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Theoretical study of the electronic and steric effects in the inter and intramolecular radical additions
Journal of Molecular Structure (Theochem),
136 (1986) 35-U
Elsevier Science Publishers B.V., Amsterdam
-Printed
in the Netherlands
THEORETICAL STUDY OF THE ELECTRONIC AND STERIC EFFECTS IN THE INTER AND INTRAMOLECULAR RADICAL ADDITIONS
JOAN IGUAL, JOSEP Ma. POBLET and J. PEDRO SARASA
Departament de Quimica Fisica, Facultat de Quimica de Tarragona, Universitat de Barcelona, Imperial Tarraco s/n, 43006 - Tarragona (Spain) (Received
15 May 1985)
ABSTRACT The intramolecular addition of the W-alkenyl radicals and the chain length influence in the cyclization process have been studied using MINDO/3 theoretical method. The partitioning of the total energy in local contributions is used to analyse the electronic and steric factors in the addition process, The free methyl radical additions to ethylene and propene have also been analysed and compared with the intramolecular additions. The comparison between the inter- and intramolecular additions shows that the first ones depend on the electronic structure of the olefin, while in the second, electronic and steric factors compete in the cycloaddition. INTRODUCTION
The addition of radicals to olefinic bonds is produced by a rapid process with generally low activation energy [ 1, 21. Theoretical and experimental studies [2, 3 ] of the intermolecular addition reactions show that the addition of the radical occurs in the less substituted carbon to give the thermodynamically more stable product radical. However, in the intramolecular cyclization reaction the attack occurs on the most substituted carbon of the double bond, giving the thermodynamically less stable product radical (exe addition). I
,--A3
(CH21n+, I
(CH&
L
I
A-B’ I
tH2
One of the most studied radicals is the 5hexenyl radical [4]. The intramolecular addition in this radical gives preferably the exe form, that is the thermodynamically less stable one [5]. A theoretical work [6] showed that the entropic factors have an important contribution in the cyclization of this radical. The introduction of a methyl group in the most substituted 5-hexenyl 0166-1280/86/$03.50
o 1986 Elsevier Science Publishers B.V.
36
olefinic carbon produces a profound effect on the regioselectivity of the ring closure [7-g]. The effect of methyl substituent and the factors which compete in this reaction have been analysed in a previous work [lo]. On the other hand, the preference for the e3co cyclization changes with the radical chain length. The abundance of experimental work on these additions proves the interest of analysing all these factors and of their role in the reaction mechanisms [ 1, 2,4, 5,7-9,11,12]. The transition states for the w-hexenyl radicals have been calculated by Bischof [6] and Dewar and Olivella [ 131. However, the electronic changes in the transition structures are not the main interest of the authors. The purpose of the present work is firstly to complete the study on the influence of the chain length in the cycloaddition and secondly to compare the interand intramolecular additions, analysing the determinant factors of these additions, THEORETICAL
PROCEDURE
The UHF version of the MIND0/3 method [14] was used. The election was justified by the results obtained in the intra- [6,13] and intermolecular [15, 161 additions. The calculated values of S2 indicated that the spin contaminations were unimportant. The equilibrium geometries were calculated by minimizing the energy with respect to all geometric variables. The geometries were determined using the Davidon, Fletcher and Powell procedure [17]. The located transition state (TS) structures were refined by minimizing the scalar gradient and lastly confirmed by diagonalizing the force constant matrix and thus determining that it has one negative eigenvalue [ 18 J . To analyse the importance of the different effects mentioned above the TS were rationalized by means of the energy partitioning in mono (EJ and bicentric (EAB) local contributions [19-221. A previous work [lo] shows that this is a good analysis method of the TS structures. The activation entropies were calculated by means of the vibrational frequencies and inertia moments of the TS structures, according to classical methods [ 231. RESULTS
AND DISCUSSION
Influence of the chain length in the alkenyl radicals cyclization The study of the influence of the chain length in the hex-5-enyl, pent-6 enyl and but-3-enyl cyclization were carried out using the energy partitioning. The activation entropy in the three cases favours the exo cyclization, although in the pen-4-enyl radical the difference is very small. The activation enthalpy favours also the exo mode except in the hex-5-enyl cyclization where the same value of the activation enthalpy has been found (Table 1).
37 TABLE 1 Activation enthalpies and entropies of the exo and endo transition states for the but-3enyl, pent-4-enyl and hex-5-enyl radicals (A& given in kJ mol-’ and A@ in J mol-’ K-l) Radical
Endo TS
EXO TS
But-3-enyl Pent-4-enyl Hex-5-enyl -
AH+
As+
51.9 78.0 69.0
-33.9 -48.1 -55.2
AH’
123.0 92.9 69.0
AS+
-40.2 -51.0 -69.0
The trend of these results is in good agreement with the estimated experimental data [ 11. In the hexd-enyl the bond in formation in the exe TS (Fig. 1) (Cl-C5 = 2.200 A) is shorter than in the endo TS (C,-C, = 2.265 A). However, these additibns of the- aIky1 distance; are shorter than in the inte&oledular
(exe)
(endo)
Q
++I?%-k 4
3
3
2
5
2
4
5
(b)
(exe)
(endo)
(exe)
(endo)
Fig. 1. Optimized structures for the ewo and endo transition states for: (a) hex-5-enyl radical cyclization; (b) pent-4-enyl radical cycliiation; (c) but-3-enyl radical cyclization.
