We have performed
m
PW1PW91 calculations to investigate the conformational characteristics and hydrogen bonds of
p

tert
butylcalix[4]arene (
1
),
p

tert
butylcalix[5]arene (
2
), calix[6]arene (
3
) and ptertbutylcalix[6]arene (
4
). The structures of the different conformers of
1

3
were optimized by using
m
PW1PW91/631+G(d,p) method. The relative stability of the four conformers of
1
is in the following order: cone (most stable) > partialcone > 1,2alternate > 1,3alternate. The relative stability of the conformers of
2
is in the following order: cone (most stable) > 1,2alternate > partialcone > 1,3alternate. The relative stability of the various conformers of
3
is in the following order: cone (
pinched
: most stable) > partialcone > cone (
winged
) ~ 1,2alternate ~ 1,2,3alternate > 1,4alternate > 1,3alternate > 1,3,5alternate. The structures of the various conformers of
4
were optimized by using the
m
PW1PW91/631G(d,p) method followed by single point calculation of
m
PW1PW91/631+G(d,p). The relative stability of the conformers of
4
is in the following order: cone (
pinched
) > 1,2alternate > cone (
winged
) > 1,4alternate ~ partialcone > 1,2,3alternate > 1,3,5alternate > 1,3alternate. The primary factor affecting the relative stabilities of the various conformers of the
1

4
are the number and strength of the intramolecular hydrogen bonds. The hydrogenbond distances are discussed based on two different calculation methods (B3LYP and
m
PW1PW91).
INTRODUCTION
Calix[n]arenes have been receiving much attention as one of the most widely employed molecular frameworks for the construction of many versatile supramolecular systems.
1
The relative stabilities of the various conformations of calix[4]aryl derivatives have been determined by experimental and theoretical methods.
2

8
Pentameric analogue calix[5]arenes
9
,
10
have received relatively less attention due to their difficulties both in the synthesis and in the selective derivatization compared to the other widely employed members of calixarenes. The conformational characteristics of calix[6]arene were studied by using the molecular mechanical method.
11
The most stable conformation of calix[6]arenes
12

14
in the solid state is called a
pinched
cone because two methylene bridges are pointing into the cavity.
Intramolecular hydrogen bond formation determines the stability of conformations of unsubstituted calix[n]arenes.
15
Recently, we have reported the
DFT
B3LYP optimization results for the conformational study and the hydrogen bonding of calix[n]arene (n = 4,5)
16
and the
m
PW1PW91 single point calculation of calix[6]arenes.
17
Density functional theory (
DFT
) is very appealing due to its excellent performancetocost ratio, and
DFT
methods are widely employed in the computational chemistry community. However, the most popular
DFT
method, B3LYP,
18
,
19
cannot successfully describe
π
hydrogen bonding
20
,
21
and B3LYP also fails badly for binding energies dominated by dispersion interactions,
22

24
Hydrogen bonding involves not only dispersion but also electrostatic interactions, polarization (induction), and charge transfer.
25
,
26
Suggestions are new hybrid HartreeFockdensity functional (HFDF) models called the modified PerdewWang 1parameter (
m
PW1) calculation methods,
27

29
such as
m
PW1B95,
m
PWB1K,
m
PW1PW91, which are suitable for hydrogen bonding. The
m
PW1PW model allows obtaining remarkable results both for covalent and noncovalent interactions.
28
The first objective of this research is to determine the relative stability of the different conformational isomers for calix[n]arene (n = 4,5,6) from the total electronic and Gibbs free energies by using the improved
m
PW1PW91 calculation method. The second objective is to compare the intramolecular hydrogen bonds by the hydroxyl groups of the
1

4
using two different calculation methods (B3LYP and
m
PW1PW91).
COMPUTATIONAL METHODS
The initial structures of
p

tert
butylcalix[4]arenes (
1
) and
p

tert
butylcalix[4]arenes (
2
) were constructed by using HyperChem.
30
The initial
pinched
conetype structures of the calix[6]arene (
3
) and
p

tert
butylcalix[6]arene (
4
) were obtained from Cambridge Structure Database (CSD
31a
entry NOBLEV
31b
(
3
) and KENBUA
31c
(
4
)), and other conformations are constructed by using the molecular mechanics (MM), molecular dynamics (MD), and AM1 semiempirical calculations of HyperChem. In order to find the optimized conformers, we executed a conformational search by using a simulated annealing method, which has been described in a previous publication.
32
The conformational isomers of
1

