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Study of the interconversion of the isomers of 14-annulene by the AM1 method
Journal of Molecular Structure (Theo&em), 204 (1990) 201-208 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
201
STUDY OF THE INTERCONVERSION OF THE ISOMERS OF 14-ANNULENE BY THE AM1 MJZTHOD
J.M. HERNANDO Departamento de Quimica Fisica, Facultad de Ciencias, Universidad de Valladolid, 47005. Valladolid (Spain) J.J. QUIRANTE* and F. ENRIQUEZ Departamento de Quimica Fisica, Facultad de Ciencias, Universidad de Mdlaga, 29071-Mdlaga (Spain) (Received 14 March 1989)
ABSTRACT The AM1 method was used to carry out a theoretical study of the reversible transformation between the two isomers of 14annulene with pyrene-like perimeter. The transition state of the process was located on the corresponding potential hypersurface.
INTRODUCTION
14-Annulene was first synthesized by Sondheimer and Gaoni [ 11, who also studied its UV absorption spectrum. As shown by the X-ray study carried out by Chiang and Paul [ 21, this compound features a pyrene like perimeter. Of its two isomers, which were characterized by Gaoni and Sondheimer [3] and result from the intramolecular repulsion of the four hydrogen atoms located inside the molecular ring, the so-called isomer A is more stable than isomer B according to these authors. This paper reports on a theoretical quantum-chemical study of both isomers carried out by using semi-empirical methods and procedures for the systematic search on stationary points on potential hypersurfaces, with special emphasis on the transition state involved in the interconversion of the two isomers. RESULTS AND DISCUSSION
The two isomers of 14-annulene with a pyrene-like perimeter, which differ in the arrangement of the hydrogen atoms inside the ring, were located on the *Author to whom correspondence should be addressed.
0166-1280/90/$03.50
0 1990 EIsevier Science Publishers B.V.
202
AM1 [4] energy hypersurface of the system by free optimization through the Davidon-Fletcher-Powell method [5,6] of all the geometric parameters of the molecule in order to minimize the energy involved. This was done by using as starting points the corresponding approximate localized geometries, namely CZhand D2, respectively. The calculated values of the most relevant geometric variables for the two isomers are listed in Tables 1-4 and the other parameters of interest related to these and to the mutual conversion process discussed below are given in Table 5. Of the two isomers, the so-called A isomer, the Cl-H1 and C4-H4 bonds of which point to one side while the C&H8 and Cll-Hll bonds point in the opposite direction, is the more stable; it has a calculated standard heat of formation of 103.33 kcal mold1 at 298.15 K, as compared with 104.08 kcal mol-’ for the B isomer. As expected, the interaction between the four inner hydrogen atoms results in a far from planar structure for 14-annulene, which is reflected in its z coordinates (Table 1 ), calculated with respect to an arbitrary chosen plane containing the maximum possible number of carbon atoms. X-ray studies [ 21 and molecular-mechanics calculations [ 71 have also yielded non-planar structures for this compound. Table 2, which lists bond lengths, also contains experimental values obtained in crystallographic studies [ 21, as well as other results found by various authors using different calculation methods [ 81. It should be noted that the CND0/2 and MINDO/S results correspond to the geometry of the more stable TABLE 1 Atomic vertical diplacementefor the stationarypointa located on the AM1 hypemurface Transition state
