A. Dieckmann et al.
between variables, possibly limiting the degree of accuracy
with which they can be determined. We have also construct-
ed other kinetic models by changing and reducing the
number of parameters directly involved in the auto- and
cross-catalytic pathways to probe different mechanisms lead-
ing to the observed diastereoselectivity, but they yield less
accurate or even unphysical results. The same is true if the
assignment of NX and XX is interchanged.
pared and pipetted into the NMR tube (ratio 1:1) just before starting the
measurement. Samples were equilibrated with respect to temperature for
6
–8 min inside the spectrometer after mixing, which is sufficient accord-
ing to information from Bruker. A spectrum with 32 scans was recorded
every 10 min. Addition of benzoic acid was done by dissolving the appro-
priate amount in CDCl and using this solution to prepare the stock solu-
3
tions of both precursors. In case of an initial addition of reaction prod-
ucts, these were taken from an identical and completed reaction, since
the products could not be dissolved again after isolation. Adding more
than 10% of pre-formed product resulted in precipitation of products at
early reaction times. Owing to poor solubility, separation of the isomers
by chromatography has not yet been achieved. ROESY spectra were
measured in CDCl
DRX 600, TXI-probehead, Topspin 1.3). Parameters were set as follows:
3
at (293ꢁ0.1) K at atmospheric pressure (Bruker
Conclusion
4
0
K data points per increment (256 increments), 48 scans, 4 dummy scans,
.1221 s acquisition time, 2.5 s relaxation delay, 5630 Hz spectral width,
We have presented a new diastereoseletive self-replicating
system based on a fulvene Diels–Alder reaction in which
two diastereomeric templates compete for common resour-
ces. The kinetics of the reaction was measured by time-re-
solved 1D NMR spectroscopy supported by ab initio chemi-
cal shifts. Different diastereomers were identified by
ROESY. Whereas in the absence of catalysis there is only a
slight diastereoselectivity of 3:2, this changes to 1:16 when
replication is enabled. We used AIMD simulations to calcu-
late free-energy profiles and dissociation potentials explain-
ing the observed behaviour: one template acts as a selfish
autocatalyst, the other as an altruistic cross-catalyst leading
to an intrinsic asymmetry. As a consequence, the autocata-
lyst dominates the system leading to the observed change in
diastereoselectivity. Based on the obtained data, we were
able to construct a kinetic model and derive rate and equi-
librium constants, which are in agreement with results from
our ab initio calculations.
The design of complex chemical reaction networks relies
heavily on understanding these systems at a very detailed
and fundamental level. However, there will be more and
more cases in which the delicate relationship between struc-
ture and physicochemical behaviour cannot be analysed by
either experiment or theory alone. The field of systems
chemistry will have to rely on an intelligent interplay of
both; this will lead to a more complete picture of dynamic
phenomena in chemistry. We believe that our method of
combining 1D and 2D NMR spectroscopic techniques sup-
ported by calculated shifts with AIMD simulations is a step
in this direction. Although experimental obstacles, namely,
the insolubility of products, prevented us from conducting
important measurements, we were able to unravel the un-
derlying reaction network and to rationalise the observed
change in diastereoselectivity. The two-pronged strategy em-
ployed herein has the potential to lead to insights at an un-
precedented level not only for other self-replicating systems
but for complex chemical networks in general.
200 ms ROESY spin-lock pulse.
The extraction of kinetic data from 1D NMR spectra was performed by
using 1D-WINNMR (Bruker Daltonik GmbH, Germany) and custom
python scripts to facilitate the manipulation of large data sets. Kinetic
[
75]
simulation and fitting of the data was performed by using Simfit.
Computational Details
General setup of constrained ab initio MD simulations: All calculations
[
76]
were carried out with the CPMD package and set up as follows: The
optimised structure was centred in a periodically repeating orthorhombic
box of an appropriate size ensuring at least a distance of 3 ꢄ between
the molecule and box boundaries. The respective reaction centres were
prearranged with a value of D=3.6 ꢄ. The system was equilibrated to an
average temperature of 300 K with a standard deviation in the order of
[
77,78]
10% by using a Nose–Hoover chain thermostat on the ions.
The cou-
pled equations of motion for nuclei and molecular orbitals were solved
by using the velocity Verlet algorithm with a timestep of 4 a.u. A ficti-
tious mass of 400 a.u was assigned to the electronic degrees of freedom.
Core electrons were treated by using Vanderbilt pseudopotentials; va-
lence orbitals were expanded in a plane wave basis with an energy cutoff
of 25 Ry. The PBE functional was used for all calculations. For each
value of D, the length of production runs was determined by the conver-
gence of the constraint force (typically 2–5 ps). After changing the value
of D the system was repeatedly quenched to the Born–Oppenheimer sur-
face. Errors for the free-energy profiles were calculated by measuring the
fluctuations of the mean constraint force over the last 0.5 ps. The mini-
mum, maximum and average forces for each value of D were integrated
to yield free energies and the respective errors. MEPs were calculated by
optimising the geometry of a snapshot randomly taken from the corre-
sponding MD run.
Calculation of thermally averaged shieldings: Thermally averaged, room-
temperature magnetic shieldings were calculated for the individual mole-
cules and selected hydrogen-bonded complexes, as well as the CDCl sol-
3
vent, at the B3LYP/6-311G* level by using the Gaussian 03 package by
[
79]
averaging over 20 AIMD snapshots for [NN·NX], 114 snapshots for XX,
and 84 snapshots for CDCl
case of [NN·NX] and XX, and by 0.5 ps in the case of CDCl
to the experimental procedure, the chemical shifts were first calculated
with respect to CDCl . To obtain the final tetramethylsilane (TMS)-
based values, a further 7.26 ppm were subtracted. The AIMD simulations
were performed by using the same computational parameters as for the
constrained AIMD runs detailed in the previous section. The standard
deviation in temperature was 25 K and 32 K for [NN·NX] and XX, re-
3
. The snapshots were separated by 1 ps in the
3
. In analogy
3
3
spectively, and 125 K for CDCl .
Experimental Section
All 1D NMR spectroscopy measurements were carried out on a Bruker
DRX 600 spectrometer (600 MHz) at 15 mm concentration of the precur-
sors in CDCl
3
(at (293ꢁ0.1) K and atmospheric pressure). For kinetic
measurements, stock solutions (ꢄ30 mm) of each substance were pre-
478
ꢀ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2011, 17, 468 – 480