Anomalous nuclear overhauser effects in carbon-substituted aziridines: Scalar cross-relaxation of the first kind

Article abstract of DOI:10.1002/anie.201410271

Anomalous NOESY cross-peaks that cannot be explained by dipolar cross-relaxation or chemical exchange are described for carbon-substituted aziridines. The origin of these is identified as scalar cross-relaxation of the first kind, as demonstrated by a com

Full text of DOI:10.1002/anie.201410271

Angewandte
Chemie
DOI: 10.1002/anie.201410271
NMR Spectroscopy
Anomalous Nuclear Overhauser Effects in Carbon-Substituted
Aziridines: Scalar Cross-Relaxation of the First Kind**
Ilya Kuprov, David M. Hodgson, Johannes Kloesges, Christopher I. Pearson, Barbara Odell, and
Timothy D. W. Claridge*
Abstract: Anomalous NOESY cross-peaks that cannot be
explained by dipolar cross-relaxation or chemical exchange are
described for carbon-substituted aziridines. The origin of these
is identified as scalar cross-relaxation of the first kind, as
demonstrated by a complete theoretical description of this
relaxation process and by computational simulation of the
NOESY spectra. It is shown that this process relies on the
stochastic modulation of J-coupling by conformational tran-
sitions, which in the case of aziridines arise from inversion at
the nitrogen center. The observation of scalar cross-relaxation
between protons does not appear to have been previously
reported for NOESY spectra. Conventional analysis would
have assigned the cross-peaks as being indicative of a chemical
exchange process occurring between correlated spins, were it
not for the fact that the pairs of nuclei displaying them cannot
undergo such exchange.
(Mr > ca. 2000 Da), aggregates or with viscous solvents, the
sign of the 1H-1H Overhauser effect undergoes a well-
documented inversion and cross-peaks become positive,
appearing similar to those arising from chemical exchange
processes.
The theory of spin relaxation processes in general[3] and of
NOEs in particular[2] is one of the most developed areas of
magnetic resonance spectroscopy, meaning deviations from
the behaviors described above are rare indeed. Herein, we
report anomalous NOESY observations for a series of C-
substituted NH aziridines 1a–d, for which the usual inter-
pretations offered no acceptable explanation.
During the development of methodology for the synthesis
and desulfinylation of N-sulfinyl terminal aziridines by some
of the current authors,[4] extensive spectroscopic analysis was
carried out to establish the integrity of the aryl-substituted
NH aziridines 1a,b (due to prior literature mischaracteriza-
tion[5]).
Among the powerful NMR structure and conformation
elucidation techniques,[1] nuclear Overhauser effect (NOE)
experiments play a central role because they map the spatial
proximity of neighboring spins.[2] The experimental tech-
niques used to observe magnetization transport due to NOEs
(NOE spectroscopy or NOESY) can also reveal the presence
of chemical exchange processes, for which the methods are
also known as exchange spectroscopy (EXSY).
For small molecules (Mr < ca. 1000 Da) in non-viscous
liquids at ambient temperatures, 1H-1H cross-peaks are
negative (opposite sign to the diagonal-peaks) for the NOE
and positive (same sign as the diagonal-peaks) for pairs of
signals undergoing chemical exchange. For large molecules
A NOESY spectrum of 2-phenylaziridine (1a) in dry
CD2Cl2 at 298 K exhibited unexpected strong positive cross-
peaks between the broad N-H resonance and all three CH
protons of the aziridine (Figure 1a), in addition to the
anticipated NOEs producing negative cross-peaks between
aziridine CH protons, characteristic of rapidly tumbling
molecules. The aziridine CH protons also produced the
expected negative cross-peaks with the nearby phenyl pro-
tons. When the temperature was reduced to 193 K, the
anomaly disappeared and only the anticipated patterns of
negative (spatial proximity) and positive (chemical exchange)
cross-peaks were apparent (Figure 1b).
[*] Prof. D. M. Hodgson, J. Kloesges, C. I. Pearson, Dr. B. Odell,
Prof. T. D. W. Claridge
Department of Chemistry, University of Oxford
Chemistry Research Laboratory
12 Mansfield Road, Oxford OX1 3TA (UK)
E-mail: tim.claridge@chem.ox.ac.uk
Dr. I. Kuprov
School of Chemistry, University of Southampton
Highfield Campus, Southampton SO17 1BJ (UK)
The exchange process observed is well understood—slow
inversion at the nitrogen center is a known feature of
aziridines,[6] and at low temperature this process gave rise to
two conformational forms (nitrogen invertomers), in a 5:1
ratio (see Figure S1 in the Supporting Information), with the
dominant isomer having the NH and phenyl group trans to
each other, as demonstrated by NOE analysis.