Isomer B
A Cl, C4, C5, C6, C8, Cll, C13, Cl4 c2, c3 c7, Cl2 c9, Cl0
0.0 -0.8 0.5 0.4
Hl, H4, H9, H10 H2, H3
0.8 -1.6
H5, H6, H7, H8,
-0.4 0.0 1.2 -0.8
H14 H13 H12 Hll
Cl, c3, c4, Hl,
C2, C5, C6, C7, C8, ClO, Cl3 c9, c12, Cl4 Cl1 H8
H2, H12, H13 H3, H6 H4, Hll H5 H7 H9 HlO H14
0.0 -0.3 -0.5 0.7 0.0 -0.3 -1.0 0.5 -0.2 -0.7 0.3 -0.8
Cl, c4, c5, Cll, Cl2 c2, c3 C6 C7, C8 c9, Cl0 Cl3 Cl4 Hl, H4, H8, HlO H2, H5 H3, Hll H6 H7 H9 H12 H13 H14
0.0 -0.4 0.3 0.5 0.4 -0.3 -0.6 0.8 -0.8 -0.7 0.3 0.7 0.2 0.0 -0.3 -1.3
203
TABLE 2 Bond lengths (A ) Bond
C2Cl C3C2 c4c3 c5c4 C6C5 C7C6 C8C7 C9C8 ClOC9 CllClO C12Cll C13C12 c14c13 C14Cl HlH4 H4H8 H8Hll HllHl H4Hll HlH8
Isomer A
B
1.446 1.348 1.446 1.346 1.449 1.348 1.445 1.346 1.448 1.346 1.445 1.348 1.449 1.346 2.040 2.311 1.958 2.311 3.056 3.055
1.450 1.346 1.450 1.344 1.449 1.348 1.443 1.345 1.457 1.345 1.443 1.348 1.449 1.344 2.509 2.164 2.451 2.165 2.322 2.237
Exp.”
CND0/2b
MIND0/3b
1.395 1.356 1.381 1.376 1.407 1.350 1.382 1.395
1.343 1.432 1.345 1.429 1.345 1.428 1.344 1.432
1.349 1.466 1.346 1.469 1.351 1.463 1.346 1.472
2.040 2.020 2.040 2.020 2.910 2.910
2.114 1.795 2.114 1.795 2.178 2.178
2.973 2.828 2.973 2.828 2.844 2.844
Transition state 1.450 1.351 1.444 1.343 1.451 1.350 1.438 1.347 1.460 1.348 1.443 1.348 1.450 1.345 1.912 1.614 2.145 2.245 2.919 2.282
“Ref. 2. bRef. 8.
isomer, which has an essentially planar structure in which only the hydrogen atoms inside the ring are free to take positions out of the molecular plane. As can be seen from the data in Table 2, the distances between the inner hydrogen atoms of isomer A calculated by the AM1 method and from crystallographic measurements are quite consistent. The AM1 results reveal alternant bond lengths, which are confirmed by experimental X-ray data; this prediction agrees with the CNDO/B and MIND0/3 results, even though, as stated above, the latter were only approximate in that they involved some constraints to the system geometry. All three methods yield similar results for the length of the double bond, but not for that of the single bond. The degree of alternancy predicted by the AM1 method is intermediate between that provided by the other two methods which appears to indicate that one of the advantages of this novel method over its most common forerunner, namely MIND0/3 (which yields marked altemancies), lies in the fact that it compensates, at least partly, for the tendency of MIND0/3 to overestimate the repulsion forces arising from non-bonding interactions [9]. In any case, the three semi-empirical methods considered in Table 2 yield very strict alternancies compared with
204 TABLE 3 Bond ar.gles (’ ) for the three stationary points Angle
Isomer
Transition state
A
B
C3-C2-Cl C4-C3-C2
123.81 123.81
122.64 122.63
124.34 121.43
c5-c4-c3 C14-Cl-C2
124.72 124.72
125.17 125.17
129.79 124.58
C6-C5-C4 c13-c14-Cl
123.55 123.55
124.26 124.23
124.59 124.57
C7-C6-C5 C14-C13-Cl2
125.06 125.06
126.17 126.15
129.98 126.69
C8-C7-C6 C13-C12-Cl1
122.37 122.37
123.27 123.28
126.07 123.65
C9-C8-C7 ClB-Cll-Cl0
125.78 125.78
126.75 126.79
130.34 126.76
ClO-c9-C8 Cll-ClO-c9
123.29 123.29
119.42 119.41
117.70 120.25
