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A MNDO and AM1 quantum chemical study of the reaction mechanism of the McLafferty type rearrangement in the butanal radical cation
Journal of Molecular Structure (Theo&m), 217 (1992) 117-127 Elsevier Science Publishers B.V., Amsterdam
117
A MNDO and AM1 quantum chemical study of the reaction mechanism of the McLafferty type rearrangement in the butanal radical cation Pedro P. Trigueros’, Jordi Casanovasa, Carlos Alem6nb and M. Cristina Vegab ‘~epurta~n~ de Quz’mica F&&a, Faeultat de Quimica, ~niversitut de BarceZona, Marti i Franques 1, Barcelona, E-~~~g (Spain) ~~epar~me~to de Ingenieria Q&mica, E.T.S.I.I.B., Uni~rsitat Politknica de C~~~a~ya, Diagonal 642, Barcelona, E-08028 (Spain) (Received 28 February 1992)
Abstract The stepwise and concerted reaction mechanisms of the McLafferty type rearrangement in the butanal radical cation have been studied by both MNDQ and AM1 (Dewar’s semiempirical methods). The calculations indicate a favored concerted reaction mechanism. Results obtained from the study of this reaction at semiempirical level were consistent with both ab initio and experimental data.
INTRODUCTION
The ~cLa~erty rearrangement [l,Z] is an important organic gas-phase reaction type extensively studied in mass spectrometry 131, in which a y-hydrogen is transfered to a double-bonded atom which leads to a p-bond cleavage in a six-membered compound (Fig. 1). Considering the importance of such a reaction, the great amount of experimental @--I23 and theoretical [X+-17] investigation focused on the elucidation of its microscopic mechanism is not surprising. Nevertheless, in spite of all these experimental and theoretical data, it has not yet been possible to establish which mechanism (concerted or stepwise) is involved in this reaction. The experimental results reported by different authors are in clear disagreement. Several experimental studies [S,ll] provide evidence that the
Correspondence to: C. Alemcin, Departamento de Ingenieria Q&mica, E.T.S.I.I.B., Universitat Politicnica de Catalunya, Diagonal 642, Barcelona, E-06026, Spain.
0166-12~~921$05.~
@ 1992 Elsevier Science Publishers
B.V. All rights reserved.
118
P.P. Trigueros el d/J.
H
l+.
A/”
A
I
II \
/“\/ R
Fig. 1. ~cLa~erty
+
Mol. Struct. ~T~eoc~em) 277 (1992) 11 F-127
l+. II
/B\,
R
type rearrangement.
McLafferty rearrangement proceeds by a concerted mechanism. Thus, in an early study Stone et al. [8] concluded, on the basis of deuterium and heavy-atom isotope effects, that in the process of elimination of acetaldehyde from benzyl ethyl ether radical cation, the concerted reaction mechanism possesses lower relative energy compared to that of the stepwise mechanism. In sharp contrast, other recent experimental investigations concluded that the McLaffe~y rearrangement occurs via a stepwise mechanism [lO,lZ]. Accordingly, from an experimental point of view, the evidence in favor of a stepwise or concerted mechanism is not conclusive. Only two theoretical studies were reported before 1985. In the first, Boer et al. [13], based on nonempirical MO calculations, postulated a stepwise mechanism. In the other, Dougherty [14], in an extended Hiickel study, found a concerted reaction mechanism for the McLafferty type rearrangement. In 1986 Ha et al. [E], based on UHF-SCF calculations at the MP2/631G* level on 3-21G optimized geometries, suggested a probable concerted transition state. In contrast, more recent ab initio calculations [16,17] suggest that the McLafferty rearrangement follows a stepwise reaction mechanism. The utility of the MNDO [18] and AM1 [19] semiempirical SCF MO treatments in the study of organic reaction mechanisms has been proved [20-261. In this paper we present MNDO and AM1 quantum mechanical studies of the stepwise and concerted mechanisms of the McLafferty rearrangement in the butanal radical cation. To our knowledge this is the first study of McLafferty type rearrangement performed by using Dewar’s MNDO and AM1 semiempirical methods. The results are compared to the experimental findings [4-121 and the ab initio [l&-17] data in the literature. Thus, we want (i) to study the suitability of these methods for describing this reaction type, and (ii) to gain some insight into the reaction mechanism of the rearrangement. COMPUTATIONAL
DETAILS
The butanal radical cation was chosen as a simple model compound to study the McLa~erty rearrangement. This molecule was selected because
PP.
Trigueros et d/J.
