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AM1 treatment of substitutionally Al and P doped cyclacenes
Journal of Molecular Structure (Theochem) 637 (2003) 189–193 www.elsevier.com/locate/theochem
AM1 treatment of substitutionally Al and P doped cyclacenes Lemi Tu¨rkera, S¸akir Erkoc¸b,* a
b
Department of Chemistry, Middle East Technical University, Ankara 06531, Turkey Department of Physics, Middle East Technical University, Inonu Bulvari, Ankara 06531, Turkey Received 24 March 2003; revised 24 March 2003; accepted 5 July 2003
Abstract Cyclacenes of the Hu¨ckel type having 3 – 8 benzenoid rings have been subjected to centric perturbations along one of the peripheral circuits such that Al and P atoms are alternatingly located. The present structure of perturbed cyclacenes let two types of isomeric compounds to arise such that in one case the peri-positions and fusion points occupied by Al and P atoms, respectively, and in the other case reversal of occupation of locations occur. For these structures, Austin model 1 (restricted Hartree-Fock) type semiempirical calculations have been carried out and the systems are analysed from various energetic points of view. q 2003 Elsevier B.V. All rights reserved. Keywords: Cyclacenes; Aluminium; Phosphorous; Substituted cyclacenes; Perturbations
1. Introduction The last few decades have evidenced piling up of various reports on cyclacenes [1 – 21], which have not been synthesized yet. Many of the studies on cyclacenes in the literature are theoretical because cyclacenes are of interest not only due to the existing similarity between the cyclacenes and the corresponding nanotubes (which have attracted attention in connection with conducting conjugated systems [6]) but also the possible utility of their cylindrical cavities in host – guest chemistry [22]. A cyclacene structure may be considered as consisting of two types of embedded structures: (1) arenoid belt (composed of benzenoid rings in the case * Corresponding author. Tel.: þ90-312-210-32-85; fax: þ 90312-210-12-81. E-mail address: [email protected] (S¸. Erkoc¸).
of simple cyclacenes) constituting the main backbone of the molecule, (2) the annulenic peripheral rings (the top and bottom rings), which become either 4m or 4m þ 2 type, depending on the number of arenoid rings ðRÞ present (Fig. 1). Some theoretical studies on cyclacenes have revealed that certain properties of cyclacenes should be dictated by the nature of their peripheral circuits (the cryptoannulenic effect [14 – 18]). It is also possible to classify cyclacenes as the Hu¨ckel or Mobius type, based on the evenness or oddness of the number of phase dislocations ðkÞ along the arenoid belt (Fig. 2). Certain interesting systems arise when a cyclacene molecule undergoes centric perturbation(s) to yield some substituted systems. One of such systems is the borazine embedded cyclacenes in which B and N atoms exist [23,24].
0166-1280/03/$ - see front matter q 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0166-1280(03)00536-0
L. Tu¨rker, S¸. Erkoc¸ / Journal of Molecular Structure (Theochem) 637 (2003) 189–193
190
3. Results and discussion
Fig. 1. Typical 4m and 4m þ 2 type cyclacenes.
The calculations (Austin model 1, AM1 and MINDO3) indicate that these structures should be stable. Phosphorous and aluminum are elements in the groups of periodic table next to nitrogen and boron, respectively. The present study considers substitutionally Al and P doped certain cyclacenes of the Hu¨ckel type for a semiempirical theoretical investigation.
2. Method In the present treatise, the geometry optimizations of all the structures leading to energy minima were achieved by using AM1 self-consistent fields molecular orbital (SCF MO) [25] method at the restricted Hartree-Fock (RHF) level [26]. The optimizations were obtained by the application of a conjugate gradient method, Polak-Ribiere (convergence limit of 4.18 £ 1024 kJ/mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 107 kJ/(mmol) (0.001 kcal/(A0 mol))). All these calculations were performed by using the Hyperchem (release 5.1) and ChemPlus (2.0) package programs.
Fig. 2. Typical Hu¨ckel and Mo¨bius type cyclacenes.
