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A simple method for the determination of rate constants at coalescence of exchanging ab systems in dynamic nmr
A SIMPLEMETHOD FORTHEDETERMINATION OF BATECONSMNTS AT COALESCENCE OF EXCHANGING AB SYSTEMS
IN DYNAMIC NMR
Daniel Kost* and Arie Zeichner Department of Chemistry, Ben Gurion University
of
the Negev,
Beersheva. Israel
(hoi-d
in UK 1 lombor 1974;roooptodfor pblioation13 Iovrber 1974)
Dynamic NMBmeasurements’ are most useful conformational
for the determination of energy barriers
changes, such as pyramidal inversions
bonds , lasgsh and ring inversions.
A
la
la,d-g
, rotations
about formal single
number of methods have been used to calculate
parameters from the temperature dependent NMBspectra of exchanging diastereotopic These methods include the complete line shape analysis entropies
of activation,
and coalescence
(CLSA), that yields
measurements, in which a single
evaluated at the temperature of highest line shape sensitivity, energy of activation
(AG# ) at this temperature. The coalescence
determined by line shape analysis, certain
spectral
unreliable
parameters. l,I
to yield
activation groups.
both enthalpies rate constant
(kc) is
rate constant can either be
Although the use of such equations has been criticized
it to as an
and by a systematic comparison,
AG’ values obtained using these equations are in good agreement with the results
in an AB spectrum, the equation shown to be restricted
kc-(n/&)/(Av*+6J*)
within certain
limits,
4
4
that
obtained by
CLSA. This is true mainly in the case of uncoupled equally populated exchanging singlets, which many of the approximate equations have been derived.
and
a value for the free
or by the use of approximate equations that relate
procedure, la it has been shown experimentally,S
to
for
For the exchange of coupled nuclei
has been employed.’
Its usefulness
was
and hence it should be used with care.
We wish to propose a method for the determination of rate constants at the coalescence of an AB spin system to a singlet. from the spectrum at the coalescence
A single point.
parameter, the width at half height
(I$),
is obtained
This is used to evaluate kc from a plot of kc against
(Figure 1). that has been calculated for various values of the coupling constant JAB by means 6 of a line shape program. The only other parameter that is needed is JAB, which must be measured
W+
4533
4534
lo.
at the slow exchange limit.
The use, at the coalescence
temperature, of a JAB value that has
been measured at lower temperature causes no difficulty, individual
however, as spin spin couplings
of
conformations are known to be temperature independent.*
The chemical shift lation
s/9
from the calculated
difference plot
(AvA8) is also obtained from the same parameters by interpo-
(Figure 2).
parameter, and its value at the coalescence
In all the approximate methods AvABis a necessary point must be extrapolated
measurements. Since AvAB is sometimes strongly
from low temperature
temperature dependent, and since the exact
nature of this dependence is unknown, a possible
error in
kc
experimental parameter. This source of error is eliminated
is introduced by using AvA8 as an
in the present method.
It is noteworthy to point out that in Figure 2 the curve for J = 2 Hz approaches a straight line with unit slope,
as is predicted
curve on Figure 1 approaches the line Av =W
c 4 singlets.
and kc=x Av/&
for the case of uncoupled singlets; kc=2.2
for the coalescence
W+ .
likewise,
This reconfirms the validity
the lowest
of the equations
of uncoupled (or, in this case, weakly coupled)
The main source of error in this method, as well as in CLSAupon which it is based, and in all other methods, remains the inaccuracy of temperature measurements. In view of this fact, it being generally
accepted that the most accurate parameter obtainable
and
from DNMR is AG’. we
believe
that the present method can be used successfully
for all simple A8 systems and yield
results
in very good agreement with those obtained from the more laborious
CLSA.
References 1. For leading references (b) R. Lynden-Bell,
on DNMR see:
(a) G. Binsch, Topics in stereo&em.,
Ports&r. (1970);
(1968);
Pergamon Press, Oxford, 1967, ch. 4;
(c) c. s.
in “Advances in Magnetic Resonance,” Vol. l_, ed. J. S. Waugh, Academic Press,
New York, 1965, ch.2; 400 (1970);
97
in “Progress in Nuclear Magnetic Resonance Spectroscopy,w Vol. &, eds.