4
obtained from the MM/MD and AM1 calculations were fully reoptimized by using the
DFT
and hybrid HFDF methods to determine the relative energies and the structures of the distinct conformations. Consecutive B3LYP optimizations followed by
m
PW1PW91calculations using Gaussian 03
33
were performed. The normal mode frequencies of the
m
PW1PW91/631G optimized structures have been calculated. Each vibrational spectrum shows no negative value of frequency, which confirms that the optimized structure exists in the energy minimum. From the zeropoint correction by the vibrational analysis and the thermal correction to free energy, Gibbs free energies at 298 K are also calculated by using the
m
PW1PW91/ 631G method.
ChemDraw structures of ptertbutylcalix[4]arene (1), ptertbutylcalix[5]arene (2), calix[6]arene (3) and ptertbutylcalix[6]arene (4)
RESULTS AND DISCUSSION
It is well known that the calix[4]arene and calix[5]arene form strong intramolecular hydrogen bonds among OH groups and represent the cone conformer as the most stable structure.
2
,
9
,
10
Substitution of all the phenolic protons of a
p

tert
butylcalix[4]arene by a bulky alkyl group generally leads to conformationally rigid structures like the tetraethyl ester of
p

tert
butylcalix[4]arene.
4
However, when the substituent is small enough such as a methyl group, the resulting tetramethyl ether of
p

tert
butylcalix[4]arene is no longer rigid, and any anisole ring can rotate
via
oxygenthroughtheannulus to give a mixture of the four possible conformers.
5

8
mPW1PW91 Optimized Total,aGibbs Free and Relative Energies, and Dipole moments of the Various Conformersbof1
^{a}The unit of total energy is in a.u. Error limits in these calculations are about 0.01 kcal/mol. ^{b}Conformer: “pc” denotes partialcone, “12a” means 1,2alternate, etc. ^{c}Total electronic energies (a.u.) at 0 K. ΔE (kcal/mol) is the relative energy with respect to the most stable cone conformation. ^{d}Sum of electronic and thermal Gibbs free energies at 298 K. ΔG (kcal/mol) is the relative free energy. ^{e}Total Dipole moment in Debye calculated from the final structure by using mPW1PW91/631+G(d,p)method.
The
p

tert
butylcalix[4]arene (
1
) and
p

tert
butylcalix[5]arene (
2
) are identical with respect to the numbers of up/down conformations that are possible, and for convenience the same descriptive names are used for both: cone, partial cone, 1,2alternate or 1,3alternate. The
DFT
optimizations without any constraint were carried out for the four conformers of the
1
and
2
.
1
reports the
m
PW1PW91/631+G(d,p) optimized total electronic and relative energies, and dipole moments of the four conformers of
1
. Sums of total electronic and thermal Gibbs free energies calculated from the
m
PW1PW91/631G method are also listed from the zeropoint correction by the vibrational analyses and thermal correction to free energy at 298 K. The calculation results suggest that the cone conformer is the most stable among the conformational isomers of
1
in the following order: cone > partialcone > 1,2alternate > 1,3alternate.
mPW1PW91 Optimized Total,aGibbs Free and Relative Energies, and Dipole moments of the Various Conformersbof2
^{ae}See the footnotes of Table 1
mPW1PW91 Optimized Totala, Gibbs Free and Relative Energies, and Dipole moments of the Various Conformersbof3
^{ae}See the footnotes of Table 1
The
m
PW1PW91/631+G(d,p) calculated relative stabilities of the conformations of
1
in
1
suggest that the cone conformer is 7.53 kcal/mol more stable than partialcone, 10.85 kcal/mol more stable than 1,2alternate, and 12.25 kcal/mol more stable than 1,3alternate analogue, respectively. In the case of the original calix[4]arene without
p

tert
butyl group, the relative stability was calculated in different order, where 1,3alternate conformer had slightly better stability than the 1,2alternate analogue.
5d
2
shows the total electronic, Gibbs free and relative energies, and dipole moments of the four distinct conformers of
p