Theoretically cyclacenes are obtained from the corresponding acenes by means of a certain intramolecular cyclization (intramolecular union process [27]) in between two identical annulene molecules. The peripheral circuits (the top and bottom) of cyclacenes are either 4m or 4m þ 2 type. These circuits are annulenic in character and electron delocalization through them lessens the aromatic behavior of the initially aromatic rings in the arenoid belt. However, certain centric perturbations in the structure of cyclacenes, such as substitution(s) of more (or less) electronegative elements or elements having different size than carbon atom should affect the conjugation in the peripheral circuits and arenoid rings. Thus, the stabilization of the substituted cyclacenes might be increased or decreased. Indeed, the calculations reveal that 4m or 4m þ 2 type nature of the peripheral circuits should affect the latitudinal and longitudinal bond lengths and the heat of formation values of unsubstituted cyclacenes [15,16, 18]. This effect is called the ‘Cryptoannulenic effect’ [11 –15]. The effect of substitutional doping of certain elements on the cyclacenes has already been reported [18,20,21]. The peripheral circuits of the Hu¨ckel type ðk ¼ 0; 2; 4; …Þ cyclacenes can be constructed as a special type of a polyene ribbon with mode 0 or 2 (modulo 4) and play an important role on the stabilities of the molecules depending on whether the peripheral circuit is of the type 4m (antiaromatic) or 4m þ 2 (aromatic) carbon atoms (m is an integer) [16,18]. In the present study, cyclacenes of the Hu¨ckel type ðk ¼ 0Þ having R ¼ 3 – 8 were considered as the starting structures and then one of the peripheries was subjected to centric perturbations in such a way that alternatingly Al and P atoms were substitutionally doped into the skeleton. This process can be achieved topologically in two different ways such that in one case Al atoms occupy the peri-positions of the cyclacene molecule and all the fusion points by are occupied by phosphorous atoms (A-type). In the other case, P and Al atoms occupy the peri- and fusion points, respectively (B-type). Fig. 3 shows a pair of representative structures. Some energies of the systems of present concern are shown in Tables 1 and 2. Note that keeping the R
L. Tu¨rker, S¸. Erkoc¸ / Journal of Molecular Structure (Theochem) 637 (2003) 189–193
191
Fig. 3. A pair of representative structures of the present concern.
constant, structures A and B constitute an isomeric pair such that only the positions of Al and P atoms are different (Fig. 3). Inspection of the total and binding energies reveals that the corresponding structures are stable but endothermic and with the exception of R ¼ 3 case, B-type structures (peri-positions occupied by P atom) are more stable than A-type (peri-positions occupied by Al).
On the other hand, for A-type structures the electronic energies are more negative and the core – core interaction energies are more repulsive as compared to B-type structures. Although, the both series of structures are endothermic, A-type structures are more endothermic than B-type structures with the exception of R ¼ 3 case. In the former case, DHf values steadily increase as R increases.
Table 1 Some energies of the structures of type A R
3
4
5
6
7
8
Total energy Binding energy Isolated atomic energy Electronic energy Core–core interaction Heat of formation
231,729.1 21614.97 230,114.1 2176,854 145,124.7 188.1644
242,264.2 22112.09 240,152.2 2278,528 236,263.3 292.0819
252,887.2 22697.01 250,190.2 2392,842 339,955.1 308.2138
263,512.6 23284.37 260,228.2 2514,972 451,459.5 321.8960
274,146.0 23879.71 270,266.3 2645,971 571,825.3 327.5932
284,709.5 24405.23 280,304.3 2777,161 692,451.2 403.1186
Energies in kcal/mol.
Table 2 Some energies of the structures of type B R
3
4
5
6
7
8
Total energy Binding energy Isolated atomic energy Electronic energy Core–core interaction Heat of formation
231,690.7 21576.62 230,114.1 2170,777 139,085.9 226.5079
242,285.7 22133.58 240,152.2 2270,597 228,310.9 270.5973
252,981.7 22791.49 250,190.2 2381,653 328,671.0 213.7349
263,619.3 23391.07 260,228.2 2502,884 439,264.2 215.1978
274,261.8 23995.49 270,266.3 2626,968 552,706.3 211.8158
284,890.0 24585.73 280,304.3 2758,590 673,700.4 222.6182
Energies in kcal/mol.