38
radicals to olefins (2.350 A) [ 31. The double bond distance C&-C6 varies slightly between the two TS structures in the hex-5-enyl. There is practically no difference in activation energy between the two transition states (Table 1) and the difference between the activation entropies favours the formation of the exo product [lo] . The energy partitioning analysis (Table 2) shows that the bond in the formation of the exo TS (C1-Cs) is more complete than in the endo TS The interaction between the SOMO of the radical and the HOMO of the olefin is the most important interaction to explain the regioselectivity in the intermolecular reactions [24]. When the attack is to the most substituted carbon, as its coefficient in the HOMO is lower [25] the HOMO-SOMO overlap is also lower and the stabilization energy for the same distance diminishes. In accord with this interpretation, the cyclization of the alkenyl radicals should happen in the less substituted carbon to give the endo product. However, both cyclizations are competitive. The reason for this is that, although the attack in the less substituted carbon is a priori more favourable, the better orientation of the p interacting orbit& in the most substituted carbon makes the two ways competitive at an electronic level. So, the size of the ring has the effect of forcing the orientation between the p orbitals of the interacting carbons in the two TS. The ES--6 term indicates that the double bond is less broken in the endo TS, and the EG5 presents a destabilization in the evolution to the exo TS. This is the result of a shift of the 0 electron density along the C&-C, bond in order to accumulate the fl charge density in C5 favouring the formation of the new bond. Table 3 shows the most important mono and bicentric contributions of the exo and endo TS of the but-3-enyl radical. The strain of this system TABLE 2 Most significative bicentric and monocentric contributions initial radical of the hex-5-enyl radical cyclization (kJ mol-‘) Initial radical
of the transition states and
Exo TS
Endo TS
-2413.5 -1533.0
-182.7 -2194.9 -1505.0
-138.5 -2232.9 -1532.3
Monocentric terms ES -9765.2 E, -9814.8 E, -10136.2
-9803.4 -9898.1 -10105.0
-9833.1 -9839.3 -10114.4
‘bndo
Bicentric terms E:_: EEs-6 E,,
*Difference between the E ,+
and E la
terms.
44.2a -37.9 -27.3 -29.7 58.8 -9.6
TS-exo
TS
39 TABLE 3 Most significative bicentric and monocentric contributions initial radical of the but-3-enyl radical cyclization (kJ mol-‘) Initial radical
Exo TS
El-3 E,-,
Endo TS
* Endo
states and
TS -Em
TS
-292.8
E
EL: Es-, E E(CHl)a - WH,), E: & E, aDifference
of the transition
between
-2413.1 -1630.4 -1532.2 -10135.6 -9669.5 -9768.8 -9814.4 the E,_,
-2161.7 -1519.8 -1399.1 46.3 -10046.2 -9690.8 -9773.9 -9926.7 and E,-,
-253.4 -2038.6 -1475.8 -1470.7 69.5 -10095.8 -9701.3 -9908.4 -9867.1
39.4a 113.1 44.0 -71.7 23.2 -60.6 -10.6 -134.8 69.6
terms.
makes the interaction distances (C1-CI = 1.918 A in exe TS and Cl-C4 = 2.064 A in the endo form) smaller than the hex-5-enyl ones and because of this the corresponding contributions E 1_-3 and E 1_-4 are more stabilizing. The comparison of the energetic contributions of the Table 3 and Table 2 shows that the electron distribution is the same as in the hex-5enyl ones. However, the endo cyclization is very unfavourable, the exo being slightly more favourable than in hex-5-enyl radical. This difference is mainly due to the more unfavourable double bond contribution in the endo TS (Table 3). This can be explained if the TS structures are considered. In the exe cyclization, rotation around the C1-C2 bond makes possible the interaction of the radical orbital with the R and a* orbitals of the olefinic fragment, and so the breaking and formation of the two bonds can occur simultaneously and without a high energy. However, in the endo TS a geometric change is needed in the HC&& dihedral angle and this produces a breaking in the double bond. This is the reason for the difference in E3--4 terms and of the high activation enthalpy in the endo cyclization. The more significative nonbonded interaction is the 2 and 4 methylene group interaction (CH,), (Table 3). This interaction is less repulsive in the exo TS because the CZ-C3--C4 angle is greater than in endo TS (132” exo and 110” endo). The analysis of the pent-4-enyl cyclization has been carried out in a similar way. The activation energy difference between the two TS is 15.9 kJ mol-’ favourable to the exo cyclization. This energy has increased with regard to both shortest and longest chain radical. This seems to indicate that there is no relation between the chain length and the activation energy in the cyclization. The most interesting term to analyse is the double bond term. Table 4 shows the values obtained for the three radicals studied. In the endo TS, the
