J. Phys. Chem. 1996, 100, 4339-4349
4339
ARTICLES Role of Spin-Orbit Coupling and Symmetry in Triplet Carbenic Addition Chemistry Ming-Der Su DRAL Daresbury Laboratory, Warrington WA4 4AD, U.K. ReceiVed: January 30, 1995; In Final Form: December 14, 1995X
The spin-orbit coupling parts in the effective one-electron Hamiltonian operator, with the inclusion of symmetry, have been used to formulate mechanisms based on the Shaik and Epiotis theory in triplet reactions for the radiationless decay of triplet complexes to singlet ground state products. This has been applied to investigate the stereochemical behavior of additions of triplet carbenes to olefins. It is shown that triplet carbene-olefin complexes can be classified according to the number and the direction of the atomic orbital rotations required to maximize spin-orbit coupling and simultaneously maintain the intermolecular binding, from which it may produce different stereoisomers. It is suggested that six spin-inversion reaction mechanisms produce geometric isomers. It is found that, as a direct of the different symmetries of the three sublevels of the triplet state (Tx, Ty, Tz) and their comparable spin-orbit coupling expressions, the triplet carbene could add to olefins nonstereospecifically. Nevertheless, it is also suggested that, because of its larger spin-orbit coupling expression as well as the less conformational change, the cycloaddition of a triplet carbene to a double bond will lead to the stereospecific cyclopropane with retention of geometry in a concerted pathway. The solvent polarity, substituent effect, and heavy atom effect must all play an important role in determining the stereoconformations of adducts. The results obtained are in agreement with the available experimental results and allow a number of predictions to be made. It is found that the approach proposed in this study is proved to be a good alternative to the traditionally accepted explanation, the Skell-Woodworth mechanism.
I. Introduction The addition of carbenes to olefins yielding cyclopropanes is both preparatively and mechanistically useful. Hence, for many years the cycloaddition of a carbene to an olefin has drawn much attention from experimentalists and theoreticians.1 It is well known that the two electrons on carbene may, of course, be spin-paired (singlet species) or have parallel spins (triplet species). The former usually arises from direct irradiation of diazo compounds, and the latter is formed either on intersystem crossing of the singlet carbene or by triplet sensitization of the chromophere.2 The reactions of singlet and triplet carbenes are typically zwitterionic and diradicaloid in nature, respectively. Thus, as mentioned in many modern textbooks,3 it was found that the addition of the former species to an olefin is stereospecific whereas the reaction of the latter yields geometric isomers (nonstereospecific). An earlier, widely accepted explanation for the stereospecificity of the addition of the different types of carbene was based on the principle of the conversion of spin. It was assumed that addition of a singlet carbene to an olefin should produce the three-membered ring adduct in one single step (i.e., in a concerted manner), thus stereospecifically. A triplet carbene, however, would add to an alkene in a stepwise fashion, initially producing a triplet 1,3-diradical (open-chain) intermediate. Here, if the rates of bond rotations are comparable to or faster than the rate of spin inversion/ring closure, the original relative geometry of the alkenic substituents will be at least partially lost upon formation of the product cyclopropane. This theory, known as the Skell-Woodworth hypothesis,4 has been persistent and used widely as a diagnostic tool5 for the identification of X
Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4339$12.00/0
spin states of carbenes using the stereochemical outcome of the additions carbene to olefins.1,6,7 Although there is a substantially larger number of examples in which careful work gives results in accord with the SkellWoodworth hypothesis, there are several examples of failure in the stereochemistry of carbene addition.8-17 For instance it was found some 15 years ago that photolysis of 9-diazoxanthene in cis-(or trans-)propenylbenzene leads to stereospecific cyclopropanation, in which triplet 9-xanthylidene was suggested to be the key intermediate in the experiments.8 Murahashi, Moritani, and Nishino reported that the triplet dibenzo[a,d]cycloheptenylidene and tribenzo[a,c,e]cycloheptenylidene are able to add to olefins stereospecifically.9 Some interesting examples can be found in refs 10-17. It is those unsuccessful applications of the Skell-Woodworth hypothesis that arouse our interest. Gaspar and Hammond have pointed out that this hypothesis does not drive from “the first principle”, albeit its utility is unquestioned and widespread.7 In fact, the SkellWoodworth hypothesis should be regarded as reasonable intuition rather than sound theory since there is no firm basis for the presumption that rotation about single bonds will necessarily be much more rapid than spin inversion.18 Furthermore, the most questionable part of Skell-Woodworth’s mechanism is that identical mixtures of cis- and trans-1,2dialkylcyclopropanes should be obtained from each of the geometrical isomers of a suitable alkene. The experimental data as collected in refs 7 and 19, however, indicate that entirely nonstereospecific addition is an exception rather than the rule. It is felt that if we could understand the basic factors governing the stereochemical course of different carbene analogs and olefins (of differing donating and accepting capability) then this would help in the design of systems which facilitate this synthetically useful reaction, in cases where at present it is © 1996 American Chemical Society
