Structural characterization of the Brooker's merocyanine/β-cyclodextrin complex using NMR spectroscopy and molecular modeling

Article abstract of DOI:10.1016/j.molstruc.2009.11.034

Brooker's merocyanine (4-[(1-methyl-4(1H)-pyridinylidene)ethylidene]-2,5-cyclohexadien-1-one) is a dye molecule that has a unique photochemical/protolytic isomerization cycle. The cis to trans isomerization of the neutral molecule occurs only in one direction with the addition of photochemical energy. When the dye molecule is complexed with β-cyclodextrin, however, the isomerization occurs spontaneously without further energy required. To understand the difference between the native dye molecule and the complex, the molecular structures of the cis and trans isomers of Brooker's merocyanine in β-cyclodextrin were optimized using the semi-empirical PM3 method as well as the hybrid ONIOM method which models the cyclodextrin at the PM3 level and the dye molecule using B3LYP/6-31g(d). The most stable complexes were similar in binding energy, although the molecular structures were quite different. The ONIOM optimized structures resulted in an increase in the planarity of the conjugated dye molecule when compared to the PM3 model. The trans isomer in the β-cyclodextrin cavity was also characterized experimentally using ¹H-NMR complexation-induced shifts, and the results were found to be in good agreement with the proposed structure from the molecular modeling. Finally, the calculated thermodynamic properties of the trans isomer complex were compared to experimental results, and it became clear that water within the cavity must be included in the analysis to obtain accurate theoretical values.

Full text of DOI:10.1016/j.molstruc.2009.11.034

Journal of Molecular Structure 965 (2010) 31–38
Contents lists available at ScienceDirect
Journal of Molecular Structure
journal homepage: www.elsevier.com/locate/molstruc
Structural characterization of the Brooker’s merocyanine/b-cyclodextrin
complex using NMR spectroscopy and molecular modeling
*
Jennifer S. Holt
School of Science, 4205 College Dr., Penn State Erie, The Behrend College, Erie, PA 16563, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Brooker’s merocyanine (4-[(1-methyl-4(1H)-pyridinylidene)ethylidene]-2,5-cyclohexadien-1-one) is a
dye molecule that has a unique photochemical/protolytic isomerization cycle. The cis to trans isomeriza-
tion of the neutral molecule occurs only in one direction with the addition of photochemical energy.
When the dye molecule is complexed with b-cyclodextrin, however, the isomerization occurs spontane-
ously without further energy required. To understand the difference between the native dye molecule
and the complex, the molecular structures of the cis and trans isomers of Brooker’s merocyanine in b-
cyclodextrin were optimized using the semi-empirical PM3 method as well as the hybrid ONIOM method
which models the cyclodextrin at the PM3 level and the dye molecule using B3LYP/6-31g(d). The most
stable complexes were similar in binding energy, although the molecular structures were quite different.
The ONIOM optimized structures resulted in an increase in the planarity of the conjugated dye molecule
when compared to the PM3 model. The trans isomer in the b-cyclodextrin cavity was also characterized
experimentally using 1H-NMR complexation-induced shifts, and the results were found to be in good
agreement with the proposed structure from the molecular modeling. Finally, the calculated thermody-
namic properties of the trans isomer complex were compared to experimental results, and it became
clear that water within the cavity must be included in the analysis to obtain accurate theoretical values.
Ó 2009 Elsevier B.V. All rights reserved.
Received 25 September 2009
Accepted 17 November 2009
Available online 20 November 2009
Keywords:
Brooker’s merocyanine
b-Cyclodextrin
Complexation-induced shifts
ONIOM
Theoretical modeling
Isomerization
x Guest þ y Cyclodextrin ¡ Guestx : Cyclodextriny
ð1aÞ
ð1bÞ
1. Introduction
½Guestx : Cyclodextrinyꢀ
K ¼
Cyclodextrin chemistry has become a prominent area of host–
guest research because of the protection afforded guest species
within the host cavity. This added stability leads to novel materials
with a wide-range of applications, including drug encapsulation
and delivery, waste treatment and odor elimination. Cyclodextrins
are torus-shaped molecules with large hydrophobic interior cavi-
ties into which a guest molecule can be inserted. Common cyclo-
y
x
½Guestꢀ ½Cyclodextrinꢀ
where K is the equilibrium binding constant, also known as the
association constant.