Mol. Struct. (Theo&em)
277 (1992) 11 F-127
119
some theoretical studies have been reported in the literature [l&-17]; consequently, the applicability of the MNDO [18] and AM1 [19] methods in this kind of rearrangement can be discussed. The calculations for open shell species were performed using an unrestricted HartreeFock (UHF) wavefunction. The geometries of stable species were computed by minimizing the energy with respect to all coordinates, using the Davidson-Fletcher-Powell (DFP) [27,28] optim~ation procedure. Transition states were located approximately by the reaction coordinate method and then refined by minimizing the scalar gradient of the energy [29]. Each transition state was characterized as such by calculating and diagonalizing the Hessian matrix, and ensuring that it had one and only one negative eigenvalue [29]. Entropies, enthalpies and free energies of reactants, products and transition states were calculated at 298 K according to the classical procedure. MNDO and AM1 calculations have been performed from the standard parameters ]18,19] by using a locally modifed 1301version of the MOPAC 1311 computer program. All calculations have been performed with the IBM3090 of the Centre d’Inform8tica de la Universitat de Barcelona. RESULTS AND DISCUSSION
The atomic rearrangements which correspond to the stepwise and concerted mechanisms of the butanal radical cation are illustrated in Fig. 2. The structures 1,2,4,5and 7 correspond to local minima; the structures 3, 6 and 8 are transition states. MNDO and AM1 are well-known methods, which provide molecular geometries very similar to those obtained from ab initio calculations 123, 321. Thus, only those geometrical parameters that are relevant to the reaction mechanism are displayed in Table 1, where the ab initio 3-21G values of Ha et al. [15] are also shown for comparison. These parameters are the distance between H, and 0 atoms (which indicates the tendency to transfer the y-hydrogen from the C4 to the 0 atom) and the distance between C2 and C3 atoms (which indicate the tendency to /?-bond cleavage in the six-membered compound). The experimental data of Djerassi and co-workers [33-351 suggest that the McLafferty rearrangement is not possible if the distance between the y-hydrogen atom and the 0 atom is greater than 1.8A. The smallest calculated distance between these two atoms is achieved using the AM1 semiempirical method. Thus, a distance of 1.82A in compound 2 (Table 1) indicates a considerable tendency to transfer the y-hydrogen atom to double-bonded oxygen atom. In contrast, the MNDO method shows a value for the hydrogen transfer which is too large (d(H,-0) = 2.36A). This discrepancy between AM1 and MNDO results is due to the planar geometry
P.P. Trigueros et al./J. Mol. Struct. (Theochem) 277 (1992) 117-127
120
(2) (3)
+
/& +0
p 3; II
H
$
.
+o/::
5
II
..d
..d\
(5)
H
-/(
*
(4) *
0
(6)
Fig. 2. Stepwise (a) and concerted (b) mechanisms for the McLafferty type rearrangement of the butanal radical cation.
obtained by AM1 in compound 2. In contrast, the MNDO method takes the cyclic conformation of structure 2 out of the plane. Thus, these MNDO results can be due to the erroneous geometries obtained when applying the MNDO method to hydrogen bonding systems. A well-known deficiency of the MNDO method is its considerable underestimation of the hydrogen bond interaction and its overestimation of the H. *.X distance (X being a
P.P. Trigueros et al.lJ. Mol. Strut.
(Theo&em)
121
277 (1992) 117-127
H
(7) (b) Fig. 2. (continued).
TABLE 1 MNDO and AM1 geometrical parameters (see text) Method
Compound
1
2
3
4
5
6
7
8
AM1 MNDO 3-21G”
_
1.82 2.36 2.06
1.55 1.22 1.40
1.00 0.96 0.99
0.99 0.96 0.99
1.00 0.96 0.98
0.99 0.96 0.98
0.99 0.96 0.98
cz-c3 AM1 MNDO 3-21G”
1.51 1.54 1.54
1.51 1.54 1.56
1.52 1.55 1.56
1.52 1.55 1.57
1.52 1.55 1.56
2.98 2.39 2.45
_
2.18 2.23 2.29
Wm-0)
“Ref. 15.
_
122
P.P. Trigueros et d/J.
