On the mechanism of action of gated molecular baskets: The synchronicity of the revolving motion of gates and in/out trafficking of guests

Article abstract of DOI:10.3762/bjoc.8.9

We used dynamic ¹H NMR spectroscopic methods to examine the kinetics and thermodynamics of CH₃CCl₃ (2) entering and leaving the gated molecular basket 1. We found that the encapsulation is first-order in basket 1 and guest 2, while the decomplexation is zeroth-order in the guest. Importantly, the interchange mechanism in which a molecule of CH₃CCl₃ directly displaces the entrapped CH ₃CCl₃ was not observed. Furthermore, the examination of the additivity of free energies characterizing the encapsulation process led to us to deduce that the revolving motion of the gates and in/out trafficking of guests is synchronized, yet still a function of the affinity of the guest for occupying the basket: Specifically, the greater the affinity of the guest for occupying the basket, the less effective the gates are in "sweeping" the guest as the gates undergo their revolving motion.

Full text of DOI:10.3762/bjoc.8.9

On the mechanism of action of gated molecular
baskets: The synchronicity of the revolving motion
of gates and in/out trafficking of guests
Keith Hermann, Stephen Rieth, Hashem A. Taha, Bao-Yu Wang,
Christopher M. Hadad and Jovica D. Badjić*
Full Research Paper
Open Access
Address:
Beilstein J. Org. Chem. 2012, 8, 90–99.
Department of Chemistry, The Ohio State University, 100 West 18th
Avenue, Columbus OH, 43210, USA
doi:10.3762/bjoc.8.9
Received: 14 October 2011
Accepted: 13 December 2011
Published: 16 January 2012
Email:
Jovica D. Badjić* - badjic@chemistry.ohio-state.edu
* Corresponding author
This article is part of the Thematic Series "Supramolecular chemistry II".
Guest Editor: C. A. Schalley
Keywords:
dynamic NMR; host–guest chemistry; linear free-energy relationships;
molecular encapsulation; recognition kinetics
© 2012 Hermann et al; licensee Beilstein-Institut.
License and terms: see end of document.
Abstract
We used dynamic 1H NMR spectroscopic methods to examine the kinetics and thermodynamics of CH3CCl3 (2) entering and
leaving the gated molecular basket 1. We found that the encapsulation is first-order in basket 1 and guest 2, while the decomplexa-
tion is zeroth-order in the guest. Importantly, the interchange mechanism in which a molecule of CH3CCl3 directly displaces the
entrapped CH3CCl3 was not observed. Furthermore, the examination of the additivity of free energies characterizing the encapsula-
tion process led to us to deduce that the revolving motion of the gates and in/out trafficking of guests is synchronized, yet still a
function of the affinity of the guest for occupying the basket: Specifically, the greater the affinity of the guest for occupying the
basket, the less effective the gates are in “sweeping” the guest as the gates undergo their revolving motion.
Introduction
Covalent and self-assembled molecules with a natural cavity, to create an opening that is large enough for a guest to
i.e., molecular capsules [1,2], employ several mechanisms to “squeeze” its way in or out of the host. In the case of self-
trap and release guests capable of residing in their inner space assembled hosts, however, the slippage, gating and possible
[3-5]. The so-called “slippage” scenario [6], in which a guest partial or full disassembly of the capsule constitute mechanistic
makes its way to and from the host by forcing the expansion of alternatives for the exchange of guests [4]. In the last decade,
its aperture [7], appears frequently. The “gating” scenario [8], we [9-14] and others [7,8,15-18] have studied gated molecular
on the other hand, includes a conformational change in the host encapsulation in artificial and natural systems [19].
90

Beilstein J. Org. Chem. 2012, 8, 90–99.
In particular, we designed gated molecular baskets (Figure 1) CH3CCl3 directly displaces another CH3CCl3 residing in the
and employed both experimental and theoretical methods to interior of the gated basket.