The guest molecule of interest in this work is Brooker’s merocy-
anine, ((4-[(1-methyl-4(1H)-pyridinylidene)ethylidene]-2,5-cyclo-
hexadien-1-one), also known as stilbazolium betaine. This dye
molecule was first synthesized in 1951 by Brooker et al. [3,4] and
is of great interest in the field of spectroscopy due to the very large
solvatochromic response to the microenvironment surrounding
the molecule [5,6]. The crystal structure indicated the most stable
form of Brooker’s merocyanine is the deprotonated, planar trans
isomer [7]. It can undergo a unique photochemical/protolytic
isomerization cycle, as shown in Fig. 1. There is no evidence for di-
rect trans to cis isomerization of Brooker’s merocyanine, but it will
photoisomerize when protonated (pKa = 8.54) [8] in solution to
create a photostationary state containing protonated cis and trans
isomers in equilibrium [9–11]. As we have previously reported
[12], when Brooker’s merocyanine is then deprotonated, the mole-
cule will photoisomerize from the cis isomer back to the stable
trans isomer when energy is added to the system. When Brooker’s
merocyanine is inserted into the b-cyclodextrin cavity, however,
dextrins include a-, b-, and c-cyclodextrin which are made of six,
seven or eight dextrin units, respectively. Interaction between
the guest molecule and the cyclodextrin occurs through hydro-
gen-bonding and weak van der Waals forces. Small molecules
can be bound completely within the cavity, which is approximately
7.8 Å in length [1], while larger molecules may be partially
inserted, with one or both ends of the guest molecule extending
beyond the cavity, allowing the external groups to be solvated.
b-Cyclodextrin has a diameter of 7.8 Å [1], and it is the appropriate
size to accommodate simple aromatic molecules, such as stilbene
[2] (similar to the guest molecule in this work). The general com-
plexation reaction is given by:
* Tel.: +1 814 898 6004; fax: +1 814 898 6213.
E-mail address: jsh18@psu.edu
0022-2860/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2009.11.034

32
J.S. Holt / Journal of Molecular Structure 965 (2010) 31–38
determined as the difference between the chemical shift of the free
- H
MH+
Mtrans
species and the complex. The structures and proton labels for both
Brooker’s merocyanine and b-cyclodextrin protons are given in
Fig. 2.
trans
Theoretical modeling was performed using Gaussian 03 soft-
ware [21]. As cyclodextrin complexes are known to have a number
of local minima, a variety of orientations were fully optimized using
the semi-empirical Parametric Method 3 (PM3) [16,17] followed by
a frequency analysis to verify true minima were found (all eigen-
values of the Hessian matrix were positive). b-Cyclodextrin was
optimized from the crystal structure obtained from the Cambridge
database [22] at the PM3 level, which resulted in an asymmetrical
cavity. The axes system was defined with the x–y plane through
the glycosidic oxygens of the cyclodextrin ring and the z-axis paral-
lel to the long axis of the cavity. Several possible orientations of
Brooker’s merocyanine within the cavity were considered, with
representative initial structures shown in Fig. 3. These structures
indicate the possible alignments of the dye with respect to the z-
axis. The trans isomer was inserted into the cavity with the car-
bonyl part of the dye molecule pointed toward either the primary
hydroxyl rim (referred to as the ‘‘down” position) or the secondary
hydroxyl groups (referred to as the ‘‘up” position). There were four
possible orientations of the cis isomer where one part of the dye
molecule (either the carbonyl or the n-methyl-pyridyl rings) was
included within the cavity, while the other part of the dye molecule
was mostly excluded and located across either the primary (down)
or secondary (up) hydroxyl groups. The dye was passed through the
cavity in 1 Å steps, as measured from the atom illustrated in Fig. 3
(+z toward the primary hydroxyl rim). The trans isomer was opti-
mized from ꢂ2 Å to 5 Å, while the cis isomer was characterized
from ꢂ2 Å to 3 Å due to the steric hinderance of the excluded ring
with the cyclodextrin hydroxyl groups. The lowest energy struc-
tures for each complex were then rotated in 45° steps around the
z-axis to further refine the model. Finally, a few additional random
cis configurations were also optimized in which the dye was tilted
further from the z-axis in order to confirm the initial angle did not
constrain the final structure.