L. Tu¨rker, S¸. Erkoc¸ / Journal of Molecular Structure (Theochem) 637 (2003) 189–193
192
Table 3 The HOMO, LUMO energies and interfrontier molecular orbital energy gaps for the presently considered structures R
3 4 5 6 7 8
A-type compounds
B-type compounds
1HOMO
1LUMO
DE
1HOMO
1LUMO
DE
8.7110, E 8.0849, A0 27.7878, A 27.7150, A 27.5587, A 27.5001, A
22.2946, A1 22.3721, A0 22.6380, A 22.3920, A 22.0829, A 22.1676, A
6.4164 5.7128 5.1498 5.3230 5.4758 5.3324
28.8467, A 27.7344, A 29.0674, A 28.9160, A 29.1768, A 28.8389, A
22.6001, A 23.2689, B 22.6265, A 22.3854, A 22.5137, A 22.8789, A
6.2465 4.4654 6.4410 6.5306 6.6631 5.9601
Energies (10219 J), symmetries.
However, this is not the case for B-type structures and indeed they exhibit cryptoannulenic effect on the heat of formation values such that the structures characterized with 4m-type peripheries (even values of R) are more endothermic than the 4m þ 2 type (odd values of R). Table 3 shows the frontier molecular orbital (the HOMO and LUMO) energies and the interfrontier molecular orbital energy gaps for A and B types structures considered. The data reveal that for Atype structures, the HOMO energy level raises up as R increases. Whereas, with increasing R; the LUMO energy level in the range of R ¼ 3 – 5 lowers down to more negative values, it raises up for R ¼ 6 – 7 then decreases algebraically. The HOMO energies of B-type compounds show some sort of cryptoannulenic effect within the series. The structures having 4m þ 2-type peripheries stand for local minima when 1HOMO vs. R graph is plotted The LUMO energies of this class is irregular in behavior. The emergence of cryptoannulenic effect in the Btype compounds indicates that they resemble the parent cyclacenes better than the others because the parent compounds are characterized with the property called the cryptoannulenic effect. The reason that Btypes mimic the parent compounds might be due to the presence of Al atoms at the fusion points which has octet hole, thus, enabling electronic effects of the carbon periphery to be coupled with the perturbed periphery. At the fusion points phosphorous atom possess lone pairs of electrons not in suitable geometry for the transmission of electronic effects of this kind.
4. Conclusion AM1 (RHF) type semiempirical calculations revealed that the presently considered structures are thermodynamically stable but endothermic. However, structures of A-type or B-type, although they are isomeric for R being the same, are considerably different from each other. B-types, whose heats of formation values exhibit the cryptoannulenic effect, possess P atoms at the peri-positions and Al atoms at the fusion points and they are generally more stable than the respective isomers of A-type.
References [1] I. Agranat, B.A. Hess Jr., L.J. Schaad, Pure Appl. Chem. 52 (1980) 1399. [2] J.L. Bergan, B.N. Cyvin, S.J. Cyvin, Acta Chim. Hung. 124 (1987) 299. [3] G. Ege, H. Vogler, Theor. Chim. Acta 35 (1974) 189. [4] E. Heilbronner, Helv. Chim. Acta 37 (1954) 921. [5] G. Derflinger, H. Sofer, Monatsh. Chem. 99 (1968) 1866. [6] S. Kivelson, O.L. Chapman, Phys. Rev. 28 (1983) 7236. [7] F.J. Zhang, S.J. Cyvin, B.N. Cyvin, Monatsh. Chem. 121 (1990) 421. [8] P.R. Ashton, N.S. Isaacs, F.H. Kohnke, A.M.Z. Slawin, C.M. Spencer, J.F. Stoddart, D.J. Williams, Angew. Chem. Int. Ed. Engl. 27 (1988) 966. [9] R.W. Alder, R.B. Sessions, J. Chem. Soc., Perkin Trans. 2 (1985) 1849. [10] R.O. Angus Jr., R.P. Johnson, J. Org. Chem. 53 (1988) 314. [11] L. Tu¨rker, Polycyclic Aromat. Compd 4 (1994) 191. [12] L. Tu¨rker, Polycyclic Aromat. Compd 8 (1996) 67. [13] L. Tu¨rker, Polycyclic Aromat. Compd 4 (1995) 231. [14] L. Tu¨rker, Polycyclic Aromat. Compd 8 (1996) 203. [15] L. Tu¨rker, J. Mol. Struct. 407 (1997) 217. [16] L. Tu¨rker, J. Mol. Struct. (Theochem) 454 (1998) 83.