gain an understanding of their mechanism of action [4]. These
Results and Discussion
dynamic hosts comprise a semirigid platform with three
The encapsulation stoichiometry and the
intrinsic binding (ΔG°)
aromatic gates appended to its rim through CH2 “hinges”
(Figure 1). The gates were set to interact by hydrogen bonding
to control the opening and closing of the basket and thereby the
rate by which a guest enters or departs the cavity of the basket
[12-14]. Indeed, the action mechanism of the basket has been
addressed [14], yet the exact role of the gates in the process of
the in/out guest exchange necessitates additional scrutiny. In
particular, a careful inspection of the additivity of free energies
[21] pertaining to the constrictive ΔG‡in/out and intrinsic ΔG°
binding energies of the guests [11] as well as the racemization
of the basket ΔG‡rac (i.e., opening and closing, see below in
Figure 6) reveals a systematic disparity (ΔG° + ΔG‡rac +
ΔG‡sterics ≠ ΔG‡out, see below in Figure 7). In order to address
this conundrum, we have employed methods of experimental
In an earlier study [13], we reported on the tendency of basket 1
to trap CH3CCl3 (2) as a guest, and we hereby elaborate on the
equilibrium thermodynamics of the recognition event
(Figure 2). The incremental addition of 2 to a CD2Cl2 solution
of 1 (0.67 mM, 298.0 K) caused considerable 1H NMR chem-
ical shifts of the resonances corresponding to the presence of
the basket (Figure 2). At 298.0 K, the formation and degrad-
ation of [basket–CH3CCl3] complex was sufficiently fast on the
“NMR time scale”: The nonlinear least-squares fitting of the
binding isotherm to a 1:1 binding model provided Ka = 54 ± 1
M−1 (R2 = 0.998, Figure 2) [23].
(dynamic NMR) and computational chemistry (steered molec- Indeed, the results of a variable temperature 1H NMR study
ular dynamics, SMD) to inspect the relationship between the (400 MHz, CD2Cl2) of 1 (0.67 mM) containing CH3CCl3 (2)
gates revolving at the rim of the host and the in/out exchange of (1.07 mM) was in line with the formation of the 1:1 complex;
guests. The results of our study suggest that for guests with a note that extrapolation of the fitted line gives Ka of 86 ± 16 M−1
greater propensity to occupy the interior of the basket (i.e., at 298.0 K, which is akin to the value obtained in the titration
more negative ΔG°) the process of gating is poorly synchro- experiment. Furthermore, the van't Hoff analysis of the 1H
nized with the guest exchange. The gates undergo a revolving NMR data revealed that the encapsulation is also driven by
motion to sweep the space but are concurrently less effective in enthalpy (ΔH° = −3.56 ± 0.06 kcal/mol, Figure 2). Indeed, the
enforcing the ejection of the guest from the cavity. Moreover, computed electrostatic potential surface (AM1, Spartan) [20] of
the results of dynamic 1H NMR measurements of CH3CCl3 (2) guest 2 is complementary to the one corresponding to the
entering and departing basket 1 (Figure 1) suggest the absence concave interior of 1 (Figure 1). Furthermore, compound 2 (93
of an interchange mechanism [22] in which a molecule of Å3, Spartan) occupies 42% of the inner space of 1 (221 ± 9 Å3)
Figure 1: Chemical structure of gated molecular basket 1 and 1,1,1-trichloroethane (2). Electrostatic potential surfaces of basket 1 and guest 2 were
computed with Spartan (AM1) [20].
91

Beilstein J. Org. Chem. 2012, 8, 90–99.
Figure 2: (Left): 1H NMR spectra (400 MHZ, CD2Cl2) of 1 (0.67 mM) obtained upon incremental addition of 1,1,1-trichloroethane (2) (0.00–0.65 M) at
298.0 K. (Middle): Nonlinear least-squares fitting (SigmaPlot) of the N–H chemical shift of 1 as a function of the concentration of 2 gave Ka = 54 ± 1
M−1 at 298.0 K [23]. (Right): The van't Hoff plot was generated from variable temperature 1H NMR measurements (400 MHz, 180–250 K) of 1 (0.67
mM) containing CH3CCl3 (1.07 mM).
[11], which is close to the packing coefficient of liquids and (250.0 ± 0.1 K) allowed us to extract (MNova software) the
thereby a good indicator of a stable assembly [24].
magnetization rate coefficients k*in and k*out (Figure 3).
The rate law characterizing guest exchange
and the constrictive binding (ΔG‡in/out)
At higher concentrations of CH3CCl3 with respect to host 1,
however, we noticed an intense T1 noise coinciding with the
We performed 1H,1H-EXSY [25] and selective inversion- [CH3CCl3]out signal, thus preventing the accurate determin-
transfer [26,27] NMR measurements (400 MHz, CD2Cl2) to ation of the volume of the corresponding cross peak. Accord-
examine the rate laws characterizing the trafficking of CH3CCl3 ingly, we had to turn to selective inversion-transfer NMR
(2) to and from basket 1. At concentrations of CH3CCl3 as a measurements to obtain the values of k*in and k*out. The
guest comparable to those of host 1, the EXSY measurements exchange rate constants k*in and k*out (characterizing the longi-
Figure 3: Chemically equivalent CH3 protons (black) in 1,1,1-trichloroethane (2) alter their magnetic environment from 2.70 ppm in bulk solvent to
−2.45 ppm inside the basket.