+ H
ν
ν
h
ν
h
h
- H
+ H
MH+
Mcis
cis
Fig. 1. The photochemical/photolytic cycle of Brooker’s merocyanine (M).
the cis to trans isomerization becomes much more facile and will
isomerize without additional photochemical energy. This cyclic
process can be used as a model to for a variety of related systems.
For example, this isomerization cycle has been suggested as a mod-
el system for naturally-occurring photocyclic systems, such as ret-
inal in rhodopsin or in the photosynthesis of Halobacterium
halobium [13]. This cyclic process in which one step proceeds in
only one direction has also been proposed as a system for informa-
tion storage [14]. Although experimental values for the thermody-
namics [12] and binding constant [15] have been reported for this
complex, a complete structural characterization has not been re-
ported for Brooker’s merocyanine with b-cyclodextrin and is
needed to understand this cyclic process.
In this work, the molecular structure of the cis and trans iso-
mers of Brooker’s merocyanine complexed to b-cyclodextrin will
be characterized. The structure of the trans isomer within the cav-
ity will be studied using NMR complexation-induced shifts (CIS) to
determine the approximate binding location. These results will be
compared to theoretical optimized geometries using the semi-
empirical Parametric Method 3 (PM3) [16,17] and the ONIOM
(our own N-layered integrated molecular orbital + molecular
mechanics) method as developed by Morokuma et al. [18]. The
hybrid ONIOM method allows for accurate modeling of the dye
molecule, while maintaining reasonable computational time. As
observed by Yan and coworkers, very few studies using this im-
proved model with cyclodextrin complexes have been undertaken
[19], leaving much to learn about the applicability of this method.
Finally, a comparison of the cis and trans isomers for the free dye
molecule and the complexes will be used to understand the differ-
ences in the isomerization process previously reported.
Several energy expressions were used to characterize the com-
plexes [23]. In addition to the absolute energy of the complex (the
HF value as reported by Gaussian), the binding energy (
DEbinding) is
defined as the difference between the energy of the complex and
the energyof theindividual components intheir optimized geometry
(Eopt.,BM or Eopt.,CD). The deformation energy is the change in energy of
eachspeciesasa resultofcomplexationandisthedifferencebetween
theoptimizedgeometryenergyandtheenergyoftheindividualcom-
ponents in their complex geometry (Especies in complex). These values
were determined by decomposing the optimized complex and per-
forming a single point energy calculation on each resulting species.
2. Experimental
Brooker’s merocyanine (Aldrich Chemicals) and b-cyclodextrin
(TCI International) were obtained and used without further purifi-
cation. All solutions were prepared using D2O (Alfa Aesar) with a
standard carbonate buffer (pHydrion buffer capsules, Micro Essen-
tials) at pH = 10.00 0.02. Carbonate buffer was chosen to ensure
that competitive binding did not occur [20]. This was verified by
comparing the binding constant to results found using a weak
solution of sodium hydroxide, reported in previous studies [12].
Concentrations of both dye and cyclodextrin solutions were chosen
to remain below the saturation limit for complexation, as well as
within the solubility limits of both species. The relative concentra-
tions of solutions containing both dye and b-cyclodextrin (between
approximately 2 ꢁ 10ꢂ3 and 5 ꢁ 10ꢂ2 M) were varied, and the 1H-
NMR spectra from these solutions were collected on a Bruker
400 MHz Avance NMR spectrometer at 20 °C. CIS values were
Fig. 2. Schematic representations of Brooker’s merocyanine and b-cyclodextrin. The
labels indicate the numbering scheme used for the 1H-NMR results.

J.S. Holt / Journal of Molecular Structure 965 (2010) 31–38
33
parameter hybrid functional of Becke with the correlation func-
tional of Lee et al. (B3LYP) [24–26] with the split-valence 6-
31G(d) basis set. The ONIOM energy is described as:
D
EONIOM ¼ Eðhigh; modelÞ þ Eðlow; realÞ ꢂ Eðlow; modelÞ
ð4Þ
where E (high, model) is the energy of the dye molecule at the
B3LYP/6-31g(d) level, E (low, real) is the energy of the complex at
the PM3 level, and E (low, model) is the energy of the b-cyclodextrin
at the PM3 level. The energy was also found by treating all atoms in
the PM3 optimized structure at the B3LYP/6-31G(d) level with BSSE
correction using the counterpoise method as implemented in
Gaussian 03 [21]. Finally, solvent effects were included using the
integral equation formalism of the polarizable continuum model
(IEFPCM) [27].