40 TABLE 4 Contribution to the activation energy of the bicentric term associated to the olefinic bond (KJ mol-I) Radical
Exo TS
Endo TS
But-benyl Pent-4-enyl Hex-5-enyl
261.4 269.9 218.6
374.6 249.5 180.7
double bond destabilization due to the distortions for the orbital overlap between the carbons is very high in the but-&enyl and practically nonexistent in the hex-5-enyl radical. Moreover, because of the smaller strength of the system, the orientation of the orbit& becomes more favourable, and the two effects make the destabilization decrease when the carbon chain is longer. Comparing the endo and exo TS, it can be seen that in the hex-5-enyl radical, the double bond term favours the endo mode, while in the but-8enyl radical it favours the exo mode. In the pent-4-enyl radical the difference of this term in the exo and endo form is minor. This indicates that in the pent4-enyl radical, we are half way between the radicals in which the activation energy difference is controlled by the orbital overlap of the interacting carbon atoms (as in the hex-5-enyl radical), and the radicals in which the difference is controlled by the destabilization of the double bond (but-3-enyl radical). So the activation energy difference is given by the necessary electronic modifications for the rupture and formation of the bonds in the three radicals and also by the nonbonded interactions in the case of the but-3enyl and pent-4-enyl radicals. Comparison of the inter and intramolecular additions With the purpose of comparing Table 5 the activation enthalpies
the inter and intramolecular additions, and activation entropies in the attack
in of
TABLE 5 Enthalpies and entropies of activation for the addition of CH, to ethylene and propene (AH+ are given in kJ mol-’ and AS+ in J mol-* K-l) Reaction
AH+
kH, + CH,=CH,
AS+
AHfxP.
33.0
-111.7
30.1-33.08
CH, + eH,=
-CH,
30.9
-109.2
30.9b
CH, + CH, b
H=&-I,
48.9
-131.8
aRef. 26. bRef. 27.
41 TABLE 6 Bond lengths and energetic contributions to the activation energy associated with bond formation (C -a C) and to the oleffnic bond (C=C) in the additions of the CH, to the ethylene and propene (bond lengths are given 10-l nm and energies in KJ mol-I) Reaction
c***c d c -*c
CH, + CH,-CH=CH,
c=c AE c **cl
dcx
A%2
2.355
-84.1
1.327
2,397
-72.5
1.340
84.4
2.296
-120.8
1.348
148.5
88.6
the methyl radical to the ethylene and propene are collected. These values have been calculated by Dewar and Olivella [3]. In Table 6 the bond in formation and olefinic bond interaction distances are given. The CHB group in the olefin produces an increase in the interaction distance C - *C when the attack is in the less substituted carbon, and a decrease when the attack is in the more substituted carbon. This can be understood if we have account of the HOMO--SOMO interaction [24]. When the addition occurs in the substituted carbon, the reactants need to be closer so that HOMO-SOMO interaction becomes sufficient for bond formation. In this case, even little, a non stabilizing secondary interaction of the SOMO of the radical with the methyl substituent also exists. In this way, in the attack to propene 01 carbon, the new bond contribution is lower than in the ethylene addition and the associated contribution to the olefinic bond is very similar. However, in the addition to /I carbon, d,,, and AE,=, are greater. At the d, ..c is smaller, and AE,..,, beginning of the reaction, the destabilization of the olefin increases rapidly when the interaction distance decreases. The deformation energy is due to the breaking of the double bond, and an accumulation of p electron density in the attacked carbon is necessary. It has also been verified that the electrostatic interactions between the radical and the substituted group are repulsive and always favour the addition to the less substituted carbon. Schematically, we can see these results from the total energy decomposition along the reaction path in three components (Fig. 2) It can be seen that the deformation energy of the methyl radical is very similar in the two attacks, and lower than the olefin deformation energy. The orientation of the addition is determined mainly by a greater deformation energy of the olefin, and a lower intermolecular stabilization energy when the addition occurs in the substituted carbon. The introduction of the CHB group in the olefin has the same consequences in the intra [lo] and in the intermolecular additions. The rate constant of the addition to the more substituted carbon is minor due to a loss of overlap between the radical and the olefinic orbitals and also to the electrostatic interaction between the radical and the substituent. The
42
E
0
-0
-I
Fig. 2. Energy descomposition along the reaction coordinate in dH, + 8H,=eHCH, additions, in three components associated to radical (ER) and olefinic (Eo) fragments and to the interaction between the radical and the olefin (IT,).
