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PM3 treatment of certain catenanes having cyclacenes and cyclotriacontene units
Journal of Molecular Structure (Theochem) 574 (2001) 177±183
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PM3 treatment of certain catenanes having cyclacenes and cyclotriacontene units Lemi TuÈrker Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey Received 14 May 2001; accepted 18 June 2001
Abstract The results of PM3 (RHF) type semiempirical quantum chemical treatment of certain catenanes which consisted of all-trans cyclotriacontene shaft and the cyclacene shuttle, having R benzenoid rings R 6±9 were reported. The results have indicated that the cryptoannulenic effect which is the characteristic property of cyclacenes is almost lost when they are incorporated into the structures of catenanes considered. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Catenanes; Rotaxanes; Cyclacenes; PM3 calculations; Cryptoannulenic effect
1. Introduction The recent discovery of networks with thousands of natural DNA-catenanes [1±3] led mechanically connected molecules to have increased signi®cance. Some proteins also form molecular knots [4,5]. Certain bacteria such as E. Coli have rotaxane-like structures in their ¯agella [6]. Rotaxanes are molecular species created when a bead-like macrocycle is trapped mechanically, without any assistance of any valance forces, on a dumbbell-shaped entity [7,8]. Recently, many protocols have been developed for the synthesis of these mechanically interlocked compounds [9±13]. The most pertinent protocol is based on the threading of a linear ®lament through the cavity of a macrocycle, by virtue of noncovalent bonds to generate the corresponding pseudorotaxene which is then transformed into a rotaxane by reaction with a suitable bulky stoppering reagent [14±16]. Rotaxanes some of which could act as molecules E-mail address: [email protected] (L. TuÈrker).
whose shape and dynamic properties can be controlled at will have recently triggered great interest [17±19] due to their potential applications [20,21]. In the present theoretical study certain catenane structures constructed from all-trans cyclotriacontene (30-annulene) and different cyclacenes were considered for PM3 type semiempirical treatment. 2. Method In the present treatise, the geometry optimizations of all the structures leading to energy minima were achieved by using PM3 self-consistent ®elds molecular orbital (SCF MO) [22,23] method at the restricted Hartree±Fock (RHF) level [24]. The optimizations were obtained by the application of the steepestdescent method followed by conjugate gradient methods, Fletcher±Rieves and Polak±Ribiere, consecutively (convergence limit of 4.18 £ 10 24 kJ/mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 10 7 kJ/M mol (0.001 kcal/A mol)). All these computations were performed by using the
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00649-2
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
178
Fig. 1. A theoretical design of presently considered catenanes.
Hyperchem (release 5.1) and ChemPlus (2.0) package programs [25].
3. Results and discussion The series of catenanes presently considered possess a cyclacene unit having certain number of benzenoid rings R R 6±9 and cyclotriacontene unit (30-annulene). The cyclotriacontene possesses all-trans oriented double bonds. It is theoretically an even annulene having 4n 1 2 p-electrons n 7: On the other hand, cyclacenes possess annulenic structures (the peripheral top and bottom rings embedded into their structures) and the peripheral circuits exert the so-called cryptoannulenic effect [26] depending Table 1 Some calculated properties of the catenanes considered (area, volume, refractivity and polarizability values are in the order of 10 220 m 2, 10 230 m 3, 10 230 and 10 230 m 3, respectively) Property
Area Volume Refractivity Polarizability LogP
R 6
7
8
9
959.8 1837.1 234.6 95.8 18.24
971.9 1917.8 238.6 103.1 12.16
1003.8 2028.1 246.3 110.3 14.63
1036.5 2143.1 254.6 117.6 17.23