MOE.Stract. ~T~~k~~
277 (1992) 117-127
hydrogen bond forming atom) in the hydrogen bond interaction [3639]. A comparison between our AM1 result and the 3-21G ab initio one proposed by Ha et al. [15] reveals a qualitative agreement, although, as can be seen, the AM1 distance is the closest to the value proposed by Djerassi and co-workers. There also exist MNDO and AM1 differences in CZ-C3 bond lengths in the 6 and 8 transition states (Table 1). Thus, the AM1 method provides a larger value for compound 6 than for 8. This indicates that the transition states 6 and 8 are clearly different and, consequently, stepwise and concerted mechanisms can be distinguished. In contrast, MNDO provides similar values for C2-C3 bond lengths in the 6 and 8 transition states. Indeed, there is no difference in the H, * * *0 interatomic distances of compounds 6 and 8. Thus, we did not find any significant geometric difference between the 6 and 8 transition states using the MNDO method. Another important fact is that it seems that the 3-21G ab initio C2-C3 bond lengths presented in Table 1 agree with the MNDO values. Figure 3 shows a schematic diagram for MNDO and AM1 relative energy profiles describing the stepwise (Fig. 3(a)) and concerted (Fig. 3(b)) reaction mechanisms of the McLafferty rearrangement of the butanal radical cation. Although the two semiempirical energy profiles present some differences, they coincide from a qualitative point of view. Both the MNDO and the AM1 methods display a clear preference for a concerted mechanism. Thus, the AM1 activation energy barrier of transition state 6 in the stepwise reaction mechanism is very high (66.3 kcal mall’) in comparison with the activation energy barrier of compound 8 (16.3 kcal mall’) in the concerted mechanism. This fact is due to the large value of the C243 bond length in transition state 6 (see Table 1). The MNDO method gives a smaller difference between the two possible reaction mechanisms (the activation energy barrier in the concerted mechanism is 14.9 kcalmoll’ lower than in the stepwise mechanism). According to both MNDO and AM1 energy profiles, the rate-determining step in the stepwise mechanism is the 5 3 7 rearrangement, owing to its high activation energy barrier. In relation to the ab initio energy profiles, the activation energy barriers reported in the literature [S--17] are quantitatively very different from the semiempirical barriers. However, ab initio MP2/6-31G* estimated profiles reported by Ha et al. [15] agree qualitatively with the MNDO and AM1 profiles. Although the MNDO and AM1 relative energy values of 2 and 3 agree qualitatively, AM1 energies are lower than MNDO ones. This is a consequence of the MNDO limitations [36-391 previously referred to. Thus, the MNDO method provides a poor treatment of the H; . +0 interaction, which leads to an overestimation of the heat of formation of some compounds. The preceding discussion has focused on electronic energy differences;
P.P. Triglseros et d/J.
Mol. Struct. ~T~~hern)
277 (1932) 117-127
123
however, at T > OK the entropy differences can play a role. Thus, the relative stabilities are best represented by relative Gibbs free enthalpies. In order to ascertain which mechanism is thermodynamically favored, entropy, enthalpy and Gibbs free enthalpy variations were computed at 298 K using MNDO and AM1 methods. According to the MNDO and AM1 values reported in Table 2, the entropic contribution is not fundamental for determining the reaction mechanism in the McLa~erty rearrangement of the butanal radical cation. MNDO and AM1 values of the relative entropy variations for 23 and 4 indicate a cyclic conformation. The increase in the number of final products in 7 gives a large positive entropy variation. MNDO and AM1 values for relative free enthalpy variations suggest that the concerted mechanism is slightly favored over the stepwise mechanism. Only a very slight difference appears in the MNDO (AG# = 15.2 kcal mall’) and AM1 (AG” = 15.3 kcal mol-‘) activation free enthalpies in the concerted mechanism, whereas notable differences are obtained in the stepwise mechanism. Thus, the MNDO method (AC+ = 30.3 kcal mol’) displays a lower activation free enthalpy than the AM1 value (AG# = 61.7 kcal moll’). CONCLUSIONS
The results presented here refer to the reaction mechanism of the McLafferty type rearrangement of the butanal radical cation. We tested the suitability of the MNDO and AM1 methods for describing this hydrogen transfer process. The condition of Djerassi et al. (33-351 for intramolecular hydrogen abstraction is observed in the AM1 method, whereas the MNDO semiempirical method shows a large distance between H, and 0 atoms. The MNDO and AM1 energy profiles lead to similar conclusions from a qualitative point of view, although their relative energy values display some differences. The reason for these discrepancies is probably the overestimation of the bielectronic repulsion in the MNDO hamiltonian, which leads to an underestimation of the hydrogen bond energy and to an overestimation of the steric hindrance. The relative energy profiles for both the stepwise and concerted mechanisms and the transition state geometries permit us to conclude that the concerted reaction mechanism is favored in this hydrogen transfer process type. The AM1 method provides important differences between the transition states of the stepwise and concerted mechanisms. Furthermore, we found an important difference (50.0 kcal mol’) between the activation energy barriers of the two possible reaction mechanisms. The MNDO method gives a lower activation energy barrier for the stepwise mechanism than AM1 does. Nevertheless, the concerted mechanism displays a lower (14.9 kcal malll) activation energy barrier than the stepwise mechanism.
