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NISHIMURA, Yasuhiro

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大嶋, 正人

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オオシマ, マサト

Oshima, Masato

Isozaki, Yoko

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*1 Associate Professor, Nanochemistry, Tokyo Polytechnic University  *2 Graduate student 
 Received Sept. 24, 2008  E-mail:oshima@nano.t-kougei.ac.jp 
 
Analysis of the α-Cyclodextrins including p-Nitrophenol  
as a Guest Molecule with DFT Calculations. 
 
Masato Oshima*1 Yoko Isozaki*2 
 
Abstract: Structure optimizations of the inclusion complex that was composed of 
α-cyclodextrin with p-nitrophenol were performed by density functional theory (DFT) with 
several calculation conditions.  These calculation conditions were evaluated by comparing the 
optimized structures with X-ray crystallographically determined structure and the interactions 
between α-cyclodextrin and p-nitrophenol were discussed using the donor-accepter interactions 
that derived from natural bond orbital (NBO) analysis. 
 
Introduction 
Cyclodextrins are macrocyclic oligosugers most commonly composed of 6-8 glucosidic units.  
Cyclodextrins and their derivatives have large cavity at the center and work as host molecules by accepting 
small molecules (called guests) forming inclusion complexes [1-3].  Although, the details of the 
interactions between the host and the guest molecules are important in the study of the inclusion complexes, 
the methods to obtain the direct information are limited.  In solution state, the important direct 
information can be obtained by the several measurement techniques of 2D nuclear magnetic resonance 
(NMR) spectroscopy [1, 4].  In solid state, X-ray single crystallographic analyses are also good method 
and it gives significant results [1, 5].  Both of these methods are useful, but is nevertheless 2D NMR 
cannot completely distinguish the complex signals, and the results of crystallographic analyses are not 
necessarily the same as in the solution state.  Commonly, ab initio and density functional theory (DFT) 
calculations are useful in this type of situation; however, the calculations of the inclusion complexes are 
one of the difficult things and most of previous studies were used semi-empirical calculations or molecular 
mechanics [1].  One of the reasons is because QM/MM [6], which combine a quantum mechanical (QM) 
method with a molecular mechanics (MM) method, and ONIOM [7], which can combine any number of 
molecular orbital method, as well as molecular mechanics 
methods, used for the calculation of the large molecules is not 
applicable.  In the both of QM/MM and ONIOM, the basic 
methodology is that to divide a large molecule into an important 
part and the part which are not so.  As for the inclusion 
complexes, the whole internal circumference of host molecule 
interacts with a guest molecule; therefore we cannot divide the 
complexes into parts.  It is insufficient for the reason of cannot 
but use a small basis set, some useful information are expected 
by the recent DFT calculation method.  In this paper, we report 
the theoretical analysis of the interaction between host and guest 
molecules with DFT calculations.  The calculations were 
performed to the inclusion complex 1 that was composed of 
α-cyclodextrin and p-nitrophenol without to divide into parts.  
 