tert
butylcalix[5]arene (
2
) optimized by the
m
PW1PW91 calculations. The cone conformer is the most stable one among the conformational isomers of
2
. However, the order (cone > 1,2alternate > partialcone > 1,3alternate) of the relative stability for the conformers of
2
is different from
1
. The
m
PW1PW91/631+G(d,p) calculated relative stabilities of the conformations of
2
in
2
suggest that the cone conformer is 4.23 kcal/mol more stable than 1,2alternate, 8.49 kcal/mol more stable than partialcone, and 13.48 kcal/mol more stable than 1,3alternate analogue, respectively.
3
shows the total electronic, Gibbs free and relative energies, and dipole moments of the conformers of calix[6]arene (
3
) calculated by the
m
PW1PW91 calculations. During the optimization of 1,2,4alternate conformation, this structure spontaneously changed to the most stable
pinched
cone. Therefore, the energy of the 1,2,4alternate conformer is omitted in
3
and
4
. The relative stabilities of
m
PW1PW91/631+G(d,p) optimization results of
3
are in the following order: cone (
pinched
: most stable) > partialcone > 1,2alternate ~ 1,2,3alternate ~ cone (
winged
) > 1,4alternate ~ 1,3alternate > 1,3,5alternate. The calculated relative stabilities of the conformations of
3
in
3
suggest that the cone (
pinched
) conformer is 9.38 kcal/mol more stable than partialcone, about 13 kcal/mol more stable than cone (
winged
), 1,2alternate and 1,2,3alternate analogues, about 17 kcal/mol more stable than 1,3alternate and 1,4alternate, and 20.48 kcal/mol more stable than 1,3,5alternate, respectively.
mPW1PW91 Optimized Totalaand Relative Energies and Dipole Momentsof the Various Conformersbof4
^{a,b,c,e}See the footnotes of Table 1. ^{d}mPW1PW91/631+G(d,p) single point calculation energy from the MPW1PW91/631G(d,p) optimized structure.
The
m
PW1PW91 calculations from three different basis sets are compared. For the relative stabilities of four different conformer in the
1

3
, Δ
E
’s calculated from 631+G(d,p) basis set are smaller than the values obtained from the 631G(d,p) and 631G basis sets in following order: 631+G(d,p) < 631G(d,p) < 631G. The higher level calculation shows less energy gap between the most stable cone conformer and the less stable analogues.
We also report the calculated results of the
m
PW1PW91 calculations for the conformers of
ptert
butylcalix[6]arene (
4
). Since the molecule
4
(156 atoms) is much bigger than the debutylated calix[6]arene
3
(84 atoms), only
m
PW1PW91/631+G(d,p) single point calculation following the
m
PW1PW91/631G(d,p) optimization of
4
was allowed with our computing resources.
4
shows the total and relative energies of the various conformers of
4
. The relative stabilities of the
m
PW1PW91/631+G(d,p) calculation results of
4
are in the following order: cone (
pinched
) > 1,2alternate > cone (
winged
) ~ 1,4alternate > partialcone > 1,2,3alternate > 1,3,5alternate ~ 1,3alternate. The
m
PW1PW91/631+G(d,p) calculated relative stabilities of the conformations of
4
in
4
suggest that the cone conformer is 7.86 kcal/mol more stable than 1,2alternate, about 13.1 kcal/mol more stable than cone (
winged
) and 1,4alternate, 15.20 kcal/mol more stable than partialcone, 19.10 kcal/mol more stable than 1,2,3alternate conformers, respectively.
One of the important factors affecting the relative stabilities of the various conformers of the calix[n]arenes is the number and strength of the intramolecular hydrogen bonds. The good stability of 1,2alternate conformer of
p

tert
butylcalix[5]arene
2
among the less stable conformers can be explained by the four hydrogen bonds, whereas
2
(partial cone) has three and
2
(1,3alternate) has one Hbonds. In
Chart 1
, we have compared the
m
PW1PW91/631+G(d,p) calculated relative energies of the conformers of
2
and the number of Hbonds to prove an excellent proportionality between two values.
Comparison of the mPW1PW91/631+G(d,p) optimized relative stabilities of the conformers of ptertbutylcalix[5]arene 2 and the number of Hbonds. The relative energies of 2 is proportional to the value which is obtained by one Hbond energy (~4.0 kcal/mol)16 multiplied by the scaled number (5 (the number of Hbonds in the most stable cone conformer)  the number of Hbonds).
Comparison of the mPW1PW91/631+G(d,p) optimized relative stabilities of the conformers of calix[6]arene 3 and the number of Hbonds. The relative energies of 3 is proportional to the value which is obtained by one Hbond energy (~4.0 kcal/mol) multiplied by the scaled number (6 (the number of Hbonds in the most stable cone conformer)  the number of Hbonds).
Again, the good stability of 1,2,3alternate conformer among the less stable conformers of
3
can be explained by the four hydrogen bonds, whereas
3
(1,3alternate) has three Hbonds and
3
(1,3,5alternate) has none. In
Chart 2
, we have compared the
m
PW1PW91/631+G(d,p) calculated relative energies of the conformers of
2
and the number of Hbonds to prove the proportionality between two values.
5
lists the
m
PW1PW91/631+G(d,p) calculated distances and angles of intramolecular hydrogen bonds of
p