polarization of the double bond also depends on the HOMO-SOMO interaction [ 241. This leads to a later TS in this case. Nevertheless, the rate constant of the addition to the unsubstituted carbon practically does not change with regard to the radical addition to ethylene. There is an important difference between the two additions: in intermolecular reactions, there is no orbital orientation effect and reaching the TS sooner or later along the reaction path depends only on the electronic structure. In the intramolecular reaction, the interaction distance is mainly controlled by the radical chain length, and in the TS this distance is shorter than in the intermolecular additions. On the other hand, the olefinic bond destabilization increases more rapidly with the shortening of the distance than the stabilization due to the new bond. Because of this, the activitation enthalpies for the intramolecular additions are greater than the intermolecular ones. The other consequence of the strength of the system in the intramolecular additions is that the orientation of the orbitals is not the same in the two
43
attacks. The addition to the carbon with a greater HOMO coefficient is also the one with a worse orientation between the orbitals that should overlap, and therefore, the polarization of the HOMO must not be used to anticipate the regioselectivity in the cyclization of the hex-5-enyl or smaller radicals. When the radical centre is a silicon atom, important changes in the regioselectivity have been observed [28]. A study on the factors determining the regioselectivity in the pent-6enylsilyl and 1,l dimethylpent-4-enylsilyl radicals is under way and will be presented in the future. ACKNOWLEDGEMENT
We thank Prs. P. Bischof and S. Olivella for communication of structural parameters. Computer time was provided by the C.P.D. of the Ministerio de Educacibn y Ciencia, made available through the terminal of the Centre de CLlcul de la Universitat Politecnica de Catalunya. REFERENCES 1 A. L. J. Beckwith, Thetrahedron, 33 (1981) 3073. 2 J. M. Tedder and J. C. Walton, Act. Chem. Res., 9 (1976) 183; Adv. Phys. Org. Chem., 16 (1978) 86. 3 M. J. S. Dewar and S. Olivella, J. Am. Chem. Sot., 100 (1978) 5290. 4 A. L. J. Beckwith, C. J. Easton and A. K. Serelis, J. Chem. Sot., Chem. Commun., (1980) 482. 5 A. L. J. Beckwith and G. Moad, J. Chem. Sot., Chem. Commun., (1974) 472. 6 P. Bischof, Helv. Chim. Acta, 63 (1980) 1434; Thetrahedron Lett., 15 (1979) 1291. 7 A. L. J. Beckwith, I. Blair and G. Phillipou, Tetrahedron Lett., 26 (1974) 2251. 8 M. Julia, C. Decoins, M. Baillarge, B. Jacquet, D. Uguen and F. A. Groeger, Tetrahedron, 31(1975) 1737. 9 A. L. J. Beckwith and T. Lawrence, J. Chem. Sot., Perkin Trans. II, (1979) 1636. 10 E. Canadell and J. IguaI, J. Chem. Sot. Perkin Trans II: (1985) 1331. 11 J. M. Tedder, Angew. Chem. Int. Ed. Engl., 21(1982) 401. 12 J. M. Tedder and J. C. Walton, Tetrahedron, 36 (1980) 701. 13 M. J. S. Dewar and S. Olivella, J. Am. Chem. Sot., 101 (1979) 4958. 14 (a) R. C!. Bingham, M. J. S. Dewar and D. H. Lo, J. Am. Chem. Sot., 97 (1975) 1286; (b) 97 (1975) 1294; (c) 97 (1975) 1302; (d) 97 (1975) 1307. 15 E. CanadeII, J. M. Poblet and S. Olivella, J. Phys. Chem., 87 (1983) 424. 16 S. Olivella, E. Canadell and J. M. Poblet, J. Org. Chem., 48 (1983) 4696. 17 R. Fletcher and M. J. D. Powell, Comput. J., (1963) 163. 18 J. W. McIver and A. Komornicki, J. Am. Chem. Sot., 94 (1972) 2625. 19 J. A. Pople, D. P. Santry and G. A. SegaI, J. Chem. Phys., 43 (1965) 5129. 20 H. Fischer and H. KoIImar, Theor. Chim. Acta, 16 (1970) 163. 21 M. J. S. Dewar and D. H. Lo, J. Am. Chem. Sot., 93 (1971) 7201. 22 L. M. Molino and E. CanadeII, Theor. Chim. Acta, 60 (1981) 299. 23F. B. Wilson Jr., J. C. Decius and P. C. Cross, Molecular Vibrations, McGraw-Hill, New York, 1976. 24 J. M. Poblet, E. Canadell and T. Sordo, Can. J. Chem., 61 (1983) 9: see ref. 29. 25 L. Libit and R. Hoffmann, J. Am. Chem. Sot., 96 (1974) 1370. 26 J. A. Kerr and M. J. Parsonage, Evaluated Kinetic Data on Gas Phase Addition Reactions: Reactions of Atoms and Radicals with Alkenes, Alkynes, and Aromatic Compounds, Butterworths, London, 1972.
44 27 R. S. Cvetzanovic and R. S. Irwin, J. Chem. Phys., 46 (1967) 1694. 28 C. Chatgilialoglu, H. Woymar, K. U. Ingold and A. G. Davies, J. Chem. Sot., Perkin Trans. II, (1983) 555; T. Barton and A. Revis, J. Am. Chem. Sot., 106 (1984) 3802. 29 For a recent discussion on the HOMO-SOMO interation in radical reactions see: F. Delbecq, D. Iiavsky, Nguyen Tronq Anh and J. M. Lefour, J. Am. Chem. Sot., 107 (1985) 1623; E. Canadell, 0. Eisenstein, G. Ohanessian and J. M. Poblet, J. Phys. Chem., 89 (1985) 4858.