on the value of R to affect some properties of cyclacene molecules [27,28]. The presently considered catenanes, theoretically related to pseudorotaxanes in which a cyclacene and all-trans triacontene units take the role of a shuttle and a shaft, respectively. The triacontene unit (shaft) is threaded through the cyclacene unit to construct the corresponding [2]pseudorotaxane and then the terminals of the shaft are connected through intramolecular union process [29] (see Fig. 1). Table 1 shows some of the calculated properties of the catenanes presently considered. As seen in Table 1, all the properties except log P values increase as the size of cyclacene moity increases. Whereas log P values in the homologous series R 6±9 ®rst decrease and then increase (the minimum occurs for R 7) as R increases. The log P value re¯ects the hydrophobicity of the system. The minimum occurring for R 7 is expected because from R 7 onwards log P values steadily increases as R increases. However, the highest value within the series (for R 6 case) is out of line. This has to be due to rather strained, thus the skew structure of the cyclacene shuttle in the case of R 6: Hence, the hydrophobic character is more pronounced. The value and direction of the dipole moments are also effective contributors to the hydrophobicity of these systems, which primarily arise from the gross topology of the catenanes considered. The contributors of the dipole moment are point charge and sp-hybrid components. Table 2 shows the
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
179
Table 2 The components and the total value of the dipole moments of the catenanes considered (dipole moments are in the order of 10 230 C m) Dipole moment
R
Direction
Component
6
7
8
9
X
Point charge sp-hybrid Point charge sp-hybrid Point charge sp-hybrid
0.7871 0.3935 1.5910 0.0867 25.0333 1.5543 5.3368 1.6044 4.0390
20.6437 0.0967 0.1367 20.0100 0.1400 0.0100 0.6737 0.0967 0.5837
20.2101 0.0600 0.3268 0.0366 0.4336 0.5737 0.5837 0.5803 1.0840
20.3468 0.0567 20.5436 0.1067 0.0933 20.0066 0.6504 0.1200 0.5303
Y Z Total Point charge Total sp-hybrid Overall Total
components and the total value of the dipole moments of the systems presently considered. Generally, the direction of the dipole moment is from some part of the periphery of the shaft, which is not inside the cyclacene moiety to the origin of the axes of inertia of the system. Fig. 2 shows the geometry optimized structures of the present systems R 6±9: Cyclacenes are characterized by the presence of two types of p-systems embedded in their skeletons. These are the benzenoid rings constituting the main backbone of a cyclacene molecule and its peripheral circuits (the top and bottom rings), which becomes 4m or 4m 1 2 depending on the number of benzenoid rings (R) present. It may be noted that the size of a peripheral circuit is equal to 2R. Various properties of the p-electron systems of cyclacenes have recently been examined [26,30,31]. Of these the
Fig. 2. The geometry optimized structures of present concern.
Fig. 3. Electrostatic potential ®eld contours for some catenanes (R 7 and 8) considered.
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
180
Table 3 Some energies of the catenanes considered (energies in kJ/mol. Symmetries below the numeric data) Energy
Total Binding Isolated atomic Electronic Core±core repulsion Heat of formation LUMO a HOMO a DE a a
R 6
7
8
9
2676438 243918 2632521 28925846 8249408 3848 22.8706 A 211.7936 A 8.9230
2725816 247843 2677972 210093038 9367221 3218 23.4899 A 211.4321 A 7.9422
2774909 251484 2723424 211188476 10413569 2874 24.9548 A 29.9761 A 5.0213
2823947 255071 2768876 212258639 11434691 2583 23.7237 A 211.2236 A 7.4999
Energies in the order of 10 219 J.
Table 4 Some energies of the cyclacene moiety (shuttle) in the catenanes considered (energies in kJ/mol) Energy
Total Binding Isolated atomic Electronic Core±core repulsion Heat of formation LUMO a HOMO a DE a a
R 6
7
8
9
2310084 217117 292968 22466348 2156264 2659 21.4338 210.6143 9.1805
2362724 220929 2341796 23135705 2772980 2143 22.2348 210.2943 8.0595
2415046 224423 2390624 23819890 3404843 1945 24.1082 29.2487 5.1405
2467394 227943 2439451 24525881 4858487 1721 23.1446 210.6820 7.5374
Energies in the order of 10 219 J.
