13462
J. Phys. Chem. 1996, 100, 13462-13465
Theoretical Analysis of the Decomposition of Episulfones D. Sua´ rez, J. A. Sordo, and T. L. Sordo* Departamento de Quı´mica Fı´sica y Analı´tica, Facultad de Quı´mica, UniVersidad de OViedo, C/ Julia´ n ClaVerı´a, 8, 33006 OViedo, Principado de Asturias, Spain ReceiVed: February 7, 1996; In Final Form: May 15, 1996X
A theoretical ab initio study of the decomposition of ethene and 2-butene episulfones was carried out by means of SCF, MP2, and MP4 methods. Both decompositions occur stereoespecifically through a nonlinear mechanism which makes possible the electronic rearrangement necessary to produce an olefin and SO2. The decomposition of cis-2-butene episulfone is faster than that of trans-2-butene episulfone. The present theoretical results suggest that this “cis effect” is, at least partly, due to the predominance of attractive dispersion forces over repulsion between the two alkyl groups at the transition state.
Introduction The cheletropic reactions of sulfur dioxide with unsaturated hydrocarbons are very useful both for the preparation of sulfones and for the stereospecific and stereoselective synthesis and manipulation of alkenes and polyenes.1 These kinds of reactions are decisively influenced by orbital symmetry, and, therefore, they offer the opportunity of gaining some insight into orbital symmetry constraints. Loss of SO2 from an episulfone is a forbidden reaction in the suprafacial mode, although it occurs readily and streospecifically. Most episulfones decompose near room temperature to give alkenes and sulfur dioxide,2-6 and the reaction seems to be a nonlinear one, at least in nonpolar solvents.7 In the reaction of acyclic R-halo sulfones with base to give olefins through episulfones, the internal displacement of halide from the halo sulfone anion, which is the rate-controlling step, appears to favor formation of the cis episulfones which then give cis olefins. In the case of the iodo ethyl sulfone the trans/ cis ratio obtained at 75° corresponds to a ∆∆Gq of 0.87 kcal/ mol favoring the cis isomer. However, thermodynamic equilibrium favors the trans episulfone by 1.0 kcal/mol at 75°.4 Therefore, the magnitude of the “cis effect” becomes 1.87 kcal/ mol, basing the estimate on the episulfones. In order to explain this cis effect, it has been suggested4 that, at the critical transition state distance during episulfone formation, there is a net force of attraction predominating over repulsion between the two alkyl groups, leading to formation of the cis episulfone. In this paper we present a theoretical study of the decomposition of episulfones. In order to address the reactivity and stereoselectivity in these processes, the following decomposition reactions were theoretically studied by means of the ab initio method: SO2
+ SO2
(1)
SO2
+ SO2
(2)
SO2
+ SO2
(3)
Our goal in this study is two-fold. On the one hand, the configurational analysis originally proposed by Fujimoto8a will be used as a tool for analyzing and for interpreting theoretical X
Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(96)00382-6 CCC: $12.00
results, trying to get a deeper understanding of the mechanism of these chemical processes and the effect of orbital symmetry constraints upon them. On the other, we will raise the question of whether there is some cis effect along the decomposition of 2-butene episulfones, too, and we will analyze its origin. Methods Ab initio calculations were carried out with the Gaussian 92/ DFT package of programs9 in which extra links for the solvent effect treatment have been added.10 Stable structures were fully optimized and transition structures located both at the RHF and MP2(FC) levels of theory using the 6-31G* basis set11 by means of Schlegel’s algorithm.12 For reaction 1 MP4SDTQ(FC)//MP2(FC)/6-31G* single point calculations were performed too. Harmonic vibrational frequency calculations characterizing reactants, products, and transition structures and giving zeropoint vibrational energies (ZPVEs) were performed at the RHF/ 6-31G* level. ∆H°, ∆S°, and ∆G° values were calculated from RHF/6-31G* frequencies scaled by 0.89,13 MP2(FC)/6-31G* electronic energies, and free energies of solvation, in order to obtain results more readily comparable with experiment. The gas-phase magnitudes were computed within the ideal gas, rigid rotor, and harmonic oscillator approximations.14 A temperature of 348.15 K and a pressure of 1 atm were assumed in the calculations. For the study of the reaction path in solution we have used a general self-consistent-reaction field (SCRF) algorithm proposed for quantum chemical computations on solvated molecules.15 This SCRF continuum model assumes a general cavity shape and a monocentric multipolar expansion of the electrostatic solvation energy.15b Free energy in solution has been obtained by adding to the gas-phase value the electrostatic free energy of solvation calculated on gas-phase MP2(FC)/6-31G* geometries. Cavitation and dispersion have not been considered. A relative permitivity of 4.20 was used to simulate diethyl ether, which is frequently used as a solvent in this kind of reactions. The HF/6-31G* wave functions of the episulfones considered and the transition structures located at the MP2(FC)/6-31G* level in the present work were analyzed by means of a theoretical method originally proposed by Fujimoto and developed by Fukui’s group.8 This method is based on the expansion of the MOs of a complex system, AB, in terms of the MOs of its constituent fragments, A and B, using the geometry each fragment has in the corresponding transition structure and the performance of the configurational analysis. The configurational analysis is performed by writting the MO wave function of the © 1996 American Chemical Society
Decomposition of Episulfones
Figure 1. MP2/6-31G* structures corresponding to reactant and transition state for reaction 1. Experimental data are given in parentheses. Distances in angstroms and angles in degrees.
