Solvent effect on kinetics and mechanism of the phospha-michael reaction of tertiary phosphines with unsaturated carboxylic acids

Article abstract of DOI:10.1002/hc.21161

In aprotic solvents, kinetics of the reaction of triphenylphosphine with acrylic acid is second order in the acid and first order in the phosphine. To find the most suitable model to describe the solvent effect on this reaction, the third-order rate constants in a series of 16 aprotic solvents were analyzed using one- and multiparameter regressions within the framework of the Kamlet-Taft, the Catalan, the Gutmann-Mayer, and the Koppel-Palm equations. The best result gives a two-parameter model constructed on the basis of the Reichardt polarity E_T and the basicity B from the Koppel-Palm equation, with the weak positive effect of the E_T parameter on the reaction rate and very strong negative effect of the B parameter. The results obtained give further evidence to the previously suggested a stepwise mechanism, which involves the initial formation of a zwitterionic intermediate, followed by the proton transfer from the second molecule of acrylic acid to the generated carbanionic center in the rate-determining step.

Full text of DOI:10.1002/hc.21161

Heteroatom Chemistry
Volume 00, Number 00, 2014
Solvent Effect on Kinetics and Mechanism
of the Phospha-Michael Reaction of Tertiary
Phosphines with Unsaturated Carboxylic Acids
Alexey V. Salin, Albert R. Fatkhutdinov, Anton V. II’in,
Vladimir I. Galkin, and Fanuza G. Shamsutdinova
BUTLEROV Institute of Chemistry, Kazan Federal University, Kazan, 420008, Russia
Received 23 January 2014; revised 17 March 2014
INTRODUCTION
ABSTRACT: In aprotic solvents, kinetics of the reac-
tion of triphenylphosphine with acrylic acid is second
order in the acid and first order in the phosphine. To
find the most suitable model to describe the solvent
effect on this reaction, the third-order rate constants
in a series of 16 aprotic solvents were analyzed using
one- and multiparameter regressions within the frame-
work of the Kamlet–Taft, the Catala´n, the Gutmann–
Mayer, and the Koppel–Palm equations. The best re-
sult gives a two-parameter model constructed on the
basis of the Reichardt polarity ET and the basicity
B from the Koppel–Palm equation, with the weak
positive effect of the ET parameter on the reaction
rate and very strong negative effect of the B parame-
ter. The results obtained give further evidence to the
previously suggested a stepwise mechanism, which
involves the initial formation of a zwitterionic inter-
mediate, followed by the proton transfer from the sec-
ond molecule of acrylic acid to the generated carban-
The Michael reaction, the conjugate addition of a
nucleophile to the α,β-unsaturated carbonyl and re-
lated compounds (Scheme 1) is one of the most ver-
satile and powerful tools in organic synthesis [1].
Undiminishing interest of chemists to this re-
action can be attributed to its several advantages,
viz. (i) the ability to combine different nucleophiles
(Michael donors) and activated alkenes (Michael ac-
ceptors) with each other, giving a rise to syntheti-
cally useful products with novel C–C, C–O, C–N, C–
P, C–S, and other bonds; (ii) the ability to achieve
highly enantioselective transformations using chiral
catalysts and auxiliaries; (iii) conformity with the
principle of atom economy; and (iv) usually mild
reaction conditions, etc. An extensive synthetic po-
tential of the Michael-type additions stimulated nu-
merous mechanistic studies carried out over the past
decades by several research groups [2–6]. However,
most of the data available are based on kinetic stud-
ies of reaction of α,β-unsaturated electrophilic sub-
strates with amine nucleophiles. Establishment of
the mechanism of this reaction was found to be a dif-
ficult problem, and alternative mechanistic hypothe-
ses including stepwise and concerted pathways were
proposed.
ꢀC
ionic center in the rate-determining step. 2014 Wiley
Periodicals, Inc. Heteroatom Chem. 00:1–12, 2014;
View this article online at wileyonlinelibrary.com.
DOI 10.1002/hc.21161
Much less information is available about the
mechanism of the phospha-Michael reaction, where
tertiary phosphine acts as a nucleophile. To fill up
the gap in the theory of the Michael-type additions,
we have recently started a systematic study of the
mechanism of the reaction of tertiary phosphines
Correspondence to: Alexey V. Salin; e-mail: salin555@mail.ru.
Contract grant sponsor: President Grant for Government
Support of Young Russian Scientists.
Contract grant number: MK-1316.2012.3.
Supporting Information is available in the online issue at
www.wileyonlinelibrary.com.
ꢀC
2014 Wiley Periodicals, Inc.
1

2
Salin et al.
relatively limited number of the solvents used for
the kinetic study. To obtain more detailed informa-
tion on the mechanism and to find the best model
of the solute–solvent interaction to describe the sol-
vent effect on the reaction, it seemed us reasonable
to expand the series of previously used aprotic sol-
vents. In this paper, we analyze the results of the
kinetic study of the reaction of triphenylphosphine
with acrylic acid in a series of 16 aprotic solvents
using various well-established one- and multipara-
meter equations.