136 (1986) 35-U
Elsevier Science Publishers B.V., Amsterdam
-Printed
in the Netherlands
THEORETICAL STUDY OF THE ELECTRONIC AND STERIC EFFECTS IN THE INTER AND INTRAMOLECULAR RADICAL ADDITIONS
JOAN IGUAL, JOSEP Ma. POBLET and J. PEDRO SARASA
Departament de Quimica Fisica, Facultat de Quimica de Tarragona, Universitat de Barcelona, Imperial Tarraco s/n, 43006 - Tarragona (Spain) (Received
15 May 1985)
ABSTRACT The intramolecular addition of the W-alkenyl radicals and the chain length influence in the cyclization process have been studied using MINDO/3 theoretical method. The partitioning of the total energy in local contributions is used to analyse the electronic and steric factors in the addition process, The free methyl radical additions to ethylene and propene have also been analysed and compared with the intramolecular additions. The comparison between the inter- and intramolecular additions shows that the first ones depend on the electronic structure of the olefin, while in the second, electronic and steric factors compete in the cycloaddition. INTRODUCTION
The addition of radicals to olefinic bonds is produced by a rapid process with generally low activation energy [ 1, 21. Theoretical and experimental studies [2, 3 ] of the intermolecular addition reactions show that the addition of the radical occurs in the less substituted carbon to give the thermodynamically more stable product radical. However, in the intramolecular cyclization reaction the attack occurs on the most substituted carbon of the double bond, giving the thermodynamically less stable product radical (exe addition). I
,--A3
(CH21n+, I
(CH&
L
I
A-B’ I
tH2
One of the most studied radicals is the 5hexenyl radical [4]. The intramolecular addition in this radical gives preferably the exe form, that is the thermodynamically less stable one [5]. A theoretical work [6] showed that the entropic factors have an important contribution in the cyclization of this radical. The introduction of a methyl group in the most substituted 5-hexenyl 0166-1280/86/$03.50
o 1986 Elsevier Science Publishers B.V.
36
olefinic carbon produces a profound effect on the regioselectivity of the ring closure [7-g]. The effect of methyl substituent and the factors which compete in this reaction have been analysed in a previous work [lo]. On the other hand, the preference for the e3co cyclization changes with the radical chain length. The abundance of experimental work on these additions proves the interest of analysing all these factors and of their role in the reaction mechanisms [ 1, 2,4, 5,7-9,11,12]. The transition states for the w-hexenyl radicals have been calculated by Bischof [6] and Dewar and Olivella [ 131. However, the electronic changes in the transition structures are not the main interest of the authors. The purpose of the present work is firstly to complete the study on the influence of the chain length in the cycloaddition and secondly to compare the interand intramolecular additions, analysing the determinant factors of these additions, THEORETICAL
PROCEDURE
The UHF version of the MIND0/3 method [14] was used. The election was justified by the results obtained in the intra- [6,13] and intermolecular [15, 161 additions. The calculated values of S2 indicated that the spin contaminations were unimportant. The equilibrium geometries were calculated by minimizing the energy with respect to all geometric variables. The geometries were determined using the Davidon, Fletcher and Powell procedure [17]. The located transition state (TS) structures were refined by minimizing the scalar gradient and lastly confirmed by diagonalizing the force constant matrix and thus determining that it has one negative eigenvalue [ 18 J . To analyse the importance of the different effects mentioned above the TS were rationalized by means of the energy partitioning in mono (EJ and bicentric (EAB) local contributions [19-221. A previous work [lo] shows that this is a good analysis method of the TS structures. The activation entropies were calculated by means of the vibrational frequencies and inertia moments of the TS structures, according to classical methods [ 231. RESULTS
AND DISCUSSION
Influence of the chain length in the alkenyl radicals cyclization The study of the influence of the chain length in the hex-5-enyl, pent-6 enyl and but-3-enyl cyclization were carried out using the energy partitioning. The activation entropy in the three cases favours the exo cyclization, although in the pen-4-enyl radical the difference is very small. The activation enthalpy favours also the exo mode except in the hex-5-enyl cyclization where the same value of the activation enthalpy has been found (Table 1).
37 TABLE 1 Activation enthalpies and entropies of the exo and endo transition states for the but-3enyl, pent-4-enyl and hex-5-enyl radicals (A& given in kJ mol-’ and A@ in J mol-’ K-l) Radical
Endo TS
EXO TS
But-3-enyl Pent-4-enyl Hex-5-enyl -
AH+
As+
51.9 78.0 69.0
-33.9 -48.1 -55.2
AH’
123.0 92.9 69.0
AS+
-40.2 -51.0 -69.0
The trend of these results is in good agreement with the estimated experimental data [ 11. In the hexd-enyl the bond in formation in the exe TS (Fig. 1) (Cl-C5 = 2.200 A) is shorter than in the endo TS (C,-C, = 2.265 A). However, these additibns of the- aIky1 distance; are shorter than in the inte&oledular
(exe)
(endo)
Q
++I?%-k 4
3
3
2
5
2
4
5
(b)
(exe)
(endo)
(exe)
(endo)
Fig. 1. Optimized structures for the ewo and endo transition states for: (a) hex-5-enyl radical cyclization; (b) pent-4-enyl radical cycliiation; (c) but-3-enyl radical cyclization.
