'One-pot' Hammett plots: A general method for the rapid acquisition of relative rate data

Article abstract of DOI:10.1039/c2cc34074g

A general 'one-pot' method for determining relative rates of reaction in complex mixtures has been established using free energy relationships to demonstrate its utility. Competition experiments involving as many as seven species gave relative rate consta

Full text of DOI:10.1039/c2cc34074g

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‘One-pot’ Hammett plots: a general method for the rapid acquisition of
relative rate dataw
Hon Man Yau,a Anna K. Croftb and Jason B. Harper*a
Received 7th June 2012, Accepted 23rd July 2012
DOI: 10.1039/c2cc34074g
A general ‘one-pot’ method for determining relative rates of
reaction in complex mixtures has been established using free
energy relationships to demonstrate its utility. Competition
experiments involving as many as seven species gave relative
rate constants that are in good agreement to those obtained from
individual kinetic analyses.
solid support was used initially in the competitive pre-attachment
of differently-substituted anilines; the resultant product distribution
was determined using ESI+-MS after liberation of species
made up of the reacted aniline and an MS sensitising moiety
(the basis of using the analytical construct). Due to the
sensitivity of this analytical method, highly accurate relative
rate information was obtained. The use of such an analytical
construct with a specific reactive functionality, which is not
necessarily trivial to prepare itself,10 poses several limitations.
In particular, the reactions are restricted to those for which
conjugation is facilitated by the particular reactive functionality,
and sample preparation is still required to remove the species to
be analysed from the solid support.
Free-energy relationships, such as the Brønsted relation1 and the
Hammett equation,2 have long been used to obtain mechanistic
information and predict reaction outcomes. The knowledge of
the relative rates of a series of reactions is necessary to establish
a free-energy relationship for a given reaction. However, the
acquisition of rate constants is not always a trivial exercise when
precise control of reaction conditions, as well as temporal
considerations in sample handling, repetition, reaction times
and data processing, are taken into account.
Binary competition experiments3–7 have been used to circumvent
some of the problems listed above. That being said, in order to
obtain relative rate information for n related species, n ꢀ 1
experiments are still necessary with the result that some of the
time-consuming procedures involved with individual kinetics
experiments still exist.
A general method that is without the limitations stated
above and allows the acquisition of relative rate information
for many species in a single competition experiment is therefore
highly desirable. Herein, we demonstrate the utility and scope
of such a method.
Key to the process described is the relationship shown as
eqn (1). Originally derived by Ingold and Shaw,11 it relates the
rate constants for the reaction of two competing substrates to
the amount of each substance present at the beginning of the
reaction and at the time of analysis (see ESIw, Appendix S1).
Various strategies have been reported in the literature for the
rapid evaluation of absolute and/or relative rate information
involving more than two competing species. One such example
has been the simultaneous kinetic analyses of the esterification
and saponification of eight different isomers of hexanoic acid and
methyl hexanoate, respectively.8 Whilst the ability to obtain eight
rate constants in a single experiment is impressive, the periodic
sampling and analysis required in this case is time consuming and
the requirement for sample preparation prior to analysis may lead
to artifacts in other cases. Further, chromatographic conditions
for optimal resolution may not always be readily available.
Another example of note is the use of a high-throughput
‘one-pot’ method in the assessment of Hammett substituent
constants.9 In this case, an ‘‘analytical construct’’ attached to a
ꢀ
ꢁ
sx
sx;t¼0
ln
ln
kx
ky
ꢀ
ꢁ
¼
ð1Þ
sy
sy;t¼0
This equation differs from the expression that is commonly
used,3–7 which equates the ratio of the products of two
competing reactions to the ratio of their rates. The latter only
holds when equimolar amounts of competing starting materials
are used and the competing starting materials are present in
large excess, relative to the common reactant. As such, an
immediately apparent advantage of using eqn (1) is that there
is no such requirement; in fact, provided the ratio of any two
competing substrates is known, the absolute concentrations
are not required. Given this, and since the extent of each
reaction is also irrelevant (provided none have gone to completion),
sub-stoichiometric amounts of the common reagent can be used for
fast reactions, whilst super-stoichiometric amounts can be used for
slow reactions. All the processes are carried out, by definition,
under the same conditions and the number of competing reactions
is only limited by the technique used to analyse the mixture;12
a School of Chemistry, University of New South Wales, Sydney,
NSW 2052, Australia. E-mail: j.harper@unsw.edu.au;
Fax: +61 2 9385 6141; Tel: +61 2 9385 4692
b School of Chemistry, University of Wales Bangor, Bangor,
Gwynedd LL57 2UW, UK
w Electronic supplementary information (ESI) available: General
procedures, NMR spectra, Hammett plots and data from all experi-
ments described in the text. See DOI: 10.1039/c2cc34074g
c
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Scheme 1 The Menschutkin reaction between the benzyl bromides
1a–g and pyridine (a R = p-OCH3, b R = p-CH3, c R = m-CH3,
d R = H, e R = p-Br, f R = p-CO2CH3, g R = p-NO2).
