CNDO/2 and INDO (intermediate neglect of differential
overlap) calculations of a reaction pathway for the sigmatropic
[1,5] hydrogen shift in cyclopentadiene
Citation for published version (APA):
de Dobbelaere, J. R., Haan, de, J. W., Buck, H. M., & Visser, G. J. (1973). CNDO/2 and INDO (intermediate neglect of differential overlap) calculations of a reaction pathway for the sigmatropic [1,5] hydrogen shift in cyclopentadiene. Theoretica Chimica Acta, 31(1), 95-99. https://doi.org/10.1007/BF00527443
DOI:
10.1007/BF00527443
Document status and date: Published: 01/01/1973
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Theoret. chim. Acta (Berl.) 31, 95--99 (1973) 9 by Springer-Verlag 1973
CNDO/2 and INDO Calculations of a Reaction Pathway
for the Sigmatropic [1, 5] H-Shift in Cyclopentadiene
J. R. de Dobbelaere*, J. W. de H a a n * * , H. M. Buck*, and G. J. Visser*** Laboratories of Organic Chemistry* and of Instrumental Analysis** and Computing Centre***,
University of Technology, Eindhoven, The Netherlands Received October 16, 1972/April 6, 1973
CNDO/2 and INDO calculations have been carried out in order to construct a suitable model for the activated complex during the reaction. In this reaction model the migrating hydrogen atom moves along an edge of the cyclopentadiene ring. An analysis of this situation suggests a partial electron transfer from the migrating hydrogen to the nascent cyclopentadienyl system. This charge transfer is discussed in terms of aromaticity. The calculated activation enthalpies are 10 kcal/mole (CNDO/2) and 17 kcal/mole (INDO), whereas the experimental value is ca. 24 kcal/mole [1].
Key words: Thermal sigmatropic hydrogen shifts - Transition state geometry - Aromaticity of odd-membered cycloradicals
Introduction
T h e r m a l [-1, 5] sigmatropic rearrangements have been reported in m a n y linear and cyclic conjugated polyenes [2, 3, 4, 5]. The kinetic activation parameters of [1, 5] H-shifts show large mutual differences, A H ~ varying between ca. 20 and 40 kcal/mole.
Starting an a t t e m p t to correlate these energy differences with transition state geometries, we performed C N D O / 2 and I N D O calculations according to Pople [6, 7].
In a similar way modified I N D O calculations have been described earlier for the Cope rearrangement [8] and the b u t a d i e n e ~ c y c l o b u t e n e isomerization [9]. Very recently the activation energy for the suprafacial and antarafacial [1, 5] H-shift in cis-piperylene has been calculated using the M I N D O / C I method [10].
Results
In the transition state of the [1, 5] sigmatropic H-shift in cyclopentadiene we assumed a three-center bond between the migrating hydrogen a t o m and two carbon atoms. This presupposition was justified by the results of Shchembelov and U s t y n y u k who considered also the four- and six-center bonds [11]. The ground state geometry was constructed using microwave spectroscopic data [12]. Concerning the b o n d lengths and angles which were varied in our minimization procedure, we used the values obtained by Shchembelov and Ustynyuk [11], see Fig. 1.
96 J.R. de Dobbelaere et al. H 6 H2 / J
"H~
H1 Hs Fig. 1 H6'\
H2
H1 ~
~
H5
Fig. 2 H3Assuming a suprafacial sigmatropic shift of H 6 from C1 to
C2,
the symmetric transition state will be as depicted in Fig. 2. In this study the reaction coordinate is defined by the angle (SRPC 0.R (SRPC1) ~
1/8 10 SR, P and H 6 are situated in a plane perpendicular to the cyclopentadiene ring, 1/4 20 while S R moves along C1-C 2 .
3/8 30 1/2 40
Energy minimization was carried out using the SIMPLEX method [13], with respect to eight geometrical parameters:
- angle
- distance S R - H 6
- angles fl and y (corresponding with out-of-plane movements of H1 and H2) - angles 6 and e (in the cyclopentadiene plane)
- distance C1-C2 (two parameters).
Other dimensions have not been optimized by CNDO/2 or INDO methods. They were derived from the ground state dimensions by applying simple geo- metric relations. See Table 1.