While the low-temperature NOESY spectrum can be
readily rationalized, the spectrum at 298 K is clearly anom-
alous; although the higher temperature accelerates the
conformational interconversion process between the inver-
[**] This work is supported by the EPSRC (EP/H003789/1). We also
thank the EPSRC, GlaxoSmithKline and AstraZeneca for studentship
support (to J.K. and C.I.P.).
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.201410271.
ꢀ 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co.
KGaA. This is an open access article under the terms of the Creative
Commons Attribution License, which permits use, distribution and
reproduction in any medium, provided the original work is properly
cited.
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peaks. The molecule is small and the solvent non-viscous,
meaning that the Overhauser effect must produce negative
cross-peaks; indeed these are apparent in Figure 1a and are
consistent with the aziridine structure. The p-chlorophenyl
aziridine (1b) showed similar behavior[7] and further inves-
tigations revealed the phenomenon is not restricted to aryl-
substituted NH aziridines, being also observed with 2-
methylaziridine (1c) and 2,2-dimethylaziridine (1d; see
Figures S2–S5), prompting us to seek a rational explanation
for this behavior.
A variety of mechanisms were considered but ruled out,
experimentally and/or theoretically. The most obvious pro-
cess of direct chemical exchange could be discounted, as there
is no chemically feasible process by which the NH and CH
protons could exchange. As evidence, samples in which the
NH proton was chemically exchanged for deuterium (by the
addition of D2O) showed no sign of loss of CH resonance
intensity on long-term storage. It is possible for relayed NOEs
to have the opposite sign to direct NOEs in small mole-
cules,[1,2] but this mechanism was also rejected because
available pathways for these effects were not consistent with
the anomalous patterns observed and because the anomalous
peaks were often of greater intensity than the NOEs present.
Further possibilities considered and rejected included quad-
rupolar effects involving 14N (15N-labelled 1a exhibited the
same phenomenon; Figure S6), all cross-correlation mecha-
nisms between quadrupole, dipole–dipole and chemical shift
anisotropy interactions, and the modulation of interproton
distances by conformational exchange.[7]
After elimination of these mechanisms, the one remaining
candidate was the stochastic modulation of J-couplings taking
place during nitrogen center inversion. This inversion process
would alter the HN-CH dihedral angles, leading to a variation
3
in the magnitude of the associated vicinal JNH-H values. This
could, in principle, cause cross-relaxation between the J-
coupled spins through the process known as scalar relaxation
of the first kind (SRFK)[2b] which, as detailed below, proved to
be the mechanism underlying the anomalous observations.
We believe this to be the first reported observation of scalar
cross-relaxation detected in 2D NOE spectra. Since this is
a little known phenomenon in mainstream NMR spectrosco-
py, it is pertinent to expand on the details of this mechanism
and we herein provide a complete theoretical rationalization
and computational simulation for this process.
Following Redfield,[3a] we split the Hamiltonian of a two-
^
spin system into the static part H0 and the centered stochastic
^
part H1ðtÞ [Eq. (1)].
D
E
^
^
^
^
HðtÞ ¼ H0 þ H1ðtÞ,
H1ðtÞ ¼ 0
ð1Þ
1
Figure 1. 2D H NOESY spectra recorded at 500 MHz with 800 ms
mixing times for 2-phenylaziridine (1a) in CD2Cl2 at a) 298 and
b) 193 K. At 298 K the two invertomers exhibit fast exchange and
anomalous cross-peaks appear between the NH and its scalar coupled
partners (red), in addition to dipolar NOE cross-peaks (blue). At 193 K
the invertomers are in slow exchange and the expected exchange
cross-peaks may be observed between these species (red) in addition
to dipolar NOE cross-peaks (blue).
