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Peripherally B and N substituted cyclacenes
Journal of Molecular Structure (Theochem) 686 (2004) 91–95 www.elsevier.com/locate/theochem
Peripherally B and N substituted cyclacenes Lemi Tu¨rker*, Selc¸uk Gu¨mu¨s¸ Department of Chemistry, Middle East Technical University, Inonu Bulvari, 06531 Ankara, Turkey Received 17 March 2004; accepted 5 July 2004
Abstract AM1 (RHF) type semiempirical quantum chemical calculations have been applied to cyclacenes whose fusion points and peri positions of one of their peripheral circuits are substituted with nitrogen and boron, respectively. The structures have been found to be stable but endothermic (except for RZ8 and 9) in nature. The nitrogen and boron (the fusion points peri positions, respectively,) substitution have been found to have stabilizing effect on the parent unsubstituted cyclacenes. Some geometrical and physicochemical data are also reported. q 2004 Elsevier B.V. All rights reserved. Keywords: Cyclacenes; Boron substitution; Nitrogen substitution; AM1 method; Semiempirical calculations
1. Introduction Cyclacenes have attracted the attention of many theoretical and experimental scientists recently, due to their resemblance to carbon nanotubes, and molecular wires [1–24]. Cyclacenes theoretically can be obtained by the intramolecular union process of polyacene molecules [25]. During this conversion, planarity of the parent polyacene structure is lost. Therefore, top and bottom peripheral circuits have been pronounced for the newly formed cyclacene molecule (Fig. 1), which constitute extra paths for the delocalization of the p-electrons in addition to the cyclic conjugation. Cyclacenes can have either 4m or 4mC2 type peripheral circuits depending on the number of benzenoid rings (R) forming the main backbone of the structure. Some properties of the cyclacenes have been related to the 4m or 4mC2 nature of their peripheral circuits (cryptoannulenic effect of the first and the second kind) [18,19,21,22]. Cyclacenes can be further classified according to the number of phase dislocations (k) in the molecule namely; the Hu¨ckel type and the Mo¨bius type [19]. The main difference between these systems is that the Hu¨ckel types * Corresponding author. Tel.: C903 122 103 244; fax: C903 122 101 280. E-mail address: [email protected] (L. Tu¨rker). 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2004.08.015
possess an even number (including zero) of phase dislocations, whereas Mo¨bius types contain an odd number of phase dislocations on the basis of molecular orbitals [26]. Although cyclacenes have still been nonexistent, Stoddart et al. [11,27,28] have achieved the synthesis of octahydro derivative of linear cyclododecacene and cyclotetradecacene. Boron (1s22s22p1) is the unique atom in the group III of the periodic table that can form aromatic molecules by doing sp2 hybridization. The remaining empty 2p atomic orbital can be used in the formation a p-bond. Boron containing aromatic systems may possess quite interesting properties because of the electron deficiency caused by the insertion of an empty 2p orbital into the conjugated structure. Nitrogen atom may have a lone pair involved in the aromatic structures like borazine. The nitrogen substituted cyclacenes should constitute interesting p-skeletons, possibly having some photoactive properties [29]. The present study deals with cyclacenes (RZ3–9) substituted in one of the peripheral rings which contain nitrogen atom in all the fusion points and boron atom in all the peri positions (Fig. 2). The structures have been subjected to AM1 (RHF) type semiempirical quantum chemical calculations in order to investigate the stabilities and the frontier molecular orbital (FMO) energies. Some physicochemical properties have also been calculated and reported.
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L. Tu¨rker, S. Gu¨mu¨s¸ / Journal of Molecular Structure (Theochem) 686 (2004) 91–95
4.18!10K4 kJ/mol (0.0001 kcal/mol) and RMS gradient of 4.18!107 kJ/Mmol (0.001 kcal/A mol)). All these computations were performed by using Hyperchem (release 5.1) package program [32].
3. Results and discussion
Fig. 1. A cyclacene with RZ6.