O
OHHO
OH
O
HO
OH
O
HO
O
HO
OH
O
HO
O
HO
OH
O
HO
O
HO
OH
O
OH
O
OH
HO
O
OH
O
OH
N
O O
A
B
C
D
E
F
 
1 
Figure 1: The inclusion complex composed 
of α−cyclodextrin and p-nitrophenol with 
glucose ring labels A to F. 
83
東京工芸大学工学部紀要 Vol. 31 No.1（2008） 
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 31 No.1 (2008) 
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 31 No.1 (2008) 
Computational Methods 
All geometry optimizations and population analyses were carried out with density functional theory 
(DFT)[8] at Becke’s three parameters (B3) exchange functional along with the Lee-Yang-Parr (LYP) 
non-local correlation functional (B3LYP) level [9, 10] or Truhalar group’s hybrid meta-GGA functional 
(MPW1B95) [11].  Split valence basis set 3-21G [12] or 3-21+G** with extra polarization [13] and 
diffuse [14] functions were used in all calculations.  The stationary points of 1b-d were confirmed as 
energy minima.  The calculations of 1e and 1f in the presence of water by IEF-PCM method [15] were not 
converged completely under the usual criteria for determining when a geometry has converged, because of 
1e and 1f were shown vary flat potential energy surface around the minimum.  These calculations were 
terminated when the forces are smaller than the cutoff value over several cycles even the displacement was 
larger than cutoff value.   Atomic Natural population analysis (NPA) and inter atomic donor-acceptor 
interactions were derived from natural bond orbital (NBO) analysis [16].  The DFT and the NBO 
calculations were performed using the Gaussian03 program package [17]. 
Results and Discussions 
Crystallographically determined structure [17] 1a provided initial geometries for the optimization of 1 
and one of the optimized structure 1b that was obtained by B3LYP level calculation with 3-21G basis set 
was shown in Figure 2. 
8.69 Å
2.4305 Å
10.34 Å
10.26 Å
2.4290 Å
9.17 Å
1a 1b
O4A
O3A
O2A
O4B
O3B
O2B
O4C
O4D
O4E
O4F
O3C
O3D
O2D
O3E
O3F
O2F
O2E
O2C
O4A
O3A
O2A
O4B
O3B
O2B
O4C
O4D
O4E
O4F
O3C
O3D
O2D
O3E
O3F
O2F
O2E
O2C
Side View
Top View
H3B
2.87 Å
H3E
H3B
H3E
 
Figure 2: Crystallographically determined structure (1a) and the optimized structure by B3LYP/3-21G (1b).  As for 
the colored ball, yellow, red, blue, and aqua express carbon, oxygen, nitrogen, and hydrogen, each. 
84 
Analysis of the α-Cyclodextrins including p-Nitrophenol as a Guest Molecule with DFT Calculations. 
It is clear from the shape of 1a and 1b, the cyclodextrin rings of 1a was transformed along the shape of 
the guest molecule.  The shape can be considered to be an oval, the major and the minor axises were 
10.34 Å and 8.69 Å, respectively.  On the other hand, the major axis of 1a became the minor axis with 1b 
and the distances of the lengthwise and crosswise directions of 1b in the 
figure 2 were 9.17 Å and 10.26 Å each.  In case of 1b, seeing from the 
top, the guest molecule was lapped over on a straight line to link the 
O4A to O4D, but moved in 1a.  The location of p-nitrophenol in 
α-cyclodextrin was illustrated in Figure 3 and the cup like structure 
showed the shape of the host.  The anomeric oxygen atoms O4A and 
O4D were close to the guest hydrogen atoms H2’ and H2, respectively.   
This previous result suggested that the interactions between O4A-H2’ 
and O4D-H2 were overestimated in this calculation conditions.  It 
seemed that the hydrogen atoms H3B and H3E of 1a were located 
closer to the aromatic ring plane of p-nitrophenol and the distances between the plane and H3B or H3E 
were 2.87 Å and 3.14 Å each (Table 1).  Meanwhile in 1b, these hydrogens were more than 3.6 Å away 
from the aromatic ring plane and the facts showed that some interactions cannot evaluated in this 
calculation. 
9.57 Å
2.4453 Å
10.46 Å
8.90 Å
2.4199 Å
10.05 Å
1c 1d
O4A
O3A
O2A O4B
O3B O2B O4C
O4D
O4EO4F
O3C
O3D
O2DO3EO3F
O2F
O2E
O2C
O4A
O3A
O2A O4B
O3B
O2B
O4C
O4D
O4E
O4F
O3C
O3D
O2D
O3E
O3F
O2F
O2E
O2C
Side View
Top View
H3B
2.89 Å
H3E
H3B
H3E
 
Figure 4: The optimized structures by B3LYP/3-21+G** (1c) and MPW1B95/3-21+G** (1d).  As for the colored 
ball, yellow, red, blue, and aqua express carbon, oxygen, nitrogen, and hydrogen, each. 
OH
N
OO
H2
H3H3'
H2' 1
2
3
4
2'
3'
O4A O4D
 