Table 5 Some energies of the cyclotriacontene (shaft) moiety in the catenanes considered (energies in kJ/mol) Energy
Total Binding Isolated atomic Electronic Core±core repulsion Heat of formation LUMO a HOMO a DE a a
R 6
7
8
9
2408557 225854 2382703 23089118 2680560 2136 21.6797 212.2660 10.5863
2408963 226260 2382703 23096515 2687552 1730 21.7161 212.4215 10.7054
2409385 226682 2382703 23099432 260047 1308 21.6997 212.2904 10.5907
2409575 226872 2302703 23099361 2689787 1118 21.6779 212.2147 10.5368
Energies in the order of 10 219 J.
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
181
Fig. 4. The distribution of molecular orbital energies as R varies.
cryptoannulenic effect [27,28], in¯uences certain properties of cyclacenes such as certain energies, HOMO±LUMO energy separation, dipole moments, bond lengths, etc. It has been one of the primary interests of the present article to investigate how the cryptoannulenic effect would display itself when a conjugated shaft, like the one presently used, is threaded through a cyclacene molecule and the shaft termini undergo an intramolecular union to yield the corresponding catenane molecule. Table 3 shows some energies of the catenanes presently considered. As seen in the table, the structures are all stable but endothermic in nature. The endogenic character decreases as the shuttle grows in size (as R increases). The thorough analysis of the data indicates that the catenanes considered exhibit almost no cryptoannulenic effect of the ®rst and second order. Note that the second order cryptoannulenic effect is de®ned as the dependence of any property of the structure on 4m or 4m 1 2 nature of the peripheral circuit per benzenoid ring (R) present [26±28]. Table 4 shows some ener-
gies of the cyclacene moiety (shuttle) in the presence of the shaft in the cyclacenes considered. In these mixed mode type calculations, the cyclacene moiety in every structure was treated quantum mechanically while the remainder (the shaft) was treated classically [32]. The data reveal that the shaft greatly affects the nature of cyclacenes (shuttle) such that only some trace of the cryptoannulenic effect on the HOMO, LUMO energies and the frontier molecular orbital (FMO) energy gap (DE) is present. Table 5 shows some energies of the cyclotriacontene unit (shaft) in the catenanes considered. This time, the HOMO, LUMO and DE values exhibit the in¯uence of the cyclacene moiety present in the structure. Thus, in the present catenene systems, the shaft and shuttle units highly in¯uence each other through space interaction [33±35]. Fig. 3 shows how the shaft and shuttle mutually exert an electrostatic potential ®eld through space. Fig. 4 shows the distribution of the molecular orbital energies of the structures. The span of the
182
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
Fig. 5. The HOMO and LUMO of the catenanes having R 7 and 8.
molecular orbital energies are in between 26.1100 and 1.0721, 26.1167 and 1.0339, 26.1160 and 1.0284 and 26.1149 and 1.0191 (all in the order of 10 218 J) for R 6±9; respectively. As for the HOMO and LUMO characteristics of the presently investigated catenanes, the PM3 treatment results in frontier molecular orbitals, such that both of them are con®ned to the shuttle (cyclacene moiety) in all the cases R 6±9: The FMO energies have been shown in Table 3. Fig. 5 shows the HOMO and LUMO of the catenanes having R 7 and 8. The symmetries of frontier molecular orbitals are all A type for R 6±9:
cryptoannulenic effect is one of the characteristic property of the cyclacenes. The shaft and shuttle in the catenanes considered affect the electronic properties of each other through space interactions. Thus, any perturbation in each moiety, such as insertion of certain heteroatoms, should affect the electronic properties of the other moiety. In other words they should be electronically (also magnetically) coupled circuits which might have certain practical applications related to molecular electronics.
