Chemical Physics Letters 383 (2004) 376–379

www.elsevier.com/locate/cplett

A new suggested class of organic tubular structures

Francesco Ferrante, Gianfranco La Manna *

Dipartimento di Chimica Fisica ‘F. Accascina’, Universit�aa degli Studi di Palermo, Viale delle Scienze, 90128 Palermo, Italy

Received 3 November 2003; in final form 17 November 2003

Published online: 5 December 2003

Abstract

A DFT study has been performed on monomers and dimers of new cyclic structures, cyclodioxabislactams, which are expected to

bring about tubular structures through a stacking process settled by hydrogen-bonding between antiparallel peptidic groups.

Different stacking modes have been found with significant effects on the energetics of the assembling process.

� 2003 Elsevier B.V. All rights reserved.

1. Introduction

Organic tubular structures are natural systems of

noticeable interest for their important functions in bi-

ology [1]. At the same time, a wide research field has

been developed on the construction of synthetic tubularstructures for several applications, in the field of the

host–guest chemistry (sensors, reaction environments,

catalysts, ionic carriers, etc.) [2–4]. Open-ended hollow

tubular structures were obtained for the first time ten

years ago from cyclic DD,LL-peptide rings [5–7] through a

stacking process due to hydrogen bonding between an-

tiparallel peptidic groups. Nowadays several classes of

organic tubular structures are known, set up by self-assembling of a macrocyclic unit [8,9].

One of the last synthesised organic tubular systems is

that set up by cyclobisamides (CBAn), having the gen-

eral formula (–CO–(CH2)n–CO[–NH–CH(CO2Me)–

CH2–S–]2), where the cavity size depends on the number

of methylene groups in the monomer; they were ob-

tained from the reaction between the acylic dichloride of

a dicarboxylic acid and LL-cystine dimethylester [10].A recent DFT computational study on monomers

and dimers of CBAn (n ¼ 4, 5, 6) by our research group

[11] allowed us to test the reliability of the method of

* Corresponding author.

E-mail address: lamanna@unipa.it (G. La Manna).

0009-2614/$ - see front matter � 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2003.11.055

calculation by the comparison of the obtained geome-

tries with the available experimental data on solid phase.

Moreover, the calculation enabled us to understand the

essential features that are needed for giving rise to an

efficient self-assembly process by hydrogen bonds be-

tween the peptidic groups. The main features we foundare the following: (1) the H-bond formation is particu-

larly efficient when the peptidic groups belonging to two

adjacent monomers are aligned along a longitudinal axis

in an antiparallel way; (2) the optimal conformation of

the monomer in the polymeric structure might have an

energy value close to that corresponding to the absolute

minimum, so the energy needed for reaching the ge-

ometry suitable for the hydrogen bond formation iseasily recovered through the polymerisation process.

Moreover, it is useful to provide cyclic monomeric

structures with an adjustable cavity size. These results

made it possible to set out on a research of new struc-

tures having the properties listed above. By examining

possible macrocyclic structures we selected some cyc-

lodioxabislactams, whose general formula is –(CH2)m–

CO–NH–(CH2)p–O–(CH2)n–O–(CH2)q–NH–CO–, wheretwo peptidic groups are present, like in CBAn, and the

variables m, n, p and q allow for a large flexibility of the

cavity shape and size. In the systems here studied, pic-

tured in Fig. 1, the p and q indexes are taken equal to

three and the considered couples of values for n and m

are (2,6), (4,6), (6,6) and (6,8), respectively. The systems

are labelled as CBL(n,m).

O(CH2)n O

(CH2)q(CH2)p

HN NH

C CO O(CH2)m

Fig. 1. Molecular structure of cyclodioxabislactams.