Figure 3: The interactions between 
O4A-H2’ and O4D-H2. 
85
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 31 No.1 (2008) 
Table 1: The structural data of 1a-f.a 
 O4A···H2’ H2···O4D Distance from H3B to aromatic ring plane
Distance from H3E to 
aromatic ring plane 
1a 
1b 
1c 
1d 
1e 
1f 
2.316 
2.078 
2.304 
2.176 
2.338 
2.364 
2.228 
2.138 
2.351 
2.203 
2.347 
2.345 
2.87 
3.70 
2.89 
2.36 
3.19 
2.85 
3.14 
3.66 
2.92 
2.57 
3.21 
2.73 
a Inter atomic distances and distances from hydrogen to aromatic ring plane are shown in Å. 
 
The 3-21G basis set was too small to calculation that including weak interactions between host and 
guest molecules and then the 3-21+G** basis set was used as an enough large one.  Furthermore, it can be 
pointed out that the B3LYP functional is not enough to calculate the molecule including weak interactions 
as the general tendency.  The MBW1B95 functional is a one of hybrid meta-GGA functional and the 
functional is improved the calculation including hydrogen bond and weak interactions.  The optimized 
structures by B3LYP level with 3-21+G** (1c) and MBW1B95 level with 3-21+G** (1d) were shown in 
Figure 4 and seemed the interaction between p-nitrophenol and glucose ring B or E were estimated than 1b.  
Comparing the structure of 1c and 1d with 1b, the distances of O4A···H2’ and H2···O4D of 1c and 1d were 
larger than that of 1b and the distances of H3B···aromatic ring plane and H3E···aromatic ring plane of 1c 
and 1d were smaller than that of 1b.  By this transform, the shapes of 1c and 1d were closer to 1a than 1b.  
However, the glucose rings B and E were bent toward p-nitrophenol.  Especially, the ring B of 1d was 
close to p-nitrophenol by the hydrogen bond between O2B and phenolic hydroxyl group. 
 
This inconvenience was resolved with the calculation including solvent effect.  The optimizations 
were performed in the presence of water (ε = 78.39) using IEF-PCM method and the shapes by B3LYP 
level with 3-21+G** (1e) and MPW1B95 level with 3-21+G** (1f) were shown in Figure 5.  Among the 
all structures obtained in this study, the shape of 1f was nearest to 1a. 
 
One of the remaining problems is the hydrogen bond between secondary hydroxyl groups.  It has 
great influences to the shape of the complex 1 was that the strength of hydrogen bond of inter-glucose rings, 
such as O2A-H···O3B etc.  The C2-OH group of one glucopyranoside unit can form a hydrogen bond with 
the C3-OH group of the adjacent glucopyranose unit.  In the cyclodextrin, a complete secondary belt is 
formed by these hydrogen bonds; therefore the estimation of the strength of hydrogen bond affects the size 
of secondary hydroxyl groups’ side.  To the analysis of the strength, the distances between oxygen atoms 
of secondary hydroxyl groups were shown in Table 2.  Normally, it is reasonable to compare the distances 
between oxygen and hydrogen atoms; however the positions of hydrogen atoms determined by X-ray 
crystallographic analysis were not enough reliability.  The overestimation of the strength of hydrogen 
bond was obvious from the results that the most of the calculated inter-oxygen atoms’ distances (1b-f) were 
smaller than that of X-ray crystallographic analysis (1a).  
 
86 
Analysis of the α-Cyclodextrins including p-Nitrophenol as a Guest Molecule with DFT Calculations. 
9.47 Å
2.4533 Å
10.28 Å
8.96 Å
2.4312 Å
10.38 Å
1e 1f
O4A
O3A
O2A
O4B
O3B
O2B
O4C
O4D
O4EO4F
O3C
O3D
O2D
O3E
O3F
O2F
O2E
O2C
O4A
O3A
O2A
O4B
O3B
O2B
O4C
O4D
O4EO4F
O3C
O3D
O2D
O3E
O3F
O2F
O2E
O2C
Side View
Top View
H3B
3.19 Å
H3E
H3B
H3E
2.85 Å
 
Figure 5: The structures by B3LYP/3-21+G** (1e) and MPW1B95/3-21+G** (1f) with solvent effect.  As for the 
colored ball, yellow, red, blue, and aqua express carbon, oxygen, nitrogen, and hydrogen, each. 
 