J. Phys. Chem., Vol. 100, No. 32, 1996 13463
Figure 2. MP2/6-31G* structures corresponding to reactant and transition state for reaction 2. Experimental data are given in parentheses. Distances in angstroms and angles in degrees.
complex system by a combination of various fragment electronic configurations:
Ψ ) C0Ψ0 + ∑CqΨq where Ψ0 (zero configuration, AB) is the state in which neither electron transfer nor electron excitation takes place and Ψq stands for monotransferred configurations Ψofu′, in which one electron in an occupied MO, o, in one of the fragments is transferred to an unoccupied MO, u′, of a different fragment (A+B-, A-B+ configurations); and monoexcited configurations, Ψofu, in which one electron in an occupied MO, o, of one of the fragments is excited to an unoccupied MO, u, of the same fragment (A*B, AB* configurations), etc. This analysis of the wave functions was performed using the ANACAL program.16 Results and Discussion Figures 1-3 display the MP2(FC)/6-31G* geometries of the reactants (episulfones) and the transition structures for reactions 1-3, respectively. Table 1 shows the energies of the reactants, transition structures, and products considered in this work, and Table 2, their relative energies and the ∆H, ∆S, and ∆G corresponding to reactions 1-3. We first discuss the results obtained for reaction 1 and then for reactions 2 and 3. We see in Figure 1 that the MP2(FC)/6-31G* geometry of the ethene episulfone (C2V) is in reasonable agreement with experimental data.17 Loss of SO2 from thiirane 1,1-dioxide, R1, goes through an asynchronous C1 transition structure, TS1, corresponding to a nonlinear cheletropic reaction.18 The energy barrier associated with this transition structure is 32.52 kcal/ mol according to MP2(FC)/6-31G* and 28.68 kcal/mol according to MP4SDTQ(FC)/6-31G*//MP2(FC)/6-31G* (see Tables 1 and 2). This energy barrier is similar to the activation energies experimentally found for the thermal dissociation of the methyldihydrothiophene 1-dioxides.19 No linear transition structure has been located in the present work. The decomposition is exoergic by -29.03 kcal/mol according to our MP2(FC)/6-31G* calculations and by -33.23 kcal/mol according to MP4SDTQ(FC)/6-31G*//MP2(FC)/6-31G* (see Tables 1 and
Figure 3. MP2/6-31G* structures corresponding to reactant and transition state for reaction 3. Distances in angstroms and angles in degrees.
2). Given the special interest of cheletropic reactions like (1) in which a three membered ring is produced or destroyed and the number of electrons of the π system is 2, we will perform a detailed analysis of this nonlinear cheletropic path. The configurational analysis of the wave function of the thiirane 1,1-dioxide (C2V) shows that the HOMO of this system is mainly a combination of the LUMOs of SO2 (b1) and ethene (b2) which are antisymmetric with respect to plane O-S-O and symmetric with respect to plane C-C-S. This fact indicates that the least motion loss of SO2 from ethene is a symmetry-forbidden process.7 In effect, along the least-motion path the two electrons in the HOMO of the episulfone would have to be delivered to the LUMOs of SO2 and C2H4, rendering excited products in contrast with experimental evidence. No linear transition structure connecting the episulfone with ethylene
13464 J. Phys. Chem., Vol. 100, No. 32, 1996
Sua´rez et al.