all that is required is that the extent of reaction in each case
can be determined accurately.z
The efficacy of the method is shown by considering the
competing Menschutkin reactions between pyridine and the
seven benzyl bromides 1a–g (Scheme 1) and comparing data
from competitive experiments with the equivalent results
obtained from individual kinetic experiments that we have
previously reported.13 The resulting Hammett plot has been
shown to be non-linear and affords an insight into how the
method performs in such a complex case (cf. the linear case).
1H NMR spectroscopy, which allowed the extent of reaction
of each of the bromides 1a–g to be determined without the need for
preparation of the reaction mixture, was chosen as the analytical
method though other methods which distinguish starting materials
1a–g and products 2a–g would also be appropriate.
Fig. 2 Hammett plots constructed from the relative rate information
obtained for the Menschutkin reactions between benzyl bromides 1a–g
and pyridine, carried out in acetonitrile at 300.7 K. Data shown is
from this work (blue) and from that reported previously (green).13
and competitive data is illustrated for the acetonitrile case in
Hammett plot form as Fig. 2. The smooth nature of the curve
likely relates to a key advantage of the competitive case, that
being that, by definition, all experiments are carried out under
identical conditions. Importantly, using this method, the time
taken from sample preparation to the construction of the
Hammett plot was no more than one day.
A sub-stoichiometric amount of pyridine was added to the
mixture of the benzyl bromides 1a–g of known composition to
initiate the competition experiment. The extent of reaction in
each case was determined using the relative amounts of each of
the starting materials 1a–g and each of the products 2a–g
present, which were in turn deduced from the 1H NMR
integrals corresponding to the resonances of the respective
benzylic protons (Fig. 1). It should be noted that although
signal overlap was observed between compounds 1a and 1d, 1c
and 1e, 2b and 2c and 2d and 2e, since the composition of
the initial reaction mixture was known, simple relationships
between the relative amounts of starting materials and products
were used to deduce the relative amounts of all species (see ESIw
for full details). Using the normalised integrals, relative rate
constants were calculated using eqn (1).
The method is further demonstrated through considering
the sodium borohydride reduction of the acetophenones 3a–d
(Scheme 2). As no reliable relative rate data was available in
the literature with ethanol as the solvent,14 binary competition
experiments were initially carried out. Subsequently, following
the procedure described above, relative rate information for the
competitive sodium borohydride reduction of acetophenones
3a–d in ethanol was obtained; in all cases a sub-stoichiometric
amount of reducing agent was used.y Along with analysis using
1H NMR spectroscopy (see ESIw), 13C NMR spectroscopy
utilising the relaxation agent tris(acetylacetonato)chromium(III)
was also used (Fig. 3). For many systems, heteronuclear MR
spectroscopy is envisaged to circumvent the issues of signal
overlap that may occur when using 1H NMR spectroscopy,
due to the wider spectral window. The results from competition
The relative rate constants obtained for the Menschutkin
reactions using the method presented in this work are in good
agreement (see ESIw) with those previously reported,13 for both
the reactions carried out in acetonitrile and in the ionic liquid
[bmim][NCF3SO2]. The latter case shows that the method can be
used with non-traditional solvents. The comparison of individual
Scheme 2 The reduction of acetophenones 3a–d using sodium boro-
hydride (a R = p-OCH3, b R = p-CH3, c R = H, d R = p-Br).
Fig. 1 A representative 1H NMR spectrum (500 MHz) showing the
final distribution of starting materials and products of the competitive
Menschutkin reaction between benzyl bromides 1a–g and pyridine to
afford the corresponding pyridinium bromide products 2a–g.