38
radicals to olefins (2.350 A) [ 31. The double bond distance C&-C6 varies slightly between the two TS structures in the hex-5-enyl. There is practically no difference in activation energy between the two transition states (Table 1) and the difference between the activation entropies favours the formation of the exo product [lo] . The energy partitioning analysis (Table 2) shows that the bond in the formation of the exo TS (C1-Cs) is more complete than in the endo TS The interaction between the SOMO of the radical and the HOMO of the olefin is the most important interaction to explain the regioselectivity in the intermolecular reactions [24]. When the attack is to the most substituted carbon, as its coefficient in the HOMO is lower [25] the HOMO-SOMO overlap is also lower and the stabilization energy for the same distance diminishes. In accord with this interpretation, the cyclization of the alkenyl radicals should happen in the less substituted carbon to give the endo product. However, both cyclizations are competitive. The reason for this is that, although the attack in the less substituted carbon is a priori more favourable, the better orientation of the p interacting orbit& in the most substituted carbon makes the two ways competitive at an electronic level. So, the size of the ring has the effect of forcing the orientation between the p orbitals of the interacting carbons in the two TS. The ES--6 term indicates that the double bond is less broken in the endo TS, and the EG5 presents a destabilization in the evolution to the exo TS. This is the result of a shift of the 0 electron density along the C&-C, bond in order to accumulate the fl charge density in C5 favouring the formation of the new bond. Table 3 shows the most important mono and bicentric contributions of the exo and endo TS of the but-3-enyl radical. The strain of this system TABLE 2 Most significative bicentric and monocentric contributions initial radical of the hex-5-enyl radical cyclization (kJ mol-‘) Initial radical
of the transition states and
Exo TS
Endo TS
-2413.5 -1533.0
-182.7 -2194.9 -1505.0
-138.5 -2232.9 -1532.3
Monocentric terms ES -9765.2 E, -9814.8 E, -10136.2
-9803.4 -9898.1 -10105.0
-9833.1 -9839.3 -10114.4
‘bndo
Bicentric terms E:_: EEs-6 E,,
*Difference between the E ,+
and E la
terms.
44.2a -37.9 -27.3 -29.7 58.8 -9.6
TS-exo
TS
39 TABLE 3 Most significative bicentric and monocentric contributions initial radical of the but-3-enyl radical cyclization (kJ mol-‘) Initial radical
Exo TS
El-3 E,-,
Endo TS
* Endo
states and
TS -Em
TS
-292.8
E
EL: Es-, E E(CHl)a - WH,), E: & E, aDifference
of the transition
between
-2413.1 -1630.4 -1532.2 -10135.6 -9669.5 -9768.8 -9814.4 the E,_,
-2161.7 -1519.8 -1399.1 46.3 -10046.2 -9690.8 -9773.9 -9926.7 and E,-,
-253.4 -2038.6 -1475.8 -1470.7 69.5 -10095.8 -9701.3 -9908.4 -9867.1
39.4a 113.1 44.0 -71.7 23.2 -60.6 -10.6 -134.8 69.6
terms.
makes the interaction distances (C1-CI = 1.918 A in exe TS and Cl-C4 = 2.064 A in the endo form) smaller than the hex-5-enyl ones and because of this the corresponding contributions E 1_-3 and E 1_-4 are more stabilizing. The comparison of the energetic contributions of the Table 3 and Table 2 shows that the electron distribution is the same as in the hex-5enyl ones. However, the endo cyclization is very unfavourable, the exo being slightly more favourable than in hex-5-enyl radical. This difference is mainly due to the more unfavourable double bond contribution in the endo TS (Table 3). This can be explained if the TS structures are considered. In the exe cyclization, rotation around the C1-C2 bond makes possible the interaction of the radical orbital with the R and a* orbitals of the olefinic fragment, and so the breaking and formation of the two bonds can occur simultaneously and without a high energy. However, in the endo TS a geometric change is needed in the HC&& dihedral angle and this produces a breaking in the double bond. This is the reason for the difference in E3--4 terms and of the high activation enthalpy in the endo cyclization. The more significative nonbonded interaction is the 2 and 4 methylene group interaction (CH,), (Table 3). This interaction is less repulsive in the exo TS because the CZ-C3--C4 angle is greater than in endo TS (132” exo and 110” endo). The analysis of the pent-4-enyl cyclization has been carried out in a similar way. The activation energy difference between the two TS is 15.9 kJ mol-’ favourable to the exo cyclization. This energy has increased with regard to both shortest and longest chain radical. This seems to indicate that there is no relation between the chain length and the activation energy in the cyclization. The most interesting term to analyse is the double bond term. Table 4 shows the values obtained for the three radicals studied. In the endo TS, the