3. Results and discussion
3.1. NMR spectroscopy
NMR spectroscopy was used to elucidate the molecular struc-
ture of the trans isomer of the Brooker’s merocyanine in b-cyclo-
dextrin. The cis isomer complex was not investigated using NMR
because it only exists in equilibrium with the trans isomer after
deprotonation from the photostationary state, leading to complex
spectra that were difficult to resolve with certainty. Brooker’s mer-
ocyanine was previously shown to form a 1:1 complex with at least
part of the dye molecule extending outside the cyclodextrin cavity
[12]. The ratio of dye to cyclodextrin was varied in order to observe
trends in the 1H-NMR complexation-induced shifts (CIS) of both
the dye and cyclodextrin peaks. The cyclodextrin region, shown
in Fig. 4, is comprised of several overlapping peaks, which makes
exact assignments and quantitative CIS values difficult. The Brook-
er’s merocyanine peak assignments were much more easily identi-
fied as there was no overlap, and the resulting chemical shifts and
CIS values are reported in Table 1. As Balabai and coworkers [28]
have previously noted for other guest:cyclodextrin complexes,
there are not two unique overlapping NMR spectra for the free
and complexed species, indicating that the equilibrium conversion
occurs more rapidly than the NMR timescale. The fact that the each
dye peak did not split into multiple peaks also indicates that there
are not multiple binding sites.
b-Cyclodextrin contains six unique hydrogen atoms that are
easily identified in the 1H-NMR spectra [29], and the pure b-cyclo-
dextrin chemical shifts were in good agreement with the literature
Fig. 3. Initial structures of the cis (A – excluded part of dye toward secondary
hydroxyl region, B – excluded part of dye toward primary hydroxyl region) and
trans (C) Brooker’s merocyanine isomers within the b-cyclodextrin cavity. All three
structures were also calculated with the dye molecule inverted in the cavity. The
arrow indicates the atom used to locate the distance from the center.
D
D
Ebinding ¼ Ecomplex ꢂ ðEopt:;BM þ Eopt:;CD
Edef ¼ Especies in complex ꢂ Eopt:;species
Þ
ð2Þ
ð3Þ
To improve the precision of the theoretical results, a QM/MM
ONIOM calculation was used to optimize the cyclodextrin mole-
cule at the PM3 level, while treating the dye molecule with quan-
tum mechanics. Specifically, the dye was treated using the three
Fig. 4. 1H-NMR spectra for the free b-cyclodextrin molecule (A) and solutions of 1:1
(B) and 10:1 (C) dye:b-cyclodextrin ratios. The spectra were normalized for
comparison using the doublets at approximately 3.53 ppm.

34
J.S. Holt / Journal of Molecular Structure 965 (2010) 31–38
Table 1
expect a similar CIS between these protons, but this is not the case.
There is a negative CIS for the H60 protons, while the H5’ protons do
not shift. In summary, the NMR results indicate that the stable
complex formed at high pH is one in which the n-methyl-pyridyl
end of the molecule is located within the cyclodextrin cavity, while
the carbonyl end remains solvated outside of the cavity. However,
further interpretation of the exact position of the dye within the
cavity requires molecular modeling to fully understand the struc-
ture of the complex.
1H-NMR CIS values assigned to Brooker’s merocyanine protons for pure dye and
complexes with varying ratios of b-cyclodextrin:dye in solution. All chemical shifts
are in ppm and referenced from the HOD peak (4.70 ppm).
Pure Dye
b-Cyclodextrin:dye
D
d (ppm)
a
dRef.
dExp.
