Molecular recognition of a transition state

Article abstract of DOI:10.1002/anie.201000656

(Figure Presented) An Inside job: The conformational interconversion of cyclohexane occurs at a higher rate in the interior of gated molecular baskets (see picture) than in bulk free solvent or a vacuum. The acceleration results from more favorable noncovalent bonding, and hence stabilization of the transition state, of the encapsulated compound.

Full text of DOI:10.1002/anie.201000656

Communications
DOI: 10.1002/anie.201000656
Encapsulation and Reactivity
Molecular Recognition of a Transition State**
´
´
Xiaoguang Bao, Stephen Rieth, Sandra Stojanovic, Christopher M. Hadad, and Jovica D. Badjic*
Self-assembled or covalent hosts capable of enclosing space
offer a confined environment for accommodating small to
medium-sized molecules.[1] When the isotropic solvent shell
around a molecule is substituted by the framework of the
host, unique properties can arise, including the stabilization of
transient intermediates[2] and catalysis of chemical reac-
tions.[3] The research groups of Cram and Sherman[4a–c] were
among the first to observe and characterize the limited
rotational mobility[4d–j] of smaller molecules residing in
carceplexes, and these seminal studies invoked steric inter-
actions as a source of the retardation. Subsequently, Rebek
and co-workers characterized encapsulation complexes with
guests having limited translational mobility, thereby estab-
lishing the phenomenon of social isomerism and revealing
new types of supramolecular chirality.[5] The conformational
interconversion of encapsulated guest(s) has also been
studied in artificial hosts,[4c,6,7] and complexation was almost
uniformly identified to retard or to have no effect, relative to
a proper reference system. The deceleration has been
speculated to arise from steric and electronic characteristics
of the hosts affecting the reactant as well as the transition
state(s) of the interconverting guest. The activation barrier
for the ring flipping of 1,4-thioxane and 1,4-dioxane required
an additional 1.6–1.8 kcalmolÀ1 (DDG°) within the restrictive
interior of carcerands.[4c] The chair–chair interconversion
process for cyclohexane was noted to occur slower in “jelly
doughnut” (DDG° ꢀ 0.3 kcalmolÀ1)[6] and resorcin[4]arene
(DDG° = 0.25 Æ 0.10 kcalmolÀ1) based cavitands.[7] In the first
[D11]cyclohexane (C6D11H) by quantitative NMR spectros-
copy and used electronic structure methods to identify the
origin of the observed acceleration.
Gated molecular baskets (Figure 1) were designed[9] as
models for examining the kinetics of molecular encapsula-
tion.[10] These dynamic hosts comprise a bowl-shaped plat-
form with three pyridine-based gates at its rim. The gates are
transiently connected through a seam of intramolecular
hydrogen bonds for controlling the in/out trafficking of
guests (Figure 1). As a prelude to studies on the relationship
À
case, this was rationalized by invoking favorable C H···p
interactions to stabilize the chair ground state. Analogous
studies on the rotation of the amide bond in encapsulated
environments showed such an interconversion occurred at a
faster/slower rate in hydrophobic, supramolecular assem-
blies[8] than in polar or nonpolar (DDG° ꢀ 1–3 kcalmolÀ1)
solvents, respectively.
In light of such discoveries, we report a rather unusual
case of accelerated ring flipping of cyclohexane inside newly
developed hosts—gated molecular baskets.[9] We measured
the kinetics of the conformational interconversion of
[*] Dr. X. Bao,[+] S. Rieth,[+] S. Stojanovic, Prof. C. M. Hadad,
´
´
Prof. J. D. Badjic
Department of Chemistry, The Ohio State University
100 West 18th Avenue, Columbus OH (USA)
Fax: (+1)614-292-1685
E-mail: badjic@chemistry.ohio-state.edu
[+] These authors contributed equally to the article.
[**] This work was financially supported with funds obtained from the
Ohio State University and the National Science Foundation under
CHE-0716355. Generous computational resources were provided by
the Ohio Supercomputer Center.