2. Method In the present treatise, the geometry optimizations of the structures under consideration leading to energy minima were achieved by using AM 1 self-consistent fields molecular orbital (SCFMO) [30] method at the restricted Hartree-Fock (RHF) level [31]. The optimizations were obtained by application of the steepest-decent method followed by conjugate gradient methods, Fletcher-Reeves and Polak-Ribiere, consecutively (convergence limit of
In the present study nitrogen (fusion points of the top periphery) and boron (peri positions of the top periphery) substituted cyclacenes (RZ3–9) have been investigated by AM1 (RHF) type semiempirical calculations. The electron deficient character of boron atom and the electronegative nature of nitrogen should lead these calculations to reveal interesting results. The geometry optimized structures of the present systems can be seen in Fig. 2. The calculations performed to investigate the charge development on each atom revealed that in all the structures under consideration, the boron and nitrogen atoms possess positive and negative charge development, respectively. On the other hand, the carbon atoms which are adjacent to
Fig. 2. The geometry optimized structures of the present cyclacene systems.
L. Tu¨rker, S. Gu¨mu¨s¸ / Journal of Molecular Structure (Theochem) 686 (2004) 91–95
93
Fig. 3. The three dimensional electrostatic maps of the structures under consideration (the dashed lines indicates the direction of the dipole moment). Table 1 Some geometrical and physicochemical properties of cyclacene systems considered presently R Area Volume Polarizability Dipole moment
3
4
5
6
7
8
9
301.08 452.33 19.18 1.37
340.59 550.96 25.57 1.74
378.25 650.91 31.96 1.52
424.21 760.70 38.35 2.02
474.45 878.06 44.74 2.30
528.67 1002.49 51.14 2.78
592.46 1128.63 57.53 3.17
Area in 10K20 m2, volume and polarizability in 10K30 m3, dipole moment in C m.
Table 2 The total energy/R, binding energy/R and heat of formation values for the structures under present consideration Energy Total/R Binding/R Heat of formation Energy values in kJ/mol.
R 3
4
5
6
7
8
9
K53762 K2570 1007
K53913 K2722 737
K54016 K2825 404
K54065 K2873 196
K54096 K2905 10
K54115 K2924 K139
K54128 K2937 K277
L. Tu¨rker, S. Gu¨mu¨s¸ / Journal of Molecular Structure (Theochem) 686 (2004) 91–95
94
Table 3 The LUMO, HOMO, and DE values for the structures presently considered R LUMO HOMO DE
3
4
5
6
7
8
9
K2.58715 K12.88170 10.29455
K2.15085 K11.38100 9.23015
K0.95672 K12.18810 11.23138
K1.47398 K11.37500 9.90102
K1.21271 K11.90660 10.69389
K1.65270 K11.30560 9.65290
K1.37255 K11.69500 10.32245
Energies in 10K19 J.
the nitrogen atoms have positive charge development whereas the carbon atoms at the peri positions of the bottom peripheral circuit are negatively charged. The hydrogen atoms in all structures are positively charged but the positive charge development is greater for the hydrogens
of the bottom periphery. Therefore, these charge separations lead to a net dipole moment directing from the top peripheral circuit to the center of the cyclacene structure. Fig. 3 shows the three dimensional electrostatic maps as well as the direction of the dipole moment for the structures
Fig. 4. The molecular orbital eigenvalue spectra of the present systems (RZ3–9).
L. Tu¨rker, S. Gu¨mu¨s¸ / Journal of Molecular Structure (Theochem) 686 (2004) 91–95
of present consideration. Table 1 gives some geometrical and physicochemical properties of the present systems. As seen in Table 1, the dipole moment values increase as R increases (except for RZ5). Table 2 gives total energy/R, binding energy/R and the heat of formation values for the cyclacenes of present study. As can be seen in Table 2, all the structures are stable but endothermic in nature (except for RZ8 and 9 which are exothermic). As the number of rings forming the main skeleton of the structure increases the total energy/R and binding energy/R values increase. This is quite reasonable because as the number of rings increases p-conjugation becomes more effective due to flattening of the benzenoid rings in the main skeleton. When the total energy/R values for the present systems are compared with the unsubstituted cyclacenes [33], it is observed that boron (peri positions) and nitrogen (fusion points) substitutions have a stabilizing effect on the parent cyclacenes. For the presently considered cyclacenes no cryptoannulenic effect is observed when the total energy/R, binding energy/R and the heat of formation values are considered. Table 3 gives the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy levels as well as the frontier molecular orbital energy gaps (DE) for the cyclacenes studied presently. The interfrontier energy gap values possess a local minimum for RZ4 and local maximum for RZ5. Moreover, the molecular orbital eigenvalue spectra of the present systems are given by Fig. 4.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
4. Conclusion [27]
AM1 (RHF) type semiempirical quantum chemical calculations have been applied to cyclacenes (whose fusion points and peri positions of the top peripheral circuit are substituted with nitrogen and boron, respectively,) are found to be more stable and less endothermic than the unsubstituted parent cyclacenes. All the structures considered presently have a dipole moment directing from the upper periphery to the center of the system thus resulting in interesting polar structures. Some geometrical and physicochemical data are also given for the present systems.