SCHEME 1 The Michael-type additions.
with unsaturated carboxylic acids and their deriva-
tives [7]. In comparison with amines, phosphines are
stronger nucleophiles, but have weaker basic char-
acter (e.g., pKa for the conjugate acid of PPh3 in
water is 2.7 [8]). It makes possible to observe the ad-
dition of tertiary phosphines to acidic unsaturated
substrates both in acidic and nonacidic solvents and
thus to extract from experimental observations more
definite information about the mechanism of proton
transfers, which accompany most of the Michael-
type reactions. The data obtained for the reaction of
tertiary phosphines with activated alkenes allowed
us to propose a stepwise mechanism, which includes
the reversible formation of zwitterionic intermedi-
ate A, followed by rate-determining proton transfer
to the generated carbanionic center from a proton
donor solvent or a second molecule of unsaturated
acid (Scheme 2).
EXPERIMENTAL
Materials
All chemicals were obtained from Acros Organics
(Geel, Belgium) or Alfa Aesar (Heysham, UK) and
were of the highest quality available. Acrylic acid
was redistilled under reduced pressure in the pres-
ence of small amounts of hydroquinone immediately
before use. Triphenylphosphine was used without
additional purification. The solvents were purified
at the day of use according to known [9] or slightly
modified procedures.
Ethylene carbonate and propylene carbonate
were redistilled under reduced pressure. Acetonitrile
and ethyl formate were distilled over CaH2.
Propionitrile was shaken twice with 5-mL por-
tions of concentrated hydrochloric acid for 5 min.
Then it was shaken with saturated potassium car-
bonate solution, and the mixture was allowed to
When unsaturated carboxylic acid is used as a
substrate, and if the addition of tertiary phosphine
proceeds in an aprotic solvent, the reaction obeys
third-order kinetics, being first order in the phos-
phine and second order in the unsaturated acid [7d,
f]. However, previous conclusions were based on a
SCHEME 2 Proposed mechanism for addition of tertiary phosphines to activated alkenes.
Heteroatom Chemistry DOI 10.1002/hc

Solvent Effect on Kinetics and Mechanism of the Phospha-Michael Reaction of Tertiary Phosphines
3
stand over anhydrous sodium sulfate for several
days. Thereafter, the solvent was decanted, distilled
from P2O5 and, finally, from CaH2.
SCHEME 3 Reaction of triphenylphosphine with acrylic acid
in aprotic solvents.
Sulfolane was vacuum distilled twice from solid
potassium hydroxide and, finally, from CaH2. Ethyl
acetate, butyl acetate, methyl acetate, and diethyl
˚
carbonate were dried over 4 A molecular sieves and
distilled.
Tetrahydrofuran (THF), 1,4-dioxane, 1,3-
dioxolane, and 1,2-dimethoxyethane were purified
by the same procedure as follows: Initially, the
solvent was distilled from benzophenone ketyl in
argon atmosphere. To remove traces of peroxides,
the distillate was then treated with triphenylphos-
phine (ꢀ2 g/L), and the solution was allowed to
stand at room temperature under argon overnight.
Finally, the solution was fractionally distilled
under reduced pressure in argon atmosphere. N,N-
Dimethylformamide (DMF) and dimethyl sulfoxide
SCHEME 4 Self-association of acrylic acid in its own solu-
tions and in non- and weakly basic solvents.
kinetic methodology are given in the Supporting
Information.
Regression Analysis
˚
(DMSO) were dried over 4 A molecular sieves and
distilled under reduced pressure.
The regression analysis was carried out using Origin
and Microsoft Excel computer software. The quality
of correlations was estimated on the basis of correla-
tion coefficient R and standard deviation s. Accord-
ing to IUPAC recommendations, a correlation was
regarded as acceptable when R ࣙ 0.95 [10].
The purity of all compounds was confirmed by
boiling or melting points and refractive indexes. The
solvent purity was additionally verified by the ab-
sence of the changes in the spectra of the prepared
solution of triphenylphosphine throughout a day.
RESULTS AND DISCUSSION
Kinetics
For practical reasons, triphenylphosphine and
acrylic acid were found to be the most easy-to-use
reactants to study the solvent effect on the kinetics
of the addition of tertiary phosphines to unsaturated
carboxylic acids (Scheme 3).