Figure 1. A) Structure of gated molecular baskets 1–3. B) Energy-mini-
mized structure of basket 1 containing cyclohexane (M06-2X/6-
31G(d)). Please note that a side of the basket is omitted for clarity.
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.201000656.
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Table 2: Thermodynamic parameters DH8, DS8, and DG8 for the binding
of [D11]cyclohexane to baskets 1–3 (DG8 and K at 188.8 K) in CD2Cl2
obtained from variable-temperature 1H NMR data (186–228 K) and
van’t Hoff plots.[17]
Basket (R) DH8 [kcalmolÀ1
]
DS8 [eu]
DG8 [kcalmolÀ1 K[a] [mÀ1
] ]
1 (CH3)
2 (Ph)
3 (CF3)
À3.88Æ0.07
À3.92Æ0.04
À3.31Æ0.05
À9.2Æ0.3 À2.15Æ0.03
À10.3Æ0.2 À1.96Æ0.02
À9.7Æ0.2 À1.48Æ0.04
314Æ29
191Æ13
52Æ5
[a] Obtained from lnK versus 1/T linear functions at 188.8 K.[17]
(Table 2). The binding free energy DG8 is less favorable as
more electron-withdrawing R groups (EWGs) are installed at
the amide position (Figure 1). It could be that the EWGs
render the hostꢀs shell less polarizable, thereby disrupting its
dispersion interactions with the guest; these interactions,
together with other factors, contribute to the DG8 values.
The rate coefficient k for [D11]cyclohexane undergoing a
chair flipping motion inside 1–3 was determined by using 1H-
1H NMR EXSY spectroscopy[16] at (188.8 Æ 0.1) K (Table 1):
Figure 2. An energy diagram for the conformational interconversion of
cyclohexane.[11b] The interconversion of ground- and transition-state
conformers can be described with two degrees of freedom f1 and
f2.[11a] Note that only one cycle of the pseudorotation is shown.
between the gating and reactivity, we decided to examine the
conformational dynamics of a well-characterized system
inside the molecular cage provided by gated baskets 1–3:
the chair-to-chair interconversion of cyclohexane (Figure 1).
The potential energy surface (PES) for the interconversion of
cyclohexane, which has been intensively studied both theo-
retically and computationally,[11] is described with two degrees
of freedom (f1 and f2, Figure 2)[11] and contains D3d-
symmetric chair and D2-symmetric twist-boat conformations
as energy minima connected by C2-symmetric half-chair and
C2v-symmetric boat transition states (Figure 2). The chair-to-
chair interconversion is characterized by the first-order rate
constant k, which on the basis of the mechanism is twice the
the first-order magnetization rate constant k*obs (k*obs = kobs
=
1
= k) was obtained for the chemical exchange of the proton
2
residing at the axial and the equatorial positions (Figure 3).[17]
At this low temperature, the rates for the entrapment and the
release of cyclohexane by the host were reduced below the
EXSY detection limit, as evidenced by the absence of the
appropriate cross-signal in the spectrum (Figure 3). The
interconversion kinetics of [D11]cyclohexane in bulk dichloro-
methane (CD2Cl2) and toluene (C6H5CD3) were measured
concurrently by using both the classical line-shape and the
EXSY methodology: the results from both analyses are
consistent and in good agreement with published data[12,13]
(Table 1). On the basis of the measurements (Table 1), it was
determined that the interconversion of cyclohexane occurs
roughly five times faster inside baskets 1–3 than in the
reference bulk solvents CD2Cl2 and C6D5CD3. What is the
origin of the acceleration?
value of the experimental kobs.
[12] By using NMR spectroscopy,
Anet et al. measured the interconversion of C6D11H in CS2 as
a solvent and found that it occurs with an activation enthalpy
(DH°) of (10.71 Æ 0.04) kcalmolÀ1 and an activation entropy
(DS°) of (2.2 Æ 0.2) eu (Table 1).[13] Importantly, the activa-
tion energy (DG°) for the process is barely a function of the
liquid phase (methylcyclohexane, acetone, and CS2);[14]
although the value of DG° is somewhat higher in the gas
phase[15] (Table 1).