95
[28]
[29] [30] [31] [32] [33]
L. Tu¨rker, J. Mol. Struct. (Theochem) 490 (1999) 55. S¸. Erkoc¸, L. Tu¨rker, Phys. E. 4 (1999) 192. R.M. Cory, L. McP, Cameron, Tetrahedron Lett. 37 (1996) 1987. I. Agranant, B.A. Hess, L.J. Schaad, Pure Appl. Chem. 52 (1980) 1399. J.L. Bergan, B.N. Cyvin, S.J. Cyvin, Acta Chim. Hung. 124 (1987) 299. G. Ege, H. Vogler, Theor. Chim. Acta 35 (1974) 189. E. Heilbronner, Helv. Chim. Acta 37 (1954) 921. G. Derflinger, H. Sofer, Monatch. Chem. 99 (1968) 1866. S. Kivelson, O.L. Chapman, Phys. Rev. B 28 (1983) 7326. F.J. Zhang, S.J. Cyvin, B.N. Cyvin, Monatch. Chem. 121 (1990) 421. P.R. Ashton, N.S. Isaac, F.H. Kohnke, A.M.Z. Slawin, C.M. Spencer, J.F. Stoddart, D.J. Williams, Angew. Chem. Int. Ed. Engl. 27 (1988) 966. R.W. Alder, R.B. Sessions, J. Chem. Soc. Perkin Trans. 2 (1985) 1849. R.O. Angus Jr., R.P. Johnson, J. Org. Chem. 53 (1988) 314. L. Tu¨rker, Polycycl. Aromat. Compd. 4 (1994) 191. L. Tu¨rker, Polycycl. Aromat. Compd. 8 (1996) 67. L. Tu¨rker, Polycycl. Aromat. Compd. 4 (1995) 231. L. Tu¨rker, Polycycl. Aromat. Compd. 8 (1996) 203. L. Tu¨rker, J. Mol. Struct. (Theochem) 407 (1997) 217. L. Tu¨rker, J. Mol. Struct. (Theochem) 454 (1998) 83. I. Gutman, P.U. Biederman, V.I. Petrovic, I. Agranat, Polycycl. Aromat. Compd. 8 (1996) 189. L. Tu¨rker, Indian J. Chem 37B (1998) 230. L. Tu¨rker, Polycycl. Aromat. Compd. 12 (1997) 213. L. Tu¨rker, J. Mol. Struct. (Theochem) 492 (1999) 159. H.S. Choi, K.S. Kim, Angew. Chem. Int. Ed. Engl. 38 (15) (1999) 2256. M.J.S. Dewar, R.C. Dougherty, PMO Theory of Organic Chemistry, Plenum-Rosetta, New York, 1975. A. Groavac, I. Gutman, N. Trinajstic, Topological Approach to the Chemistry of Conjugated Molecules, Springer, Berlin, 1977. P.R. Ashton, G.R. Brown, N.S. Isaacs, D. Giuffrida, F.H. Kohnke, J.P. Mathias, A.M.Z. Slavin, D.R. Smith, J.F. Stoddart, D.J. Williams, J. Am. Chem. Soc. 114 (1992) 6330. P.R. Ashton, U. Girreser, D. Giuffrida, F.H. Kohnke, J.P. Mathias, F.M. Raymo, A.M.Z. Slavin, J.F. Stoddart, D.J. Williams, J. Am. Chem. Soc. 115 (1993) 5422. B. Dietrich, P. Viout, J.M. Lehn, Macrocyclic Chemistry, VCH Publications, New York, 1993. M.J.S. Dewar, E.G. Zoebish, E.F. Healey, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. A.R. Leach, Molecular Modelling, Longman, Essex, 1997. Hyperchem, Hypercube Inc., Gainesville, FL, USA. L. Tu¨rker, J. Mol. Struct.(Theochem) 535 (2001) 151.
