalyzed [3+2] cycload-
dition reaction suggest that formation of the 1,3-dipole from
allenoate and phosphine and its stepwise [3+2] cycloaddi-
tion to an electron-deficient alkene are energy-demanding
processes with Gibbs free energies of about 20 kcalmolꢀ1 in
benzene solution.
The information obtained from the mechanistic studies of
phosphine-catalyzed [3+2] cycloaddition reactions, both
computationally and experimentally, will greatly deepen our
understanding of other related phosphine-catalyzed reac-
tions and assist the design of novel phosphine-catalyzed re-
actions. The discovery that a trace amount of water acts as a
catalyst in [1,2]- and [1,3]-proton shifts will prompt chemists
to rethink the role of water and other protic sources in or-
ganic reactions.[49]
Conclusion
The detailed mechanism of Luꢀs phosphine-catalyzed [3+2]
cycloaddition reaction between allenoates and electron-defi-
cient alkenes has been investigated. The generation of a 1,3-
dipole is the first step of the phosphine-catalyzed [3+2] cy-
cloaddition reaction and is also key to all nucleophilic phos-
phine-catalyzed reactions. Through computational studies
(DFT calculations and FMO analysis), the thermodynamics
and kinetics relating to the formation of the 1,3-dipole have
been obtained and suggest that electron-withdrawing groups
in allenes can stabilize both the transition state and the 1,3-
dipole. The relationship between all the possible structures
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4371

Z.-X. Yu et al.
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Acknowledgements
We are indebted to generous financial support from a new faculty grant
from the 985 Program for Excellent Research in Peking University, the
Natural Science Foundation of China (20772007 and 20672005), and the
Scientific Research Foundation for Returned Overseas Chinese Scholars,
State Education Ministry of China.
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4372
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Cycloaddition of Allenoates and Alkenes
FULL PAPER
dipole. The activation energy of the former is lower than that of the
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molꢀ1 in benzene and an activation enthalpy of 14.8 kcalmolꢀ1. This
can be explained by FMO theory: the LUMO of 20 is higher than 1
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[36] Previous calculations demonstrated that the intermolecular hydro-
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with the water-catalyzed process. For details, see the Supporting In-
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[45] A similar water-assisted [1,3]-H shift was also found by Padwa et al.
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[37] We repeated the PPh3-catalyzed [3+2] cycloaddition of deuterium-
labeled reactants 7 and 8 which had been stored in the refrigerator
for 14 months in benzene (refluxed with sodium and freshly distilled
prior to use). It was found that the ratio of the 4-H-substituted prod-
uct 10 had increased from the previous 25% to a new value of 52%.
We attributed the increase in the percentage of 10 in the final prod-
ucts to an increase of moisture in 7 and 8 during storage. This indi-
cates that the level of incorporation of protons in the final cycload-
duct depends on their content (from H2O) in the reaction system.
[38] One equivalent of H2O can provide twice as many protons as
MeOH. This suggests that 0.5 equivalents of H2O is as effective as
1 equivalent of MeOH in providing the same number of protons for
the water-catalyzed [1,2]-proton shift. This was supported by the
comparison experiment: when 0.5 equivalents of H2O was added to
the [3+2] cycloaddition reaction between 7 and 8, the ratio of the
4-D and 4-H substituted products 9 and 10 was 24:76. This ratio is
coincidently the same as that of reaction III in Scheme 4, in which
1 equivalent of MeOH was added as the additive.
[46] After many attempts, the transition state TS10 could not be located.
However, the reaction between the olefinic anion and water is ex-
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[47] In this isotopic labeling experiment, both [1,3]- and [1,2]-hydrogen
shifts are involved. According to the computational results, both of
these hydrogen shifts are catalyzed by water which is supported by
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Received: November 1, 2007
Published online: March 20, 2008
Chem. Eur. J. 2008, 14, 4361 – 4373
ꢁ 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
4373