124
I.--
18.4
(r
/ I , 7.8
$7.7
1 \
(7)
\
,’
\ \ f+
I t
1
\
1
2.0
\ t \ t
~
\ ’
-13.6 (4) ’ t -17.8 \
(5)
f I
Fig. 3. Schematic plot of the MNDO and AM1 calculated energies of stable species and transition states in stepwise {a) and concerted (b) reaction mechanisms of the McLafferty type rearrangement of the butanal radical cation.
P.P. Trigueros
et al./J.
Mol. Struct.
(Theochem)
277 (1992) 117-127
125
AM1
23.0
(b) Fig. 3. (continued).
The thermodynamic study of the reaction points out that the concerted mechanism is favored over the stepwise by both entropic and enthalpic terms. The results emphasize the enthalpy-guided nature of these reactions, demonstrated by the fact that it is possible to neglect the entropic effect TABLE 2 Thermodynamic MNDO and AM1 parameters with respect to 1 (taken as zero) for the McLafferty type rearrangement of the butanal radical cation Method
Compound 1
2
3
(Cal K-‘molC’) MNDO AM1
0.0 0.0
- 1.3 - 5.1
- 8.0 - 4.8
- 4.1 - 2.4
2.1 - 1.1
1.7 14.4
34.5 36.0
- 1.7 0.1
A(AH)(kcal molC’) MNDO AM1
0.0 0.0
7.8 2.8
18.4 3.5
- 17.6 - 13.6
- 21.3 - 15.6
8.8 50.7
23.0 19.1
2.0 17.7
A(AG)(kcalmol-‘) MNDO AM1
0.0 0.0
8.2 4.3
20.7 4.9
- 16.4 - 12.3
- 21.9 - 15.3
8.4 46.4
- 8.3 7.0
23.5 19.5
4
5
6
6
7
NW
126
P.P. Trigueros et al./J. Mot. Struct. (Theochem) 277 (1992) 117-127
without introducing major changes in the qualitative discussion of both mechanisms. These calculations are in agreement with recent experimental findings 18,111, in which the modeled concerted mechanism leads to predicted isotope effects in agreement with the experimental results. Our results are also in good agreement with those presented by Ha et al. [15]. These facts clearly demonstrate the efficacy of Dewar’s semiempirica~ methods (especially AMl) for studying this kind of rea~ang~ment. ACKNOWLEDGMENTS
The authors would like to thank Dr. S. Olivella and Dr. J.M. Bofill for making available their particular version of the MOPAC program. We are also indebted to Dr. F.J. Luque and Dr. M. Orozco for their stimulating, valuable and critical comments on this paper.
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
F.W. McLafferty, Anal. Chem., 28 (1956) 306. F.W. McLafferty, Anal. Chem., 31 (1959) 82. D.G.I. Kingston, J.T. Bursey and M.M. Bursey, Chem. Rev., 74 (1974) 215. C. Fenselan, J.L. Young, S. Meyerson, W.R. Landis, E. Selke and C. Lertch, J. Am. Chem. Sot., 91 (1969) 6847. P. Brown, A.H. Albert and G.R. Petit& J. Am. Chem. Sot., 92 (1970) 3212. G.S. Smith and F.W. McLafferty, Org. Mass Spectrom., 5 (1971) 483. P.J. Derrick, A.M. Falick and A.L. Burlingame, J. Am. Chem. Sot., 96 (1974) 615. D.J.M. Stone, J.H. Bowie, D.J. Underwood, K-F. Donchi, C.E. Allison and P.J. Derrick, J. Am. Chem. Sot., 105 (1983) 1688. II. Muto, K. Toriyama, K. Nunome and M. Iwasaki, Chem. Phys. Lett., 105 (1984) 592. C. Wesdemiotis, R. Feng and F.W. MeLafferty, J. Am. Chem. Sot., 107 (1985) 715. C.E. Allison, M.B. Stringer, J.H. Bowie and P.J. Derrick, J. Am. Chem. Sot., 110 (1988) 6291. T.H. Osterheld and J.I. Brauman, J.Am. Chem. Sot., 112 (1990) 2014. F.B. Boer, T.W. Shannon and F.W. McLafferty, J. Am. Chem. Sot., 90 (1968) 7239. R.C. Dougherty, J. Am. Chem. Sot., 96 (1968) 5780. T-K. Ha, C. Radloff and M.T. Nguyen, J. Phys. Chem., 96 (1986) 2991. C.E. Hudson, L.L. Griffin and D.J. McAdoo, Org. Mass Spectrom., 24 (1989) 866. A.E. Dorigo, M.A. McCarrick, R.J. Loncharich and K.N. Houk, J. Am. Chem. Sot., 112 (1990) 7508. M.J.S. Dewar and W. Thiel, J. Am. Chem. Sot., QQ(1977) 4899. M.J.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P. Stewart, J. Am. Chem. Sot., 107 (1985) 3902. M.J.S. Dewar and C. Doubleday, J. Am. Chem. Sot., 100 (1978) 4935. M.J.S. Dewar, D.J. Nelson, P.B. Shevlin and K.A. Biesiada, J. Am. Chem. Sot., 103 (1981) 2802. S. Schtider and W. Thiel, J. Am. Chem. Sot., 107 (1985) 4422. J.M. Bofill, J. Castells, S. Olivella and A. Sole, J. Org. Chem., 53 (1988) 5148. M. Grozco, E.I. Canela and R. France, Mol. Pharmacol., 35 (1989) 257.