Table 1

Energy values, in kJ mol�1, of the studied systems (see text for

definitions)

Conf. Edim � EmðdÞ Edef DE

[CBL(2,6)]2 a )42.2 6.9 )35.3[CBL(2,6)]2 b )40.9 8.6 )32.3[CBL(2,6)]3 b )90.5 17.7 )72.8[CBL(4,6)]2 b )38.2 14.1 )24.1[CBL(6,6)]2 a )40.3 1.1 )39.2[CBL(6,8)]2 a )41.5 3.2 )38.3

OH

O

O

O

OH

H

H

O

O

O

O

H

H

F. Ferrante, G. La Manna / Chemical Physics Letters 383 (2004) 376–379 377

2. Methods of calculation

The geometries of the monomers were fully optimised

starting from suitable conformations, which were de-

rived from an analysis performed by using a home-made

program based on the intersection algorithm [12]. In

particular, a conformational analysis at PM3 level was

performed on all possible fragments of five connectedatoms of the backbone and on the intersections of

fragments at lowest energies with the constraint of the

ring closure. The atoms of the monomers are close to an

average molecular plane and the peptidic groups are

antiparallel with respect to the plane. Afterwards the

electrostatic potential concerning some molecular sec-

tions was examined, since it turned out to be a very

useful tool for checking the ability of a given confor-mation to provide an efficient stacking process. Finally,

two monomers with the same geometry were aligned

along the polymerisation direction and the geometry of

the dimer was optimised.

The geometry optimisations of the considered mono-

meric cyclic systems CBL(n,m), as well as that of the di-

mers, were carried out by using the Resolution of Identity

Density Functional Theory (RI-DFT) method [13,14].The Generalized Gradient Approximation (GGA) BP86

functional [15,16] was adopted, with a split-valence plus

polarisation basis set (7s4p1d/4s2p) contracted to

[3s2p1d/2s1p] [17]. The RI-DFT method is implemented

in the program package TURBOMOLEURBOMOLE [18–20]; its reli-

ability was verified in the literature [21,22] and tested by

comparing the optimised geometrical values of the sim-

plest monomers as obtained by standard DFT and RI-DFT calculations (root mean square deviation¼ 0.006 �AAfor bond lengths and 0.3� for bond and dihedral angles).

The energy values, at the optimised geometries, were

obtained by using the hybrid functional B3LYP within

the DFT approach with the cc-PVDZ basis set, as im-

plemented in the GAUSSIANAUSSIAN 98W package [23].

O

O

OH O

O

O

O

H

Fig. 2. Dimers of CBL-a(2,6) (a) and CBL-b(2,6) (b).

3. Results and discussion

The smallest system examined was CBL(2,6), for

which two conformations were found suitable to set up a

polymeric tubular structure. In the first conformation,

CBL-a(2,6), the amidic groups are antiparallel and

normal to the average plane of the macrocycle (angle

between carboxylic C@O and average plane equal to

102�), whereas in the other, CBL-b(2,6), the antiparallelamidic groups show an angle of 63� with the same plane.

Consequently, the average molecular plane is approxi-

mately perpendicular to the polymerisation direction in

the first case and tilted in the other. The dimerisation

energy values, corrected from the BSSE by the

counterpoise method, are evaluated as DE ¼ Edim�EmðdÞ þ Edef , where Edim is the total energy of the dimer,

EmðdÞ is the sum of the energy values of the monomers,BSSE corrected, at the geometries assumed in the dimer

and Edef is the sum of the energy differences due to the

changes of geometries when going to the absolute min-

imum of the monomers to the dimer. The relevant en-

ergy values are reported in Table 1 and the two dimers

are shown in Fig. 2.

Hydrogen bond lengths, reported in Table 2 along

with some geometrical data, are 2.008, 2.009 �AA in [CBL-a(2,6)]2, and 2.043, 2.027 �AA in [CBL-b(2,6)]2.

It is worthwhile to point out that the dimerisation

process of CBL-a(2,6) involves some changes of the

monomer geometries mainly concerning the torsional

angles about the bond between the amidic nitrogen and

the adjacent methylenic carbon, resulting in a rear-

rangement of the outer peptidic groups, which lose the

property to be antiparallel. This seems to rule out the

O

N O

O

N

O

H

H

O

N

O

O N

O

H

H

O

N

O

O

N

OO

N

OO

N

O

.

(a)

(b)

Fig. 4. Dimer of CBL(6,8).