that derived from the experimental bond-length values which, despite the slight differences between single and double bonds, are not in a regular sequence. Loos and Legka [lo] originally attributed these divergences to a potential difference in the molecular geometry of the compound in the solid and the gas phase, on which the quantum-mechanical calculations were made. However, more recent work [11,12] has shown the relevance of explicitly considering electron correlation in studying rings of this size. Thus, Jug and Fasold [ 121 demonstrated such a correlation to be greater for delocalized forms: by applying the semi-empirical SINDO/l method including a large number of configurations they obtained virtually delocalized forms for both isomers. However, insofar as the electron correlation was introduced to such calculations by applying CI (configuration interaction) at different levels to the geometries previously optimized with no CI and imposing symmetries C,, and C, for isomer A and symmetry DZ for the localized form of isomer B, the bond lengths calculated by these authors cannot be granted absolute validity unless geometries had been optimized on a CI hypersurface. On the basis of the above considerations, the AM1 results show that for this type of molecule, electron correlation
205 TABLE 4 Dihedral angles ( ’ ) Dihedral angle
Transition
Isomer
State
A C4,C3-C2,Cl Cll, ClO-C9, C8
B 0.00 0.00
355.17 313.97
1.47 322.81
C5,C4-C3,C2 C14,Cl-C2,C3
209.83 150.18
141.92 141.76
206.84 148.55
C6,C5-C4,C3 C13,C14-Cl,CZ
173.99 185.99
183.86 183.89
170.28 186.48
C7$6-C5,C4 ClZ,C13-C14,Cl
324.02 35.97
35.37 35.46
333.80 39.79
CS,C7-C6,C5 C14$13-C12,Cll
358.59 1.42
0.61 0.61
4.11 0.00
C9,C8-C7,C6 C13,C12-Cll,ClO
143.05 216.95
205.85 205.99
204.35 202.80
ClO,C9-C8,C7 C12,Cll-ClO,C9
192.85 167.15
172.23 172.30
176.12 171.04
Hl,Cl-C4,H4” H8,C8-Cll,Hll” H&Cl-Cll,Hll” H4,C4-C8,HS”
0.00 0.01 61.92 61.93
80.55 74.70 74.05 74.09
1.45 64.89 72.14 22.01
*Not according the MOPAC sign convention.
is underestimated if calculations are limited to those included in the parametrization of the method. Tables 3 and 4, which list the calculated bond and dihedral angles, show the minimization process to have led, with no imposition whatsoever on the system geometry, to a structure with a C, symmetry for isomer A. As shown below, the geometry obtained for isomer B has no symmetry; yet, its bond angles fulfil the same equalities as those of isomer A (e.g. the angles formed by the bonds C3-C4-Cl and C!&C4-C3 are equal to those of C4-C3-C2 and C14-Cl-C2, respectively, etc.). By adding up pairs of symmetry related dihedral angles of isomer A, the values of which are specified according to the sign convention of the MOPAC program [ 131, a constant value of 360” is obtained, which definitively confirms the C, symmetry of this isomer. Should isomer B have a C2 symmetry with a binary axis intercepting the C2-C3 and C9-Cl0 bonds me-
206 TABLE 5 Energetic properties
and dipolar moment Isomer
Heat of formation (kcal mol-‘) Relative energy (kcal mol-‘) Electronic energy (eV ) Core-core repulsion (eV) P(D) Ionization potential (eV) HOMO (eV) LUMO (eV)
Transition
A
B
103.33 0.00 - 11774.760035 9792.894283 0.271 8.330 - 8.330 -0.417
104.08 0.75 - 11763.76237 9781.927374 0.134 8.503 - 8.503 - 0.349
state
109.70
6.37 - 11711.38644 9729.79704 0.204 8.387 -8.387 -0.530
dially, it would also have, according to the above-mentioned sign convention, equal values for symmetry related pairs of dihedral angles; this is the case with some, but not all, such angles. Hence, strictly speaking, isomer B has no de& nite symmetry, essentially as a result of the molecular region defined by atoms Cl, C2, C3 and C4 not undergoing a strain similar to that of the region bound by atoms C8, C9, Cl0 and Cl1 because of the above-mentioned alternancy of bond lengths. The more stable isomer, A, is also that with the smaller electronic energy and the less marked alternancy of carbon-carbon bond lengths, which suggests a somewhat more aromatic structure