All kinetic data were obtained spectrophotomet-
rically on a Perkin–Elmer Lambda 35 UV/vis
spectrometer with 1 cm, thermostated ( 0.1°C),
quarts cells within a general temperature interval
10–70°C, corrected for each solvent according to its
melting or boiling point (for details, see Fig. 2). The
reaction was studied under pseudo–first-order con-
ditions, in which the acrylic acid concentration was
at least 100 times greater than the concentration of
triphenylphosphine, [PPh3] ꢀ 10−4 M. The reaction
was followed by monitoring the decrease in the
absorbance of triphenylphosphine at λ = 300 nm to
over 80% completion. The pseudo–first-order rate
constants kꢁ were determined from the slope of the
plot (R > 0.9998) ln(Ax − Aꢁ) versus time t, where Ax
From viewpoint of the reaction mechanism, this
choice of reactants, as will be shown later, is not
crucial. However, it is advantageous that the rate of
chosen reaction is within the range suitable for the
experimental measurement for a wide series of sol-
vents, and pseudo–first-order condition in the phos-
phine can be excellently complied. Another advan-
tage is that there is no restriction in solubility of
substrates in solvents of different classes. The use
of the monocarboxylic acid is also preferred, since
it allows to avoid the complication of the reaction
kinetics due to appearance of the parallel channels
of proton transfer, as observed for the dicarboxylic
acids [7a].
However, there are a number of restrictions
that complicate the application of some solvents for
the kinetic study. The ability of carboxylic acids to
self-associate via intermolecular hydrogen bonding
(Scheme 4) limits the use of non- and weakly ba-
sic solvents, such as hydrocarbons and halogenated
hydrocarbons.
and A are the measured absorbances at time t, and
∞
completion of the reaction, respectively. Standard
deviations in kꢁ in individual runs were less than
3%. The third-order rate constants kIII were obtained
from the slope of a plot (R > 0.999) kꢁ versus [acrylic
acid]2 with ࣙ5 concentrations. Activation parame-
ters were calculated from standard Arrhenius plots
(R > 0.9995) with seven different temperatures,
values of ꢀH and ꢀS are within 2 kJ mol−1 and
ࣔ
ࣔ
7 J mol−1 −1, respectively. Examples of the
K
Heteroatom Chemistry DOI 10.1002/hc

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Salin et al.
Acrylic acid associated with a solvent or a sec-
It is noteworthy that a comparison of the ki-
netic parameters strongly suggests that the reaction
involves an identical mechanism for all the apro-
tic solvents used. For example, an isokinetic plot of
ond molecule of acrylic acid behaves differently in
the addition step (that reflects on k1/k–1) and the pro-
tonation step (that reflects on k2). If the solvent is not
able to specific solvation of the acid, the equilibrium
in solution is not shifted exclusively toward the acid
associated with this solvent, and the reaction shows
very complex kinetics, as observed for hydrocarbons
and their halogenated derivatives. Simplification of
the reaction kinetics in this case could be achieved
using highly diluted solutions of acrylic acid, [acrylic
acid] → 0; however, such a situation becomes impos-
sible under the pseudo–first-order condition in the
phosphine that requires [acrylic acid] >> [PPh3].
However, the problem of self-association of acrylic
acid can be solved by application of proton acceptor
solvents; these were used in our study.
Moreover, it should be noted that the use of
acyclic monoethers, such as Et2O and n-Bu2O, is im-
possible due to insolubility of the reaction product.
Ketones are not appropriate solvents for spectropho-
tometric measurements because of their absorption
at the operating wavelength of 300 nm.
Despite the above restrictions, the scope of sol-
vents suitable for the kinetic study remains suffi-
ciently broad; this allowed us to expand considerably
the series of seven aprotic solvents used previously
[7d] by adding ethylene carbonate, propylene car-
bonate, methyl acetate, ethyl formate, propionitrile,
1,4-dioxane, 1,3-dioxolane, 1,2-dimethoxyethane,
and THF.
T+30
log k
versus log kITII, also known as the Exner cri-
III
terion [11], exhibits the excellent linear character, as
shown in Fig. 2 and Eq. (2).
T+30
log k
= (0.901 0.012) log kITII + (0.416 0.030)
III
N= 16, R= 0.99975, s= 5.04 × 10−4
(2)
where kITIIand kITII+30are third-order rate constants at
temperatures T and T+30, respectively.
Interestingly, Eq. (2) is identical to those ones
obtained previously for the same reaction carried out
in protic solvents (alcohols and carboxylic acids [7c])
and for the similar reactions with other activated
alkenes [7h] and tertiary phosphines [7f]. Therefore,
solvents and substituents do not have a primary ef-
fect on the energy surface (i.e., do not change the
rate-determining step and the structure of the in-
termediate), and following conclusions about the
mechanism of the reaction of triphenylphosphine
with acrylic acid are valid for other examples of this
type of phospha-Michael reaction.
Two main conclusions about the mechanism fol-
low from the kinetic equation (1); they are in accor-
dance with our previous observations:
(i) The rate-determining step is the proton transfer,
and this is not a function of solvent properties
(e.g., basicity and/or polarity);
(ii) The proton transfer proceeds exclusively via a in-
termolecular pathway with assistance of a second
proton donor molecule (in this case, the second
molecule of acrylic acid).