Then, for the case of stochastically modulated J-coupling, one
obtains Equation (2),
ð1Þ
ð2Þ
^
^
^
^
^
^
H0 ¼ w1SZ þ w2SZ þ 2pJ0V, H1ðtÞ ¼ 2pJ1V
V ¼ SX SX þ SY SY þ SZ SZ
ð2Þ
ð1Þ ð2Þ
ð1Þ ð2Þ
ð1Þ ð2Þ
^ ^
^
^
^
^
^
,
hJ1ðtÞi ¼ 0
tomers, there can be no chemical exchange of any kind
between the CH and NH protons linked by the positive cross-
where angular brackets denote ensemble average, w1,2 are
Zeeman frequencies of the two spins, SXYZ are spin operators,
ð1;2Þ
^
2
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J0 is the static part of the J-coupling and J1(t) is its time
dependent part. Formal application of Bloch-Redfield-
Wangsness relaxation theory[3a] then leads to the following
expression for the relaxation superoperator given in Equa-
tion (3).
at low temperatures, due to a lack of resolved coupling
structure). The caveat is that the correlation time tin of the
nitrogen center inversion in aziridines is seven orders of
magnitude longer than the rotational correlation time tR,
meaning the contribution from scalar cross-relaxation
becomes significant.
In liquid-state NMR systems, both the dipole-dipole cross-
relaxation and the scalar cross-relaxation of the first kind
derived above are very well researched individually.[9] The
salient point here is that for small values of the rotational
correlation time tR (i.e. for small molecules in non-viscous
liquids), the corresponding rates have opposite signs
[Eq. (6)],
1
Z
^
^
^
^
^
^
^
^
2
ꢀiH0t
þiH0
Ve tdt
^
^
R ¼ ꢀ4p
hJ1ðtÞJ1ðt ꢀ tÞiVe
ð3Þ
0
Assuming an exponential correlation function for the sto-
chastic part of the J-coupling [Eq. (4)],
4p2hJ1ðtÞJ1ðt ꢀ tÞi ¼ D2J expðꢀt=tinÞ
ð4Þ
ꢀ
ꢀ
ꢀ
ꢀ
D
E
ꢂ
g21g22ꢀh2 ꢁm0 tR
ð1Þꢀ^
ð2Þ
^
^
^
SZ
R
S
¼ ꢀ
ꢁ
ꢀ
DD
Z
r16;2
10
4p
the automatic symbolic processing system developed by
Kuprov et al.[8] returned the expression defining the “scalar
cross-relaxation” rate between the two spins [Eq. (5)],
ꢃ
ꢄ
6
1
ꢀ
ð6Þ
2
2
1 þ ðw1 þ w2Þ t2R 1 þ ðw1 ꢀ w2Þ t2R
ꢀ
ꢀ
D
E
D2J tin
1
ð1Þꢀ^
ꢀ
ꢀ
ð2Þ
^
^
^
SZ
R
S
¼ þ
ꢀ
ꢀ
ꢀ
ꢀ
D
E
D2J tin
1
SRFK
Z
2
1 þ ðw1 ꢀ w2Þ t2in
2
ð1Þꢀ^
^
^ ^ð2Þ
ð5Þ
SZ R S
¼
ꢀ
ꢀ
Z
2
1 þ ðw1 ꢀ w2Þ t2in
2
where g1,2 are magnetogyric ratios of the two nuclei and r1,2 is
the internuclear distance. Thus, as illustrated below, it is
possible for these two processes to compete with each other.
Under appropriate experimental conditions it is also possible
for the SRFK term to dominate the dipolar term and produce
the unexpected cross-peak sign inversion described above.
All parameters required by the formalism presented
above are either known or could be estimated with sufficient
accuracy from electronic structure theory calculations,[7] and
the J-coupling modulation depth was estimated at 15 Hz
(Figure 2).
where tin is the correlation time of the nitrogen inversion
process and DJ is the modulation depth of the scalar coupling.
The difficulty with this expression is that D2J is tiny—about
15 Hz variation in the J-coupling was estimated from a DFT
calculation on 2-methylaziridine (Figure 2)—and therefore
cannot be expected to compete with dipole–dipole (DD)
cross-relaxation process with its 10 kHz modulation depth
(for computational simplicity 2-methylaziridine (1c) was
used; J values could not be measured experimentally, even
Figure 3 shows the derived cross-relaxation rates for the
dipolar process (blue curve), and scalar process (red curve)
between the amine proton and a vicinal CH proton in 2-
methylaziridine (1c). It is clear that, while the purely dipolar
process gives the expected negative cross-relaxation rate
(negative cross-peaks in NOESY), the apparent cross-relax-
ation rate between the protons with modulated J-couplings is
predicted to be positive (positive cross-peaks in NOESY).
Also positive would be the cross-peaks correlating nuclei that
undergo chemical exchange during the nitrogen ring-inver-
sion process.