than that of its counterpart, B. Nuclear repulsion, obviously stronger in isomer A, compensates, although not completely, for the energetic implications of the above-mentioned effect, so that the calculated energy difference between the two isomers is 0.76 kcal mol-‘. The dipole moments obtained for the two isomers allow it to be stated that isomer A will prevail in polar solvents. The analysis of the two-centre contribution of each isomer to the overall SCF energy in a one-centre and two-centre term partition, typical of ZDO methods, showed the repulsion between the inner hydrogens to account for over 50% of the energy difference calculated for the two isomers. In fact, the sum of the different possible two-centre contributions involving hydrogen atoms Hl, H4, H8 or Hll was 0.017 eV more repulsive (ca. 0.39 kcal mol-‘) for isomer B than for A. As far as the isomerization process is concerned, a transition state is located on the AM1 potential hypersurface. From the minimum-energy geometries of both isomers and using the technique developed by Dewar et al. [ 141 to study elementary processes, an approximate point in the vicinity of the true transition state was obtained. By minimizing the Euclidean energy-gradient norm from this point a stationary point was finally obtained which was classed as a
207
saddle point on account of the force constants and transition vectors obtained. This point, according to the transition vector shown in Fig. 1, turned out to be the transition state of the interconversion process. The process A-B was found to have an activation energy of about 6.2 kcal mol-’ at 298.15 K. The reaction coordinate for isomer A reveals the C5-H5 bond to be the first to change its position with respect to the reference plane in such a way that, already in the transition state, it lies slightly above such a plane, as do atoms Hl and H4. After the transition state (see Fig. 1 ), the C4-H4 bond shifts markedly to its final position in isomer B. This is also the case, although to a smaller extent, with the other three bonds involving inner hydrogen atoms. This process must be accompanied by ring relaxation, which should chiefly affect the region close to atoms H4 and HS, i.e. those exchanging their relative positions with respect to the reference plane. In fact, the angles of the bonds involving atoms C3, C4,
Fig. 1. Geometry calculated for the AM1 transition state for the interconversion of the two isomers of 14-annulene. Arrows illustrate the form of the normal mode which corresponds to the reaction coordinate.
208
C5, C6, C7, C8 and C9 are somewhat larger in the transition state than at equilibrium (Table 3 ) .
REFERENCES
5 6 7 8 9 10 11 12 13 14
F. Sondheimer and Y. Gaoni, J. Am. Chem. Sot., 82 (1960) 5765. C.C. Chiang and I.C. Paul, J. Am. Chem. Sot., 94 (1972) 4741. Y. Gaoni and F. Sondheimer, Proc. Chem. Sot. London, (1964) 229. M.J.S. Dewar, E.G. Zoebisch, E.F. HeaIy and J.J.P. Stewart, J. Am. Chem. Sot., 107 (1985) 3902. W.C. Davidon, Comput. J., 10 (1968) 406. R. Fletcher and J.J. Powell, Comput. J., 6 (1963) 163. N.L. Allinguer and J.P. Sprague, J. Am. Chem. kc., 95 (1973) 3893. H. Vogler, J. Mol. Struct., 51 (1979) 289. R.C. Bingham, M.J.S. DewarandD.H. Lo, J. Am. Chem. Soc.,97 (1975) 1285,1294. D. Loos and J. Leiika, Collect. Czech. Chem. Commun., 47 (1982) 1705. H. Baumann, J. Am. Chem. Sot., 100 (1978) 7196. K. Jug and E. Fasold, J. Am. Chem. Sot., 109 (1987) 2263. Dewar Research Group and J.J.P. Stewart, Q.C.P.E. (1986) program No. 506. M.J.S. Dewar, E.F. HeaIy and J.J.P. Stewart, J. Chem. Sot., Faraday Trans. 2, 80 (1984) 227.