Kinetic Equation and Reaction Mechanism
As previously described, clear nonlinear depen-
dences of the pseudo–first-order rate constant kꢁ on
the concentration of acrylic acid in the aprotic sol-
vent were found (examples for ethylene carbonate
and propylene carbonate are given in Fig. 1A), and
a plot of log kꢁ versus log[acrylic acid] gives a slope
close to 2, indicating that the reaction is second or-
der in acrylic acid (Fig. 1B). Thus, the third-order
kinetic equation (1) is general for the reaction of
acrylic acid with triphenylphosphine carried out in
any aprotic solvent, if the kinetics is not complicated
by self-association of the acid in solution, as men-
tioned above.
Since the rate-determining protonation of the
carbanionic center in acidic media seems quite sur-
prising, it was important for us to demonstrate in
the current study the generality of this mechanism
for a wide series of solvents. Recently, we also at-
tracted additional experimental and theoretical facts
[7g] to support this mechanistic proposal. The data
obtained allowed us to conclude that such a mecha-
nism is the result of high lability of the phospho-
nium zwitterion, whereby the decomposition rate
k–1 becomes much greater than the rate of proton
transfer k2 (Scheme 2). The attempts to explain the
reaction mechanism without assignment of the rate-
determining step to the protonation of carbanionic
center are not satisfactory, and most realistic ones
are presented below.
k1
Rate =
k2[PPh3][acrylic acid]2
k
−1
= kIII[PPh3][acrylic acid]2
(1)
One can assume that the second molecule
of acrylic acid becomes involved in the reaction
where kIII = k1k2/k–1 is the third-order rate constant.
Heteroatom Chemistry DOI 10.1002/hc

Solvent Effect on Kinetics and Mechanism of the Phospha-Michael Reaction of Tertiary Phosphines
5
FIGURE 1 Plots of kꢁ versus [acrylic acid] (A) and log kꢁ versus log [acrylic acid] (B) for the reaction of triphenylphosphine with
acrylic acid in aprotic solvents at 30°C (for ethylene carbonate, at 40°C). (a) propylene carbonate: log kꢁ + 1 = 1.88 log[acrylic
acid] – 1.114 (R2 = 0.9999, y = 1); (b) ethylene carbonate: log kꢁ = 1.90 log[acrylic acid] – 0.777 (R2 = 0.9999, y = 0); (c)
propionitrile: log kꢁ = 1.90 log[acrylic acid] – 1.319 (R2 = 0.9988, y = 0); (d) ethyl formate: log kꢁ = 1.80 log[acrylic acid] –
1.987 (R2 = 0.9992, y = 0); (e) 1,3-dioxolane: log kꢁ – 0.2 = 2.09 log[acrylic acid] – 1.960 (R2 = 0.9993, y = –0.2); (f) methyl
acetate: log kꢁ – 0.5 = 1.98 log[acrylic acid] – 2.009 (R2 = 0.9995, y = –0.5); (g) 1,4-dioxane: log kꢁ = 2.09 log[acrylic acid] –
2.781 (R2 = 0.9996, y = 0); (h) THF: log kꢁ = 2.09 log[acrylic acid] – 3.139 (R2 = 0.9996, y = 0); (i) 1,2-dimethoxyethane: log kꢁ
– 1 = 2.07 log[acrylic acid] – 2.702 (R2 = 0.9998, y = −1).
kinetic equation would have form (3) with the zero
order in the phosphine that contradicts the experi-
mental observations.
Rate =kobs[Acrylic Acid]2
(3)
The scenario of the specific-acid catalysis, pre-
sented in Scheme 6, would result in a kinetic
equation (4), which is also inconsistent with the
experimental data, because for a weak acrylic
acid the following expression is true: [H+] =
ꢀ
=
Kdis[acrylic acid] = [acrylic acid] (where Kdis is
a dissociation constant of acrylic acid in a given
solvent):
T+30
FIGURE 2 Isokinetic plot of log k
versus log kITII for the
III
reaction of triphenylphosphine with acrylic acid in aprotic sol-
vents (T = 283 K for acetonitrile, ethyl formate, 1,3-dioxolane,
methyl acetate, ethyl acetate, 1,2-dimethoxyethane, THF; T =
293 K for propionitrile, diethyl carbonate, butyl acetate, DMF,
DMSO; T = 294 K for 1,4-dioxane; T = 298 K for propylene
carbonate, T = 303 K for sulfolane; T = 313 K for ethylene
carbonate). For solvent numbering, see Table 1.
Rate =kobs[PPh3][Acrylic Acid][H+]
(4)
The third-order kinetic equation (1) could be
explained in terms of hydrogen bonding between
two molecules of acrylic acid with only partial
protonation of the carbonyl oxygen atom followed
by the rate-determining addition of the phosphine
(Scheme 7).