References 4. Conclusions The present PM3 type calculations revealed that the considered catenanes having the cyclacene shuttle are stable but endogenic structures possessing almost no
[1] J. Chen, C.A. Rauch, J.H. White, P.T. Englund, N.R. Cozzarelli, Cell 80 (1985) 61. [2] J. Chen, P.T. Englund, N.R. Cozzarelli, EMBO J. 14 (1995) 6339. [3] D.E. Adams, E.M. Shekhtman, E.L. Zechiedrich, M.B. Schmid, N.R. Cozzarelli, Cell 71 (1992) 277. [4] C. Liang, K. Mislow, J. Am. Chem. Soc. 116 (1994) 11189.
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183 [5] F. Takusagawa, S. Kamitori, J. Am. Chem. Soc. 118 (1996) 8945. [6] L. Stryer, Biochemie, Spektrum, Heildelberg, 1991. [7] D.A. Amabilino, J.F. Stoddart, Chem. Rev. 95 (1995) 2725. [8] H.W. Gibson, in: J.A. Semlyn (Ed.), Large Ring Molecules, Wiley, Chichester, 1996, pp. 191±262. [9] S.J. Cantrill, D.A. Fulton, M.C.T. Fyfe, J.F. Stoddart, A.J.P. White, D.J. Williams, Tetrahedron Lett. 40 (1999) 3669. [10] M. Fujite, Acc. Chem. Res. 32 (1999) 53. [11] M.M. Conn, J. Rebek Jr., Chem. Rev. 97 (1997) 1647. [12] R.E. Gillard, F.M. Raymo, J.F. Stoddart, Chem. Eur. J. 3 (1997) 1933. [13] R. Jager, F. VoÈgtle, Angew. Chem., Int. Ed. Engl. 36 (1997) 930. [14] J.M. Lehn, Supramolecular Chemistry, VCH, Weinheim, 1995. [15] M.C.T. Fyfe, J.F. Stoddart, Acc. Chem. Res. 30 (1997) 393. [16] P.R. Ashton, P.T. Glink, J.F. Stoddart, P.A. Tasker, A.J.P. White, D.J. Williams, Chem. Eur. J. 2 (1996) 729. [17] M.C. Jime'nez, C. Dietrich-Buchecker, J.P. Sauvage, Angew. Chem. Int. Ed. 39 (18) (2000) 3284. [18] S.I. Jun, J.W. Lee, S. Sakamoto, K. Yamaguchi, K. Kim, Tetrahedron Lett. 41 (2000) 471.
183
[19] M. Di Ventra, S.T. Pantelides, N.D. Lang, Appl. Phys. Lett. 76 (23) (2000) 3448. [20] M.J. Marsella, P.J. Carroll, T.M. Swager, J. Am. Chem. Soc. 116 (1994) 9347. [21] S.S. Zhu, P.J. Carroll, T.M. Swager, J. Am. Chem. Soc. 118 (1996) 8713. [22] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209. [23] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 221. [24] A.R. Leach, Molecular Modelling, Longman, Essex, 1997. [25] Hyperchem, Hypercube Inc., Gainesville, Florida, USA, 1998. [26] L. TuÈrker, Polycycl. Aromat. Compd. 4 (1994) 191. [27] L. TuÈrker, J. Mol. Struct. 407 (1997) 217. [28] L. TuÈrker, N. C Ë elebi, Ind. J. Chem. 39B (2000) 410. [29] M.J.S. Dewar, R.C. Dougherty, PMO Theory of Organic Chemistry, Plenum-Rosetta, New York, 1975. [30] J. Aihara, J. Chem. Soc., Perkin Trans. (1994) 971. [31] J. Aihara, J. Chem. Soc. Faraday Trans. 91 (1995) 237. [32] Hyperchem, Computational Chemistry, Hypercube Inc., Gainesville, Florida, USA, 1998. [33] R. Hoffmann, Acc. Chem. Res. 4 (1971) 1. [34] R. Gleither, Tetrahedron Lett. (1969) 4453. [35] R. Boschi, W. Schmidth, Angew. Chem. 83 (1973) 408.