1:1
2:1
10:1
20:1
Dye
H20
H30
H50
H60
H80
H90
8.13
7.65
6.79
7.48
7.34
6.57
8.111
8.095
7.617
7.609
6.744
6.705
7.474
7.434
7.312
7.290
6.506
6.485
ꢂ0.120
ꢂ0.119
ꢂ0.073
ꢂ0.072
+0.004
+0.005
ꢂ0.031
ꢂ0.031
ꢂ0.008
ꢂ0.008
+0.022
+0.022
ꢂ0.178
ꢂ0.177
ꢂ0.108
ꢂ0.106
+0.002
+0.003
ꢂ0.051
ꢂ0.052
ꢂ0.007
ꢂ0.007
+0.047
+0.047
ꢂ0.196
ꢂ0.203
ꢂ0.204
ꢂ0.120
ꢂ0.120
+0.004
+0.004
ꢂ0.059
ꢂ0.058
+0.005
+0.003
+0.068
+0.067
ꢂ0.195
ꢂ0.115
ꢂ0.113
+0.002
+0.003
ꢂ0.057
ꢂ0.058
+0.005
+0.005
+0.070
+0.070
3.2. Theoretical models
The cis and trans isomers were optimized at the PM3 level be-
fore insertion into the cyclodextrin cavity. The trans isomer was
planar except for a slight tip of the –N–CH3 group. The optimized
cis isomer had a 60° dihedral angle across the central C5–C6 bond
due to steric effects. The NMR results indicated that the dye mole-
cule was inserted into the cyclodextrin cavity, so capping and
external binding complexes were not considered. Results from
the lowest energy structures for each of the possible conformations
of the dye within the cavity are given in Table 2. The binding en-
ergy for each of the possible complexes was negative, which indi-
cates that complex formation is energetically favored. The most
stable inclusion complex of the trans isomer resulted in an overall
energy as well as a binding energy that was very similar to the
most stable cis isomer complex. The binding energies for the most
stable complexes of the two isomers differed by only 3.72 kJ molꢂ1
(at the PM3 level), and both of these structures are shown in Fig. 5.
It has been reported that the dipole of guest molecules align anti-
parallel to the dipole of the cyclodextrin cavity, which points to-
ward the primary hydroxyl rim [34]. This is in agreement with
the observation that the most stable structures for all configura-
tions have the carbonyl end of Brooker’s merocyanine, and there-
fore the molecular dipole, directed away from the primary
hydroxyl groups. The energy difference between the carbonyl up
versus down in the complex containing the trans isomer was
17.6 kJ molꢂ1 lower in energy for the up position, while the cis iso-
mer complex was 21.6 kJ molꢂ1 lower in energy for the up align-
ment if part of the dye extended beyond the secondary hydroxyl
rim initially. There was no difference in energy for the cis isomer
in which the dye molecule initially protruded from the cyclodex-
trin at the primary hydroxyl region.
a
From Ref. 35.
assignments, using the HOD peak position as a common reference.
It is well known that if a complex is formed by inserting the guest
molecule into the cavity, the interior protons of the cyclodextrin
(H3 and H5) are considerably shielded leading to an upfield chem-
ical shift, as first observed by Demarco and Thakkar [30,31], and
subsequently reviewed by Schneider and coworkers [29]. Fig. 4
shows the cyclodextrin proton region of the NMR spectra for both
the free b-cyclodextrin as well as 1:1 and 10:1 dye:b-cyclodextrin.
It is apparent that there are some peaks that exhibit dramatic
shifts, while others remain constant. The cyclodextrin H3 proton,
found at approximately 3.85 ppm shifted upfield by up to
0.07 ppm upon complexation, indicating that the dye does indeed
enter the cyclodextrin cavity. In the free b-cyclodextrin solution,
the H5 and H6 cyclodextrin proton peaks were superimposed at
approximately 3.75 ppm. Upon complexation, the H5 protons be-
came resolved and shifted by more than 0.10 ppm upfield. The
spectral pattern follows that reported for b-cyclodextrin com-
plexed with benzoic acid [32], although the H5 shift for the litera-
ture complex is approximately double the current CIS values for
comparable guest:host ratios. This is likely due to the smaller size
of the benzoic acid, which allows it to be inserted more easily deep
within the cavity where the H5 proton is located and interact more
strongly. The H6 proton peak also splits and has a smaller CIS than
the H5 proton peak. In contrast, the peaks centered at 3.51 ppm
was assigned to the H2 protons and differed by no more than
0.004 ppm upon complexation, and the signal at approximately
3.45 ppm, which was assigned to the H4 protons, had a CIS that
was at most 0.018 ppm for the ratios investigated. These protons
are located on the outside of the cyclodextrin, so it can be con-
cluded that there is no external complexation. It is clear from these
results that this complex is formed by inserting the dye molecule
into the cyclodextrin cavity such that it can interact with both
the H3 and H5 cyclodextrin protons.