However, it seems doubtful that such partial pro-
tonation can significantly increase the electrophilic-
ity of the terminal carbon atom of the C=C bond in
comparison with the non-hydrogen bonded acrylic
acid (i.e., to make ꢀ+ >> δ+; Scheme 7); the
non-hydrogen bonded acrylic acid must be consid-
ered as unreactive in this scenario to provide “pure”
second-order kinetics in the acid. Moreover, the sol-
vent effect on this reaction, as will be seen later,
mechanism as a result of general- or specific-acid
catalysis, in which the first molecule of the acid pro-
tonates the second one at the carbonyl oxygen atom
and, thus, increases the electrophilicity of the C=C
bond in the latter molecule. According to the well-
known theory of acid–base catalysis [12], the sce-
nario of general acid catalysis requires the involve-
ment of the proton transfer in the rate-determining
step; this step would have occurred here prior the
attack of the phosphine (Scheme 5). As a result, the
Heteroatom Chemistry DOI 10.1002/hc

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Salin et al.
SCHEME 5 The general-acid-catalyzed reaction scenario.
SCHEME 6 The specific-acid-catalyzed reaction scenario.
SCHEME 7 The reaction scenario involving hydrogen bonding between two molecules of acrylic acid.
definitely requires the proton transfer to be the rate-
determining step.
considered as the most likely in our initial reports
[7a–c].
The absence of intramolecular proton migra-
One more possible scenario involves the gener-
ation of a low-polarity prereaction complex C be-
tween the phosphine and acrylic acid, in which the
formation of covalent P–C bond proceeds relatively
synchronous with the proton transfer to the incip-
ient carbanionic center from a second molecule of
acrylic acid (Scheme 8). However, the strong sub-
stituent effect [7f, h] and solvent effect (see below)
forced us to abandon such a concerted mechanism,
tion within the zwitterionic intermediate A (EWG
= CO2H) (Scheme 2), as follows from the kinetic
equation (1), is also quite remarkable. Now we
can summarize that it is a general phenomenon
for all types of solvents, both aprotic and pro-
tic ones [7c, h]. The quantum chemical calcula-
tions, carried out for a model reaction in the gas
phase showed [7g] that the involvement of a second
Heteroatom Chemistry DOI 10.1002/hc

Solvent Effect on Kinetics and Mechanism of the Phospha-Michael Reaction of Tertiary Phosphines
7
SCHEME 8 The reaction scenario involving the low-polarity prereaction complex between triphenylphosphine and acrylic
acid.
TABLE 1 Kinetic and Activation Parameters for the Reaction of Triphenylphosphine with Acrylic Acid in Aprotic Solvents (30°C)
ࣔ
ࣔ
Entry
Solvent
103 kIII (M−2 s−1)
ꢀH (kJ mol−1
)
–ꢀS (J mol−1 K−1
)
Reference
1
2
3
4
5
6
7
8
Ethylene carbonate
Propylene carbonate
Acetonitrile
Propionitrile
Sulfolane
Diethyl carbonate
Ethyl formate
1,3-Dioxolane
Butyl acetate
Methyl acetate
Ethyl acetate
1,2-Dimethoxyethane
1,4-Dioxane
THF
(143)a
27.4
29.1
29.3
29.2
32.4
31.3
36.7
36.9
35.7
31.9
34.0
39.1
39.0
42.5
47.8
43.5
171
169
172
173
165
173
160
161
165
178
172
168
169
165
161
180
This work
This work
[7d]
This work
[7d]
93.1
56.9
55.2
40.3
25.4
13.2
10.7
10.6
9.83
9.14
2.03
1.67
0.742
0.138
0.081
1.1
0.7b
0.7
0.5
0.5
0.2
0.3
0.05
0.05
0.04
0.03
0.02
0.009
0.005
0.004
[7d]
This work
This work
[7d]
This work
[7d]
This work
This work
This work
[7d]
9
10
11
12
13
14
15
16
DMF
DMSO
[7d]
aValue extrapolated from 40–70°C temperature interval.
bRefined value compared with the previously reported [7d].
proton donor molecule in the reaction is a result
of kinetic forbiddance for intramolecular proton
transfer via four-membered cyclic transition state B
(Scheme 2). Evidently, this tendency is valid when
the gas phase is replaced by any solvent. Interest-
ingly, the four-membered cyclic transition state for
a proton transfer was proposed for the Michael-
type reaction of primary and secondary amines
with activated alkenes [5], but the reaction mecha-
nism remains controversial [4d]. For the phospha-
Michael reaction of tertiary phosphines with
activated alkenes, the third-order kinetic equation
allows us to explicitly exclude a similar cyclic tran-
sition state from the mechanism.
