SUPPORTING INFORMATION
Kinetic analysis of the racemization process
Circular dichroism was used to follow the racemisation process in time, since
racemisation results in a decrease of the CD-intensity.
The activation energy, Ea, and the pre-exponential factor A:
The racemization of assembly (P)-13•(BuCYA)6 was measured at 70, 60, 50 and 40 C,
respectively. For each temperature the rate constant, kobs, was obtained by fitting the data
to the following model using Micromath Scientist for Windows 2.01 (Table 1):
kobs
(P)-13•(BuCYA)6
kobs
(M)-13•(BuCYA)6
Table 1 Rate constant kobs (with error Δkobs) as a function of temperature.
T(K)
kobs (s-1)
Δkobs (s-1)
343
6.70x10-4
3.04x10-6
333
2.06x10-4
7.52x10-7
-5
323
8.23x10
4.55x10-7
313
1.75x10-5
3.19x10-7
Analysis of these data using the Arrhenius-equation resulted in values for Eact and A of
105.9 kJ.mol-1 and 9.07006E+12, respectively (figure 1).
-6
y = -12736x + 29.836
ln k
-7
-8
-9
- 10
- 11
- 12
0.0029
0.0030
0.0031
0.0032
-1
1/T (K )
Figure 1 Plot of ln kobs vs T-1
The half-life time, t1/2, is defined as the time required for a 50% decrease in enantiomeric
excess ([(P)-13•(BuCYA)6]t=0.75 [(P)-13•(BuCYA)6]0) and can be calculated from
ln( 2)
t1/ 2 
2k obs
Determination of the order in (P)-13•(BuCYA)6 and (S)-BAR
The racemisation rate of (P)-13•(BuCYA)6 was measured as a function of the initial
concentration of (P)-13•(BuCYA)6 at 50 C. The order, n, in the (P)-13•(BuCYA)6 was
determined with
d ([( P ) - 13(BuCYA) 6]
 k obs [( P ) - 13(BuCYA) 6]0n
dt
Data were fitted using the Scientist model and the logarithm of the calculated initial rate,
ln Rt=0, was plotted as a function of ln [(P)-13•(BuCYA)6]0 giving a straight line
(R2=0.99) with slope n=1.8 (Figure 2).
Rt 0  
-8.5
-8
-7.5
-7
-15
-6 -15.5-5.5
-6.5
-7.8
-7.6
-7.4
-16
-7.2
-7
-6.8
-16
-6.6
-6.4
-16.5
y = 1.7512x - 4.7776
-16.5
y = 1.8182x - 3.9242
-17
2
R = 0.9999
-17.5
-17
R2 = 0.9932
-17.5
-18
-18
-18.5
-19
-18.5
Figure 2 Duplo measurements (x-axis: ln[(P)-13•(BuCYA)6]0 ; y-axis: ln Rt=0)
An order of 1.8 in the assembly concentration at first was puzzling, until we started to
examine the role of the other species present, i.e. BuCYA and (S)-BAR. Although
BuCYA quantitatively replaces (S)-BAR no free BuCYA excess is present in the
solution, because of the low solubility of BuCYA in benzene. This is confirmed by 1H
NMR spectroscopy, which does not show any signals for free BuCYA. Consequently,
free BuCYA can not play a role in the racemisation mechanism. The expelled (S)-BAR,
however, is soluble in benzene at these concentrations and signals for the free (S)-BAR
are clearly observed in the 1H NMR spectrum. In order to determine if the presence of
(S)-BAR affects the racemisation rate, we studied the racemisation of [(P)-13•(BuCYA)6]
at a constant concentration in the presence of different amounts of (S)-BAR. Similar
treatment of the data as before (Scientist-fit and a plot of ln Rt=0 vs ln [(S)-BAR]0)
resulted in an order 0.9 (Figure 3).