L. Tu¨rker, S¸. Erkoc¸ / Journal of Molecular Structure (Theochem) 637 (2003) 189–193 [17] I. Gutman, P.U. Biederman, V.I. Petrovic’, I. Agranat, Polycyclic Aromat. Compd 8 (1996) 189. [18] L. Tu¨rker, Indian J. Chem. 37B (1998) 230. [19] L. Tu¨rker, Polycyclic Aromat. Compd 12 (1997) 213. [20] L. Tu¨rker, Theochem 492 (1999) 159. [21] H.S. Choi, K.S. Kim, Angew. Chem. Int. Ed. 38 (15) (1999) 2256. [22] R.M. Cory, C.L. McPhail, Tetrahedron Lett. 37 (1996) 1987.
193
[23] L. Tu¨rker, S¸. Erkoc¸, J. Mol. Struct. (Theochem) 578 (2002) 65. [24] L. Tu¨rker, S¸. Erkoc¸, J. Mol. Struct. (Theochem) 531 (2000) 401. [25] M.J.S. Dewar, E.G. Zoebisch, E.F. Healey, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [26] A.R. Leach, Molecular Modelling, Longman, Essex, 1997. [27] M.J.S. Dewar, R.C. Dougherty, PMO Theory of Organic Chemistry, Plenum-Rosetta, New York, 1975.
AM1 treatment of substitutionally Al and P doped cyclacenes Lemi Tu¨rkera, S¸akir Erkoc¸b,* a
b
Department of Chemistry, Middle East Technical University, Ankara 06531, Turkey Department of Physics, Middle East Technical University, Inonu Bulvari, Ankara 06531, Turkey Received 24 March 2003; revised 24 March 2003; accepted 5 July 2003
Abstract Cyclacenes of the Hu¨ckel type having 3 – 8 benzenoid rings have been subjected to centric perturbations along one of the peripheral circuits such that Al and P atoms are alternatingly located. The present structure of perturbed cyclacenes let two types of isomeric compounds to arise such that in one case the peri-positions and fusion points occupied by Al and P atoms, respectively, and in the other case reversal of occupation of locations occur. For these structures, Austin model 1 (restricted Hartree-Fock) type semiempirical calculations have been carried out and the systems are analysed from various energetic points of view. q 2003 Elsevier B.V. All rights reserved. Keywords: Cyclacenes; Aluminium; Phosphorous; Substituted cyclacenes; Perturbations
1. Introduction The last few decades have evidenced piling up of various reports on cyclacenes [1 – 21], which have not been synthesized yet. Many of the studies on cyclacenes in the literature are theoretical because cyclacenes are of interest not only due to the existing similarity between the cyclacenes and the corresponding nanotubes (which have attracted attention in connection with conducting conjugated systems [6]) but also the possible utility of their cylindrical cavities in host – guest chemistry [22]. A cyclacene structure may be considered as consisting of two types of embedded structures: (1) arenoid belt (composed of benzenoid rings in the case * Corresponding author. Tel.: þ90-312-210-32-85; fax: þ 90312-210-12-81. E-mail address: [email protected] (S¸. Erkoc¸).