Fig. 3 A representative 13C NMR spectrum (150 MHz) showing the
signals used to calculate relative rate constants of the competitive
sodium borohydride reduction of acetophenones 3a–d.
c
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Table 1 Relative rate constants for the competitive sodium boro-
hydride reduction, in ethanol at 295 K, of either all four acetophenones
3a–d simultaneously or binary combinations of the acetophenones
3a–d
superior technique in that it is more suitable for the rapid
accrual of relative rate information where it is applicable.
Whilst stoichiometric processes have been demonstrated
here, there is clear application of this method to catalytic
systems. For example, relative rates of conversion of a range
of substrates by a given catalyst (be it biological, metallic or
organic) could be readily determined, although the contribution
to the selectivity by binding and reactivity effects would require
some deconvolution. While the presence of intermediates may
complicate analysis, use of an appropriate analytical technique
with sufficient resolution (such as 13C NMR spectroscopy and
HPLC – it does not matter what the analytical procedure is as
the method itself is general) should overcome this.
Acetophenone
k/kH (1H)
k/kH
(
13C)
k/kH (Binary)
3a
3b
3c
3d
0.19 (0.03)
0.44 (0.12)
1
0.17 (0.04)
0.43 (0.03)
1
0.17 (0.07)
0.36 (0.04)
1
3.62 (0.21)
3.42 (0.21)
3.74 (0.29)
experiments containing all four acetophenones 3a–d are shown
in Table 1 along with those obtained from binary competition
experiments carried out under the same conditions.
The relative rate constants obtained from all the competition
experiments with either all of the acetophenones 3a–d or two at a
time are the same within the uncertainties of the measurement,
irrespective of the analytical method used. Likewise, the Hammett
plots constructed from the different data sets have similar r
values; 2.46 (1H) and 2.42 (13C) in the presence of all the
acetophenones 3a–g and 2.65 in the binary case.
In summary, a general method for the rapid assessment
of relative rate information from competition experiments
involving multiple competing species has been validated.
Along with being inherently more flexible than existing methods
in terms of the ratio of reagents present, both competing and not,
there are clear temporal benefits over existing methodologies. All
that is required is an analytical technique through which the
extent of reaction can be determined; herein the utility of direct
analysis using NMR spectroscopy has been highlighted.
These results illustrate the ability of this method to afford
relative rate information for reactions with lifetimes much
shorter than the timescale of the analytical method used;
that is, it demonstrates that the absolute values of the rate
constants are unimportant to the performance of the method.
It is also worth noting the difference in rate between the fastest
and the slowest reactions in this case is a factor of 20,
demonstrating that such differences can be accurately determined
using these analytical techniques. While not necessary in these
cases, the range of accessible rates can be extended by increasing
the proportion of the slower reacting substrate in the initial
mixture.
Notes and references
z It is worth noting that such an analysis assumes that there is no
reaction between each of the competing substrates, that there is no
reaction between any of the substrates and any of the products, and
that the competing species do not alter the reactivities of one another.
Within these limitations, the method is general.
y As a sub-stoichiometric amount of sodium borohydride is used, the
observed rate constants are a composite of each of the possible
reduction steps. However, this does not affect the method of analysis
as is demonstrated by agreement between binary and competition
experiments.
As a comparison between spectroscopic and chromato-
graphic analytical techniques, analysis of the competitive
sodium borohydride reduction of acetophenones 3a–d was
also carried out using reverse phase HPLC. Along with
requiring sample treatment prior to analysis, despite much
effort being spent on optimising elution conditions, it was not
possible to directly observe phenylethanol 4b, which had to be
extrapolated from the known quantities of other species at
multiple wavelengths. The errors involved with extrapolation
likely result in the significant deviation of the relative rate
constant for the acetophenone 3b–phenylethanol 4b pair from
that obtained using 1H NMR spectroscopy (see ESIw). Otherwise,
the relative rate constants obtained using reverse-phase HPLC
are in good agreement with those obtained using NMR
spectroscopy. While reverse-phase HPLC (and other chromato-
graphic techniques) can potentially achieve better resolution of
signals than NMR spectroscopy, and hence may be used in
circumstances where NMR spectroscopy is simply not suitable,
it should be noted that the time involved with the former is
often substantially more than the latter. Also, NMR spectro-
scopy does not require pre-analysis work-up, so that quantita-
tion can be performed in the native state of the reaction mixture
and, more importantly, does not suffer from matrix effects. For
these reasons, it is our opinion that NMR spectroscopy is a
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c
This journal is The Royal Society of Chemistry 2012
Chem. Commun., 2012, 48, 8937–8939 8939