TABLE 1: Energies (au) of Reactants, Transition Structures, and Products Considered in This Work
a
structures
HF/6-31G*
ZPVE
MP2(FC)/6-31G*
MP4/6-31G* a
ethene episulfone cis-2-butene episulfone trans-2-butene episulfone TS1 TS2 TS3 SO2 ethene cis-2-butene trans-2-butene
-625.160 947 -703.238 221 -703.239 988 -625.096 092 -703.182 171 -703.184 019 -547.169 006 -78.031 718 -156.107 856 -156.110 408
0.069 037 0.129 381 0.129 225 0.065 853 0.125 848 0.125 855 0.008 020 0.054 766 0.115 887 0.115 686
-625.921 250 -704.265 526 -704.266 994 -625.869 430 -704.222 232 -704.223 038 -547.682 480 -78.285 028 -156.623 473 -156.625 924
-625.977 760 -625.932 050 -547.710 882 -78.319 830
MP4SDTQ(FC)/6-31G*//MP2(FC)/6-31G* single point calculations.
TABLE 2: Relative Energies and Gibbs Free Energies (kcal/mol), ∆G, and Its Components of Transition Structures and Products with Respect to the Corresponding Episulfones Considered in This Work
a
structures
HF/6-31G*
MP2(FC)/6-31G*
∆H
∆S (eu)
∆∆Gsol
∆G a
TS1 ethene + SO2 TS2 cis-2-butene + SO2 TS3 trans-2-butene + SO2
40.70 -24.96 35.17 -24.25 35.12 -24.74
32.52 -29.03 27.17 -25.37 27.58 -25.98
31.03 -31.12 25.51 -27.46 25.94 -28.12
3.77 41.93 3.87 45.47 2.41 44.40
0.30 2.34 0.08 2.15 0.10 2.01
30.01 -43.38 24.25 -41.14 25.20 -41.57
∆G ) ∆H - T∆S + ∆∆Gsol.
TABLE 3: Change in Electronic Population for HOMO and LUMO of C2H4 and SO2 in a C2W Structure Located at a C-S Distance of 2.4 Å along the Least-Motion Path for Reaction 1 HOMO LUMO total charge
C2H4
SO2
0.0 0.0 -0.01
-0.03 0.0 +0.01
TABLE 4: Coefficients of the Most Important Fragment Configurations (A ) SO2; B ) C2H4) in a C2W Structure Located at a C-S Distance of 2.4 Å along the Least-Motion Path for Reaction 1 (HO ) HOMO; NLU, NNLU, ... ) NEXT-LUMO, NEXT-NEXT-LUMO, ... (See Figure 4)) configuration
coefficient
weight
AB A*B (HO-NNLU) A-B+ (HO-NNLU) A+B+ (HO-NLU) AB* (NNHO-NLU)
1.0328 0.0699 -0.0692 0.0341 0.0062
1.0000 0.0046 0.0045 0.0011 0.0000
+ SO2 has been located. Structures at C-S distances expected for hypothetical linear transition structures present no binding interaction between C2H4 and SO2 fragments (see Tables 3 and 4 and Figure 4). Equivalently, as SO2 and C2H4 approach each other in a linear (C2V) way to form the episulfone, it is found that no important electronic interchange takes place (see Table 3) and the energy of the system increases monotonously owing to the four-electron repulsion interaction between the HOMOs of SO2 and C2H4. As a consequence, we see from Table 4 that, in a C2V structure corresponding to a C-S distance of 2.4 Å (the average of the two C-S distances in TS1) along the leastmotion (linear) path, no important progress has taken place toward the formation of the thiirane 1,1-dioxide, the wave function of the system being practically the zero configuration AB. This symmetry-forbidden linear path can be circumvented by a reduction in the symmetry of the system, which makes possible a favorable orbital interaction. This reduction of symmetry should occur at the transition state according to theoretical arguments.20 Our calculations show that this is the case, of course. Table 5 clearly shows the important electronic rearrangement taking place at TS1 and, consequently, we see from Table 6 that the wave function of TS1 is a combination
Figure 4. Frontier MOs of fragments CH2dCH2 and SO2 in the transition structure TS1 and in the C2V structure at a C-S distance of 2.4 Å.