The trans isomer of the dye molecule fit relatively easily within
the cavity with little steric hinderance. As the trans isomer was
moved through the cyclodextrin cavity, the absolute energy of
the optimized structures varied by approximately 30 kJ molꢂ1, as
Table 2
Relative energies of the lowest energy states for each complex at the PM3 level. For
the cis isomer, one of the dye phenyl rings is located within the cavity, while the other
is initially excluded at either the primary or secondary hydroxyl region of the
cyclodextrin cavity. All energies are in kJ molꢂ1
.
Absolute
energy
D
Ebinding
D
Edef,CD
DEdef,dye
The chemical shifts and coupling constants for Brooker’s mero-
cyanine protons in D2O were in good agreement with the literature
values [33], as shown in Table 1. Unlike the cyclodextrin protons
that generally shifted upfield, guest molecule protons exhibited a
downfield shift upon complexation. The dye peaks that were most
affected upon complex formation were H20 and H30, which corre-
spond to the hydrogens on the n-methyl-pyridyl ring. The negative
CIS for both protons indicates a strong interaction within the cyclo-
dextrin cavity. The H90 protons had a positive CIS, indicating very
different behavior from the H20 and H30 protons. It is clear by the
sign change that the H90 protons were excluded from the cavity.
The H50 and H60 protons should be located in approximately the
same location within the cyclodextrin cavity. Therefore, one would
Trans isomer
n-Methyl-pyridyl end
down
Carbonyl end down
ꢂ5959.9
ꢂ5942.4
ꢂ69.58
ꢂ52.10
ꢂ0.617
+2.860
ꢂ2.493 +0.934
Cis isomer, excluded at primary OH rim
n-Methyl-pyridyl end
down
Carbonyl end down
ꢂ5932.4
ꢂ61.54
ꢂ62.32
ꢂ1.103
+1.388
+1.429
ꢂ5933.2
+2.999
Cis isomer, excluded at secondary OH rim
n-Methyl-pyridyl end
down
Carbonyl end down
ꢂ5944.1
ꢂ73.30
ꢂ51.75
ꢂ0.555
+2.255
+2.644
ꢂ5922.6
+0.717

J.S. Holt / Journal of Molecular Structure 965 (2010) 31–38
35
Fig. 5. Optimized geometry for the most stable trans (A) and cis (B) isomers within the b-cyclodextrin cavity, shown from the equatorial and axial direction. Optimization
performed at the PM3 level.
shown in Fig. 6. When the molecule was rotated around the z-axis,
the energy difference was approximately 25 kJ molꢂ1. The most
stable trans isomer complex, shown in Fig. 5A, resulted in a slight
tilt of the dye molecule within the cavity to maximize intermolec-
ular interactions. The methyl group extended beyond the primary
hydroxyl rim, while most of the phenyl ring with the carbonyl ex-
tended beyond the secondary hydroxyl rim. One downfall of the
PM3 optimization was that the dye molecule became slightly non-
planar. For example, a dihedral angle of ꢂ178.2° was observed
across the C5–C6 bond, and the C2–C3–C4–C5 dihedral angle was
ꢂ174.5°. In the free trans isomer optimized at the PM3 level, these
dihedral angles were both ꢂ180°. This bend in the dye molecule re-
sults in a positive dye deformation energy for this complex.
The energy of the cis isomer complex was slightly higher than
the trans isomer, but the binding energy was actually lower for
the most stable cis isomer complex. If the dye molecule was cen-
tered relative to the x–y plane within the cavity, the optimization
process oriented the dye molecule at an angle within the cavity
so both end groups could interact with the cyclodextrin hydroxyl
regions without causing large deformations in either molecule. If
the dye molecule was offset from the central x–y plane of the
cyclodextrin initially, the excluded part of the dye remained out-
side the cavity in the optimized structure, but was no longer
aligned along the z-axis in order to maximize the dye-hydroxyl
interactions. As noted earlier, several random structures were also
tested, and no further refinement of the complex was obtained by
aligning the dye molecule off-axis before the optimization process
occurred. The most stable cis isomer complex is shown in Fig. 5B.
The dihedral angle across the central C5–C6 bond was slightly
twisted from 60° in the free molecule to 55° in the complex. The
dye molecule remained more planar in this complex as compared
to the trans isomer complex, with the C2–C3–C4–C5 dihedral angle
equal to ꢂ176.2°, but there was still deformation, as seen in the po-
sitive deformation energy of the dye molecule.