201
STUDY OF THE INTERCONVERSION OF THE ISOMERS OF 14-ANNULENE BY THE AM1 MJZTHOD
J.M. HERNANDO Departamento de Quimica Fisica, Facultad de Ciencias, Universidad de Valladolid, 47005. Valladolid (Spain) J.J. QUIRANTE* and F. ENRIQUEZ Departamento de Quimica Fisica, Facultad de Ciencias, Universidad de Mdlaga, 29071-Mdlaga (Spain) (Received 14 March 1989)
ABSTRACT The AM1 method was used to carry out a theoretical study of the reversible transformation between the two isomers of 14annulene with pyrene-like perimeter. The transition state of the process was located on the corresponding potential hypersurface.
INTRODUCTION
14-Annulene was first synthesized by Sondheimer and Gaoni [ 11, who also studied its UV absorption spectrum. As shown by the X-ray study carried out by Chiang and Paul [ 21, this compound features a pyrene like perimeter. Of its two isomers, which were characterized by Gaoni and Sondheimer [3] and result from the intramolecular repulsion of the four hydrogen atoms located inside the molecular ring, the so-called isomer A is more stable than isomer B according to these authors. This paper reports on a theoretical quantum-chemical study of both isomers carried out by using semi-empirical methods and procedures for the systematic search on stationary points on potential hypersurfaces, with special emphasis on the transition state involved in the interconversion of the two isomers. RESULTS AND DISCUSSION
The two isomers of 14-annulene with a pyrene-like perimeter, which differ in the arrangement of the hydrogen atoms inside the ring, were located on the *Author to whom correspondence should be addressed.
0166-1280/90/$03.50
0 1990 EIsevier Science Publishers B.V.
202
AM1 [4] energy hypersurface of the system by free optimization through the Davidon-Fletcher-Powell method [5,6] of all the geometric parameters of the molecule in order to minimize the energy involved. This was done by using as starting points the corresponding approximate localized geometries, namely CZhand D2, respectively. The calculated values of the most relevant geometric variables for the two isomers are listed in Tables 1-4 and the other parameters of interest related to these and to the mutual conversion process discussed below are given in Table 5. Of the two isomers, the so-called A isomer, the Cl-H1 and C4-H4 bonds of which point to one side while the C&H8 and Cll-Hll bonds point in the opposite direction, is the more stable; it has a calculated standard heat of formation of 103.33 kcal mold1 at 298.15 K, as compared with 104.08 kcal mol-’ for the B isomer. As expected, the interaction between the four inner hydrogen atoms results in a far from planar structure for 14-annulene, which is reflected in its z coordinates (Table 1 ), calculated with respect to an arbitrary chosen plane containing the maximum possible number of carbon atoms. X-ray studies [ 21 and molecular-mechanics calculations [ 71 have also yielded non-planar structures for this compound. Table 2, which lists bond lengths, also contains experimental values obtained in crystallographic studies [ 21, as well as other results found by various authors using different calculation methods [ 81. It should be noted that the CND0/2 and MINDO/S results correspond to the geometry of the more stable TABLE 1 Atomic vertical diplacementefor the stationarypointa located on the AM1 hypemurface Transition state
Isomer B
A Cl, C4, C5, C6, C8, Cll, C13, Cl4 c2, c3 c7, Cl2 c9, Cl0
0.0 -0.8 0.5 0.4
Hl, H4, H9, H10 H2, H3
0.8 -1.6
H5, H6, H7, H8,
-0.4 0.0 1.2 -0.8