92

Beilstein J. Org. Chem. 2012, 8, 90–99.
tudinal magnetization of the hydrogen nuclei in CH3CCl3 tion of CH3CCl3. At higher concentrations of CH3CCl3,
altering the chemical/magnetic environment) are by the nature however, there should be a negligible variation in the concentra-
of the experiment pseudo-first-order in character (see below) tion of basket–CH3CCl3 and the magnetization rate coefficient
[25,26].
k*in becomes inversely proportional to the concentration of
CH3CCl3.
On the basis of the reaction stoichiometry (Figure 2), we
initially made the assumption that the entrapment is first-order
in both [basket] and [CH3CCl3]. Accordingly, the rate of the
forward reaction is given as:
(1)
As per the earlier discussion, the pseudo-first-order constant
k*in describes the longitudinal magnetization of the hydrogen
nuclei in CH3CCl3 transferring from the bulk solvent (δ = 2.70
ppm, Figure 3) to the interior of 1 (δ = −2.45 ppm, Figure 3).
Correspondingly, the rate of the forward reaction (entrapment)
can be formulated as:
Figure 4: Nonlinear least-squares fitting (SigmaPlot) of magnetization
rate constants k*in (2-D EXSY, 250.0 ± 0.1 K) as a function of the
concentration of the free basket to a linear function gives a slope of kin
= 2.1 ± 0.3 × 103 M−1·s−1.
(2)
From Equation 1 and Equation 2, we furthermore derive:
In accordance with this theoretical model, we completed a
series of selective inversion-transfer [27] NMR measurements
of 1 (1.65 mM) and CH3CCl3 (16–200 mM) in CD2Cl2 at 250.0
± 0.1 K (Figure 5). In the experiment, the proton resonance
corresponding to [CH3CCl3]out was selectively inverted,
resulting in the perturbation of the longitudinal relaxation of
(3)
If the proposed model is valid, then the experimentally deter- both [CH3CCl3]out and [CH3CCl3]in due to chemical exchange
mined k*in will be linearly proportional to the concentration of over the course of variable delay time τ (180° x (selective) – τ –
free basket 1. Indeed, when the value of k*in is plotted against 90° x (nonselective) – τd). Upon the integration of both signals
the concentration of free basket 1, there is an apparent linear (Iin and Iout), we subjected the data to nonlinear least-squares
dependence, with the slope of the fitted curve kin = 2.1 ± 0.3 × fitting of Iin/out versus τ using the proposed solutions of the
103 M−1·s−1 (at 250 ± 0.1 K, Figure 4). Using Equation 4, we McConnell equations [27] describing the relaxation of the
derive Equation 5, which upon insertion into Equation 3 gives hydrogen nucleus residing in two environments (Figure 5A).
Equation 6:
For the fitting, the longitudinal relaxation rate (1/T1) of
hydrogen nuclei in CH3CCl3 was determined separately by
using a classical selective inversion-recovery NMR pulse
sequence. When the experimental k*in was plotted against the
equilibrium concentration of CH3CCl3, there indeed appeared a
hyperbolic dependence (Figure 5B) in agreement with
(4)
(5)
(6)
Equation 6 (k*in
1/[CH3CCl3]). The fitting of the data to
Equation 6 was inaccurate as only a few experimental points
characterize the dependence (Figure 5B), although computing
kin from each data point would give a value of this coefficient
(~2 × 103 M−1·s−1) similar to that determined in the EXSY
This particular dependence suggests that k*in should be directly experiment (Figure 4). In accordance with the 2-D EXSY and
proportional to the concentration of the host–guest complex, selective inversion-transfer results, we conclude that the entrap-
[basket–CH3CCl3], but inversely proportional to the concentra- ment is first-order in both basket 1 and guest 2.
93

Beilstein J. Org. Chem. 2012, 8, 90–99.
Figure 5: (A): Nonlinear least-squares fitting of 1H NMR signal intensities (Iin/out) of [CH3CCl3]in/out as function of the time variable τ (250.0 ± 0.1 K)
was completed with the assistance of the Bloch–McConnell equations [27,28] describing the relaxation of hydrogen nuclei in two different environ-
ments; in this particular experiment [basket]0 = 1.65 mM and [CH3CCl3]0 = 50.0 mM. Magnetization transfer rate coefficients k*in (B) and k*out (C)
were further obtained [27,28] from selective inversion-transfer measurements and plotted as a function of the concentration of free CH3CCl3.