J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Johnson, jr.,
2,
(d) A. Rauk, L. C. Allen and K. Mislow, Anqsw. Chew
(a) J. 8. Lambert, mpics in Stereochem.. 5, 19 (1971);
Chem. Forsch., E,
311 (1970);
(g) H. Kessler,
(h) W. E. Stewart and T. H. Siddal,
III,
Internet. E&I.. 2,
(f) J.-M. Lehn,
Allgear. Chum. Internat.
Chem. Rev., z,
715 (1970).
Bdn.. z, 219
of an AB quartet
with various JAB values (JAB given in Hz).
half height at the coalescence
Figure 1: A plot of rate constants vs. line widths at
IO
w+
20
differences
Hi0
in Hz).
.&Bquartet with various JAB values
1 (JAB given
of an
vs. line
40
widths at half height at the coalescence
Figure 2: A plot of chemical shift
20
30
N40
4
I
so
60
Y
ei
lto.51/32
4536
2. V. S.
Dimitrov,
Org.
Mag. Resonance, 2,
16 (1974).
3. (a) K.-I. Dahlqvist,S. Porsen and T. Alm, Acta Cbem. &and., 24, 651 (1970); (b) E. H. Carlson, F. B. Jones, jr., and M. Raban, C&m. Comm.,1235 (1969); (c) M. Raban, F. B. Jones, jr., E. H. Carlson, E. Banucci,and N. A. LeBel, J. Org. Chem., ?i& 1496 (1970); (d) W. Egan, R. Tang, G. Zen, and
K.
Mislow, J. Amer. Chem. Sot., E,
6205 (1971); (e) R. C. Neuman, jr.,
and V. Jonas, J. Org. Chem., 39, 925 (1974). 4. D. Kost, E. H. Carlson and M. Raban, Chem. Comm., 656 (1971). 5. R. J. Kurland,M. B. Rubin and M. B. Wise, J. Chem. Phys., 40, 2426 (1964). 6. We have used a modificationof program Quabex from referencela, p. 180. A reasonablevalue of T2 = 0.4 s has been used throughoutthe calculations.It has been noted7 that the line shape near coalescenceis insensitiveto small changes in T2. The usual definitionof coalescencehas been used, as in reference4. 7. T. Drakenberg,K.-I. Dahlqvistand S. Forsen,Acta Chem. Scami., 24, 694 (1970). 8. J. W. Emsley, J. Feeney and L. H. Sutcliffe,"High ResolutionNuclear Magnetic Resonance Spectroscopy",Vol. 1, PergamonPress, Oxford, 1965, p. 63.
IN DYNAMIC NMR
Daniel Kost* and Arie Zeichner Department of Chemistry, Ben Gurion University
of
the Negev,
Beersheva. Israel
(hoi-d
in UK 1 lombor 1974;roooptodfor pblioation13 Iovrber 1974)
Dynamic NMBmeasurements’ are most useful conformational
for the determination of energy barriers
changes, such as pyramidal inversions
bonds , lasgsh and ring inversions.
A
la
la,d-g
, rotations
about formal single
number of methods have been used to calculate
parameters from the temperature dependent NMBspectra of exchanging diastereotopic These methods include the complete line shape analysis entropies
of activation,
and coalescence
(CLSA), that yields
measurements, in which a single
evaluated at the temperature of highest line shape sensitivity, energy of activation
(AG# ) at this temperature. The coalescence
determined by line shape analysis, certain
spectral
unreliable
parameters. l,I
to yield
activation groups.
both enthalpies rate constant
(kc) is
rate constant can either be
Although the use of such equations has been criticized
it to as an
and by a systematic comparison,
AG’ values obtained using these equations are in good agreement with the results
in an AB spectrum, the equation shown to be restricted
kc-(n/&)/(Av*+6J*)
within certain
limits,
4
4
that
obtained by
CLSA. This is true mainly in the case of uncoupled equally populated exchanging singlets, which many of the approximate equations have been derived.
and
a value for the free
or by the use of approximate equations that relate
procedure, la it has been shown experimentally,S
to
for
For the exchange of coupled nuclei
has been employed.’
Its usefulness
was
and hence it should be used with care.
We wish to propose a method for the determination of rate constants at the coalescence of an AB spin system to a singlet. from the spectrum at the coalescence
A single point.
parameter, the width at half height
(I$),
is obtained
This is used to evaluate kc from a plot of kc against
(Figure 1). that has been calculated for various values of the coupling constant JAB by means 6 of a line shape program. The only other parameter that is needed is JAB, which must be measured
W+
4533
4534
lo.
at the slow exchange limit.