An elevated pressure was earlier demonstrated to facil-
itate the interconversion of cyclohexane.[14] Originally, the
There is moderate thermodynamic affinity for
[D11]cyclohexane occupying the interior of baskets 1–3
Table 1: Activation parameters DH°, DS°, and DG° (188.8 K) for the
conformational interconversion of [D11]cyclohexane (2D EXSY NMR,
400 MHz, CD2Cl2, 188.8Æ0.1 K) inside baskets 1–3 in CS2, the gas
phase, CD2Cl2, and C6D5CD3.
Solvent
DH° [kcalmolÀ1
]
DS° [eu] DG° [kcalmolÀ1 k [sÀ1
] ]
[a]
CS2
10.71Æ0.04
2.2Æ0.2 10.29Æ0.06
5.7Æ0.5 10.6Æ0.5
4.7Æ0.7
2.1Æ1.5
43Æ3
gas phase[b] 12.1Æ0.5
basket 1
basket 2
basket 3
–
–
–
–
–
–
9.43Æ0.03
9.45Æ0.02
9.56Æ0.04
41Æ2
30Æ3
Figure 3. A 2D NMR EXSY spectrum (400 MHz, 188.8Æ0.1 K) of a
14.0 mm solution (CD2Cl2) of [D11]cyclohexane and basket 2
(1.40 mm). The volumes of the diagonal and cross-signals were used
to extract the magnetization rate constant k*obs that characterized the
conformational interconversion.[17]
[c]
CH2Cl2
C6D5CD3
10.2Æ0.1
0.4Æ0.4 10.1Æ0.1
6.9Æ2.2
7.9Æ4.3
[c]
10.3Æ0.2
1.2Æ0.7 10.1Æ0.2
[a] See Ref. [13]. [b] See Ref. [15]. [c] Obtained from Eyring plots and line-
1
shape analysis of H NMR signals (197 to 236 K).[17]
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Communications
stochastic model for isomerization reactions[11g,f] was used to
studying noncovalent interactions between organic molecules
(see the Supporting Information). To assess the role of the
basket as a host, we obtained optimized geometries for the
cyclohexane guest inside the basket (for chair and half-chair
TS structures) and then recomputed the energies of the static
chair and half-chair in a vacuum (that is, without the basket)
relative to fully optimized M06-2X calculations of cyclohex-
ane in a vacuum. According to the DFT results, the chair is
slightly destabilized in the basket relative to the isolated chair
conformer in a vacuum (DE = 0.25 kcalmolÀ1; Figure 4B).
Further inspection of the interatomic distances (Figure 4A)
explain such a result. In contrast to conventional transition-
state theory, this model takes into account the recrossing of
the activation barrier and proposes a dependence of the
transmission coefficient k (the fraction of successful trajecto-
ries) on the collisional frequency of molecules; in conven-
tional transition-state theory k = 1. That is to say, the reaction
coordinate becomes coupled to the surrounding medium
through collisions between solvent and solute molecules. The
unimolecular kinetics that describes the isomerization of
cyclohexane[11c] in the liquid phase conflicts with statistical
RRKM theory, and the transmission coefficient k is a function
of the external pressure or coupling of the solvent and solute.
As the framework of the basket is in intimate and prolonged
contact with the entrapped and rapidly fluctuating cyclohex-
ane, the collisional contribution to the reaction coordinate
could be sufficient[18] to affect the interconversion and thereby
control the isomerization rate. Our computational results,
however, offer an alternative explanation.
The acceleration of cyclohexaneꢀs interconversion in the
interior of these molecular baskets is due to a) a reduced
energy barrier from the chair local minimum to the half-chair
transition state or b) to a more efficient transmission coef-
ficient k.[11b] The basket could contribute energetically in two
ways: the destabilization of the chair conformer and the
stabilization of the half-chair transition state (Figure 4).