www.elsevier.com/locate/theochem
PM3 treatment of certain catenanes having cyclacenes and cyclotriacontene units Lemi TuÈrker Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey Received 14 May 2001; accepted 18 June 2001
Abstract The results of PM3 (RHF) type semiempirical quantum chemical treatment of certain catenanes which consisted of all-trans cyclotriacontene shaft and the cyclacene shuttle, having R benzenoid rings R 6±9 were reported. The results have indicated that the cryptoannulenic effect which is the characteristic property of cyclacenes is almost lost when they are incorporated into the structures of catenanes considered. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Catenanes; Rotaxanes; Cyclacenes; PM3 calculations; Cryptoannulenic effect
1. Introduction The recent discovery of networks with thousands of natural DNA-catenanes [1±3] led mechanically connected molecules to have increased signi®cance. Some proteins also form molecular knots [4,5]. Certain bacteria such as E. Coli have rotaxane-like structures in their ¯agella [6]. Rotaxanes are molecular species created when a bead-like macrocycle is trapped mechanically, without any assistance of any valance forces, on a dumbbell-shaped entity [7,8]. Recently, many protocols have been developed for the synthesis of these mechanically interlocked compounds [9±13]. The most pertinent protocol is based on the threading of a linear ®lament through the cavity of a macrocycle, by virtue of noncovalent bonds to generate the corresponding pseudorotaxene which is then transformed into a rotaxane by reaction with a suitable bulky stoppering reagent [14±16]. Rotaxanes some of which could act as molecules E-mail address: [email protected] (L. TuÈrker).
whose shape and dynamic properties can be controlled at will have recently triggered great interest [17±19] due to their potential applications [20,21]. In the present theoretical study certain catenane structures constructed from all-trans cyclotriacontene (30-annulene) and different cyclacenes were considered for PM3 type semiempirical treatment. 2. Method In the present treatise, the geometry optimizations of all the structures leading to energy minima were achieved by using PM3 self-consistent ®elds molecular orbital (SCF MO) [22,23] method at the restricted Hartree±Fock (RHF) level [24]. The optimizations were obtained by the application of the steepestdescent method followed by conjugate gradient methods, Fletcher±Rieves and Polak±Ribiere, consecutively (convergence limit of 4.18 £ 10 24 kJ/mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 10 7 kJ/M mol (0.001 kcal/A mol)). All these computations were performed by using the
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00649-2
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
178
Fig. 1. A theoretical design of presently considered catenanes.
Hyperchem (release 5.1) and ChemPlus (2.0) package programs [25].
3. Results and discussion The series of catenanes presently considered possess a cyclacene unit having certain number of benzenoid rings R R 6±9 and cyclotriacontene unit (30-annulene). The cyclotriacontene possesses all-trans oriented double bonds. It is theoretically an even annulene having 4n 1 2 p-electrons n 7: On the other hand, cyclacenes possess annulenic structures (the peripheral top and bottom rings embedded into their structures) and the peripheral circuits exert the so-called cryptoannulenic effect [26] depending Table 1 Some calculated properties of the catenanes considered (area, volume, refractivity and polarizability values are in the order of 10 220 m 2, 10 230 m 3, 10 230 and 10 230 m 3, respectively) Property
Area Volume Refractivity Polarizability LogP
R 6
7
8
9
959.8 1837.1 234.6 95.8 18.24
971.9 1917.8 238.6 103.1 12.16
1003.8 2028.1 246.3 110.3 14.63
1036.5 2143.1 254.6 117.6 17.23