-5.2
-5
-4.8
y = 0.7996x - 12.653
2
R = 0.9814
-4.6
-4.4
-16.1
-16.2-4.2
-5.2
-5
-4.8
-16.3
y = 0.9596x - 11.86
-16.4
R2 = 0.9896
-16.5
-16.6
-16.7
-16.8
Figure 3 Duplo measurements (x-axis: ln[(S)-BAR] ; y-axis: ln Rt=0)
-4.6
-4.4
-15.9
-16-4.2
-16.1
-16.2
-16.3
-16.4
-16.5
-16.6
-16.7
-16.8
-16.9
Based on these results we propose a new model to describe the racemisation pathway.
kuncat
(P)-13•(BuCYA)6
kuncat
(M)-13•(BuCYA)6
(P)-13•(BuCYA)6 + (S)-BAR
kcat
kcat
(M)-13•(BuCYA)6 + (S)-BAR
Racemisation can occur both via an uncatalyzed and a catalyzed pathway, in which (S)BAR acts as a catalyst. Both pathways are first order in (P)-13•(BuCYA)6. The
uncatalyzed pathway cannot be studied independently as a result of the preparation
method. Assembly (P)-13•(BuCYA)6 is prepared by exchanging (S)-BAR for BuCYA in
assembly (P)-13•((S)-BAR)6. When the initial concentration (P)-13•((S)-BAR)6 is
increased, more (S)-BAR is expelled, which accelerates racemisation. The racemisation
rate can be written as:
Rt 0  k cat [( S )  BAR ][( P ) - 13(BuCYA) 6]0  k uncat [( P) - 13(BuCYA) 6]0
 (k cat [( S )  BAR ]  k uncat )[( P) - 13(BuCYA) 6]0
The rate constants kcat and kuncat can be determined by plotting kobs vs [(S)-BAR] for both
the concentration dependent CD-studies discussed above. This results in averaged values
of 7.4x10-3 l mol-1 s-1 and 1.1x10-5 s-1 for kcat and kuncat, respectively.
The nature of our experiments do not permit to determine kuncat, independently, since (S)BAR can not be removed after the exchange process. However, 1H NMR spectroscopy
was used to study the exchange of calix[4]arene dimelamines in the absence of (S)-BAR
and to determine the rate constant for this process. Assemblies 13•(BuCYA)6 and
23•(BuCYA)6 (see manuscript) were mixed in a 1:1 ratio at different initial concentrations
in benzene-d6. 1H NMR spectra were recorded at regular time intervals at 70 C. Due to
exchange of dimelamines 1 and 2, new heteromeric assemblies 1221•(BuCYA)6 and
1122•(BuCYA)6 are formed. The concentration of both homomeric and heteromeric
assemblies can be measured since well-seperated NMR signals can be found for all
species. The resulting curves are fitted in the following way. Assemblies 13•(BuCYA)6
and 23•(BuCYA)6 are regarded as one species (homomer) and assemblies 1221•(BuCYA)6
and 1122•(BuCYA)6 as well (heteromer). These are in equilibrium via
3 kobs
homomer
kobs
heteromer
and thus
Rt 0  
d ([homomer]
 3k obs [hom omer] 0n
dt
The factor 3 is present to account for the statistical preference for the heteromeric
assemblies (1:3). The dissociation is first order (1.1) in 13•(BuCYA)6 (Figure 4).
A value for kobs of 7.04x10-5 s-1 is found. This value perfectly agrees with the value for
kuncat found for the racemization mechanism. (The slightly higher value for kobs is caused
by the higher temperature during the 1H NMR experiment (70 vs 50 C).
-7.2
-7
-6.8
-6.6
-6.4
-15.4
-6.2 -15.6 -6
-15.8
y = 1.1421x - 8.4623
2
R = 0.9929
-16
-16.2
-16.4
-16.6
-16.8
Figure 4 1H NMR exchange experiment (x-axis: ln[homomers] ; y-axis: ln Rt=0)
In a similar manner the rate of exchange was measured at constant initial concentrations
of 13•(BuCYA)6 and 23•(BuCYA)6 in the presence of different amounts of (S)-BAR.
Again kobs was determined and plotted as a function of (S)-BAR. From this it can be
concluded that (S)-BAR accelerates exchange of dimelamines in a similar manner as
racemisation (kcat = 14.7x10-3 l mol-1 s-1).
1.20E-04
1.00E-04y = 1.470E-02x + 4.267E-05
8.00E-05
R2 = 9.769E-01
6.00E-05
4.00E-05
2.00E-05
0.00E+00
0.00E+ 1.00E00
03
2.00E- 3.00E03
03
4.00E- 5.00E03
03
Figure 5 1H NMR exchange experiment (x-axis: [(S)-BAR] ; y-axis: kobs)