H14 H13 H12 Hll
Cl, c3, c4, Hl,
C2, C5, C6, C7, C8, ClO, Cl3 c9, c12, Cl4 Cl1 H8
H2, H12, H13 H3, H6 H4, Hll H5 H7 H9 HlO H14
0.0 -0.3 -0.5 0.7 0.0 -0.3 -1.0 0.5 -0.2 -0.7 0.3 -0.8
Cl, c4, c5, Cll, Cl2 c2, c3 C6 C7, C8 c9, Cl0 Cl3 Cl4 Hl, H4, H8, HlO H2, H5 H3, Hll H6 H7 H9 H12 H13 H14
0.0 -0.4 0.3 0.5 0.4 -0.3 -0.6 0.8 -0.8 -0.7 0.3 0.7 0.2 0.0 -0.3 -1.3
203
TABLE 2 Bond lengths (A ) Bond
C2Cl C3C2 c4c3 c5c4 C6C5 C7C6 C8C7 C9C8 ClOC9 CllClO C12Cll C13C12 c14c13 C14Cl HlH4 H4H8 H8Hll HllHl H4Hll HlH8
Isomer A
B
1.446 1.348 1.446 1.346 1.449 1.348 1.445 1.346 1.448 1.346 1.445 1.348 1.449 1.346 2.040 2.311 1.958 2.311 3.056 3.055
1.450 1.346 1.450 1.344 1.449 1.348 1.443 1.345 1.457 1.345 1.443 1.348 1.449 1.344 2.509 2.164 2.451 2.165 2.322 2.237
Exp.”
CND0/2b
MIND0/3b
1.395 1.356 1.381 1.376 1.407 1.350 1.382 1.395
1.343 1.432 1.345 1.429 1.345 1.428 1.344 1.432
1.349 1.466 1.346 1.469 1.351 1.463 1.346 1.472
2.040 2.020 2.040 2.020 2.910 2.910
2.114 1.795 2.114 1.795 2.178 2.178
2.973 2.828 2.973 2.828 2.844 2.844
Transition state 1.450 1.351 1.444 1.343 1.451 1.350 1.438 1.347 1.460 1.348 1.443 1.348 1.450 1.345 1.912 1.614 2.145 2.245 2.919 2.282
“Ref. 2. bRef. 8.
isomer, which has an essentially planar structure in which only the hydrogen atoms inside the ring are free to take positions out of the molecular plane. As can be seen from the data in Table 2, the distances between the inner hydrogen atoms of isomer A calculated by the AM1 method and from crystallographic measurements are quite consistent. The AM1 results reveal alternant bond lengths, which are confirmed by experimental X-ray data; this prediction agrees with the CNDO/B and MIND0/3 results, even though, as stated above, the latter were only approximate in that they involved some constraints to the system geometry. All three methods yield similar results for the length of the double bond, but not for that of the single bond. The degree of alternancy predicted by the AM1 method is intermediate between that provided by the other two methods which appears to indicate that one of the advantages of this novel method over its most common forerunner, namely MIND0/3 (which yields marked altemancies), lies in the fact that it compensates, at least partly, for the tendency of MIND0/3 to overestimate the repulsion forces arising from non-bonding interactions [9]. In any case, the three semi-empirical methods considered in Table 2 yield very strict alternancies compared with
204 TABLE 3 Bond ar.gles (’ ) for the three stationary points Angle
Isomer
Transition state
A
B
C3-C2-Cl C4-C3-C2
123.81 123.81
122.64 122.63
124.34 121.43
c5-c4-c3 C14-Cl-C2
124.72 124.72
125.17 125.17
129.79 124.58
C6-C5-C4 c13-c14-Cl
123.55 123.55
124.26 124.23
124.59 124.57
C7-C6-C5 C14-C13-Cl2
125.06 125.06
126.17 126.15
129.98 126.69
C8-C7-C6 C13-C12-Cl1
122.37 122.37
123.27 123.28
126.07 123.65
C9-C8-C7 ClB-Cll-Cl0
125.78 125.78
126.75 126.79
130.34 126.76
ClO-c9-C8 Cll-ClO-c9
123.29 123.29
119.42 119.41
117.70 120.25
that derived from the experimental bond-length values which, despite the slight differences between single and double bonds, are not in a regular sequence. Loos and Legka [lo] originally attributed these divergences to a potential difference in the molecular geometry of the compound in the solid and the gas phase, on which the quantum-mechanical calculations were made. However, more recent work [11,12] has shown the relevance of explicitly considering electron correlation in studying rings of this size. Thus, Jug and Fasold [ 121 demonstrated such a