P.P. Trigueros et al@. 25 26 27 28 29 30 31 32 33 34 35 36 31 36 39
MoE. Struct. ~The~che~) 277 fl992) fl F-127
M. Orozco, E.I. Canela, J. Mallol, C. Lluis and R. France, J. Org. Chem., 55 (1990) 753. M. Orozco, E.I. Canela and R. France, J. Org. Chem., 55 (1996) 2630. R. Fletcher and M.J.D. Powell, Comput. J., 6 (1963) 163. W.C. Davidson, Comput. J., 6 (1968) 466. J.W. McIver and A. Komornicki, J. Am. Chem. Sot., 94 (1972), 2625; 95 (1973) 4512. S. Olivella, Q.C.P.E. Bull., 4 (19&Q)10. J.J.P. Stewart, Q.C.P.E. Bull., 3 (1983) 43. S. Topiol, J. Comput. Chem., 8 (1987) 142. D.H. WiIliams, J.M. Wilson, H. Budzikiewicz and C. Djerassi, J. Am. Chem. Sot., 85 (1963) 2091. D.H. Williams and C. Djerassi, Steroids, 3 (1964) 259. C. Djerassi, G.v. Mutzenbacher, J. Fajkos, D.H. Williams and H. Budzikiewicz, J. Am. Chem. Sot., 87 (1985) 817. G.E. Schultz and R.M. Schirme, Principles of Protein Structure, Springer-Verlag, New York, 1979 pp. 34, 35. A.A. Voitynk and A.A. Blizuyuk, Theor. Chim. Acta, 72 (1987) 223. A.R. Fersht, J.-P. Shi, J. Knill-Jones, D.M. Lowe, A.J. Wilkinson, D.M. Blow, P. Brick, P. Carter, M.M.Y. Wayne and G. Winter, Nature, 314 (1985) 235. M. Moot-Ner, J. Am. Chem. Sot., 106 (1984) 1257.
117
A MNDO and AM1 quantum chemical study of the reaction mechanism of the McLafferty type rearrangement in the butanal radical cation Pedro P. Trigueros’, Jordi Casanovasa, Carlos Alem6nb and M. Cristina Vegab ‘~epurta~n~ de Quz’mica F&&a, Faeultat de Quimica, ~niversitut de BarceZona, Marti i Franques 1, Barcelona, E-~~~g (Spain) ~~epar~me~to de Ingenieria Q&mica, E.T.S.I.I.B., Uni~rsitat Politknica de C~~~a~ya, Diagonal 642, Barcelona, E-08028 (Spain) (Received 28 February 1992)
Abstract The stepwise and concerted reaction mechanisms of the McLafferty type rearrangement in the butanal radical cation have been studied by both MNDQ and AM1 (Dewar’s semiempirical methods). The calculations indicate a favored concerted reaction mechanism. Results obtained from the study of this reaction at semiempirical level were consistent with both ab initio and experimental data.
INTRODUCTION
The ~cLa~erty rearrangement [l,Z] is an important organic gas-phase reaction type extensively studied in mass spectrometry 131, in which a y-hydrogen is transfered to a double-bonded atom which leads to a p-bond cleavage in a six-membered compound (Fig. 1). Considering the importance of such a reaction, the great amount of experimental @--I23 and theoretical [X+-17] investigation focused on the elucidation of its microscopic mechanism is not surprising. Nevertheless, in spite of all these experimental and theoretical data, it has not yet been possible to establish which mechanism (concerted or stepwise) is involved in this reaction. The experimental results reported by different authors are in clear disagreement. Several experimental studies [S,ll] provide evidence that the
Correspondence to: C. Alemcin, Departamento de Ingenieria Q&mica, E.T.S.I.I.B., Universitat Politicnica de Catalunya, Diagonal 642, Barcelona, E-06026, Spain.
0166-12~~921$05.~
@ 1992 Elsevier Science Publishers
B.V. All rights reserved.
118
P.P. Trigueros el d/J.
H
l+.
A/”
A
I
II \
/“\/ R
Fig. 1. ~cLa~erty
+
Mol. Struct. ~T~eoc~em) 277 (1992) 11 F-127
l+. II
/B\,
R
type rearrangement.