On the basis of the reaction stoichiometry (Figure 2), the rate NMR pulse sequence. Markedly, there was essentially no inter-
law for 2 leaving the encapsulation complex can be described dependence between k*out (21 ± 3 s−1) and the concentration of
as:
guest 2 (Figure 5C); the curve indeed shows a small slope, but
the intercept of 18.1 suggests that this is likely an artifact. 2-D
EXSY measurements would give a rate coefficient k*out = 10 ±
0.1 s−1, which was also found to be independent of the external
concentration of the basket/guest (Figure 4). The departure of
(7)
Alternatively, the rate of the same process expressed through CH3CCl3 from its complexed form [basket–CH3CCl3], there-
the NMR magnetization transfer rate coefficient k*out is:
fore, follows a dissociative mechanism [4]. Notably, a mole-
cule of solvent CD2Cl2 and not another CH3CCl3 (interchange
mechanism) displaces the encapsulated guest. In fact, the
inspection of CPK models as well as molecular dynamics
studies (see below) revealed that the departure of CH3CCl3 (93
(8)
As in the case above, the manipulation of Equation 7 and Equa- Å3) demands (a) “opening” of at least two gates, (b) disruption
tion 8 gives Equation 9:
of internal N–H…N hydrogen bonds, and (c) distortion of the
framework of the basket. We further reason that in the case of a
direct exchange of two CH3CCl3 molecules, the departure of
CH3CCl3 would create an empty host, and therefore vacuum,
(9)
In accordance with this theoretical model, we increased the before another guest of the same kind can take its place. Note
concentration of guest 2 (16–200 mM) with respect to 1 (1.65 that two large compounds (overall ~186 Å3) cannot simultane-
mM) and measured k*out using the selective inversion-transfer ously occupy the interior of 1 (~220 Å3).
94

Beilstein J. Org. Chem. 2012, 8, 90–99.
Computational examination of the in/out traf-
ficking
displacing the entrapped CH3CCl3, as suggested by the kinetic
study. The substitution of the guest by the solvent should
To gain mechanistic insight into the departure of CH3CCl3 (2) perhaps cause an even greater distortion of the framework of the
from the interior of basket 1, we completed a series of steered basket.
molecular dynamics (SMD) simulations using the AMBER 10.0
The revolving of the gates and the racemiza-
suite of programs [29-32]. Without applying any external force
on the entrapped CH3CCl3, we first found that this guest would, tion of basket 1
within 10 ns, adopt many positions inside host 1, although the The aromatic gates in basket 1 interact through hydrogen
one depicted in Figure 6A is obtained after 1 ns (Supporting bonding, as exemplified by a large downfield shift of the signal
Information File 1). The N–H…N hydrogen bond contacts along corresponding to (O=C)N−H protons (δ = 11.6 ppm at 298.0 K,
the top of the basket were also monitored throughout the 10 ns Figure 2) [13]. In addition, the aromatic gates are dynamic, each
simulation. Importantly, the distance between each pair of one revolving about its axis to give rise to two enantiomeric
amide-hydrogen and pyridine-nitrogen atoms was found to be conformers 1A and 1B (Figure 7A). The interconversion kinetics
invariant (~2 Å, see Supporting Information File 1).
of the 1A/B racemization can be followed by dynamic NMR
spectroscopy in which a singlet corresponding to Ha/Hb nuclei
In addition, the width of each side aperture (the span between at high temperatures is seen to split into two doublets at low
adjacent carbonyl oxygen atoms) also remained constant at temperatures. In particular, the revolving rate of the gates is
~6.3 Å throughout the simulation (Figure S3, see Supporting temperature dependent, thereby governing the lifetime of Ha or
Information File 1). We then selected multiple trajectories for Hb nuclei, each residing in a particular chemical environment (τ
“pulling” the guest from the host (Figure 6A). Markedly, the = 1/krac); the hydrogen nuclei are observed as separate reso-
departure of CH3CCl3 necessitated the cleavage of at least two nances when τ >> 1/Δν(Ha/b) [33]. Accordingly, we performed
intramolecular N–H…N hydrogen bonds in 1 (Figure 6B) with a the classical line-shape analysis of Ha/Hb resonances
simultaneous expansion of the host (Figure 6B). That is to say, (WinDNMR-Pro software) to obtain the rate constants (krac)
the “slippage” of CH3CCl3 (with gates in the “closed” position) and corresponding activation energies ΔG‡rac characterizing the
does not appear to be a viable mechanistic scenario. Note that racemization of basket 1 (Figure 7B). Evidently, the rate at
our simulation did not include solvent molecules (CD2Cl2) which the aromatic gates in 1 revolve is a function of the com-
Figure 6: (A) Four different trajectories were used for examining the departure of CH3CCl3 guest from basket 1 with steered molecular dynamics. (B)
The variation in N–H…N and –C=O…O=C– distances during SMD simulation with CH3CCl3 being pulled on the side.