Although PM3 has been shown to be adequate to model cyclo-
dextrin complexes, it does have limitations. Therefore, more ad-
vanced methods, including density functional methods are
necessary to refine the geometries that have been discussed thus
far. It has been shown that B3LYP is the best of the density func-
tionals to determine relative conformational energies [35], but
for large systems like cyclodextrin complexes, optimization and
frequency calculations are prohibitively expensive. Therefore, the
hybrid ONIOM method was employed to optimize the dye at the
B3LYP level and the cyclodextrin at the PM3 level, thereby reduc-
ing the computational cost while increasing the accuracy of the
resulting structure. The ONIOM results follow the same trend as
the PM3 optimizations, where the absolute energy of the most sta-
ble trans isomer complex was very slightly lower in energy than
the cis isomer complex, as shown in Table 3. However, the struc-
ture was improved by increasing the planarity of Brooker’s mero-
cyanine in the complex. The –N–CH3 end group and the central
C5–C6 bond were especially affected as a result of the increase in
the theory level. All of the dihedral angles in the dye molecule were
within 2° of planar. Therefore, the ONIOM methodology provided
reasonable improvements in the model with minimal increase in
the computation time. To further refine the energy differences, a
single point calculation using B3LYP/6-31g(d) for the entire com-
plex was calculated and the results for the cis and trans isomers
were also reported in Table 3. This led to virtually no difference be-
tween the energy of both complexes.
To observe the effect of water on the relative stabilities of the
Brooker’s merocyanine isomers in the complex, a solvation model
was chosen to improve the single point B3LYP calculations. The
IEFPCM model was chosen because it represents the solvent as sur-
face charges spread over the surface of a cavity that contains the
molecule of interest. However, the addition of this term was rela-
tively minimal, and the absolute energy did not vary by much
when the complex was hydrated using this model. In the future,

36
J.S. Holt / Journal of Molecular Structure 965 (2010) 31–38
with b-cyclodextrin has not been characterized experimentally.
The simple equilibrium of dye insertion, as shown in Eq. (1), was
evaluated using the thermodynamic values calculated from the
most stable trans isomer complex. The resulting
dicted the complex would not form spontaneously. Both the mag-
nitude and the sign of the S° and G° values were very different
DG° value pre-
D
D
from the experimental values [12], as shown in Table 4. It has been
reported that the entropy of complexation depends on both the
insertion of the dye molecule and the concurrent displacement of
water molecules that are trapped within the cyclodextrin cavity.
Experimental results from X-ray [36] and neutron diffraction
[22,37] as well as theoretical studies [38,39] have indicated that
there are seven water molecules, on average, within the cyclodex-
trin cavity when in solution. Therefore, the thermodynamic values
for the hydrated complex were calculated according to:
Guest þ b-cyclodextrin ꢃ 7H2O ¡ Guest : b-cyclodextrin þ 7H2O
ð5Þ
When the water molecules were included in the analysis, the
resulting thermodynamic values were much closer to the experi-
mental results, and the sign matched the reported values in all
cases. These results indicate the complex is thermodynamically fa-
vored (negative
DG°), exothermic, and is both an enthalpy and en-
tropy driven process. Further refinement would be possible by
treating these systems at the B3LYP level with solvent effects, as
solvation is known to play an important role in the thermodynam-
ics of complex formation, but these calculations at this level proved
to be cost prohibitive.
4. Discussion
The theoretical model and the 1H-NMR CIS values can be com-
bined to obtain a consistent representation for the trans isomer of
Brooker’s merocyanine within the b-cyclodextrin cavity. The low-
est energy complex, as shown in Fig. 5, matches the structure de-
scribed by the CIS values. Both experimental and theoretical
models result in the n-methyl-pyridyl ring bound near the primary
hydroxyl region of the cyclodextrin cavity, while the H9’ protons
are excluded from the cavity. Even the difference in CIS values be-
tween the H50 and H60 protons can be explained with the opti-
mized theoretical structure. According to the model, these
protons have very different intermolecular interactions with the
cyclodextrin ring. The H60 dye proton is within 2.88 Å and 3.22 Å
of two oxygen atoms in the secondary hydroxyl groups, leading
to attractive intermolecular forces, while the H5’ proton is located
much further from the two closest glycosidic oxygen atoms at 3.16
Å and 3.47 Å. This interaction causes the CIS values to differ. In
addition, the NMR spectra predicted that the H9’ protons had dif-
ferent behavior from the other protons. According to the model,
the H9’ protons are excluded from the cavity and are easily hy-
drated, which was in agreement with the NMR CIS sign change,
while the H8’ protons, which are again close to the H90 in space,
have much stronger interactions with the secondary hydroxyl re-
gion of the cyclodextrin. Therefore, the model is in excellent agree-
Fig. 6. The energy of the optimized structure of Brooker’s merocyanine:b-
cyclodextrin complex as the dye was passed through the center of the cavity (A)
and rotated around the z-axis (B) for the trans isomer (solid line) and the cis isomer
(dotted line). Both isomers had the carbonyl in the up position, and the cis isomer
had the carbonyl extending beyond the secondary hydroxyl region.