McLafferty rearrangement proceeds by a concerted mechanism. Thus, in an early study Stone et al. [8] concluded, on the basis of deuterium and heavy-atom isotope effects, that in the process of elimination of acetaldehyde from benzyl ethyl ether radical cation, the concerted reaction mechanism possesses lower relative energy compared to that of the stepwise mechanism. In sharp contrast, other recent experimental investigations concluded that the McLaffe~y rearrangement occurs via a stepwise mechanism [lO,lZ]. Accordingly, from an experimental point of view, the evidence in favor of a stepwise or concerted mechanism is not conclusive. Only two theoretical studies were reported before 1985. In the first, Boer et al. [13], based on nonempirical MO calculations, postulated a stepwise mechanism. In the other, Dougherty [14], in an extended Hiickel study, found a concerted reaction mechanism for the McLafferty type rearrangement. In 1986 Ha et al. [E], based on UHF-SCF calculations at the MP2/631G* level on 3-21G optimized geometries, suggested a probable concerted transition state. In contrast, more recent ab initio calculations [16,17] suggest that the McLafferty rearrangement follows a stepwise reaction mechanism. The utility of the MNDO [18] and AM1 [19] semiempirical SCF MO treatments in the study of organic reaction mechanisms has been proved [20-261. In this paper we present MNDO and AM1 quantum mechanical studies of the stepwise and concerted mechanisms of the McLafferty rearrangement in the butanal radical cation. To our knowledge this is the first study of McLafferty type rearrangement performed by using Dewar’s MNDO and AM1 semiempirical methods. The results are compared to the experimental findings [4-121 and the ab initio [l&-17] data in the literature. Thus, we want (i) to study the suitability of these methods for describing this reaction type, and (ii) to gain some insight into the reaction mechanism of the rearrangement. COMPUTATIONAL
DETAILS
The butanal radical cation was chosen as a simple model compound to study the McLa~erty rearrangement. This molecule was selected because
PP.
Trigueros et d/J.
Mol. Struct. (Theo&em)
277 (1992) 11 F-127
119
some theoretical studies have been reported in the literature [l&-17]; consequently, the applicability of the MNDO [18] and AM1 [19] methods in this kind of rearrangement can be discussed. The calculations for open shell species were performed using an unrestricted HartreeFock (UHF) wavefunction. The geometries of stable species were computed by minimizing the energy with respect to all coordinates, using the Davidson-Fletcher-Powell (DFP) [27,28] optim~ation procedure. Transition states were located approximately by the reaction coordinate method and then refined by minimizing the scalar gradient of the energy [29]. Each transition state was characterized as such by calculating and diagonalizing the Hessian matrix, and ensuring that it had one and only one negative eigenvalue [29]. Entropies, enthalpies and free energies of reactants, products and transition states were calculated at 298 K according to the classical procedure. MNDO and AM1 calculations have been performed from the standard parameters ]18,19] by using a locally modifed 1301version of the MOPAC 1311 computer program. All calculations have been performed with the IBM3090 of the Centre d’Inform8tica de la Universitat de Barcelona. RESULTS AND DISCUSSION
The atomic rearrangements which correspond to the stepwise and concerted mechanisms of the butanal radical cation are illustrated in Fig. 2. The structures 1,2,4,5and 7 correspond to local minima; the structures 3, 6 and 8 are transition states. MNDO and AM1 are well-known methods, which provide molecular geometries very similar to those obtained from ab initio calculations 123, 321. Thus, only those geometrical parameters that are relevant to the reaction mechanism are displayed in Table 1, where the ab initio 3-21G values of Ha et al. [15] are also shown for comparison. These parameters are the distance between H, and 0 atoms (which indicates the tendency to transfer the y-hydrogen from the C4 to the 0 atom) and the distance between C2 and C3 atoms (which indicate the tendency to /?-bond cleavage in the six-membered compound). The experimental data of Djerassi and co-workers [33-351 suggest that the McLafferty rearrangement is not possible if the distance between the y-hydrogen atom and the 0 atom is greater than 1.8A. The smallest calculated distance between these two atoms is achieved using the AM1 semiempirical method. Thus, a distance of 1.82A in compound 2 (Table 1) indicates a considerable tendency to transfer the y-hydrogen atom to double-bonded oxygen atom. In contrast, the MNDO method shows a value for the hydrogen transfer which is too large (d(H,-0) = 2.36A). This discrepancy between AM1 and MNDO results is due to the planar geometry
P.P. Trigueros et al./J. Mol. Struct. (Theochem) 277 (1992) 117-127
120
(2) (3)
+
/& +0
p 3; II
H
$
.