95

Beilstein J. Org. Chem. 2012, 8, 90–99.
Figure 7: (A) The interconversion of conformational enantiomers 1A and 1B, having anticlockwise and clockwise senses in the orientation of the
intramolecular N–H…N hydrogen bonds, contributes to the process of racemization, i.e., the opening and closing of the basket [13]. (B) Eyring plots
describing the linear relationship between ln(krac/T) and temperature for basket 1 containing CH3CCl3 (black squares) and solvent CD2Cl2 (red trian-
gles). The plots were generated from the results of the line-shape analysis (WinDNMR-Pro) of 1H NMR Ha/b signals of 1 (1.65 mM, CD2Cl2) at vari-
able temperatures.
pound occupying the inner space: With CH3CCl3 the gates are the statistical correction to the measured krac to obtain krac′ (krac′
less dynamic than with CD2Cl2 occupying the cavity = 2krac = 616 s−1, Figure 7B) [34]. This particular rate coeffi-
(Figure 7B).
cient should more precisely describe the process of racemiza-
tion.
On the action mechanism of the basket
Is there a relationship between the aromatic gates sweeping the One could describe the free energy characterizing the guest
space and guests trafficking to and from the basket [11]? That is departure (ΔG‡out) as a linear combination of ΔG‡rac′ + ΔG° +
to say, will the gates expel the entrapped guest each time that ΔG‡sterics representing (1) the opening of the gates (ΔG‡rac′), (2)
they alter their propeller-like orientation (Figure 8)? First, our the decomplexation of the guest (ΔG°), and (3) the “slippage”
kinetic measurements suggest that guest CH3CCl3 (2) enters of the guest while exiting the open host (ΔG‡sterics)
basket 1 by substituting solvent (CD2Cl2) molecule(s), while [8,11,21,35]. The encapsulation kinetics is first-order in guest
exactly the opposite occurs during the dissociation (Figure 8). CH3CCl3 suggesting that this species creates van der Waals
Given this exchange scenario, we deduce that 1A–CH3CCl3 strain (friction) during the in/out trafficking, thereby justifying
shall transform into 1B–CH3CCl3 via intermediate 1–CD2Cl2 the use of the ΔG‡sterics term.
(Figure 8). That is, the formation of 1–CD2Cl2 from
1A–CH3CCl3 is accompanied by either reorientation or rein- In addition, the decomplexation of CH3CCl3 follows a late tran-
statement of the gates, and therefore, there is an equal likeli- sition state [14] whereby its affinity for populating the interior
hood that 1–CD2Cl2 will yield 1A–CH3CCl3 or 1B–CH3CCl3 of the basket should decrease to a somewhat smaller value than
(Figure 8); this reasoning is also supported by the fact that the described by ΔG°. Given the delicacy of the proposed parti-
gates of the solvated basket revolve at a higher rate (Figure 7B). tioning, will the additivity of free energies and the relationship
In accordance with such a racemization mechanism, we apply ΔG‡rac′ + ΔG° + ΔG‡sterics ~ ΔG‡out still hold?
96

Beilstein J. Org. Chem. 2012, 8, 90–99.
Figure 8: The departure of CH3CCl3 from 1A–CH3CCl3 gives rise to the less stable 1–CD2Cl2, which upon entrapment of another CH3CCl3 gives
either 1A–CH3CCl3 or 1B–CH3CCl3. The 1A/B–CH3CCl3 interconversion occurs with CH3CCl3 departing (BR1 mechanism) or remaining (BR2 mecha-
nism) in the cavity.
When ΔG‡rac′ of 11.4 ± 0.1 kcal/mol (at 250.0 ± 0.1 K, In one of our prior studies [13,14], we measured kinetic and
Figure 7) is added to the intrinsic binding energy of CH3CCl3 thermodynamic parameters pertaining to the exchange of five
(│ΔG°│ = 2.79 ± 0.09 kcal/mol at 250.0 ± 0.1 K, Figure 2), a isosteric (same-size) guests 3–7 to and from basket 1 (Figure 9).
value of 14.2 kcal/mol is obtained. Without even including When ΔG‡rac′ + ΔG° is computed for each guest and the values
ΔG‡sterics (as a positive number), there is an apparent disagree- plotted against ΔG‡out, a linear relationship appears (R2 = 0.99,
ment between the sum value (≥14.2 kcal/mol) and the experi- Figure 9A). Note that ΔG‡sterics is not included in this analysis
mentally determined ΔG‡out = 13.4 ± 0.1 kcal/mol (from 2-D as it is unknown; however, we anticipate that the value of the
EXSY, kout = 10 ± 1 s−1). Is there a missing factor needed in parameter should show minimal fluctuations for the series of
order to understand this phenomenon?