Peripherally B and N substituted cyclacenes Lemi Tu¨rker*, Selc¸uk Gu¨mu¨s¸ Department of Chemistry, Middle East Technical University, Inonu Bulvari, 06531 Ankara, Turkey Received 17 March 2004; accepted 5 July 2004
Abstract AM1 (RHF) type semiempirical quantum chemical calculations have been applied to cyclacenes whose fusion points and peri positions of one of their peripheral circuits are substituted with nitrogen and boron, respectively. The structures have been found to be stable but endothermic (except for RZ8 and 9) in nature. The nitrogen and boron (the fusion points peri positions, respectively,) substitution have been found to have stabilizing effect on the parent unsubstituted cyclacenes. Some geometrical and physicochemical data are also reported. q 2004 Elsevier B.V. All rights reserved. Keywords: Cyclacenes; Boron substitution; Nitrogen substitution; AM1 method; Semiempirical calculations
1. Introduction Cyclacenes have attracted the attention of many theoretical and experimental scientists recently, due to their resemblance to carbon nanotubes, and molecular wires [1–24]. Cyclacenes theoretically can be obtained by the intramolecular union process of polyacene molecules [25]. During this conversion, planarity of the parent polyacene structure is lost. Therefore, top and bottom peripheral circuits have been pronounced for the newly formed cyclacene molecule (Fig. 1), which constitute extra paths for the delocalization of the p-electrons in addition to the cyclic conjugation. Cyclacenes can have either 4m or 4mC2 type peripheral circuits depending on the number of benzenoid rings (R) forming the main backbone of the structure. Some properties of the cyclacenes have been related to the 4m or 4mC2 nature of their peripheral circuits (cryptoannulenic effect of the first and the second kind) [18,19,21,22]. Cyclacenes can be further classified according to the number of phase dislocations (k) in the molecule namely; the Hu¨ckel type and the Mo¨bius type [19]. The main difference between these systems is that the Hu¨ckel types * Corresponding author. Tel.: C903 122 103 244; fax: C903 122 101 280. E-mail address: [email protected] (L. Tu¨rker). 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2004.08.015
possess an even number (including zero) of phase dislocations, whereas Mo¨bius types contain an odd number of phase dislocations on the basis of molecular orbitals [26]. Although cyclacenes have still been nonexistent, Stoddart et al. [11,27,28] have achieved the synthesis of octahydro derivative of linear cyclododecacene and cyclotetradecacene. Boron (1s22s22p1) is the unique atom in the group III of the periodic table that can form aromatic molecules by doing sp2 hybridization. The remaining empty 2p atomic orbital can be used in the formation a p-bond. Boron containing aromatic systems may possess quite interesting properties because of the electron deficiency caused by the insertion of an empty 2p orbital into the conjugated structure. Nitrogen atom may have a lone pair involved in the aromatic structures like borazine. The nitrogen substituted cyclacenes should constitute interesting p-skeletons, possibly having some photoactive properties [29]. The present study deals with cyclacenes (RZ3–9) substituted in one of the peripheral rings which contain nitrogen atom in all the fusion points and boron atom in all the peri positions (Fig. 2). The structures have been subjected to AM1 (RHF) type semiempirical quantum chemical calculations in order to investigate the stabilities and the frontier molecular orbital (FMO) energies. Some physicochemical properties have also been calculated and reported.
92
L. Tu¨rker, S. Gu¨mu¨s¸ / Journal of Molecular Structure (Theochem) 686 (2004) 91–95
4.18!10K4 kJ/mol (0.0001 kcal/mol) and RMS gradient of 4.18!107 kJ/Mmol (0.001 kcal/A mol)). All these computations were performed by using Hyperchem (release 5.1) package program [32].
3. Results and discussion
Fig. 1. A cyclacene with RZ6.