+o/::
5
II
..d
..d\
(5)
H
-/(
*
(4) *
0
(6)
Fig. 2. Stepwise (a) and concerted (b) mechanisms for the McLafferty type rearrangement of the butanal radical cation.
obtained by AM1 in compound 2. In contrast, the MNDO method takes the cyclic conformation of structure 2 out of the plane. Thus, these MNDO results can be due to the erroneous geometries obtained when applying the MNDO method to hydrogen bonding systems. A well-known deficiency of the MNDO method is its considerable underestimation of the hydrogen bond interaction and its overestimation of the H. *.X distance (X being a
P.P. Trigueros et al.lJ. Mol. Strut.
(Theo&em)
121
277 (1992) 117-127
H
(7) (b) Fig. 2. (continued).
TABLE 1 MNDO and AM1 geometrical parameters (see text) Method
Compound
1
2
3
4
5
6
7
8
AM1 MNDO 3-21G”
_
1.82 2.36 2.06
1.55 1.22 1.40
1.00 0.96 0.99
0.99 0.96 0.99
1.00 0.96 0.98
0.99 0.96 0.98
0.99 0.96 0.98
cz-c3 AM1 MNDO 3-21G”
1.51 1.54 1.54
1.51 1.54 1.56
1.52 1.55 1.56
1.52 1.55 1.57
1.52 1.55 1.56
2.98 2.39 2.45
_
2.18 2.23 2.29
Wm-0)
“Ref. 15.
_
122
P.P. Trigueros et d/J.
MOE.Stract. ~T~~k~~
277 (1992) 117-127
hydrogen bond forming atom) in the hydrogen bond interaction [3639]. A comparison between our AM1 result and the 3-21G ab initio one proposed by Ha et al. [15] reveals a qualitative agreement, although, as can be seen, the AM1 distance is the closest to the value proposed by Djerassi and co-workers. There also exist MNDO and AM1 differences in CZ-C3 bond lengths in the 6 and 8 transition states (Table 1). Thus, the AM1 method provides a larger value for compound 6 than for 8. This indicates that the transition states 6 and 8 are clearly different and, consequently, stepwise and concerted mechanisms can be distinguished. In contrast, MNDO provides similar values for C2-C3 bond lengths in the 6 and 8 transition states. Indeed, there is no difference in the H, * * *0 interatomic distances of compounds 6 and 8. Thus, we did not find any significant geometric difference between the 6 and 8 transition states using the MNDO method. Another important fact is that it seems that the 3-21G ab initio C2-C3 bond lengths presented in Table 1 agree with the MNDO values. Figure 3 shows a schematic diagram for MNDO and AM1 relative energy profiles describing the stepwise (Fig. 3(a)) and concerted (Fig. 3(b)) reaction mechanisms of the McLafferty rearrangement of the butanal radical cation. Although the two semiempirical energy profiles present some differences, they coincide from a qualitative point of view. Both the MNDO and the AM1 methods display a clear preference for a concerted mechanism. Thus, the AM1 activation energy barrier of transition state 6 in the stepwise reaction mechanism is very high (66.3 kcal mall’) in comparison with the activation energy barrier of compound 8 (16.3 kcal mall’) in the concerted mechanism. This fact is due to the large value of the C243 bond length in transition state 6 (see Table 1). The MNDO method gives a smaller difference between the two possible reaction mechanisms (the activation energy barrier in the concerted mechanism is 14.9 kcalmoll’ lower than in the stepwise mechanism). According to both MNDO and AM1 energy profiles, the rate-determining step in the stepwise mechanism is the 5 3 7 rearrangement, owing to its high activation energy barrier. In relation to the ab initio energy profiles, the activation energy barriers reported in the literature [S--17] are quantitatively very different from the semiempirical barriers. However, ab initio MP2/6-31G* estimated profiles reported by Ha et al. [15] agree qualitatively with the MNDO and AM1 profiles. Although the MNDO and AM1 relative energy values of 2 and 3 agree qualitatively, AM1 energies are lower than MNDO ones. This is a consequence of the MNDO limitations [36-391 previously referred to. Thus, the MNDO method provides a poor treatment of the H; . +0 interaction, which leads to an overestimation of the heat of formation of some compounds. The preceding discussion has focused on electronic energy differences;
P.P. Triglseros et d/J.