Table 2: The distances (Å) of oxygen atoms of inter-glucose rings 
 O2F···O3A O2A···O3B O2B···O3C O2C···O3D O2D···O3E O2E···O3F 
1a 
1b 
1c 
1d 
1e 
1f 
3.068 
2.725 
2.803 
2.768 
2.740 
2.787 
2.862 
2.771 
2.722 
2.690 
2.711 
2.748 
3.135 
2.793 
2.756 
2.732 
2.724 
2.781 
2.846 
2.882 
2.795 
2.706 
2.757 
2.777 
2.650 
2.724 
2.723 
2.667 
2.691 
2.755 
2.859 
2.763 
2.755 
2.706 
2.728 
2.765 
 
As the detail interactions between host and guest molecules, the donor-accepter interactions of 1f were 
analyzed using NBO program.  The obtained stabilization energies by the electron donation were 9.11 and 
21.01 kcal/mol from the host to the guest and from the guest to the host, respectively.  The principal 
interactions of 9.11 kcal/mol were 1.95 and 2.11 kcal/mol stabilization energies from the lone pair on O4A 
and O4D to σ*-H2’-C2’ and σ*-H2-C2, respectively (Table 3).   The details of the 21.01 kcal/mol were 
also shown in Table 4.  The vacant σ*-H3-C3 and σ*-H5-C5 orbitals on each glucopyranoside unit 
expanded to inside and these orbitals worked as main electron accepters from p-nitrophenol.  The 
87
ACADEMIC REPORTS Fac. Eng. Tokyo Polytech. Univ. Vol. 31 No.1 (2008) 
electrons at π-orbitals and σ-H-C orbitals 
of aromatic ring were donated to mainly 
the σ*-H3-C3 and σ*-H5-C5 orbitals on 
glucopyranoside units A, C, D, and F.  
The orbitals σ*-H5A-C5A, σ*-H5C-C5C, 
σ*-H5D-C5D, and σ*-H5F-C5F were 
accepted additional electron donations 
from lone pairs at oxygen atoms of NO2 
group, therefore the large stabilization 
energies were obtained. 
 
Conclusion 
The structure optimizations of the 
large inclusion complex composed of 
α-cyclodextrin with p-nitrophenol were 
carried out by density functional theory 
and the result of the calculation using 
recently reported new functional 
MBW1B95 level with 3-21+G** basis set 
showed basically good correspondence to 
the X-ray crystallographically determined 
structure.  Using the obtained structure, 
the detail analyses between donor and 
accepter orbitals were performed.  The 
stabilization energies were obtained 
mainly by the electron donation from the 
guest molecule to the vacant σ*-H3-C3 
and σ*-H5-C5 orbitals, and additionally 
by the electron donation from the lone 
pairs on anomeric O4s, σ-H3-C3, and 
σ-H5-C5 orbitals to the guest molecule.  
 
Acknowledgment 
The authors are grateful to Professor Keiko Takahashi for helpful suggestions.  This work was 
partially supported by the “Academic Frontier” Project for Private Universities (2006-2008), matching 
fund subsidy from Ministry of Education, Culture, Sports Science and Technology. 
 
References 
[1] H. Dodziuk (Ed.), Cyclodextrins and Their Complexes, Wiley-VCH Verlag GmbH & Co. KGaA, 
Weinheim (2006). 
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Table 3: The stabilization energies from the host to the guest 
Donor Accepter 
Stabilization energy 
[kcal/mol] 
O4A 
O4D 
σ-C5A-H5A 
σ-C5C-H5C 
σ-C5D-H5D 
σ-C5F-H5F 
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88 
Analysis of the α-Cyclodextrins including p-Nitrophenol as a Guest Molecule with DFT Calculations. 
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90 


Analysis of the α-Cyclodextrins including p-Nitrophenol as a Guest Molecule with DFT Calculations.

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