on the value of R to affect some properties of cyclacene molecules [27,28]. The presently considered catenanes, theoretically related to pseudorotaxanes in which a cyclacene and all-trans triacontene units take the role of a shuttle and a shaft, respectively. The triacontene unit (shaft) is threaded through the cyclacene unit to construct the corresponding [2]pseudorotaxane and then the terminals of the shaft are connected through intramolecular union process [29] (see Fig. 1). Table 1 shows some of the calculated properties of the catenanes presently considered. As seen in Table 1, all the properties except log P values increase as the size of cyclacene moity increases. Whereas log P values in the homologous series R 6±9 ®rst decrease and then increase (the minimum occurs for R 7) as R increases. The log P value re¯ects the hydrophobicity of the system. The minimum occurring for R 7 is expected because from R 7 onwards log P values steadily increases as R increases. However, the highest value within the series (for R 6 case) is out of line. This has to be due to rather strained, thus the skew structure of the cyclacene shuttle in the case of R 6: Hence, the hydrophobic character is more pronounced. The value and direction of the dipole moments are also effective contributors to the hydrophobicity of these systems, which primarily arise from the gross topology of the catenanes considered. The contributors of the dipole moment are point charge and sp-hybrid components. Table 2 shows the
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
179
Table 2 The components and the total value of the dipole moments of the catenanes considered (dipole moments are in the order of 10 230 C m) Dipole moment
R
Direction
Component
6
7
8
9
X
Point charge sp-hybrid Point charge sp-hybrid Point charge sp-hybrid
0.7871 0.3935 1.5910 0.0867 25.0333 1.5543 5.3368 1.6044 4.0390
20.6437 0.0967 0.1367 20.0100 0.1400 0.0100 0.6737 0.0967 0.5837
20.2101 0.0600 0.3268 0.0366 0.4336 0.5737 0.5837 0.5803 1.0840
20.3468 0.0567 20.5436 0.1067 0.0933 20.0066 0.6504 0.1200 0.5303
Y Z Total Point charge Total sp-hybrid Overall Total
components and the total value of the dipole moments of the systems presently considered. Generally, the direction of the dipole moment is from some part of the periphery of the shaft, which is not inside the cyclacene moiety to the origin of the axes of inertia of the system. Fig. 2 shows the geometry optimized structures of the present systems R 6±9: Cyclacenes are characterized by the presence of two types of p-systems embedded in their skeletons. These are the benzenoid rings constituting the main backbone of a cyclacene molecule and its peripheral circuits (the top and bottom rings), which becomes 4m or 4m 1 2 depending on the number of benzenoid rings (R) present. It may be noted that the size of a peripheral circuit is equal to 2R. Various properties of the p-electron systems of cyclacenes have recently been examined [26,30,31]. Of these the
Fig. 2. The geometry optimized structures of present concern.
Fig. 3. Electrostatic potential ®eld contours for some catenanes (R 7 and 8) considered.
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
180
Table 3 Some energies of the catenanes considered (energies in kJ/mol. Symmetries below the numeric data) Energy
Total Binding Isolated atomic Electronic Core±core repulsion Heat of formation LUMO a HOMO a DE a a
R 6
7
8
9
2676438 243918 2632521 28925846 8249408 3848 22.8706 A 211.7936 A 8.9230
2725816 247843 2677972 210093038 9367221 3218 23.4899 A 211.4321 A 7.9422
2774909 251484 2723424 211188476 10413569 2874 24.9548 A 29.9761 A 5.0213
2823947 255071 2768876 212258639 11434691 2583 23.7237 A 211.2236 A 7.4999
Energies in the order of 10 219 J.
Table 4 Some energies of the cyclacene moiety (shuttle) in the catenanes considered (energies in kJ/mol) Energy
Total Binding Isolated atomic Electronic Core±core repulsion Heat of formation LUMO a HOMO a DE a a
R 6
7
8
9
2310084 217117 292968 22466348 2156264 2659 21.4338 210.6143 9.1805
2362724 220929 2341796 23135705 2772980 2143 22.2348 210.2943 8.0595
2415046 224423 2390624 23819890 3404843 1945 24.1082 29.2487 5.1405
2467394 227943 2439451 24525881 4858487 1721 23.1446 210.6820 7.5374
Energies in the order of 10 219 J.