of simple cyclacenes) constituting the main backbone of the molecule, (2) the annulenic peripheral rings (the top and bottom rings), which become either 4m or 4m þ 2 type, depending on the number of arenoid rings ðRÞ present (Fig. 1). Some theoretical studies on cyclacenes have revealed that certain properties of cyclacenes should be dictated by the nature of their peripheral circuits (the cryptoannulenic effect [14 – 18]). It is also possible to classify cyclacenes as the Hu¨ckel or Mobius type, based on the evenness or oddness of the number of phase dislocations ðkÞ along the arenoid belt (Fig. 2). Certain interesting systems arise when a cyclacene molecule undergoes centric perturbation(s) to yield some substituted systems. One of such systems is the borazine embedded cyclacenes in which B and N atoms exist [23,24].
0166-1280/03/$ - see front matter q 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0166-1280(03)00536-0
L. Tu¨rker, S¸. Erkoc¸ / Journal of Molecular Structure (Theochem) 637 (2003) 189–193
190
3. Results and discussion
Fig. 1. Typical 4m and 4m þ 2 type cyclacenes.
The calculations (Austin model 1, AM1 and MINDO3) indicate that these structures should be stable. Phosphorous and aluminum are elements in the groups of periodic table next to nitrogen and boron, respectively. The present study considers substitutionally Al and P doped certain cyclacenes of the Hu¨ckel type for a semiempirical theoretical investigation.
2. Method In the present treatise, the geometry optimizations of all the structures leading to energy minima were achieved by using AM1 self-consistent fields molecular orbital (SCF MO) [25] method at the restricted Hartree-Fock (RHF) level [26]. The optimizations were obtained by the application of a conjugate gradient method, Polak-Ribiere (convergence limit of 4.18 £ 1024 kJ/mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 107 kJ/(mmol) (0.001 kcal/(A0 mol))). All these calculations were performed by using the Hyperchem (release 5.1) and ChemPlus (2.0) package programs.
Fig. 2. Typical Hu¨ckel and Mo¨bius type cyclacenes.
Theoretically cyclacenes are obtained from the corresponding acenes by means of a certain intramolecular cyclization (intramolecular union process [27]) in between two identical annulene molecules. The peripheral circuits (the top and bottom) of cyclacenes are either 4m or 4m þ 2 type. These circuits are annulenic in character and electron delocalization through them lessens the aromatic behavior of the initially aromatic rings in the arenoid belt. However, certain centric perturbations in the structure of cyclacenes, such as substitution(s) of more (or less) electronegative elements or elements having different size than carbon atom should affect the conjugation in the peripheral circuits and arenoid rings. Thus, the stabilization of the substituted cyclacenes might be increased or decreased. Indeed, the calculations reveal that 4m or 4m þ 2 type nature of the peripheral circuits should affect the latitudinal and longitudinal bond lengths and the heat of formation values of unsubstituted cyclacenes [15,16, 18]. This effect is called the ‘Cryptoannulenic effect’ [11 –15]. The effect of substitutional doping of certain elements on the cyclacenes has already been reported [18,20,21]. The peripheral circuits of the Hu¨ckel type ðk ¼ 0; 2; 4; …Þ cyclacenes can be constructed as a special type of a polyene ribbon with mode 0 or 2 (modulo 4) and play an important role on the stabilities of the molecules depending on whether the peripheral circuit is of the type 4m (antiaromatic) or 4m þ 2 (aromatic) carbon atoms (m is an integer) [16,18]. In the present study, cyclacenes of the Hu¨ckel type ðk ¼ 0Þ having R ¼ 3 – 8 were considered as the starting structures and then one of the peripheries was subjected to centric perturbations in such a way that alternatingly Al and P atoms were substitutionally doped into the skeleton. This process can be achieved topologically in two different ways such that in one case Al atoms occupy the peri-positions of the cyclacene molecule and all the fusion points by are occupied by phosphorous atoms (A-type). In the other case, P and Al atoms occupy the peri- and fusion points, respectively (B-type). Fig. 3 shows a pair of representative structures. Some energies of the systems of present concern are shown in Tables 1 and 2. Note that keeping the R
L. Tu¨rker, S¸. Erkoc¸ / Journal of Molecular Structure (Theochem) 637 (2003) 189–193
191
Fig. 3. A pair of representative structures of the present concern.
constant, structures A and B constitute an isomeric pair such that only the positions of Al and P atoms are different (Fig. 3). Inspection of the total and binding energies reveals that the corresponding structures are stable but endothermic and with the exception of R ¼ 3 case, B-type structures (peri-positions occupied by P atom) are more stable than A-type (peri-positions occupied by Al).