it may be necessary to include explicit solvent molecules in and
around the cyclodextrin cavity during the optimization process
to improve the hydration model.
3.3. Thermodynamics of binding
The thermodynamic parameters (DH°, DS°, and DG°) that
describe the 1:1 dye:b-cyclodextrin complexation process have
previously been characterized experimentally [12,15]. Again, as
was the case with the NMR data, the cis isomer could not be iso-
lated, so the thermodynamics of the complexation of the cis isomer
Table 3
Relative energies of the PM3 optimized cis and trans isomers in b-cyclodextrin at higher levels of theory. The structures reported are the lowest energy optimized structures at the
PM3 level (n-methyl-pyridyl group of Brooker’s merocyanine pointed toward the primary hydroxyl groups of the cyclodextrin cavity in both cases). All energies are in hartrees.
Trans isomer complex
Cis isomer complex
PM3 energy
ꢂ2.270
ꢂ2.264
ONIOM energy for PM3 optimized structure
ONIOM energy for ONIOM optimized structure
B3LYP single point energy with BSSE correction
B3LYP single point energy with solvation (IEFPCM–water)
ꢂ673.581
ꢂ673.596
ꢂ4946.277
ꢂ4946.307
ꢂ673.574
ꢂ673.587
ꢂ4946.237
ꢂ4946.281

J.S. Holt / Journal of Molecular Structure 965 (2010) 31–38
37
Table 4
Thermodynamic values for the complexation of Brooker’s merocyanine with b-cyclodextrin. The simple complex does not account for water in the cyclodextrin cavity, while the
hydrated complex includes seven waters displaced during complexation of the dye molecule. G° is calculated at 298 K.
D
D
H° (kJ molꢂ1
)
D
S° (J molꢂ1 Kꢂ1
)
D
G° (kJ molꢂ1
)
Simple complex (Eq. (1))
ꢂ60.8
ꢂ16.4
ꢂ11.2
ꢂ252
29
12
14.5
Complex with hydrated cyclodextrin (Eq. (6))
ꢂ25.1
Experimental resultsa
ꢂ14.8
a
From Ref. [12].
Table 5
Energy, Gibbs free energy, and equilibrium constants for the cis to trans isomerization of Brooker’s merocyanine when free and complexed to b-cyclodextrin.
Brooker’s merocyanine
Cis isomer
Complex
Cis isomer
ꢂ2.264
Trans isomer
0.079
Trans isomer
Energy (hartrees)
G° (kJ molꢂ1
Keq
0.086
ꢂ2.270
D
)
ꢂ15.3
ꢂ27.0
4.88 ꢁ 102
5.34 ꢁ 104
ment with the 1H-NMR results for the trans isomer of Brooker’s
merocyanine within b-cyclodextrin.
tails of the photochemical/protolytic isomerization process of
Brooker’s merocyanine using host–guest chemistry.
The cis-to-trans isomerization was also characterized in order
to understand the differences in the behavior between the free
and complexed dye molecule. The optimized trans isomer is
slightly lower in energy than the optimized cis isomer for either
the free molecule or the dye within the cyclodextrin cavity, as
summarized in Table 5. Therefore, it follows that the cis isomer will
ultimately convert to the trans isomer, as long as the transition
state energy is not too large. The Gibbs free energy for the cis to
trans isomerization process is spontaneous for both the free dye
and the dye in the complex, as given in Table 5. Using the standard
thermodynamic relationship in Eq. (6), the equilibrium constant at
298 K was determined.
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