2. Method In the present treatise, the geometry optimizations of the structures under consideration leading to energy minima were achieved by using AM 1 self-consistent fields molecular orbital (SCFMO) [30] method at the restricted Hartree-Fock (RHF) level [31]. The optimizations were obtained by application of the steepest-decent method followed by conjugate gradient methods, Fletcher-Reeves and Polak-Ribiere, consecutively (convergence limit of
In the present study nitrogen (fusion points of the top periphery) and boron (peri positions of the top periphery) substituted cyclacenes (RZ3–9) have been investigated by AM1 (RHF) type semiempirical calculations. The electron deficient character of boron atom and the electronegative nature of nitrogen should lead these calculations to reveal interesting results. The geometry optimized structures of the present systems can be seen in Fig. 2. The calculations performed to investigate the charge development on each atom revealed that in all the structures under consideration, the boron and nitrogen atoms possess positive and negative charge development, respectively. On the other hand, the carbon atoms which are adjacent to
Fig. 2. The geometry optimized structures of the present cyclacene systems.
L. Tu¨rker, S. Gu¨mu¨s¸ / Journal of Molecular Structure (Theochem) 686 (2004) 91–95
93
Fig. 3. The three dimensional electrostatic maps of the structures under consideration (the dashed lines indicates the direction of the dipole moment). Table 1 Some geometrical and physicochemical properties of cyclacene systems considered presently R Area Volume Polarizability Dipole moment
3
4
5
6
7
8
9
301.08 452.33 19.18 1.37
340.59 550.96 25.57 1.74
378.25 650.91 31.96 1.52
424.21 760.70 38.35 2.02
474.45 878.06 44.74 2.30
528.67 1002.49 51.14 2.78
592.46 1128.63 57.53 3.17
Area in 10K20 m2, volume and polarizability in 10K30 m3, dipole moment in C m.
Table 2 The total energy/R, binding energy/R and heat of formation values for the structures under present consideration Energy Total/R Binding/R Heat of formation Energy values in kJ/mol.
R 3
4
5
6
7
8
9
K53762 K2570 1007
K53913 K2722 737
K54016 K2825 404
K54065 K2873 196
K54096 K2905 10
K54115 K2924 K139
K54128 K2937 K277
L. Tu¨rker, S. Gu¨mu¨s¸ / Journal of Molecular Structure (Theochem) 686 (2004) 91–95
94
Table 3 The LUMO, HOMO, and DE values for the structures presently considered R LUMO HOMO DE
3
4
5
6
7
8
9
K2.58715 K12.88170 10.29455
K2.15085 K11.38100 9.23015
K0.95672 K12.18810 11.23138
K1.47398 K11.37500 9.90102
K1.21271 K11.90660 10.69389
K1.65270 K11.30560 9.65290
K1.37255 K11.69500 10.32245
Energies in 10K19 J.
the nitrogen atoms have positive charge development whereas the carbon atoms at the peri positions of the bottom peripheral circuit are negatively charged. The hydrogen atoms in all structures are positively charged but the positive charge development is greater for the hydrogens
of the bottom periphery. Therefore, these charge separations lead to a net dipole moment directing from the top peripheral circuit to the center of the cyclacene structure. Fig. 3 shows the three dimensional electrostatic maps as well as the direction of the dipole moment for the structures
Fig. 4. The molecular orbital eigenvalue spectra of the present systems (RZ3–9).
L. Tu¨rker, S. Gu¨mu¨s¸ / Journal of Molecular Structure (Theochem) 686 (2004) 91–95
of present consideration. Table 1 gives some geometrical and physicochemical properties of the present systems. As seen in Table 1, the dipole moment values increase as R increases (except for RZ5). Table 2 gives total energy/R, binding energy/R and the heat of formation values for the cyclacenes of present study. As can be seen in Table 2, all the structures are stable but endothermic in nature (except for RZ8 and 9 which are exothermic). As the number of rings forming the main skeleton of the structure increases the total energy/R and binding energy/R values increase. This is quite reasonable because as the number of rings increases p-conjugation becomes more effective due to flattening of the benzenoid rings in the main skeleton. When the total energy/R values for the present systems are compared with the unsubstituted cyclacenes [33], it is observed that boron (peri positions) and nitrogen (fusion points) substitutions have a stabilizing effect on the parent cyclacenes. For the presently considered cyclacenes no cryptoannulenic effect is observed when the total energy/R, binding energy/R and the heat of formation values are considered. Table 3 gives the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy levels as well as the frontier molecular orbital energy gaps (DE) for the cyclacenes studied presently. The interfrontier energy gap values possess a local minimum for RZ4 and local maximum for RZ5. Moreover, the molecular orbital eigenvalue spectra of the present systems are given by Fig. 4.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
4. Conclusion [27]
AM1 (RHF) type semiempirical quantum chemical calculations have been applied to cyclacenes (whose fusion points and peri positions of the top peripheral circuit are substituted with nitrogen and boron, respectively,) are found to be more stable and less endothermic than the unsubstituted parent cyclacenes. All the structures considered presently have a dipole moment directing from the upper periphery to the center of the system thus resulting in interesting polar structures. Some geometrical and physicochemical data are also given for the present systems.