On the other hand, for A-type structures the electronic energies are more negative and the core – core interaction energies are more repulsive as compared to B-type structures. Although, the both series of structures are endothermic, A-type structures are more endothermic than B-type structures with the exception of R ¼ 3 case. In the former case, DHf values steadily increase as R increases.
Table 1 Some energies of the structures of type A R
3
4
5
6
7
8
Total energy Binding energy Isolated atomic energy Electronic energy Core–core interaction Heat of formation
231,729.1 21614.97 230,114.1 2176,854 145,124.7 188.1644
242,264.2 22112.09 240,152.2 2278,528 236,263.3 292.0819
252,887.2 22697.01 250,190.2 2392,842 339,955.1 308.2138
263,512.6 23284.37 260,228.2 2514,972 451,459.5 321.8960
274,146.0 23879.71 270,266.3 2645,971 571,825.3 327.5932
284,709.5 24405.23 280,304.3 2777,161 692,451.2 403.1186
Energies in kcal/mol.
Table 2 Some energies of the structures of type B R
3
4
5
6
7
8
Total energy Binding energy Isolated atomic energy Electronic energy Core–core interaction Heat of formation
231,690.7 21576.62 230,114.1 2170,777 139,085.9 226.5079
242,285.7 22133.58 240,152.2 2270,597 228,310.9 270.5973
252,981.7 22791.49 250,190.2 2381,653 328,671.0 213.7349
263,619.3 23391.07 260,228.2 2502,884 439,264.2 215.1978
274,261.8 23995.49 270,266.3 2626,968 552,706.3 211.8158
284,890.0 24585.73 280,304.3 2758,590 673,700.4 222.6182
Energies in kcal/mol.
L. Tu¨rker, S¸. Erkoc¸ / Journal of Molecular Structure (Theochem) 637 (2003) 189–193
192
Table 3 The HOMO, LUMO energies and interfrontier molecular orbital energy gaps for the presently considered structures R
3 4 5 6 7 8
A-type compounds
B-type compounds
1HOMO
1LUMO
DE
1HOMO
1LUMO
DE
8.7110, E 8.0849, A0 27.7878, A 27.7150, A 27.5587, A 27.5001, A
22.2946, A1 22.3721, A0 22.6380, A 22.3920, A 22.0829, A 22.1676, A
6.4164 5.7128 5.1498 5.3230 5.4758 5.3324
28.8467, A 27.7344, A 29.0674, A 28.9160, A 29.1768, A 28.8389, A
22.6001, A 23.2689, B 22.6265, A 22.3854, A 22.5137, A 22.8789, A
6.2465 4.4654 6.4410 6.5306 6.6631 5.9601
Energies (10219 J), symmetries.
However, this is not the case for B-type structures and indeed they exhibit cryptoannulenic effect on the heat of formation values such that the structures characterized with 4m-type peripheries (even values of R) are more endothermic than the 4m þ 2 type (odd values of R). Table 3 shows the frontier molecular orbital (the HOMO and LUMO) energies and the interfrontier molecular orbital energy gaps for A and B types structures considered. The data reveal that for Atype structures, the HOMO energy level raises up as R increases. Whereas, with increasing R; the LUMO energy level in the range of R ¼ 3 – 5 lowers down to more negative values, it raises up for R ¼ 6 – 7 then decreases algebraically. The HOMO energies of B-type compounds show some sort of cryptoannulenic effect within the series. The structures having 4m þ 2-type peripheries stand for local minima when 1HOMO vs. R graph is plotted The LUMO energies of this class is irregular in behavior. The emergence of cryptoannulenic effect in the Btype compounds indicates that they resemble the parent cyclacenes better than the others because the parent compounds are characterized with the property called the cryptoannulenic effect. The reason that Btypes mimic the parent compounds might be due to the presence of Al atoms at the fusion points which has octet hole, thus, enabling electronic effects of the carbon periphery to be coupled with the perturbed periphery. At the fusion points phosphorous atom possess lone pairs of electrons not in suitable geometry for the transmission of electronic effects of this kind.