A simulation, shown in Figure 4, incorporating the SRFK
contribution to the relaxation superoperator and the nitrogen
ring-inversion contribution to the chemical kinetics super-
operator, using the standard functionality available in Spi-
nach,[15] was capable of reproducing simultaneously the
regular-looking NOESY (Figure 1b) and the anomalous
NOESY (Figure 1a) for 2-phenylaziridine (1a). The sign of
every single cross-peak is correctly reproduced, and the role
played by the SRFK process is essential in reproducing the
anomalous cross-peaks—when SRFK terms are removed
from the relaxation superoperator, the agreement with the
experiment disappears (Figure S8; the simulation source code
is a part of the example set included with Spinach library
versions 1.5 and later). The SRFK process has no dependence
on inter-nuclear distance, but requires that the scalar coupling
between two spins is modulated at a rate that is comparable to
Figure 2. Modulation of three-bond 1H-1H J-couplings to the amine
proton during aziridine nitrogen center inversion. The minimum-
energy reaction path was obtained for 2-methylaziridine (1c) with
STQN DFT M06/cc-pVTZ method[10] in Gaussian09 with solvent effects
accounted for using SCIPCM model.[11] J-couplings were then com-
puted for each point on the reaction path using GIAO DFT M06/cc-
pVTZ method with IEFPCM solvent model.[12] The Fermi contact
contribution to the J-coupling was evaluated with a decontracted basis
set augmented with tight basis functions.[13] The points in the Figure
are interpolated with a cubic spline. See Figure S7 in the Supporting
Information for the modulation graphs for J-couplings not involving
the amino proton.
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Figure 3. Dipolar (blue curve) and SRFK (red curve) longitudinal cross-
relaxation rates between the amine proton and the CH2 proton trans to
the methyl group in 2-methylaziridine (1c), as functions of rotational
correlation time tR and nitrogen inversion correlation time tin. The
curves were obtained from Equation (6) with the following parameters:
NMR magnet induction of 11.75 Tesla, proton Zeeman frequency
difference of 1000 Hz, interproton distance of 2.33 ꢁ, J-coupling
modulation depth of 15 Hz. The experimentally reported[14] range of
times tin characteristic of the inversion process in aziridines is shown
with a red line in the upper part of the graph. The rotational correlation
times tR of 2-methylaziridine (1c) in four solvents shown in the lower
part of the graph were estimated using the Stokes–Einstein equation,
for which the molecular volume of 108 ꢁ3 was computed as the PCM
DFT solvent-excluded volume.[12] Room-temperature dynamic viscosi-
ties of 0.224, 0.604, 0.890, and 2.544 MPas were used for ether,
benzene, water, and 1-butanol, respectively.
the frequency difference between the coupled spins, and that
the coupling constant has significant magnitude relative to the
shift difference. These factors have meant that scalar relax-
ation effects have been considered unlikely to be apparent in
NOE experiments performed with modern high-field spec-
trometers.[16]
We believe scalar cross-relaxation of the first kind has not
previously been reported as being observed in 2D NOESY
spectra and, it appears, the effect has only rarely been
detected experimentally. The clearest example of this appears
to be the work of Fukumi et al.[17] over forty years ago in
which negative NOEs were observed between the coupled
CH-OH protons of methanol and ethanol and attributed to
scalar relaxation. The effect occurred only at acidic pH where
the hydroxyl proton exchange rates fulfilled the SRFK
requirements, outside which only conventional dipolar
NOEs were detected.
1
Figure 4. Theoretical H NOESY spectra of 2-phenylaziridine (1a),
simulated using Spinach library,[15] with the conditions matching the
experimental conditions reported in Figure 1, magnetic interaction
parameters computed as described for 2-methylaziridine (1c) in the
caption to Figure 3 and the following additional assumptions: for
a) forward nitrogen inversion rate constant 1.2 kHz, backward nitrogen
inversion rate constant 1.2 kHz, rotational correlation time 50 ps; for
b) forward nitrogen inversion rate constant 4 Hz, backward nitrogen
inversion rate constant 20 Hz, rotational correlation time 50 ps.