isosteric guests 3–7. Importantly, the greater the affinity of a
particular guest for occupying the interior of the basket (ΔG°),
the greater the deviation of the calculated ΔG‡rac′ + ΔG° (black
line, Figure 9A) from the experimental ΔG‡out (red line,
Figure 9A). The variation of ΔΔG = (ΔG‡rac′ + ΔG°) − ΔG‡out
with intrinsic binding energies ΔG° of 3–7 is shown in
Figure 9B. The trend is evident, supporting the notion that for
guests having greater propensity to occupy the basket (ΔG°) the
BR2 pathway is more greatly involved in the 1A–CH3CCl3/
1B–CH3CCl3 racemization. As already discussed, the BR2
pathway contributes to the measured ΔG‡rac′, yet it is not
involved in the exchange of guests.
In reality, when the internal hydrogen bonds are broken and the
gates open up the guest does not have to depart the basket
cavity. That is to say, the gates should be able to revolve to
allow the interconversion of 1A–CH3CCl3 into 1B–CH3CCl3
without even ejecting the guest. Accordingly, we hereby
propose that the conversion of 1A–CH3CCl3 into 1B–CH3CCl3
(i.e., racemization) occurs by two routes, BR1 and BR2, one
with (BR1) and another without (BR2) the concomitant guest
exchange (Figure 8).
It follows that, during the departure of CH3CCl3, the measured
racemization of 1 (ΔGrac′) includes energetic contributions from Conclusion
two pathways (ΔG‡rac′ = ΔG‡BR1 + ΔG‡BR2) of which only BR1 Describing mechanisms by which dynamic hosts entrap/release
should be incorporated in the additivity assessment. It is there- guests is a challenging task necessitating experimental and
fore convenient to partition the energetic contribution of the two computational scrutiny. Notably, one can use NMR spectro-
“competing” BR1 and BR2 routes to ΔG‡rac′ (ΔG‡rac′ = ΔG‡BR1 scopic methods for understanding the equilibrium kinetics char-
+ ΔG‡BR2) to corroborate fully the role of the gates. However, acterizing the rate law of molecular encapsulation processes.
this is a difficult task, but for guest molecules holding strongly Our study, accordingly, describes the rate law characterizing the
onto the basket (more negative ΔG°) there should be a greater encapsulation of guest CH3CCl3 by the gated basket 1. Impor-
contribution from the RG2 pathway during the racemization.
tantly, the entrapment reaction is first-order in each compound,
97

Beilstein J. Org. Chem. 2012, 8, 90–99.
Figure 9: (A): Kinetic and thermodynamic parameters [13,14] characterizing the departure of isosteric guests 3–7 from the basket. (B): The computed
ΔΔG = (ΔG‡rac′ + ΔG°) − ΔG‡out is apparently a linear function of ΔG‡out.
while the complex dissociation is zeroth-order in guest each mixing time τm, calculated by using the EXSYCalc
CH3CCl3. Furthermore, examination of the additivity of free program (Mestrelab Research). The mean values of k*in and
energies corresponding to different molecular events can assist k*out are reported with the standard deviation as an experi-
in the understanding of the operation of gated hosts and, in par- mental error.
ticular, can help to reveal the explicit role of the gates. On the
basis of these results, we deduced that the synchronicity in the Procedure for 1H-selective inversion-transfer experiments
revolving motion of the gates and in/out trafficking of guests is [27]: A solution of basket 1 and guest 2 in CD2Cl2 (J. Young
a function of the affinity of the guest for occupying the gated NMR tube) was cooled to 250.0 ± 0.1 K inside the NMR probe
basket. The greater the affinity, the less effective the gates are in and allowed to equilibrate for 1.0 h. The 1H spin–lattice relax-
“sweeping” the guest as the gates undergo their revolving ation time (T1 = 3.30 s) for the free guest was determined by a
motion. This result is important for exploring the utility of standard inversion-recovery pulse sequence with a relaxation
gating for controlling the outcome of chemical reactions occur- delay (τd) of at least 5 × T1. By using a selective 1-D inversion-
ring in confined space but also for the understanding of the recovery pulse sequence [180° x (selective) – τ – 90° x (nonse-
effective conversion of energy at the molecular level and the lective) – τd], 32 transients were obtained for each variable
preparation of molecular machines [36,37].