correlation to be greater for delocalized forms: by applying the semi-empirical SINDO/l method including a large number of configurations they obtained virtually delocalized forms for both isomers. However, insofar as the electron correlation was introduced to such calculations by applying CI (configuration interaction) at different levels to the geometries previously optimized with no CI and imposing symmetries C,, and C, for isomer A and symmetry DZ for the localized form of isomer B, the bond lengths calculated by these authors cannot be granted absolute validity unless geometries had been optimized on a CI hypersurface. On the basis of the above considerations, the AM1 results show that for this type of molecule, electron correlation
205 TABLE 4 Dihedral angles ( ’ ) Dihedral angle
Transition
Isomer
State
A C4,C3-C2,Cl Cll, ClO-C9, C8
B 0.00 0.00
355.17 313.97
1.47 322.81
C5,C4-C3,C2 C14,Cl-C2,C3
209.83 150.18
141.92 141.76
206.84 148.55
C6,C5-C4,C3 C13,C14-Cl,CZ
173.99 185.99
183.86 183.89
170.28 186.48
C7$6-C5,C4 ClZ,C13-C14,Cl
324.02 35.97
35.37 35.46
333.80 39.79
CS,C7-C6,C5 C14$13-C12,Cll
358.59 1.42
0.61 0.61
4.11 0.00
C9,C8-C7,C6 C13,C12-Cll,ClO
143.05 216.95
205.85 205.99
204.35 202.80
ClO,C9-C8,C7 C12,Cll-ClO,C9
192.85 167.15
172.23 172.30
176.12 171.04
Hl,Cl-C4,H4” H8,C8-Cll,Hll” H&Cl-Cll,Hll” H4,C4-C8,HS”
0.00 0.01 61.92 61.93
80.55 74.70 74.05 74.09
1.45 64.89 72.14 22.01
*Not according the MOPAC sign convention.
is underestimated if calculations are limited to those included in the parametrization of the method. Tables 3 and 4, which list the calculated bond and dihedral angles, show the minimization process to have led, with no imposition whatsoever on the system geometry, to a structure with a C, symmetry for isomer A. As shown below, the geometry obtained for isomer B has no symmetry; yet, its bond angles fulfil the same equalities as those of isomer A (e.g. the angles formed by the bonds C3-C4-Cl and C!&C4-C3 are equal to those of C4-C3-C2 and C14-Cl-C2, respectively, etc.). By adding up pairs of symmetry related dihedral angles of isomer A, the values of which are specified according to the sign convention of the MOPAC program [ 131, a constant value of 360” is obtained, which definitively confirms the C, symmetry of this isomer. Should isomer B have a C2 symmetry with a binary axis intercepting the C2-C3 and C9-Cl0 bonds me-
206 TABLE 5 Energetic properties
and dipolar moment Isomer
Heat of formation (kcal mol-‘) Relative energy (kcal mol-‘) Electronic energy (eV ) Core-core repulsion (eV) P(D) Ionization potential (eV) HOMO (eV) LUMO (eV)
Transition
A
B
103.33 0.00 - 11774.760035 9792.894283 0.271 8.330 - 8.330 -0.417
104.08 0.75 - 11763.76237 9781.927374 0.134 8.503 - 8.503 - 0.349
state
109.70
6.37 - 11711.38644 9729.79704 0.204 8.387 -8.387 -0.530
dially, it would also have, according to the above-mentioned sign convention, equal values for symmetry related pairs of dihedral angles; this is the case with some, but not all, such angles. Hence, strictly speaking, isomer B has no de& nite symmetry, essentially as a result of the molecular region defined by atoms Cl, C2, C3 and C4 not undergoing a strain similar to that of the region bound by atoms C8, C9, Cl0 and Cl1 because of the above-mentioned alternancy of bond lengths. The more stable isomer, A, is also that with the smaller electronic energy and the less marked alternancy of carbon-carbon bond lengths, which suggests a somewhat more aromatic structure than that of its counterpart, B. Nuclear repulsion, obviously stronger