The ONIOM[19a] (MP2/6-31G(d):AM1) method was
employed to investigate the complex formed between the
basket and cyclohexane as a guest. Unfortunately, only very
small differences in the geometry and energy for both the
chair and half-chair conformers were seen between calcula-
tions on cyclohexane in a vacuum and in the basket. An
inadequate treatment of the host–guest interactions may be
the main reason for the inability of the ONIOM method to
provide an explanation to this experimental observation (see
Tables S1 and S2 in the Supporting Information).[17] Unfortu-
nately, we were unable to evaluate the system with the MP2
level of theory because of its size.[19b] Thus, we employed
density functional theory (DFT) calculations using the M06-
2X functional,[22] as this method has been optimized for
À
reveal three (cyclohexane) C H···p (basket) contacts
(<2.7 ꢁ from hydrogen to the p centroid)[21] for the encapsu-
lated chair conformation, which leads to the C1 symmetry of
the chair in the basket but a D3d symmetry in a vacuum.
Conversely, relative to the half-chair conformer in a vacuum,
the half-chair transition state of the guest is a more stabilized
structure (DE = À0.90 kcalmolÀ1) in the interior of basket 1.
Examination of the encapsulated half-chair conformation
(Figure 4C) showed that three dihedral angles of the carbon
skeleton changed significantly as a consequence of the
À
“fourth” C H···p interaction with the upper pyridine gate
(see Table S3 in the Supporting Information). This additional
À
C H···p contact may play a role in assisting the “distortion”
of the half-chair conformation, thereby moving it along the
reaction coordinate to more closely resemble the twist-boat
product. Our computational studies implied that the encap-
sulated chair conformation is slightly destabilized and that the
half-chair TS is stabilized in the basket relative to that in a
vacuum. The activation barrier DE° for the interconversion of
cyclohexane was thus computed to be 10.87 kcalmolÀ1 in the
interior of basket 1 (Table 3), which is a significant reduction
from the calculated barrier (12.02 kcalmolÀ1) in a vacuum. A
more favorable conversion of the chair into the half-chair TS
while inside the basket (DDE° = 1.15 kcalmolÀ1, Figure 4B)
is consistent with the experimental finding (DDG° ꢀ 0.5 kcal
molÀ1).
The computational study revealed two Heq atoms and one
À
H
ax atom of the chair conformation making C H···p contacts
with the basket (Figure 4A). This result is in agreement with a
greater difference in the
chemical shift Ddax/eq of the
axial/equatorial protons of
C6D11H inside baskets 1–3
(227 Hz) than in bulk sol-
vent (190 Hz, Figure 3).
Moreover, the splitting
pattern of the 1H NMR
signals of the entrapped
C6D11H did not alter at
lower temperatures, thus
suggesting a low activation
barrier for this compound
tumbling in the interior of
1–3. The results of molec-
ular dynamics (MD) simu-
lations[17] are consistent
Figure 4. Energy-optimized structures of chair (left) and half-chair (right) conformers inside gated molecular
with this observation, dis-
closing a random fluctua-
À
basket 1 (M06-2X/6-31G(d)); note that some structural features are omitted for clarity. Host–guest C H···p
contacts and the dihedral angle f (Df=4.18) are also shown.
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31G(d)) for the conformational interconversion of cyclohexane in a
vacuum and inside basket 1.[a]
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Conformation
Vacuum [kcalmolÀ1
]
Basket 1 [kcalmolÀ1
]
chair
0
0
half-chair
twist-boat
boat
12.02
6.19
7.51
10.87
6.05
–
[a] For comparison, the computed energy corresponding to the chair
conformational state was in each case set at zero.
tion of cyclohexane (111 ꢁ3) inside closed 1–3 (ca. 221 ꢁ3)
over a period of 10 ns.
The molecular framework of gated baskets was herein
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Received: February 3, 2010
Published online: May 28, 2010
Keywords: host–guest systems · molecular dynamics ·
.
molecular recognition · supramolecular catalysis ·
transition states
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