tants (i.e., having polar intermediates in the path-
way) than for reactions involving low-polarity in-
termediates with partially broken or formed bonds
(e.g., complex C from Scheme 8). According to the
rate constant kIII, aprotic solvents can be roughly
divided into three groups. The first group consists
of “fast” solvents (kIII > 3 × 10−2 M−2
s
−1), such as
ethylene and propylene carbonates, nitriles, and sul-
folane. Notably, this group contains solvents with
weak basic characteristics and sufficiently large di-
electric constants (Table 2). Such solvents may be
recommended for this type phospha-Michael reac-
tion. The second group of solvents with “medium”
rates (3 × 10−4 ࣘ kIII ࣘ 3 × 10−2 M−2
s
−1) contains
esters (except for ethylene and propylene carbon-
ates) and ethers. As compared with the first group
of solvents, esters of this group have much smaller
dielectric constants but possess approximately the
same basic properties (Table 2). Polarity and basic-
ity of ethers are very varied and depend on the struc-
ture of carbon chain (cyclic or acyclic) and relative
position of oxygen atoms. If a series of ethers with
very similar dielectric constants is considered, 1,3-
dioxolane–1,2-dimethoxyethane–THF, one can no-
tice that the reaction rate slows down as the solvent
basicity increases (Table 1). DMF and DMSO belong
to the third group of “slow” solvents (kIII < 3 × 10−4
Solvent Effect on the Reaction Kinetics
The influence of the solvent on the kinetic and acti-
vation parameters of the studied reaction is summa-
rized in Table 1, where both previously and currently
obtained data for aprotic solvents were collected for
convenience.
As follows from Table 1 with the rate constants
varying over a 1500-fold range, the reaction is very
sensitive to the solvent effect. The strong solvent
effect is typical for reactions involving significant
redistribution of electron density among the reac-
Heteroatom Chemistry DOI 10.1002/hc

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Salin et al.
TABLE 2 Solvent Parameters Used in the Koppel–Palm Equation
Solvent
ε [9]
89.78
64.92
35.94
28.86
43.26
2.82
n [9]
ET [13]
48.6
46.0
45.6
43.6
44.0
36.7
40.9
43.1
38.5
38.9
38.1
38.2
36.0
37.4
43.2
45.1
Ya
Pb
E [14]
6.7d
4.3d
5.2
3.2
2.3
3.7d
3.7d
5.8d
2.6d
2.0d
1.6
0
B [15]
–
Ethylene carbonate
Propylene carbonate
Acetonitrile
Propionitrile
Sulfolane
Diethyl carbonate
Ethyl formate
1,3-Dioxolane
Butyl acetate
Methyl acetate
Ethyl acetate
1,2-Dimethoxyethane
1,4-Dioxane
THF
1.4195
1.4215
1.3441
1.3658
1.4833
1.3851
1.3599
1.3992
1.3942
1.3614
1.3724
1.3796
1.4224
1.4076
1.4305
1.4793
0.4917
0.4885
0.4794
0.4745
0.4829
0.2741
0.4021
0.3997
0.3639
0.3955
0.3850
0.4026
0.2231
0.4049
0.4798
0.4840
0.33665
0.33789
0.28740
0.30202
0.37503
0.31472
0.29808
0.32381
0.32060
0.29908
0.30639
0.31113
0.33845
0.32916
0.34347
0.37271
176e
160
162
157
145
185e
196
158
170
181
238
237
287
291
362
7.16
6.98c
5.01
6.68
6.02
7.20
2.209
7.39
36.71
46.45
4.2
0
2.6
3.2
DMF
DMSO
aCalculated by Eq. (17).
bCalculated by Eq. (19).
cTaken from [16].
d Calculated by Eq. (20).
eData obtained from Prof. G. Midyana.
M−2 −1). Apparently, high polarity is incapable of
s
formation. We can speculate that the absence of elec-
trostriction is a result of high lability of the zwitteri-
onic intermediate A, which reconverts to the starting
materials or transforms to the reaction product with
very large rate constants k–1 and k2, respectively. The
lifetime of this zwitterions is not long enough to pro-
duce ordering of polar solvent molecules around the
separated charges.
compensating strong deceleration of the rate as a re-
sult of very high basicity of these solvents. For syn-
thetic purposes, the use of solvents from the third
group should be avoided in the phospha-Michael re-
action.
The activation parameters presented in Table 1
give interesting information about the reaction inter-
mediate. As seen from Table 1, the values of entropy
of activation are always very negative and for this
To obtain further information on the reaction
mechanism, we analyzed the solvent effect using a
linear free energy relationship on the basis of differ-
ent empirical models of solute–solvent interactions.
The attempts to correlate the reaction rate with only
one solvent parameter were not satisfactory, sug-
gesting that different specific and nonspecific inter-
ࣔ
reason the ꢀS term contributes significantly to the
ࣔ
ࣔ
ࣔ
Gibbs free energy of activation (ꢀG = ꢀH – TꢀS )
at ambient temperatures. Large negative values of
the ꢀS are typical for reactions involving polar in-
ࣔ
termediates and usually arise from solvation effects,
viz. electrostriction of the solvent [13], the ordering
of polar solvent molecules around the charged cen-
ters appearing in the reaction pathway. However,
ࣔ
actions contribute to the ꢀG of this reaction. To
achieve correlations of better quality, multiparame-
ter equations were applied. It should be noted that
we knowingly did not use the opportunity to improve
the quality of the correlations by exclusion the most
deviating points for some of the solvents, since the
presence of the general isokinetic plot (Fig. 2, Eq. (2))
discredits such efforts. The only reason why not all
of the solvents were used in a correlation was the
lacking of a solvent parameter in the literature. The
solvent parameters of the Koppel–Palm equation are
given in Table 2, and other solvent parameters used
in this study are presented in the Supporting Infor-
mation. The results of one- and multiparameter re-
gression analysis are summarized in Table 3.