Mol. Struct. ~T~~hern)
277 (1932) 117-127
123
however, at T > OK the entropy differences can play a role. Thus, the relative stabilities are best represented by relative Gibbs free enthalpies. In order to ascertain which mechanism is thermodynamically favored, entropy, enthalpy and Gibbs free enthalpy variations were computed at 298 K using MNDO and AM1 methods. According to the MNDO and AM1 values reported in Table 2, the entropic contribution is not fundamental for determining the reaction mechanism in the McLa~erty rearrangement of the butanal radical cation. MNDO and AM1 values of the relative entropy variations for 23 and 4 indicate a cyclic conformation. The increase in the number of final products in 7 gives a large positive entropy variation. MNDO and AM1 values for relative free enthalpy variations suggest that the concerted mechanism is slightly favored over the stepwise mechanism. Only a very slight difference appears in the MNDO (AG# = 15.2 kcal mall’) and AM1 (AG” = 15.3 kcal mol-‘) activation free enthalpies in the concerted mechanism, whereas notable differences are obtained in the stepwise mechanism. Thus, the MNDO method (AC+ = 30.3 kcal mol’) displays a lower activation free enthalpy than the AM1 value (AG# = 61.7 kcal moll’). CONCLUSIONS
The results presented here refer to the reaction mechanism of the McLafferty type rearrangement of the butanal radical cation. We tested the suitability of the MNDO and AM1 methods for describing this hydrogen transfer process. The condition of Djerassi et al. (33-351 for intramolecular hydrogen abstraction is observed in the AM1 method, whereas the MNDO semiempirical method shows a large distance between H, and 0 atoms. The MNDO and AM1 energy profiles lead to similar conclusions from a qualitative point of view, although their relative energy values display some differences. The reason for these discrepancies is probably the overestimation of the bielectronic repulsion in the MNDO hamiltonian, which leads to an underestimation of the hydrogen bond energy and to an overestimation of the steric hindrance. The relative energy profiles for both the stepwise and concerted mechanisms and the transition state geometries permit us to conclude that the concerted reaction mechanism is favored in this hydrogen transfer process type. The AM1 method provides important differences between the transition states of the stepwise and concerted mechanisms. Furthermore, we found an important difference (50.0 kcal mol’) between the activation energy barriers of the two possible reaction mechanisms. The MNDO method gives a lower activation energy barrier for the stepwise mechanism than AM1 does. Nevertheless, the concerted mechanism displays a lower (14.9 kcal malll) activation energy barrier than the stepwise mechanism.
124
I.--
18.4
(r
/ I , 7.8
$7.7
1 \
(7)
\
,’
\ \ f+
I t
1
\
1
2.0
\ t \ t
~
\ ’
-13.6 (4) ’ t -17.8 \
(5)
f I
Fig. 3. Schematic plot of the MNDO and AM1 calculated energies of stable species and transition states in stepwise {a) and concerted (b) reaction mechanisms of the McLafferty type rearrangement of the butanal radical cation.
P.P. Trigueros
et al./J.
Mol. Struct.
(Theochem)
277 (1992) 117-127
125
AM1
23.0
(b) Fig. 3. (continued).
The thermodynamic study of the reaction points out that the concerted mechanism is favored over the stepwise by both entropic and enthalpic terms. The results emphasize the enthalpy-guided nature of these reactions, demonstrated by the fact that it is possible to neglect the entropic effect TABLE 2 Thermodynamic MNDO and AM1 parameters with respect to 1 (taken as zero) for the McLafferty type rearrangement of the butanal radical cation Method
Compound 1
2
3
(Cal K-‘molC’) MNDO AM1
0.0 0.0
- 1.3 - 5.1
- 8.0 - 4.8
- 4.1 - 2.4
2.1 - 1.1
1.7 14.4
34.5 36.0
- 1.7 0.1
A(AH)(kcal molC’) MNDO AM1
0.0 0.0
7.8 2.8
18.4 3.5
- 17.6 - 13.6
- 21.3 - 15.6
8.8 50.7
23.0 19.1
2.0 17.7
A(AG)(kcalmol-‘) MNDO AM1
0.0 0.0
8.2 4.3
20.7 4.9
- 16.4 - 12.3
- 21.9 - 15.3
8.4 46.4
- 8.3 7.0
23.5 19.5
4
5
6
6
7
NW
126
P.P. Trigueros et al./J. Mot. Struct. (Theochem) 277 (1992) 117-127
without introducing major changes in the qualitative discussion of both mechanisms. These calculations are in agreement with recent experimental findings 18,111, in which the modeled concerted mechanism leads to predicted isotope effects in agreement with the experimental results. Our results are also in good agreement with those presented by Ha et al. [15]. These facts clearly demonstrate the efficacy of Dewar’s semiempirica~ methods (especially AMl) for studying this kind of rea~ang~ment. ACKNOWLEDGMENTS
The authors would like to thank Dr. S. Olivella and Dr. J.M. Bofill for making available their particular version of the MOPAC program. We are also indebted to Dr. F.J. Luque and Dr. M. Orozco for their stimulating, valuable and critical comments on this paper.
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
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