delay time (τ) with a relaxation delay (τd) of at least 5 × T1. The
absolute integrals corresponding to encapsulated and free guest
molecules were, at each mixing time, determined by using
Experimental
Procedure for 2-D EXSY experiments [25]: A solution of TopSpin software from Bruker, and the resulting data was fitted
basket 1 and guest 2 in CD2Cl2 (J. Young NMR tube) was by using the two-site exchange equations described by Led et
cooled to 250.0 ± 0.1 K inside the NMR probe and allowed to al. [27] to obtain magnetization exchange rate constants k*in
equilibrate for 1.0 h. A series of gradient NOESY experiments and k*out.
was run with a relaxation delay of 5 × T1 and mixing times (τm)
of 0 ms and three others ranging from 40 ms to 250 ms, such
Supporting Information
that the cross-peaks were clearly resolved; the spin–lattice
relaxation time (T1 = 3.30 s) for the free guest was determined
Supporting Information contains details of the
by performing a standard inversion-recovery pulse sequence
computational studies.
with a relaxation delay (τd) of at least 5 × T1. Each of
Supporting Information File 1
the 128 F1 increments represented the accumulation
of at least two scans. The corresponding integrals were deter-
mined by using MNova software from Mestrelab Research,
after phase and baseline corrections in both dimensions. The
magnetization exchange rate constants (k*in and k*out) were, at
Details of the computational studies.
[http://www.beilstein-journals.org/bjoc/content/
supplementary/1860-5397-8-9-S1.pdf]
98

Beilstein J. Org. Chem. 2012, 8, 90–99.
24.Mecozzi, S.; Rebek, J., Jr. Chem.–Eur. J. 1998, 4, 1016.
Acknowledgements
doi:10.1002/(SICI)1521-3765(19980615)4:6<1016::AID-CHEM1016>3.
0.CO;2-B
This work was financially supported with funds obtained from
the National Science Foundation under CHE-1012146 (to
J.D.B.). We thank the Ohio Supercomputer Center for generous
allocations of computational resources.
25.Perrin, C. L.; Dwyer, T. J. Chem. Rev. 1990, 90, 935.
doi:10.1021/cr00104a002
26.Lian, L. Y. In NMR of macromolecules : a practical approach;
Roberts, G. C. K., Ed.; IRL Press: Oxford, 1993; pp 153 ff.
27.Led, J. J.; Gesmar, H.; Abildgaard, F. Methods Enzymol. 1989, 176,
311. doi:10.1016/0076-6879(89)76017-1
References
1. Badjić, J. D.; Stojanović, S.; Ruan, Y. Adv. Phys. Org. Chem. 2011, 45,
28.Hansen, D. F.; Led, J. J. J. Magn. Reson. 2003, 163, 215.
doi:10.1016/S1090-7807(03)00062-4
1. doi:10.1016/B978-0-12-386047-7.00001-1
2. Hof, F.; Craig, S. L.; Nuckolls, C.; Rebek, J., Jr. Angew. Chem., Int. Ed.
2002, 41, 1488.
29.Duan, Y.; Wu, C.; Chowdhury, S.; Lee, M. C.; Xiong, G.; Zhang, W.;
Yang, R.; Cieplak, P.; Luo, R.; Lee, T.; Caldwell, J.; Wang, J.;
Kollman, P. J. Comput. Chem. 2003, 24, 1999. doi:10.1002/jcc.10349
30.Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A.
J. Comput. Chem. 2004, 25, 1157. doi:10.1002/jcc.20035
31.Isralewitz, B.; Gao, M.; Schulten, K. Curr. Opin. Struct. Biol. 2001, 11,
224. doi:10.1016/S0959-440X(00)00194-9
doi:10.1002/1521-3773(20020503)41:9<1488::AID-ANIE1488>3.0.CO;
2-G
3. Palmer, L. C.; Rebek, J., Jr. Org. Biomol. Chem. 2004, 2, 3051.
doi:10.1039/b412510j
4. Rieth, S.; Hermann, K.; Wang, B.-Y.; Badjić, J. D. Chem. Soc. Rev.
2011, 40, 1609. doi:10.1039/c005254j
32.Sotomayor, M.; Schulten, K. Science 2007, 316, 1144.
doi:10.1126/science.1137591
5. Pluth, M. D.; Raymond, K. N. Chem. Soc. Rev. 2007, 36, 161.
doi:10.1039/b603168b
33.Sandström, J. Dynamic NMR Spectroscopy; Academic Press: London,
1982.