TABLE 5: Change in Electronic Population for HOMO and LUMO of C2H4 and SO2 in the C1 Transition Structure TS1 for Reaction 1 HOMO LUMO total charge
C2H4
SO2
-0.63 +0.57 -0.10
-0.59 +0.83 +0.10
of the zero configuration, charge transfer configurations, excited configurations, and so on. A LUMO-LUMO orbital control takes place, leading to the interaction diagram described above for the thiirane 1,1-dioxide. This is the pseudoexcitation mechanism proposed by Fukui.21 In effect, as Table 6 displays, local excitations both at SO2 and C2H4 play an important role at TS1. Further, the analysis of atomic orbital overlap population between atomic orbitals on C1 or C2 and on S shows that
Decomposition of Episulfones
J. Phys. Chem., Vol. 100, No. 32, 1996 13465
TABLE 6: Coefficients of the Most Important Fragment Configurations (A ) SO2; B ) C2H4) at TS1 for Reaction 1 (HO ) HOMO; LU ) LUMO) configurations
coefficient
weight
AB A-B+ (HO-LU) A+B- (HO-LU) A*B (HO-LU) A*B* (HO-LU/HO-LU) AB* (HO-LU) A-*B+ (HO-LU/HO-LU) A2-B2+ (HO-LU/HO-LU) A+*B- (HO-LU/HO-LU)
0.2623 -0.2347 0.1962 0.1711 0.1535 -0.1219 -0.1104 0.1003 0.0895
1.0000 0.8004 0.5597 0.4253 0.3423 0.2162 0.1773 0.1463 0.1165
the LUMO-LUMO interaction is important in the formation of C1-S and C2-S bonds at TS1. Figures 2 and 3 display the geometry of reactants (cis- and trans-2-butene episulfones, R2 and R3), and transition structures, TS2 and TS3, corresponding to reactions 2 and 3, respectively. These processes proceed again through a nonlinear mechanism. The energy barriers corresponding to TS2 and TS3 are, respectively, 27.17 and 27.58 kcal/mol according to MP2(FC)/6-31G* calculations. ZPVE, thermal energy, and entropy as well as the electrostatic solvent effect further favor the cis decomposition so that, according to our calculations, although the trans episulfone is 0.89 kcal/mol more stable in free energy than the cis one, and trans-2-butene is 1.32 kcal/mol lower in free energy than cis-2-butene, TS2 is 0.06 kcal/mol more stable in free energy than TS3. Thus, decomposition of the cis sulfone is faster than that of the trans sulfone, and the magnitude of this cis effect is 0.95 kcal/mol, basing the estimate on the episulfones. Both reactions 2 and 3 are less exoergic than reaction 1 according to the MP2 calculations (see Table 2). It is interesting to note that HF/6-31G* electronic energies favor the trans process, whereas the MP2(FC)/6-31G* level favors the cis one (see Table 2). In fact, at the HF level the trans transition structure, TS3, is 1.16 kcal/mol more stable than the cis one, TS2, while TS3 is only 0.51 kcal/mol more stable than TS2 at the MP2(FC)/6-31G* level (see Table 1). These theoretical results support the interpretation of the nature of the cis effect as due to the predominance of the dispersion attractive forces between the two methyl groups at the transition state.4 Comparing the geometries of the episulfones intervening in reaction 1 and in reactions 2 and 3, we see that the ethene episulfone presents a tighter structure than the cis- and trans1,2-dimethylethene episulfones. It is remarkable the relative increase in the C-C distance of ethene in the cis episulfone. The C-C distance of ethene decreases continuously along the decomposition process; from 1.586 Å for the trans-2-butene episulfone, R3, through 1.450 Å at TS3, to 1.340 Å for the trans-2-butene molecule and from 1.595 Å for the cis episulfone, R2, through 1.453 Å at TS2, to 1.343 Å for the cis-2-butene molecule. The distance between the C atoms of the two methyl groups increases from 3.901 Å for the trans episulfone, R3, to 3.917 Å at TS3, whereas it decreases from 3.118 Å for the cis episulfone, R2, to 3.088 Å at TS2. This different evolution would make possible the predominance of attractive forces between the two methyl groups at TS2. The configurational analysis of the wave function of reactants and transition structures corresponding to reactions 2 and 3