40 TABLE 4 Contribution to the activation energy of the bicentric term associated to the olefinic bond (KJ mol-I) Radical
Exo TS
Endo TS
But-benyl Pent-4-enyl Hex-5-enyl
261.4 269.9 218.6
374.6 249.5 180.7
double bond destabilization due to the distortions for the orbital overlap between the carbons is very high in the but-&enyl and practically nonexistent in the hex-5-enyl radical. Moreover, because of the smaller strength of the system, the orientation of the orbit& becomes more favourable, and the two effects make the destabilization decrease when the carbon chain is longer. Comparing the endo and exo TS, it can be seen that in the hex-5-enyl radical, the double bond term favours the endo mode, while in the but-8enyl radical it favours the exo mode. In the pent-4-enyl radical the difference of this term in the exo and endo form is minor. This indicates that in the pent4-enyl radical, we are half way between the radicals in which the activation energy difference is controlled by the orbital overlap of the interacting carbon atoms (as in the hex-5-enyl radical), and the radicals in which the difference is controlled by the destabilization of the double bond (but-3-enyl radical). So the activation energy difference is given by the necessary electronic modifications for the rupture and formation of the bonds in the three radicals and also by the nonbonded interactions in the case of the but-3enyl and pent-4-enyl radicals. Comparison of the inter and intramolecular additions With the purpose of comparing Table 5 the activation enthalpies
the inter and intramolecular additions, and activation entropies in the attack
in of
TABLE 5 Enthalpies and entropies of activation for the addition of CH, to ethylene and propene (AH+ are given in kJ mol-’ and AS+ in J mol-* K-l) Reaction
AH+
kH, + CH,=CH,
AS+
AHfxP.
33.0
-111.7
30.1-33.08
CH, + eH,=
-CH,
30.9
-109.2
30.9b
CH, + CH, b
H=&-I,
48.9
-131.8
aRef. 26. bRef. 27.
41 TABLE 6 Bond lengths and energetic contributions to the activation energy associated with bond formation (C -a C) and to the oleffnic bond (C=C) in the additions of the CH, to the ethylene and propene (bond lengths are given 10-l nm and energies in KJ mol-I) Reaction
c***c d c -*c
CH, + CH,-CH=CH,
c=c AE c **cl
dcx
A%2
2.355
-84.1
1.327
2,397
-72.5
1.340
84.4
2.296
-120.8
1.348
148.5
88.6
the methyl radical to the ethylene and propene are collected. These values have been calculated by Dewar and Olivella [3]. In Table 6 the bond in formation and olefinic bond interaction distances are given. The CHB group in the olefin produces an increase in the interaction distance C - *C when the attack is in the less substituted carbon, and a decrease when the attack is in the more substituted carbon. This can be understood if we have account of the HOMO--SOMO interaction [24]. When the addition occurs in the substituted carbon, the reactants need to be closer so that HOMO-SOMO interaction becomes sufficient for bond formation. In this case, even little, a non stabilizing secondary interaction of the SOMO of the radical with the methyl substituent also exists. In this way, in the attack to propene 01 carbon, the new bond contribution is lower than in the ethylene addition and the associated contribution to the olefinic bond is very similar. However, in the addition to /I carbon, d,,, and AE,=, are greater. At the d, ..c is smaller, and AE,..,, beginning of the reaction, the destabilization of the olefin increases rapidly when the interaction distance decreases. The deformation energy is due to the breaking of the double bond, and an accumulation of p electron density in the attacked carbon is necessary. It has also been verified that the electrostatic interactions between the radical and the substituted group are repulsive and always favour the addition to the less substituted carbon. Schematically, we can see these results from the total energy decomposition along the reaction path in three components (Fig. 2) It can be seen that the deformation energy of the methyl radical is very similar in the two attacks, and lower than the olefin deformation energy. The orientation of the addition is determined mainly by a greater deformation energy of the olefin, and a lower intermolecular stabilization energy when the addition occurs in the substituted carbon. The introduction of the CHB group in the olefin has the same consequences in the intra [lo] and in the intermolecular additions. The rate constant of the addition to the more substituted carbon is minor due to a loss of overlap between the radical and the olefinic orbitals and also to the electrostatic interaction between the radical and the substituent. The
42
E
0
-0
-I
Fig. 2. Energy descomposition along the reaction coordinate in dH, + 8H,=eHCH, additions, in three components associated to radical (ER) and olefinic (Eo) fragments and to the interaction between the radical and the olefin (IT,).