ࣔ
one can notice that the ꢀS values do not increase
as the polarity of solvent increases (e.g., compare the
ࣔ
ꢀS values for low-polarity 1,4-dioxane and highly
polar propylene carbonate; see Table 1). Taking into
account the experimental error in the determination
ࣔ
of ꢀS ( 7 J mol−1
K
−1), the reaction series may
be regarded as isoentropic; this leads to the general
isokinetic plot shown in Fig. 2. The assignment of
large negative values of entropy of activation to the
electrostriction of the solvents in such a situation
ࣔ
is doubtful. Most probably, these ꢀS values are a
result of highly organized structures of the reaction
intermediate and transition states themselves that
require rigorous arrangement of reactants relative
to each other for the efficient P–C and C–H bonds
As follows from Table 3, there is only a weak
positive correlation between the reaction rate and
the solvent polarity, defined either as the Kirkwood
Heteroatom Chemistry DOI 10.1002/hc

Solvent Effect on Kinetics and Mechanism of the Phospha-Michael Reaction of Tertiary Phosphines
9
Heteroatom Chemistry DOI 10.1002/hc

10 Salin et al.
function (Eq. (17) [17]), or the Reichardt parameter
ET [13], as confirmed by very low coefficients of the
pair correlations: 0.121 and 0.309, respectively (Eqs.
(5) and (6); Table 3).
tetrachloromethane solution and phenol in tetra-
chloromethane solution (Eq. (21)).
CC14
CC14
CC14
B = ꢀv¯
= v¯
− v¯
(21)
PhOH
PhOH
PhOH−Solv
The correlation coefficient for the full, four-
parameter Koppel–Palm regression is 0.958 (Eq.
(10), Table 3). The exclusion of the statistically
insignificant P and E parameters gives Eq. (15)
(Table 3) with satisfactory R = 0.952. Although
the parameter Y in Eq. (15) is also weakly signif-
icant, the exclusion of this parameter leads to one-
parameter correlation (16) (Table 3) with unsatisfac-
tory R = 0.935. Therefore, the success of the Koppel–
Palm equation compared with other multiparameter
equations is mainly a result of a very strong correla-
tion of the rate constants with the parameter B.
Further improvement of the quality of correla-
tion can be achieved by using the Reichardt param-
eter ET instead of the Y, P, and E parameters (R =
0.961, Eq. (11), Table 3). Such transformation seems
reasonable, since the use of procedure described by
Eq. (20) makes the E parameter less reliable than the
ET parameter [23].
Presented quantitative analysis of the solvent
effect on the reaction rate is a good evidence to
the mechanism proposed in Scheme 2. An obvi-
ous considerable impact of the solvent basicity on
the reaction rate proves the assignment of the rate-
determining step to the proton transfer. A pro-
nounced decrease in the reaction rate with the in-
crease in the solvent basicity can be assigned to the
double negative effect of this parameter on the rate
constant kIII = k1k2/k–1. The solvent basicity not only
decreases the protonation rate k2 but also retards
the nucleophilic attack of the phosphine k1, since
hydrogen bond with a proton acceptor solvent stabi-
lizes the ground state of acrylic acid and reduces the
electron-withdrawing effect of the carboxyl group
attached to the C=C bond. Therefore, the attempts
to accelerate reaction using highly polar solvents to
make smaller the decomposition rate k–1 are failed,
when the solvent possesses highly basic properties,
as observed for DMF and DMSO.
ε − 1
Y =
(17)
2ε + 1
where ε is a dielectric constant.
However, there are strong negative correlations
(0.8 < R < 0.95) with the solvent basicity expressed
in any of the scales used (i.e., DN, β, SB, B, see
Eqs. (12)—(14) and (16) and Table 3). The Kamlet–
Taft and the Catala´n multiparameter equations do
not describe satisfactory the solvent effect; even if
the parameters responsible for solvent dipolarity–
polarizability (π*, SPP) and Lewis acidity (α, SA)
are included into correlations, the correlation coeffi-
cient remains less than 0.9 (Eqs. (7) and (8); Table 3).
The Gutmann–Mayer equation based on the donor
numbers (DN) as a measure of the Lewis basicity of
the solvent and the acceptor numbers (AN) as a mea-
sure of the Lewis acidity of solvent allows to achieve
better correlation (R = 0.939, Eq. (9), Table 3), but it
still cannot be regarded as satisfactory. The Koppel–
Palm equation was found to be a more appropriate
model to describe the solvent effect.
In the Koppel–Palm model, the total solvent ef-
fect on a reaction rate is determined by the four-
parameter equation (18) [17].
log k = log k0 + yY + pP + eE + bB
(18)
where polarity Y and polarizability P describe
nonspecific components of solute–solvent interac-
tions; electrophilicity/acidity E and nucleophilic-
ity/basicity B describe specific components of these
interactions; y, p, e, b characterize the sensitivity of
a given reaction toward the corresponding solvation
effect; k0 formally conforms to rate constant in the
gas phase.