tert
butylcalix[4]arene (
1
). In general, if O…..O distance is less than 3.0 A, one interprets that the (OH…O) hydrogen bond is relatively strong for this intramolecular case.
34
The O..…O distances of
2
.645 ~ 2.777 A in
5
suggest that our calculated distances of
1
are in accord with the experimental distances (2.727 ~ 2.779 A in
8
) of the intramolecular hydrogen bonds (O..…O) of the
p

tert
butylcalix [4]arene and calix[4]crown5ether obtained from Cambridge Structure Database.
31
mPW1PW91/631+(d,p) Optimized Distances (Å) and Angles of Hydrogen Bonds of1
mPW1PW91/631+(d,p) Optimized Distances (Å) and Angles of Hydrogen Bonds of 1
In order to compare our calculated Hbond distances of
t
butylcalix[4]arene (
2
)with the values of the strong intramolecular hydrogen bonds of tbutylcalix[4]arene (
1
), we have tabulated the
m
PW1PW91/631+G(d,p) calculated Hbond distances of
2
in
6
. The average calculated distances (2.753 ~ 2.846 A in
6
) of the intramolecular hydrogen bonds of tbutylcalix[5]arene (
2
) are longer than the values (2.645 ~ 2.777 A in
5
) of
p

tert
butylcalix[4]arene (
1
). FTIR studies already confirmed the intramolecular character of the Hbonding and showed that it is strongest for the cyclic tetramer (
1
) and weakest for the cyclic pentamer (
2
).
39
mPW1PW91/631+(d,p) Optimized Distances (Å) and Angles of Hydrogen Bonds of2
mPW1PW91/631+(d,p) Optimized Distances (Å) and Angles of Hydrogen Bonds of 2
mPW1PW91 Optimized Distances (Å) and Angles (°) of Intramolecular Hydrogen Bonds of3
mPW1PW91 Optimized Distances (Å) and Angles (°) of Intramolecular Hydrogen Bonds of 3
7
lists the
m
PW1PW91/631+G(d,p) optimized distances and angles of intramolecular hydrogen bonds of
3
. The O..…O distances of 2.614 ~ 2.790 Å in
7
suggest that these calculated values in the calix[6]arene (
3
) display strong hydrogen bonds. The calculated O…..O distances (2.687 ~ 2.790 Å) of the less stable conformations of
3
are 0.07 ~ 0.15 Å longer than the value (2.614 Å) of the most stable cone conformer.
Experimental Distances(O..…O) of Intramolecular Hydrogen Bonds of the Cone Conformers of Calix[n]arenes
Experimental Distances(O..…O) of Intramolecular Hydrogen Bonds of the Cone Conformers of Calix[n]arenes
mPW1PW91Optimized Average O…O Distances (Å) of Intramolecular (OH…O) Hydrogen Bonds of1,2and3
^{a}B3LYP calculated O…O distances are obtained from references 16 and 17. ^{b}Difference: mPW1PW91 optimized distance minus B3LYP calculated value.
Since the
m
PW1PW91/631+G(d,p) optimization of the bigger
t
butylcalix[6]arene (
4
) was not possible due to our limited computational resources, the distances and angles of the intramolecular hydrogen bonds of
4
are not listed in this publication. The average calculated O…..O distances (2.614 Å of calix[6]arene (
3
) in
7
and 2.640 Å of tbutylcalix[6]arene (
4
) from the B3LYP optimization in reference 17) of the intramolecular hydrogen bonds of the cone conformers are slightly longer than the experimental crystal structure values (2.585 and 2.597 Å, respectively) in
8
.
We have compared the
m
PW1PW91 optimized hydrogenbond distances of
1
,
2
and
3
with the values obtained from previous B3LYP calculation method.
9
shows the
m
PW1PW91 optimized average O…..O distances (2.645 ~ 2.777 Å) in
1
are about 0.015 Å shorter than the values (2.650 ~ 2.796 Å) of B3LYP method. The
m
PW1PW91 optimized average O…..O distances (2.754 ~ 2.846 Å) in
2
are also shorter than the values (2.765 ~ 2.861 Å) of B3LYP method. The
m
PW1PW91 optimized average O…..O distances (2.614 ~ 2.790 Å) in
3
are about 0.022 Å shorter than the values (2.640 ~ 2.795 Å) of B3LYP method. Those
m
PW1PW91 optimized distances in
3
are closer to the experimental results (2.585 Å in
8
).
Comparison betweenmPW1PW91aand B3LYPbmethods for the Calculated Relative Energies of the conformers of14
^{a}mPW1PW91/631+(d,p) calculated relative energies are copied from Tables 14. ^{b}B3LYP calculated relative energies are obtained from references 16 and 17. ^{c}Difference: mPW1PW91 optimized relative energy minus B3LYP calculated value.
In
10
, we have compared the relative energies of
m
PW1PW91 calculations of the various conformers of
1

