´
J. D. Badjic and S. Rieth
ing isosteric 4–8. That is to say, the encapsulation of 4–8 by
basket 1 occurred at more similar rates than by baskets 2
and 3. The greater gate activity is therefore associated with
greater encapsulation selectivity and vice versa. The binding
of isosteric 4–8 to basket 1 (R=CF3) is furthermore slowed
down when compared to basket 3 (R=CH3, Figure 1). A
trend whereby a host with more dynamic gates also ex-
changes guests at a faster rate ought to be reasoned from
the standpoint of the gate dynamics.[10] Namely, the aromatic
gates revolving at a slower rate, that is, 1, would spend
longer time in the “closed” position, hence more effectively
restricting the access to the hostꢂs inner space.
To further inspect the relationship between the entrap-
ment selectivity and the basketꢂs gate dynamics, we scruti-
nised the rates describing the entrance/departure of guests
9–11 (Figure 2B). Comparatively smaller 9 (93 ꢀ3) was
found to enter/exit 1–3 at rates greater than expected from
the linear relationship established for 4–8 (106–107 ꢀ3,
Figure 3). The entrance/departure of bigger tetramethylsi-
lane (10) would, however, take place at slower rates.[14] At
this point, we reasoned that the magnitude of the deviation
of the exchange rate of 9–11 from the established linear re-
lationship for 4–8 (described with the equation DG°
=
in/out
1DG8+d) would suggest the selectivity by which the basket
operates. In other words, a gated basket incapable of effec-
tively discriminating guests on the basis of the size/shape
would solely promote their in/out exchange on the basis of
the encapsulation potential DG8, and closely abiding to the
established LFER.
To quantitatively ascertain the distribution of the encap-
sulation rates for 9–11, we first computed 90% confidence
band (SigmaPlot) for each of the fitted regression lines per-
taining to 4–8 entering/departing 1–3 (Figure 3).[13] This par-
ticular statistical method is useful for revealing the distribu-
tion of data having 90% certainty with reference to the ex-
perimental values. Accordingly, the activation energies
Figure 3. The activation energies for the entrapment (DG°in) and the de-
parture (DG°out) of isosteric guests 4–8 (black circles) abide to a linear
free energy relationship described with the equation DG°in/out =1DG8+d.
Note that the experimental data were fit to a linear function correspond-
ing to A) basket 1 (Ri2n =0.69; Ro2ut =1.00), B) basket 2 (R2in =0.93; R2out
=
0.99) and C) basket 3 (R2in =0.94; Ro2ut =0.99). The kinetic data for the ex-
change of 9–11 are shown in blue. The computed 90% confidence bands
(SigmaPlot) of the linear regression lines are also shown in blue.
DG°
of 9–11 entering/exiting the less dynamic basket 1
in/out
appeared more within the band when compared to those re-
garding baskets 2 and 3 (Figure 3); the rates for 1,1-dibro-
mo-1-chloroethane (11) were, for all three baskets, posi-
tioned quite close to the fitted lines, which is likely due to
the very small difference in volume between this (102 ꢀ3)
and the guests from the isosteric series (106–107 ꢀ3). Fur-
thermore, we determined the difference (DDG°in/out) be-
tween the experimental activation energy, DG°in/out, for the
entrance/departure of 9/10 and the corresponding hypotheti-
cal guests having identical DG8 while abiding to the free
energy relationship DG°in/out =1DG8+d (Table 3). In particu-
lar, one notes an increasingly larger jDDG°in/out j values and,
therefore, greater deviations for non-spherical guest 9 going
from the less dynamic 1 to the more dynamic 3 (Table 3).
The spherical tetramethylsilane (10, akin to 4–8), however,
was to a much smaller degree (if any) discriminated by bas-
kets 1–3. Nonetheless, the experimental observations still in-
dicate a feasible correlation between the dynamics of the
gates and the basketꢂs kinetic selectivity such that more dy-
namic gates afford greater entrapment selectivity.
function of the binding energies (DG8). We reason that the
slope (1) of the fitted lines depicts the susceptibility by
which DG°
responds to the changes in DG8, therefore
in/out
reporting on the nature of the encapsulationꢂs transition
state; thus, a small slope 1in would concur with an early tran-
sition state. Second, the intercept (d) describes the energy
required for the entry/departure of a hypothetical guest
having the same size/shape as 4–8 but no binding affinity
(DG8=0). For each host, the two DG°in/out/DG8 regression
lines converge at d, whose value increased with slower gate
dynamics (Figure 3).
Interestingly, baskets 2 and 3, having more dynamic gates
(R=CH3 and Ph), exhibited similar 1 values of roughly
1in =0.25 for the ingress and 1out =ꢀ0.76 for the egress of 4–
8 (Table 1). Basket 1, however, with slower revolving gates
(R=CF3) showed distinctively different values: 1in =0.08
and 1out =ꢀ0.93. Evidently, host 1 with gates revolving at
the slowest rate had also the lowest capacity for distinguish-
2564
ꢃ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2011, 17, 2562 – 2565