render the same features as in reaction 1. When passing from reaction 1 to reactions 2 and 3, we find a transition structure which presents more important weights for the transference and excited configurations. This would imply a stronger interaction between the zero configuration and the A-B+, A+B-, etc., configurations at TS2 and TS3 than at TS1 and, accordingly, a lower energy barrier as displayed by Table 2. In summary, the decomposition of ethene and 2-butene episulfones occur stereoespecifically through a nonlinear mechanism which makes possible the electronic rearrangement necessary to reach the corresponding olefin and SO2. A hypothetical linear path is completely blocked by symmetry constraints. The decomposition of cis-2-butene episulfone takes place faster than that of trans-2-butene episulfone. Our theoretical results (energies and geometries) support the idea that this cis effect is, at least partly, due to the predominance of attractive dispersion forces over repulsion between the two alkyl groups at the transition state. References and Notes (1) Neureiter, N. P.; Bordwell, F. G. J. Am. Chem. Soc. 1963, 85, 1209. (2) Opitz, H.; Fischer, H. Angew. Chem., Int. Ed. Engl. 1965, 4, 70. (3) Carpino, L. A.; McAdams, L. V., III. J. Am. Chem. Soc. 1965, 87, 5804. (4) Neureiter, N. P. J. Am. Chem. Soc. 1966, 88, 558. (5) Tokura, N.; Nagai, T.; Matsumura, S. J. Org. Chem. 1966, 31, 349. (6) Bordwell, F. G., Williams, J. M., Jr.; Hoyt, E. B., Jr.; Jarvis, B. B. J. Am. Chem. Soc. 1968, 90, 429. (7) Pearson, P. G. Symmetry Rules for Chemical Reactions; Wiley; New York, 1976; pp 372-374. (8) (a) Hoffmann, R.; Fujimoto, H.; Swenson, J. R.; Wan, Ch. J. Am. Chem. Soc. 1973, 95, 7644. (b) Fujimoto, H.; Kato, S.; Yamabe, S.; Fukui, K. J. Chem. Phys. 1974, 60, 572. (9) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Hill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92; Gaussian, Inc.: Pittsburgh, PA, 1992. (10) Adapted by D. Rinaldi from: Rinaldi, D.; Pappalardo, R. R. Quantum Chemistry Program Exchange; Program No. 622; Indiana University: Bloomington, IN, 1992. (11) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (12) Schlegel, H. B. J. Comput. Chem. 1982, 3, 211. (13) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A.; Hout, R. F.; Hehre, W. J. Int. J. Quantum Chem., Quantum Chem. Symp. 1981, 15, 269. (14) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley-Interscience: New York, 1976. (15) (a) Rivail, J. L.; Rinaldi, D.; Ruiz-Lo´pez, M. F. In Theoretical and Computational Model for Organic Chemistry; Formosinho, S. J., Csizmadia, I. G., Arnaut, L., Eds.; NATO ASI Series C, Vol. 339; Kluwer: Dordrecht, The Netherlands, 1991; pp 79-92. (b) Dillet, V.; Rinaldi, D.; Angya´n, J. G.; Rivail, J. L. Chem. Phys. Lett. 1993, 202, 18. (16) Lo´pez, R.; Mene´ndez, M. I.; Sua´rez, D.; Sordo, T. L.; Sordo, J. A. Comput. Phys. Commun. 1993, 76, 235. (17) Nakano, Y.; Saito, S.; Morino, Y. Bull. Chem. Soc. Jpn. 1968, 43, 368. (18) Woodward, R. B.; Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1969, 8, 781. (19) Grummitt, O.; Ardis, A. E.; Fick, J. J. Am. Chem. Soc. 1950, 72, 5167. (20) (a) Pearson, R. G. Theoret. Chim. Acta 1970, 16, 107. (b) Pearson, R. G. Symmetry Rules for Chemical Reactions; Wiley: New York, 1976. (21) Fukui, K. Theory of Orientation and Stereoselection; Springer Verlag: Berlin, 1975.
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