4. Conclusion AM1 (RHF) type semiempirical calculations revealed that the presently considered structures are thermodynamically stable but endothermic. However, structures of A-type or B-type, although they are isomeric for R being the same, are considerably different from each other. B-types, whose heats of formation values exhibit the cryptoannulenic effect, possess P atoms at the peri-positions and Al atoms at the fusion points and they are generally more stable than the respective isomers of A-type.
References [1] I. Agranat, B.A. Hess Jr., L.J. Schaad, Pure Appl. Chem. 52 (1980) 1399. [2] J.L. Bergan, B.N. Cyvin, S.J. Cyvin, Acta Chim. Hung. 124 (1987) 299. [3] G. Ege, H. Vogler, Theor. Chim. Acta 35 (1974) 189. [4] E. Heilbronner, Helv. Chim. Acta 37 (1954) 921. [5] G. Derflinger, H. Sofer, Monatsh. Chem. 99 (1968) 1866. [6] S. Kivelson, O.L. Chapman, Phys. Rev. 28 (1983) 7236. [7] F.J. Zhang, S.J. Cyvin, B.N. Cyvin, Monatsh. Chem. 121 (1990) 421. [8] P.R. Ashton, N.S. Isaacs, F.H. Kohnke, A.M.Z. Slawin, C.M. Spencer, J.F. Stoddart, D.J. Williams, Angew. Chem. Int. Ed. Engl. 27 (1988) 966. [9] R.W. Alder, R.B. Sessions, J. Chem. Soc., Perkin Trans. 2 (1985) 1849. [10] R.O. Angus Jr., R.P. Johnson, J. Org. Chem. 53 (1988) 314. [11] L. Tu¨rker, Polycyclic Aromat. Compd 4 (1994) 191. [12] L. Tu¨rker, Polycyclic Aromat. Compd 8 (1996) 67. [13] L. Tu¨rker, Polycyclic Aromat. Compd 4 (1995) 231. [14] L. Tu¨rker, Polycyclic Aromat. Compd 8 (1996) 203. [15] L. Tu¨rker, J. Mol. Struct. 407 (1997) 217. [16] L. Tu¨rker, J. Mol. Struct. (Theochem) 454 (1998) 83.
L. Tu¨rker, S¸. Erkoc¸ / Journal of Molecular Structure (Theochem) 637 (2003) 189–193 [17] I. Gutman, P.U. Biederman, V.I. Petrovic’, I. Agranat, Polycyclic Aromat. Compd 8 (1996) 189. [18] L. Tu¨rker, Indian J. Chem. 37B (1998) 230. [19] L. Tu¨rker, Polycyclic Aromat. Compd 12 (1997) 213. [20] L. Tu¨rker, Theochem 492 (1999) 159. [21] H.S. Choi, K.S. Kim, Angew. Chem. Int. Ed. 38 (15) (1999) 2256. [22] R.M. Cory, C.L. McPhail, Tetrahedron Lett. 37 (1996) 1987.
193
[23] L. Tu¨rker, S¸. Erkoc¸, J. Mol. Struct. (Theochem) 578 (2002) 65. [24] L. Tu¨rker, S¸. Erkoc¸, J. Mol. Struct. (Theochem) 531 (2000) 401. [25] M.J.S. Dewar, E.G. Zoebisch, E.F. Healey, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [26] A.R. Leach, Molecular Modelling, Longman, Essex, 1997. [27] M.J.S. Dewar, R.C. Dougherty, PMO Theory of Organic Chemistry, Plenum-Rosetta, New York, 1975.