in isomer A, compensates, although not completely, for the energetic implications of the above-mentioned effect, so that the calculated energy difference between the two isomers is 0.76 kcal mol-‘. The dipole moments obtained for the two isomers allow it to be stated that isomer A will prevail in polar solvents. The analysis of the two-centre contribution of each isomer to the overall SCF energy in a one-centre and two-centre term partition, typical of ZDO methods, showed the repulsion between the inner hydrogens to account for over 50% of the energy difference calculated for the two isomers. In fact, the sum of the different possible two-centre contributions involving hydrogen atoms Hl, H4, H8 or Hll was 0.017 eV more repulsive (ca. 0.39 kcal mol-‘) for isomer B than for A. As far as the isomerization process is concerned, a transition state is located on the AM1 potential hypersurface. From the minimum-energy geometries of both isomers and using the technique developed by Dewar et al. [ 141 to study elementary processes, an approximate point in the vicinity of the true transition state was obtained. By minimizing the Euclidean energy-gradient norm from this point a stationary point was finally obtained which was classed as a
207
saddle point on account of the force constants and transition vectors obtained. This point, according to the transition vector shown in Fig. 1, turned out to be the transition state of the interconversion process. The process A-B was found to have an activation energy of about 6.2 kcal mol-’ at 298.15 K. The reaction coordinate for isomer A reveals the C5-H5 bond to be the first to change its position with respect to the reference plane in such a way that, already in the transition state, it lies slightly above such a plane, as do atoms Hl and H4. After the transition state (see Fig. 1 ), the C4-H4 bond shifts markedly to its final position in isomer B. This is also the case, although to a smaller extent, with the other three bonds involving inner hydrogen atoms. This process must be accompanied by ring relaxation, which should chiefly affect the region close to atoms H4 and HS, i.e. those exchanging their relative positions with respect to the reference plane. In fact, the angles of the bonds involving atoms C3, C4,
Fig. 1. Geometry calculated for the AM1 transition state for the interconversion of the two isomers of 14-annulene. Arrows illustrate the form of the normal mode which corresponds to the reaction coordinate.
208
C5, C6, C7, C8 and C9 are somewhat larger in the transition state than at equilibrium (Table 3 ) .
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F. Sondheimer and Y. Gaoni, J. Am. Chem. Sot., 82 (1960) 5765. C.C. Chiang and I.C. Paul, J. Am. Chem. Sot., 94 (1972) 4741. Y. Gaoni and F. Sondheimer, Proc. Chem. Sot. London, (1964) 229. M.J.S. Dewar, E.G. Zoebisch, E.F. HeaIy and J.J.P. Stewart, J. Am. Chem. Sot., 107 (1985) 3902. W.C. Davidon, Comput. J., 10 (1968) 406. R. Fletcher and J.J. Powell, Comput. J., 6 (1963) 163. N.L. Allinguer and J.P. Sprague, J. Am. Chem. kc., 95 (1973) 3893. H. Vogler, J. Mol. Struct., 51 (1979) 289. R.C. Bingham, M.J.S. DewarandD.H. Lo, J. Am. Chem. Soc.,97 (1975) 1285,1294. D. Loos and J. Leiika, Collect. Czech. Chem. Commun., 47 (1982) 1705. H. Baumann, J. Am. Chem. Sot., 100 (1978) 7196. K. Jug and E. Fasold, J. Am. Chem. Sot., 109 (1987) 2263. Dewar Research Group and J.J.P. Stewart, Q.C.P.E. (1986) program No. 506. M.J.S. Dewar, E.F. HeaIy and J.J.P. Stewart, J. Chem. Sot., Faraday Trans. 2, 80 (1984) 227.