Table 1
R = 0 R = 1 / 8 R = 1 / 4 R = 3 / 8 R = 1 / 2 R = 1
C3-C 4 (A) 1.460 1.450 1.441 1.411 1.402 1.344
C4-C 5 (~) 1.344 1.366 1.370 1.383 1.399 1.460
H-Shift in Cyclopentadiene Table 2. CNDO/2 results
97
R CI_C 2 SR_H6(z~t) 0~(o) j~(o) ,~(o) ~(o) E:(o) C1C2C3(~ AE ~H 6
(kcal/mole) 0 1.470 1.090 53.0 -53.0 0.0 127.3 124.4 108.3 0.0 0.97 1/8 1.465 1.138 63.3 -36.2 - 1.9 1 2 7 . 7 122.7 109.8 6.0 0.95 1/4 1 . 4 6 0 1.119 71.0 -25.9 - 2 . 2 1 2 9 . 4 123.5 109.6 10.0 0.90 3/8 1 . 4 6 0 1.075 76.1 - 13.4 - 3 . 2 1 2 7 . 6 123.3 108.4 10.4 0.85 1/2 1 . 4 7 0 1.050 76.6 - 6.3 -6.9 126.7 125.5 107.6 10.0 0.83
Table 3. INDO results
R CI_C2(A) SR_H6(A) e(o) /~(o) y(o) ~(o) ~(o) C1C2C3(~ zJE 0H6 (kcal/mole) 0 1.470 1.090 53.0 -53.0 0.0 127.3 124.4 108.3 0.0 1.00 1/8 1.470 1.146 62.9 -36.8 1.8 1 2 7 . 6 122.7 109.7 6.7 0.98 1/4 1.463 1.130 69:6 -26.6 - 1 . 4 128.6 123.6 109.5 t2.9 0.93 3/8 1.468 1.079 74.4 -13.8 - 2 . 7 1 2 6 . 4 124.5 108.2 16.5 0.88 1/2 1.471 1.058 76.0 - 8.8 -5.8 125.9 125.3 107.0 17.2 0.86 E kcal,/'mote B IND0 l o CND0 - 2 20 15 10 5 0 1/8 1~ 3/8 1/2 5,/8 3/z 7/8 I ~ R Fig. 3 I n fact, v a r i a t i o n o f t h e s e d i m e n s i o n s is b o u n d to h a v e s o m e i n f l u e n c e o n t h e t o t a l e n e r g y . H o w e v e r , a v e r y s i m i l a r i n f l u e n c e is to be e x p e c t e d in t h e t o t a l e n e r g y o f t h e g r o u n d s t a t e m o l e c u l e , t h u s t h e e n e r g y d i f f e r e n c e is n o t affected. T h e r e s u l t i n g e n e r g i e s , g e o m e t r i e s a n d e l e c t r o n d e n s i t i e s o n t h e m i g r a t i n g h y d r o g e n a t o m a r e s h o w n in T a b l e s 2 a n d 3 a n d F i g . 3.
98 J.R. de Dobbelaere et al.
Discussion
The results of the CNDO/2 and INDO calculations for the reaction pathway indicate that the electron density on the migrating hydrogen varies between 1.0 and 0.8. This is immediately reminiscent of one of Woodward and Hoffmann's early remarks: "In the [1,j] sigmatropic migration of hydrogen within an
all-cis-
polyene framework, R2CI=CH--(CH=CH)k--CJHR2, one may envisage the transition state as made up by the combination of the orbital of a hydrogen atom with those of a radical containing 2k + 3n-electrons".
Generally, at each point of the reaction coordinate a charge transfer process takes place which can be described as a "hybrid" of two configurations. The intermediate position (R = 1/2) can be indicated as follows:
~ H e
In this situation all carbon atoms are sp2-hybridized, thus creating optimal conditions for charge delocalization. In the CNDO/2 approximation this situation is calculated to be an intermediate. This intermediate is probably inherent to the CNDO/2 method, it does not appear in the INDO-calculations. The weights for the "no-bond" configuration and the ~'dative" configuration are approximately in the ratio 6 : 1. The relatively small contribution of the latter "aromatic" configu- ration is due to the high ionization potential of hydrogen and its small penetration magnitude. If one uses aromaticity as a criterion for predicting the course of the reaction, the question whether radicals containing 2 n + 3 conjugated carbon atoms and 2n + 3n-electrons are aromatic, should be solved first. Dewar suggests that Hiickel 4 n + 3-radicals are probably aromatic although there might be some doubt about the cyclopropenyl radical [14] 1.
Simple PPP calculations indeed predict aromaticity for the cyclopropenyl and cyclopentadienyl radicals, compared with the open structure radicals. The aromaticity of the cycloheptatrienyl radical has been concluded after resonance energy determining experiments [ 15].
We might conclude that in our picture a suprafacial hydrogen shift is only thermally allowed when both the "dative" and the "no-bond" configurations are aromatic.
The reason why "4n + 2" aromaticity may be used as a criterion for an allowed sigmatropic process in cyclic systems, seems to be that cycloradicals containing 2n + 3 carbon atoms and 2n + 3n-electrons are aromatic.
The reaction pathway borne out by our calculations may be visualized as follows: between R - - 0 and R = l / 2 the atom H1 shifts gradually towards the plane of the cyclopentadiene ring, while H2 will stay in or close to that plane (C 2
sp2-hybridized).
This leads to a symmetrical state with both H 1 and H2 close to (within 0.1A) the plane of the ring when R = 1/2 (C 1 and C 2 sp2-hybridized). The angle c~ increases gradually from 53 to 77 ~1 In this respect it m a y be of interest to note that ( + ) - l - b r o m o - 2 - m e t h y l b u t a n e reacts with Br' and DBr under formation of ( + ) - l - b r o m o - 2 - m e t h y l - 2 - D - b u t a n e with retention of configuration [16].
H-Shift in Cyclopentadiene 99 This discussion is substantiated by preliminary calculations on the 1,3- cyclohexadiene system. We find analogous parameters with ringbending as an extra feature. The electron density on the migrating hydrogen ranges between 0.8 and 0.9 in the transition state. Mechanistic implications of the shifts in the cyclohexadiene ring are apparently very similar to those described for the cyclo- pentadiene system. A detailed description and kinetic parameters of the 1,3- cyclohexadiene system will be published in due course.
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J. R. de Dobbelaere
Laboratory of Organic Chemistry
University of Technology