Table 5 Some energies of the cyclotriacontene (shaft) moiety in the catenanes considered (energies in kJ/mol) Energy
Total Binding Isolated atomic Electronic Core±core repulsion Heat of formation LUMO a HOMO a DE a a
R 6
7
8
9
2408557 225854 2382703 23089118 2680560 2136 21.6797 212.2660 10.5863
2408963 226260 2382703 23096515 2687552 1730 21.7161 212.4215 10.7054
2409385 226682 2382703 23099432 260047 1308 21.6997 212.2904 10.5907
2409575 226872 2302703 23099361 2689787 1118 21.6779 212.2147 10.5368
Energies in the order of 10 219 J.
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
181
Fig. 4. The distribution of molecular orbital energies as R varies.
cryptoannulenic effect [27,28], in¯uences certain properties of cyclacenes such as certain energies, HOMO±LUMO energy separation, dipole moments, bond lengths, etc. It has been one of the primary interests of the present article to investigate how the cryptoannulenic effect would display itself when a conjugated shaft, like the one presently used, is threaded through a cyclacene molecule and the shaft termini undergo an intramolecular union to yield the corresponding catenane molecule. Table 3 shows some energies of the catenanes presently considered. As seen in the table, the structures are all stable but endothermic in nature. The endogenic character decreases as the shuttle grows in size (as R increases). The thorough analysis of the data indicates that the catenanes considered exhibit almost no cryptoannulenic effect of the ®rst and second order. Note that the second order cryptoannulenic effect is de®ned as the dependence of any property of the structure on 4m or 4m 1 2 nature of the peripheral circuit per benzenoid ring (R) present [26±28]. Table 4 shows some ener-
gies of the cyclacene moiety (shuttle) in the presence of the shaft in the cyclacenes considered. In these mixed mode type calculations, the cyclacene moiety in every structure was treated quantum mechanically while the remainder (the shaft) was treated classically [32]. The data reveal that the shaft greatly affects the nature of cyclacenes (shuttle) such that only some trace of the cryptoannulenic effect on the HOMO, LUMO energies and the frontier molecular orbital (FMO) energy gap (DE) is present. Table 5 shows some energies of the cyclotriacontene unit (shaft) in the catenanes considered. This time, the HOMO, LUMO and DE values exhibit the in¯uence of the cyclacene moiety present in the structure. Thus, in the present catenene systems, the shaft and shuttle units highly in¯uence each other through space interaction [33±35]. Fig. 3 shows how the shaft and shuttle mutually exert an electrostatic potential ®eld through space. Fig. 4 shows the distribution of the molecular orbital energies of the structures. The span of the
182
L. TuÈrker / Journal of Molecular Structure (Theochem) 574 (2001) 177±183
Fig. 5. The HOMO and LUMO of the catenanes having R 7 and 8.
molecular orbital energies are in between 26.1100 and 1.0721, 26.1167 and 1.0339, 26.1160 and 1.0284 and 26.1149 and 1.0191 (all in the order of 10 218 J) for R 6±9; respectively. As for the HOMO and LUMO characteristics of the presently investigated catenanes, the PM3 treatment results in frontier molecular orbitals, such that both of them are con®ned to the shuttle (cyclacene moiety) in all the cases R 6±9: The FMO energies have been shown in Table 3. Fig. 5 shows the HOMO and LUMO of the catenanes having R 7 and 8. The symmetries of frontier molecular orbitals are all A type for R 6±9:
cryptoannulenic effect is one of the characteristic property of the cyclacenes. The shaft and shuttle in the catenanes considered affect the electronic properties of each other through space interactions. Thus, any perturbation in each moiety, such as insertion of certain heteroatoms, should affect the electronic properties of the other moiety. In other words they should be electronically (also magnetically) coupled circuits which might have certain practical applications related to molecular electronics.
References 4. Conclusions The present PM3 type calculations revealed that the considered catenanes having the cyclacene shuttle are stable but endogenic structures possessing almost no
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