polarization of the double bond also depends on the HOMO-SOMO interaction [ 241. This leads to a later TS in this case. Nevertheless, the rate constant of the addition to the unsubstituted carbon practically does not change with regard to the radical addition to ethylene. There is an important difference between the two additions: in intermolecular reactions, there is no orbital orientation effect and reaching the TS sooner or later along the reaction path depends only on the electronic structure. In the intramolecular reaction, the interaction distance is mainly controlled by the radical chain length, and in the TS this distance is shorter than in the intermolecular additions. On the other hand, the olefinic bond destabilization increases more rapidly with the shortening of the distance than the stabilization due to the new bond. Because of this, the activitation enthalpies for the intramolecular additions are greater than the intermolecular ones. The other consequence of the strength of the system in the intramolecular additions is that the orientation of the orbitals is not the same in the two
43
attacks. The addition to the carbon with a greater HOMO coefficient is also the one with a worse orientation between the orbitals that should overlap, and therefore, the polarization of the HOMO must not be used to anticipate the regioselectivity in the cyclization of the hex-5-enyl or smaller radicals. When the radical centre is a silicon atom, important changes in the regioselectivity have been observed [28]. A study on the factors determining the regioselectivity in the pent-6enylsilyl and 1,l dimethylpent-4-enylsilyl radicals is under way and will be presented in the future. ACKNOWLEDGEMENT
We thank Prs. P. Bischof and S. Olivella for communication of structural parameters. Computer time was provided by the C.P.D. of the Ministerio de Educacibn y Ciencia, made available through the terminal of the Centre de CLlcul de la Universitat Politecnica de Catalunya. REFERENCES 1 A. L. J. Beckwith, Thetrahedron, 33 (1981) 3073. 2 J. M. Tedder and J. C. Walton, Act. Chem. Res., 9 (1976) 183; Adv. Phys. Org. Chem., 16 (1978) 86. 3 M. J. S. Dewar and S. Olivella, J. Am. Chem. Sot., 100 (1978) 5290. 4 A. L. J. Beckwith, C. J. Easton and A. K. Serelis, J. Chem. Sot., Chem. Commun., (1980) 482. 5 A. L. J. Beckwith and G. Moad, J. Chem. Sot., Chem. Commun., (1974) 472. 6 P. Bischof, Helv. Chim. Acta, 63 (1980) 1434; Thetrahedron Lett., 15 (1979) 1291. 7 A. L. J. Beckwith, I. Blair and G. Phillipou, Tetrahedron Lett., 26 (1974) 2251. 8 M. Julia, C. Decoins, M. Baillarge, B. Jacquet, D. Uguen and F. A. Groeger, Tetrahedron, 31(1975) 1737. 9 A. L. J. Beckwith and T. Lawrence, J. Chem. Sot., Perkin Trans. II, (1979) 1636. 10 E. Canadell and J. IguaI, J. Chem. Sot. Perkin Trans II: (1985) 1331. 11 J. M. Tedder, Angew. Chem. Int. Ed. Engl., 21(1982) 401. 12 J. M. Tedder and J. C. Walton, Tetrahedron, 36 (1980) 701. 13 M. J. S. Dewar and S. Olivella, J. Am. Chem. Sot., 101 (1979) 4958. 14 (a) R. C!. Bingham, M. J. S. Dewar and D. H. Lo, J. Am. Chem. Sot., 97 (1975) 1286; (b) 97 (1975) 1294; (c) 97 (1975) 1302; (d) 97 (1975) 1307. 15 E. CanadeII, J. M. Poblet and S. Olivella, J. Phys. Chem., 87 (1983) 424. 16 S. Olivella, E. Canadell and J. M. Poblet, J. Org. Chem., 48 (1983) 4696. 17 R. Fletcher and M. J. D. Powell, Comput. J., (1963) 163. 18 J. W. McIver and A. Komornicki, J. Am. Chem. Sot., 94 (1972) 2625. 19 J. A. Pople, D. P. Santry and G. A. SegaI, J. Chem. Phys., 43 (1965) 5129. 20 H. Fischer and H. KoIImar, Theor. Chim. Acta, 16 (1970) 163. 21 M. J. S. Dewar and D. H. Lo, J. Am. Chem. Sot., 93 (1971) 7201. 22 L. M. Molino and E. CanadeII, Theor. Chim. Acta, 60 (1981) 299. 23F. B. Wilson Jr., J. C. Decius and P. C. Cross, Molecular Vibrations, McGraw-Hill, New York, 1976. 24 J. M. Poblet, E. Canadell and T. Sordo, Can. J. Chem., 61 (1983) 9: see ref. 29. 25 L. Libit and R. Hoffmann, J. Am. Chem. Sot., 96 (1974) 1370. 26 J. A. Kerr and M. J. Parsonage, Evaluated Kinetic Data on Gas Phase Addition Reactions: Reactions of Atoms and Radicals with Alkenes, Alkynes, and Aromatic Compounds, Butterworths, London, 1972.
44 27 R. S. Cvetzanovic and R. S. Irwin, J. Chem. Phys., 46 (1967) 1694. 28 C. Chatgilialoglu, H. Woymar, K. U. Ingold and A. G. Davies, J. Chem. Sot., Perkin Trans. II, (1983) 555; T. Barton and A. Revis, J. Am. Chem. Sot., 106 (1984) 3802. 29 For a recent discussion on the HOMO-SOMO interation in radical reactions see: F. Delbecq, D. Iiavsky, Nguyen Tronq Anh and J. M. Lefour, J. Am. Chem. Sot., 107 (1985) 1623; E. Canadell, 0. Eisenstein, G. Ohanessian and J. M. Poblet, J. Phys. Chem., 89 (1985) 4858.