The polarity Y is the Kirkwood function; the
polarizability P is defined by Eq. (19):
n2 − 1
P =
(19)
n2 + 1
From viewpoint of the proposed reaction mech-
anism, the polarity of the solvent expressed either
in the Y or the ET scale favors the reaction due to
more efficient stabilization of the zwitterionic inter-
mediate A and reduction of the decomposition rate
k–1 (positive signs before these parameters in Eqs.
(11) and (15)). Such additional stabilization can be
achieved both by a dipole–dipole interaction with
the solvent and an interaction of the solvent as a
Lewis acid with the anionic moiety of the intermedi-
ate. Evidently, the “overall solvation” ET parameter
describes better the interaction of the solvent with
where n is the refractive index.
The electrophilicity/acidity E is expressed by the
Reichardt parameter ET, improved by subtraction of
the nonspecific interaction in accordance with Eq.
(20).
ε − 1
ε + 2
n2 − 1
E = ET − 25.10 − 14.84
− 9.59
(20)
n2 + 2
The nucleophilicity/basicity B is based on the
shift of the OH stretching vibration of phenol
within the complex with a solvent molecule in
Heteroatom Chemistry DOI 10.1002/hc

Solvent Effect on Kinetics and Mechanism of the Phospha-Michael Reaction of Tertiary Phosphines 11
this mechanism, the second-order kinetics in the
acid arises from one molecule being a reactant with
the phosphine and the other as a proton source in the
rate-determining step. Alternative mechanistic pro-
posals are also considered, but neither of them are
in agreement with the scope of the experimental ob-
servations. The reaction rate is very sensitive to the
solvent effect; this effect was analyzed using the
linear free energy relationship on the basis of
the one- and multiparameter equations, such as the
Kamlet–Taft, the Catala´n, the Gutmann–Mayer, and
the Koppel–Palm equations. The results obtained
showed that the solvent basicity defined in any of the
scales has the dominant and negative effect on the
reaction rate, confirming the assignment of the rate-
determining step to the proton transfer. The solvent
polarity expressed by the Kirkwood function or the
Reichardt ET parameter has only weak positive ef-
fect on the rate; this was assigned to extremely labile
character of the reaction intermediate that makes
solvation effects negligible for this zwitterions. This
conclusion is supported by the nearly isoentropic
character of the reaction studied in the solvents
with different polarities. The combination of the
Reichardt ET parameter with the Koppel–Palm ba-
sicity parameter B gives a two-parameter equation,
which in the best way describes the solvent effect.
The presence of the general isokinetic plot makes
the conclusions about the reaction mechanism and
solvent effects valid for other tertiary phosphines
and unsaturated carboxylic acids. The most appro-
priate aprotic solvents for this phospha-Michael
reactions are cyclic carbonates (ethylene carbonate
and propylene carbonate), nitriles, and sulfolane
due to their weak basic properties and high polarity.
The information obtained can be useful for planning
similar reactions, where phosphonium zwitterion
of type A is involved as a deprotonating agent, for
example, phosphine-catalyzed additions of alcohols
and CH acids to activated alkenes [24].
FIGURE 3 The relationship between experimental and
calculated rate constants on the basis of correlation Eq. (11)
(for solvent numbering, see Table 1).
this zwitterion than it does the Kirkwood function
Y (or free of nonspecific contribution, the parameter
E).
Most probably, the small statistical significances
of the Y and ET parameters in Eqs. (11) and (15)
come from high lability of the reaction intermedi-
ate; its very short lifetime does not allow the solvent
to be efficiently involved in the interaction. This as-
sumption is supported by the nearly constant values
of the entropy of activation for the solvents with very
different polarity, as discussed above.
Thus, Eq. (11) may be regarded as the best-fit
model to describe the solvent effect. Figure 3 illus-
trates a satisfactory relationship between the exper-
imental rate constants and those ones calculated by
this equation. The presented study allowed us to re-
fine the previous conclusions [7d, f] about the in-
dividual contribution of solvent parameters to the
overall effect on the reaction rate, when a fewer num-
ber of solvents was used.
ACKNOWLEDGMENTS
CONCLUSIONS
SAV gratefully thanks Dr. Alexandr Kuz’min for
generous financial support. We thank Prof. Galina
Midyana for her useful suggestions.
The kinetics of the reaction of triphenylphosphine
with acrylic acid was studied in a series of aprotic
solvents. The rate equation has general third order,
first order in the phosphine, and second order in
the acid. This equation was interpreted in terms of
previously suggested a stepwise mechanism with
the initial nucleophilic attack of the phosphine on
the terminal carbon atom of the C=C bond of the
acid, followed by rate-determining proton transfer
to the generated carbanionic center from the second
molecule of acrylic acid as shown in Scheme 2. In
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