4
with the values obtained from previous B3LYP method. The differences in
10
tell us that the relative energies obtained from the
m
PW1PW91 method always give smaller gap than the B3LYP calculated values. The range is ‒0.44 ~ ‒2.96 kcal/mol (average ‒1.2 kcal/mol) except one case (‒7.01 kcal/mol) of
4
(1,3,5alternate).
Since the
m
PW1PW91 optimized lowresolution figures of the various conformers of
1

4
are very similar to the structures obtained from previously published B3LYP calculations,
16
,
17
we report the structures of the most stable cone conformers for the respective molecules of
1

4
in
. 1
. The cone conformer (
1
(cone):
. 1)
(a) having four hydrogen bonds and
2
(cone) (
. 1
(c)) having five hydrogen bonds are the most stable, as shown in experimental studies.
2h
,
18
,
19
The
pinched
cone conformations of calix[6]arene (
1
(e) and
1
(g)) having six hydrogen bonds are the most stable conformers of
3
and
4
, respectively.
mPW1PW91/631+G(d,p) optimized molecular structures of the cone conformers of 13. (a) Bottom view of 1 (ptertbutylcalix[4]arene) by PosMol40 with hydrogen bonds shown, (b) side view of 1 (ptertbutylcalix[4]arene) by Chem3D41 without hydrogen atoms, (c) bottom view of 2 (ptertbutylcalix[5]arene) by PosMol, (d) side view of 2 (ptertbutylcalix[5]arene), (e) bottom view of 3 pinched cone (calix[6]arene) by PosMol, (f) side view of 3 pinched cone (calix[6]arene) by Chem3D. (g) mPW1PW91/631G(d,p) optimized molecular structures of bottom view of 4 pinched cone (ptertbutylcalix[6]arene) by PosMol and (h) side view of 4 pinched cone (ptertbutylcalix[6]arene) by Chem3D. Atoms that are within a certain distance (the bond proximate distance) from one another were automatically marked as bonded.40
CONCLUSION
The relative stabilities of the conformers of
p

tert
butylcalix[4]arene (
1
),
p

tert
butylcalix[5]arene (
2
), calix[6]arene (
3
) and
p

tert
butylcalix[6]arene (
4
) were calculated by using
m
PW1PW91/631+G(d,p) method. The relative stability of four conformers of
1
is in the following order: cone (most stable) > partialcone > 1,2alternate > 1,3alternate. The relative stability of the various conformers of
2
is in the following order: cone (most stable) > 1,2alternate > partialcone > 1,3alternate. The relative stability of the conformers of
3
is in the following order: cone (
pinched
: most stable) > partialcone > cone (
winged
) ~ 1,2alternate ~ 1,2,3alternate > 1,4alternate > 1,3alternate > 1,3,5alternate.
The structures of different conformers of
4
were optimized by using the
m
PW1PW91/631G(d,p) method followed by single point calculation of
m
PW1PW91/631+G(d,p). The relative stability of the conformers of
4
is in the following order: cone (
pinched
) > 1,2alternate > cone (
winged
) > 1,4alternate ~ partialcone > 1,2,3alternate > 1,3,5alternate > 1,3alternate.
The primary factor affecting the relative stabilities of the various conformers of the
1

4
are the number and strength of the intramolecular hydrogen bonds. Each hydrogen bond contributes about 4 kcal/mol for the stability of the conformers of these calix[n]arenes.
The
m
PW1PW91 optimized average Hbond distances (2.645 ~ 2.846 Å) in
1

4
are slightly shorter than the values (2.640 ~ 2.861 Å) calculated from B3LYP method.
Acknowledgements
This work was supported by the Young Investigator Research Program of ChungAng University 2007 year. The large portions of the computations were carried out with use of the computer facilities at the Research Center for Computational Science of the Okazaki National Research Institutes in Japan.
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