We are also not aware of the scalar cross-relaxation
process being previously reported for nitrogen NH groups. In
the case of the aziridines, as noted earlier, it is well-
documented that inversion of the pyramidal nitrogen center
is a relatively slow process,[6] and it appears that the reported
rates for this process are appropriate to induce the observed
SRFK effects detailed herein.[14] In a relevant NMR study of
H-N inversion in 2,2-dimethylaziridine (1d),[18] the unimo-
lecular inversion mechanism gave an inversion rate constant
of 1.6 sꢀ1 at 304 K and an activation free energy at this
temperature of 73 kJmolꢀ1. This slow inversion rate when
compared to other amines is attributed to the small 608 C-N-C
angle (q) at the inverting center which destabilizes the planar
transition state relative to the pyramidal nitrogen.[6b] By
comparison, the inversion barrier for ammonia is significantly
lower at 24 kJmolꢀ1,[19] for pyrrolidines, where q = 1058, itꢀs
a comparable 25 kJmolꢀ1 and for azetidines, where q ꢂ 908,
4
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Chemie
the barrier rises slightly to 30 kJmolꢀ1.[20] We note that in
control experiments with azetidine and pyrrolidine the
anomalous cross-peaks were not observed (Figure S9).
[3] a) A. G. Redfield, IBM J. Res. Dev. 1957, 1, 19 – 31; b) R. K.
Wangsness, F. Bloch, Phys. Rev. 1953, 89, 728 – 739.
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2009, 1923 – 1932.
Although the intramolecular inversion process is there-
fore a likely and appropriate mechanism to modulate the J-
couplings of the NH-CH protons, we cannot completely
exclude the role of intermolecular NH exchange in these
systems that would also lead to similar inversion and J-
modulation, since bimolecular NH exchange between azir-
idine molecules can occur[18]—a process which may also be
catalyzed by water. Indeed, NH exchange with residual water
is sometimes observed in NOESY spectra of the aziridines,
although its presence was not a requirement for the anom-
alous cross-peaks to be observed as these were also seen in
samples subjected to drying conditions (Figures S2–S6).
Nonetheless, the salient point we seek to highlight here is
that the anomalous cross-peaks observed in the NOESY
spectra of aziridine derivatives owe their presence to scalar
cross-relaxation of the first kind. Through a specific combi-
nation of parameters, the resulting cross-relaxation process
becomes strong enough to overpower the dipolar NOE and
invert the sign of the NOESY cross-peak. This phenomenon is
likely to be observed in any NMR system where homonuclear
J-couplings are modulated on a millisecond time scale. We
anticipate others will recognize these effects in small mole-
cule NOESY data, now that these apparently anomalous
peaks have been reported and rationalized; other similar
results from our laboratory will be reported in due course.
[5] B. Denolf, E. Leemans, N. De Kimpe, J. Org. Chem. 2007, 72,
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[7] See the Supporting Information for details.
[8] I. Kuprov, N. Wagner-Rundell, P. J. Hore, J. Magn. Reson. 2007,
184, 196 – 206.
[9] a) A. Abragam, The principles of nuclear magnetism, Clarendon
Press, Oxford, 1961; b) R. Brꢁschweiler in Understanding
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drecht, 1994; c) R. Brꢁschweiler, R. R. Ernst, J. Chem. Phys.
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Received: October 20, 2014
Revised: November 24, 2014
Published online: && &&, &&&&
Keywords: aziridines · NMR spectroscopy · NMR theory ·
.
Overhauser effect · scalar relaxation
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[1] T. D. W. Claridge, High-resolution NMR techniques in organic
chemistry, 2nd ed., Elsevier, Oxford, 2009.
[2] a) D. Neuhaus, M. P. Williamson, The nuclear Overhauser effect
in structural and conformational analysis, 2nd ed., Wiley, New
York, 2000; b) J. H. Noggle, R. E. Schirmer, The nuclear Over-
hauser effect: chemical applications, Academic Press, New York,
1971.
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Communications
NMR Spectroscopy
Scalar relaxation: Apparently anomalous
cross-peaks in 2D H NOESY spectra of
1
I. Kuprov, D. M. Hodgson, J. Kloesges,
C. I. Pearson, B. Odell,
carbon-substituted aziridines are shown
to arise from scalar cross-relaxation of the
first kind (SRFK; see picture), due to
modulation of scalar coupling constants
between protons. Such effects will likely
be seen in NOESY spectra of other small
molecules experiencing dynamic
T. D. W. Claridge*
&&& — &&&
Anomalous Nuclear Overhauser Effects
in Carbon-Substituted Aziridines: Scalar
Cross-Relaxation of the First Kind
exchange modulation of scalar 1H-1H
coupling constants.
6
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