Table 2

Hydrogen bond lengths (�AA) and relevant bond angles and dihedral

angles (�)

H� � �O N–H� � �O N–H� � �O@C

[CBL-a(2,6)]2 2.008; 2.009 165.6; 166.7 31; 0

[CBL-b(2,6)]2 2.043; 2.027 158.0; 161.1 151; 165

[CBL-b(2,6)]3 2.007; 1.993 160.5; 160.1 175; 163

1.992; 2.000 157.5; 161.5 166; )171[CBL(4,6)]2 2.053; 2.045 160.6; 166.9 127; )113[CBL(6,6)]2 2.031; 2.024 168.9; 168.5 )141; )121[CBL(6,8)]2 2.037; 2.030 167.1; 168.0 160; 179

378 F. Ferrante, G. La Manna / Chemical Physics Letters 383 (2004) 376–379

possibility of building a H-bond network without fur-

ther geometrical rearrangements.

On the contrary, the geometrical changes in the dimer

of CBL-b(2,6) are noticeably lower and the outer amidic

groups maintain their antiparallelism. In this case athird monomer approaching the dimer finds favourable

conditions to build up a polymeric structure without

being forced to significant geometrical changes. To

confirm the possibility of an easy bonding interaction

with another unity, the geometry optimisation of the

trimer of CBL-b(2,6) was performed and the obtained

structure is shown in Fig. 3. As expected, only slight

changes with respect to the dimer were observed, con-firming that in this case the presence of a third unit does

not give rise to appreciable distortions of the structure.

Hydrogen bond lengths are lower than in the dimer,

ranging from 1.992 to 2.007 �AA.

The dimerisation energy values are evaluated as

35.3 kJ mol�1 for CBL-a and 32.3 kJ mol�1 for CBL-b.

Considering that these values contain the relaxation

contributions of the monomers, the energy gain ob-tained from the H-bond formation is about 40 kJ mol�1

in both cases, corresponding to 20 kJ mol�1 per H-bond.

In the trimer, the net interaction energy is 90.5 kJ

mol�1, corresponding to 22.6 kJ mol�1 per H-bond, a

value higher than that evaluated for the dimer.

Fig. 3. Trimer of CBL-b(2,6).

This cooperative effect can be explained as the con-

sequence of the enhanced polarisation within the amidic

groups because of the H-bond formation, as it is con-

firmed by the observation of the electrostatic potential

values at the nuclei involved in the H-bonds.Starting from the optimised structure of CBL(4,6),

where the amidic groups are perpendicular to the aver-

age molecular plane, a dimeric structure is obtained

showing geometrical features similar to those of {CBL-

b(2,6)}2. Thus, in this case the deformation energy

connected to the geometrical variations of the mono-

mers is noticeably larger than in the previous case, giv-

ing an interaction energy of only 24 kJ mol�1.Finally, preliminary calculations on dimers whose

single units have n ¼ 6 and m ¼ 6 and 8, show a stacking

mode which is close to the one observed in the dimer of

CBL-a(2,6). A large conformational flexibility is to be

expected in these cases, allowing for an assembling

process without significant modifications of the geome-

try of the monomer, as confirmed from the low defor-

mation energy values (see Table 1). It is to be observedthat the single monomeric units of CBL(6,8) in the di-

mer, reported in Fig. 4, show a relative rotation angle

about the stacking direction by approximately 20�.

4. Conclusion

A set of macrocyclic monomeric units, whose generalformula is –(CH2)m–CO–NH–(CH2)p–O–(CH2)n–O–

(CH2)q–NH–CO–, has been theoretically studied and

proposed as constituents of new organic tubular struc-

F. Ferrante, G. La Manna / Chemical Physics Letters 383 (2004) 376–379 379

tures. The features of the monomeric unit should allow

to build up a series of tubular systems whose cavity size

can be tuned by varying the values of some of m, n, p

indexes within the monomers. This can be of particular

importance when interactions with guest moleculesinside the cavity are taken into account.

Acknowledgements

This work has been performed by the research funds

of Italian MURST (60% – 1998).

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