The use, at the coalescence
temperature, of a JAB value that has
been measured at lower temperature causes no difficulty, individual
however, as spin spin couplings
of
conformations are known to be temperature independent.*
The chemical shift lation
s/9
from the calculated
difference plot
(AvA8) is also obtained from the same parameters by interpo-
(Figure 2).
parameter, and its value at the coalescence
In all the approximate methods AvABis a necessary point must be extrapolated
measurements. Since AvAB is sometimes strongly
from low temperature
temperature dependent, and since the exact
nature of this dependence is unknown, a possible
error in
kc
experimental parameter. This source of error is eliminated
is introduced by using AvA8 as an
in the present method.
It is noteworthy to point out that in Figure 2 the curve for J = 2 Hz approaches a straight line with unit slope,
as is predicted
curve on Figure 1 approaches the line Av =W
c 4 singlets.
and kc=x Av/&
for the case of uncoupled singlets; kc=2.2
for the coalescence
W+ .
likewise,
This reconfirms the validity
the lowest
of the equations
of uncoupled (or, in this case, weakly coupled)
The main source of error in this method, as well as in CLSAupon which it is based, and in all other methods, remains the inaccuracy of temperature measurements. In view of this fact, it being generally
accepted that the most accurate parameter obtainable
and
from DNMR is AG’. we
believe
that the present method can be used successfully
for all simple A8 systems and yield
results
in very good agreement with those obtained from the more laborious
CLSA.
References 1. For leading references (b) R. Lynden-Bell,
on DNMR see:
(a) G. Binsch, Topics in stereo&em.,
Ports&r. (1970);
(1968);
Pergamon Press, Oxford, 1967, ch. 4;
(c) c. s.
in “Advances in Magnetic Resonance,” Vol. l_, ed. J. S. Waugh, Academic Press,
New York, 1965, ch.2; 400 (1970);
97
in “Progress in Nuclear Magnetic Resonance Spectroscopy,w Vol. &, eds.
J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Johnson, jr.,
2,
(d) A. Rauk, L. C. Allen and K. Mislow, Anqsw. Chew
(a) J. 8. Lambert, mpics in Stereochem.. 5, 19 (1971);
Chem. Forsch., E,
311 (1970);
(g) H. Kessler,
(h) W. E. Stewart and T. H. Siddal,
III,
Internet. E&I.. 2,
(f) J.-M. Lehn,
Allgear. Chum. Internat.
Chem. Rev., z,
715 (1970).
Bdn.. z, 219
of an AB quartet
with various JAB values (JAB given in Hz).
half height at the coalescence
Figure 1: A plot of rate constants vs. line widths at
IO
w+
20
differences
Hi0
in Hz).
.&Bquartet with various JAB values
1 (JAB given
of an
vs. line
40
widths at half height at the coalescence
Figure 2: A plot of chemical shift
20
30
N40
4
I
so
60
Y
ei
lto.51/32
4536
2. V. S.
Dimitrov,
Org.
Mag. Resonance, 2,
16 (1974).
3. (a) K.-I. Dahlqvist,S. Porsen and T. Alm, Acta Cbem. &and., 24, 651 (1970); (b) E. H. Carlson, F. B. Jones, jr., and M. Raban, C&m. Comm.,1235 (1969); (c) M. Raban, F. B. Jones, jr., E. H. Carlson, E. Banucci,and N. A. LeBel, J. Org. Chem., ?i& 1496 (1970); (d) W. Egan, R. Tang, G. Zen, and
K.
Mislow, J. Amer. Chem. Sot., E,
6205 (1971); (e) R. C. Neuman, jr.,
and V. Jonas, J. Org. Chem., 39, 925 (1974). 4. D. Kost, E. H. Carlson and M. Raban, Chem. Comm., 656 (1971). 5. R. J. Kurland,M. B. Rubin and M. B. Wise, J. Chem. Phys., 40, 2426 (1964). 6. We have used a modificationof program Quabex from referencela, p. 180. A reasonablevalue of T2 = 0.4 s has been used throughoutthe calculations.It has been noted7 that the line shape near coalescenceis insensitiveto small changes in T2. The usual definitionof coalescencehas been used, as in reference4. 7. T. Drakenberg,K.-I. Dahlqvistand S. Forsen,Acta Chem. Scami., 24, 694 (1970). 8. J. W. Emsley, J. Feeney and L. H. Sutcliffe,"High ResolutionNuclear Magnetic Resonance Spectroscopy",Vol. 1, PergamonPress, Oxford, 1965, p. 63.