95
[28]
[29] [30] [31] [32] [33]
L. Tu¨rker, J. Mol. Struct. (Theochem) 490 (1999) 55. S¸. Erkoc¸, L. Tu¨rker, Phys. E. 4 (1999) 192. R.M. Cory, L. McP, Cameron, Tetrahedron Lett. 37 (1996) 1987. I. Agranant, B.A. Hess, L.J. Schaad, Pure Appl. Chem. 52 (1980) 1399. J.L. Bergan, B.N. Cyvin, S.J. Cyvin, Acta Chim. Hung. 124 (1987) 299. G. Ege, H. Vogler, Theor. Chim. Acta 35 (1974) 189. E. Heilbronner, Helv. Chim. Acta 37 (1954) 921. G. Derflinger, H. Sofer, Monatch. Chem. 99 (1968) 1866. S. Kivelson, O.L. Chapman, Phys. Rev. B 28 (1983) 7326. F.J. Zhang, S.J. Cyvin, B.N. Cyvin, Monatch. Chem. 121 (1990) 421. P.R. Ashton, N.S. Isaac, F.H. Kohnke, A.M.Z. Slawin, C.M. Spencer, J.F. Stoddart, D.J. Williams, Angew. Chem. Int. Ed. Engl. 27 (1988) 966. R.W. Alder, R.B. Sessions, J. Chem. Soc. Perkin Trans. 2 (1985) 1849. R.O. Angus Jr., R.P. Johnson, J. Org. Chem. 53 (1988) 314. L. Tu¨rker, Polycycl. Aromat. Compd. 4 (1994) 191. L. Tu¨rker, Polycycl. Aromat. Compd. 8 (1996) 67. L. Tu¨rker, Polycycl. Aromat. Compd. 4 (1995) 231. L. Tu¨rker, Polycycl. Aromat. Compd. 8 (1996) 203. L. Tu¨rker, J. Mol. Struct. (Theochem) 407 (1997) 217. L. Tu¨rker, J. Mol. Struct. (Theochem) 454 (1998) 83. I. Gutman, P.U. Biederman, V.I. Petrovic, I. Agranat, Polycycl. Aromat. Compd. 8 (1996) 189. L. Tu¨rker, Indian J. Chem 37B (1998) 230. L. Tu¨rker, Polycycl. Aromat. Compd. 12 (1997) 213. L. Tu¨rker, J. Mol. Struct. (Theochem) 492 (1999) 159. H.S. Choi, K.S. Kim, Angew. Chem. Int. Ed. Engl. 38 (15) (1999) 2256. M.J.S. Dewar, R.C. Dougherty, PMO Theory of Organic Chemistry, Plenum-Rosetta, New York, 1975. A. Groavac, I. Gutman, N. Trinajstic, Topological Approach to the Chemistry of Conjugated Molecules, Springer, Berlin, 1977. P.R. Ashton, G.R. Brown, N.S. Isaacs, D. Giuffrida, F.H. Kohnke, J.P. Mathias, A.M.Z. Slavin, D.R. Smith, J.F. Stoddart, D.J. Williams, J. Am. Chem. Soc. 114 (1992) 6330. P.R. Ashton, U. Girreser, D. Giuffrida, F.H. Kohnke, J.P. Mathias, F.M. Raymo, A.M.Z. Slavin, J.F. Stoddart, D.J. Williams, J. Am. Chem. Soc. 115 (1993) 5422. B. Dietrich, P. Viout, J.M. Lehn, Macrocyclic Chemistry, VCH Publications, New York, 1993. M.J.S. Dewar, E.G. Zoebish, E.F. Healey, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. A.R. Leach, Molecular Modelling, Longman, Essex, 1997. Hyperchem, Hypercube Inc., Gainesville, FL, USA. L. Tu¨rker, J. Mol. Struct.(Theochem) 535 (2001) 151.