6. Davis, A. V.; Raymond, K. N. J. Am. Chem. Soc. 2005, 127, 7912.
doi:10.1021/ja051037s
34.Bao, X.; Rieth, S.; Stojanović, S.; Hadad, C. M.; Badjić, J. D.
Angew. Chem., Int. Ed. 2010, 49, 4816. doi:10.1002/anie.201000656
35.Christensen, T.; Gooden, D. M.; Kung, J. E.; Toone, E. J.
J. Am. Chem. Soc. 2003, 125, 7357. doi:10.1021/ja021240c
36.Northrop, B. H.; Braunschweig, A. B.; Mendes, P. M.; Dichtel, R. W.;
Stoddart, J. F. Molecular Machines. In Handbook of Nanoscience,
Engineering, and Technology, 2nd ed.; Goddard, W. A.;
Brenner, D. W.; Lyshevski, S. E.; Iafrate, G. J., Eds.; CRC Press: Boca
Raton, 2007; 11-1–11-50.
7. Raymo, F. M.; Houk, K. N.; Stoddart, J. F. J. Am. Chem. Soc. 1998,
120, 9318. doi:10.1021/ja9806229
8. Houk, K. N.; Nakamura, K.; Sheu, C.; Keating, A. E. Science 1996,
273, 627. doi:10.1126/science.273.5275.627
9. Maslak, V.; Yan, Z.; Xia, S.; Gallucci, J.; Hadad, C. M.; Badjić, J. D.
J. Am. Chem. Soc. 2006, 128, 5887. doi:10.1021/ja060534l
10.Wang, B.-Y.; Bao, X.; Stojanovic, S.; Hadad, C. M.; Badjić, J. D.
Org. Lett. 2008, 10, 5361. doi:10.1021/ol802199t
11.Wang, B.-Y.; Bao, X.; Yan, Z.; Maslak, V.; Hadad, C. M.; Badjić, J. D.
J. Am. Chem. Soc. 2008, 130, 15127. doi:10.1021/ja8041977
12.Wang, B.-Y.; Rieth, S.; Badjić, J. D. J. Am. Chem. Soc. 2009, 131,
7250. doi:10.1021/ja9023868
37.Saha, S.; Stoddart, J. F. Molecular Motors and Muscles. In Functional
Organic Materials; Müller, T. J. J.; Bunz, U. H. F., Eds.; Wiley-VCH:
Weinheim, Germany, 2007; pp 295 ff.
13.Rieth, S.; Badjić, J. D. Chem.–Eur. J. 2011, 17, 2562.
doi:10.1002/chem.201003138
14.Rieth, S.; Bao, X.; Wang, B.-Y.; Hadad, C. M.; Badjić, J. D.
J. Am. Chem. Soc. 2010, 132, 773. doi:10.1021/ja908436c
15.Helgeson, R. C.; Hayden, A. E.; Houk, K. N. J. Org. Chem. 2010, 75,
570. doi:10.1021/jo9012496
License and Terms
This is an Open Access article under the terms of the
Creative Commons Attribution License
16.Sheu, C.; Houk, K. N. J. Am. Chem. Soc. 1996, 118, 8056.
doi:10.1021/ja9535423
(http://creativecommons.org/licenses/by/2.0), which
permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
17.Wang, X.; Houk, K. N. Org. Lett. 1999, 1, 591. doi:10.1021/ol9900820
18.Hooley, R. J.; Van Anda, H. J.; Rebek, J., Jr. J. Am. Chem. Soc. 2006,
128, 3894. doi:10.1021/ja058727g
19.Zhou, H.-X.; McCammon, J. A. Trends Biochem. Sci. 2010, 35, 179.
doi:10.1016/j.tibs.2009.10.007
The license is subject to the Beilstein Journal of Organic
Chemistry terms and conditions:
20.Kamieth, M.; Klärner, F.-G.; Diederich, F. Angew. Chem., Int. Ed. 1998,
37, 3303.
(http://www.beilstein-journals.org/bjoc)
doi:10.1002/(SICI)1521-3773(19981217)37:23<3303::AID-ANIE3303>3
.0.CO;2-T
The definitive version of this article is the electronic one
which can be found at:
21.Dill, K. A. J. Biol. Chem. 1997, 272, 701. doi:10.1074/jbc.272.2.701
22.Craig, S. L.; Lin, S.; Chen, J.; Rebek, J., Jr. J. Am. Chem. Soc. 2002,
124, 8780. doi:10.1021/ja025672z
doi:10.3762/bjoc.8.9
23.Wilcox, C. S. In Frontiers in supramolecular organic chemistry and
photochemistry; Schneider, H.-J; Dürr, H., Eds.; VCH: Weinheim,
Germany, 1991; pp 123 ff.
99