4340 J. Phys. Chem., Vol. 100, No. 11, 1996
Su
difficult to obtain or unobserved. Thus, in this work we have attempted to study such carbene additions using spin-orbit (SO) coupling terms and simple group theory. To our knowledge, theoretical analyses of this crucial triplet carbene addition reaction are still lacking, with the exception of some works done by Hoffmann,20 Dewar et al.,21 Halvei and Trindle,22 Moreno et al.,23a Kirmse, Houk, et al.,23b and Engles et al.23c In those theoretical studies only Halvei and Trindle24 have considered SO coupling terms. Our aim is therefore to search for a general theory of reactivity for such addition reactions from a unified point of view and to delineate the significant role played by SO coupling. To highlight the questions which formed the basis for our study, it is perhaps worthwhile to review briefly some of the necessary formulas. The theory can be traced back to previous papers by Lin25 and Salem and Rowland26 as well as Shaik and Epiotis27 and has been extensively applied in this work. It has to be pointed that the concept of spin-inversion mechanisms in such triplet carbenic addition reactions was expressed for the first time by Shaik and Epiotis27a,c and then by Shaik.27b Hence, we shall cite the theory by Shaik and Epiotis27 as follows. Consider a reaction system on a triplet surface (T1). After completing a sequence of events (e.g., bond reorganization), the reaction system reaches a region where it inverts a spin and relaxes to the ground state (S0) in a radiationless manner. A very clear discussion of spin-orbit coupling in molecules has been provided by McGlynn et al.28 It was shown that the probability of such a spin inversion process occurring is directly ˆ SO|S0〉 and proportional to the SO coupling matrix element 〈T1|H inversely proportional to the energy gap separating the two states.28a Hence, in order to obtain an efficient spin inversion, the system must adopt a geometry for which the SO coupling matrix element is maximized and the T1-S0 separation is minimized.26 Furthermore, the SO coupling operator can be written as a double sum over the interaction of all electrons, i, with all nuclei, N:28
H ˆ SO ) ∑∑ i
N
Z*Ne2 ˆl (i)‚sˆ(i) 2m c
∑i ∑N K
(
ˆl (i)‚sˆ(i) riN3
K)
2 Z* Ne
)
2m2c2
(1)
where Z* N represents the effective nuclear charge of nucleus N, and riN represents the distance between electron i and nucleus N. The ˆl(i) and sˆ(i) are the orbital and spin angular momentum operators for electron i, respectively. It should be stated that eq 1 is an approximation to the total SO coupling operator.28 We note that the SO coupling operator (eq 1) is also a sum of one-electron operators. It is therefore easily verified that the SO matrix elements vanish if the two configurations involved differ by more than one pair of MOs.29 Accordingly, the relative SO coupling efficiency of the mechanisms can be reduced to evaluate the matrix elements described below
〈
In this equation the ˆl components operate only on the spatial (orbital) parts and sˆ components only on the spin parts of the wave functions. Upon operation on a real p-type atomic orbital (AO) the ˆlk operators rotate the orbital by (90° about the axis specified by the operator subscript, k() x, y, z). Hence, it is easily proved that eq 2 can be rewritten in terms of the atomic integrals. Thus, the only significant contributions to 〈H ˆ SO〉k arise from two-center integrals over two perpendicular p AOs on two neighboring centers.26 In addition, the interaction terms which arise from the relationship of those p AOs can be classified as being, σ and ω, as follows,
1 1 + | 〈 r r |p 〉 1 1 + ) p | 〈 r r |p 〉, etc.
σ ) pmy Vmn
3
π Vmn
mz
n
3
m
ny
3
m
nz
3
| r |LUMO〉
(
K)
(4)
n
where m and n are the positions of the atomic centers. For example, pmy is the py AO on the C-m atom. For convenience, from now on we shall use Vσ and Vπ to describe σ- and π-interactions, respectively,26 where Vσ and Vπ behave similarly π is to the corresponding AO overlap integrals. For instance Vmn approximately proportional to the π-type overlap between the pz AOs on C-m and C-n atoms. Thus, in general, we may obtain the following relationships.27b,c
(5)
On the other hand, the SO coupling matrix element of the two states (here we are interested in only two particular states T1 and S0) can be expanded as 0 ˆ SO + H ˆ SO ) H
( ) ∂H ˆ SO ∂Qj
Qj + ...
(6)
where Qj stands for the normal coordinate of the jth vibrational mode. This leads to the final form of the SO coupling matrix elements as follows
〈| |〉
0 ˆ SO|S0〉 ) 〈T01|H ˆ SO |S00〉 + T01 〈T1|H
∂H ˆ SO ∂Qj
S00 Qj + ... (7)
We may therefore obtain the intersystem crossing rule as25,27b
ˆ SO|S00〉 f Γ(T10,ν) × Γ(Rk) × Γ(S0) ) A 〈T01|H
ˆl ksˆk 2
(3)
σ π σ | > Vmn > 0, Vmn a, this implies that the reaction would be suitable for a polar solvent event.27b,c Then, as polarity increases b2 becomes larger than 2ab,33 which is able to decrease the magnitude of the SO coupling expression in eq 14, especially for high polarity. It is therefore predicted that a nonpolar (b ≈ a) environment will encourage the case A(i) mechanism. The reaction mechanism on this pathway for the carbenic cycloaddition is shown schematically in 7. The coloring convention of the p orbitals
Alternatively, there is the second motion case B, which also meets with the A′′ symmetry requirement, involving a single rotation as depicted in 9. Thus, the MOs of the complex, after conrotation by R in the direction shown in 9, may be written as
HOMO ) ap1x - b(p2y cos R + p2z sin R - p3y) (16) LUMO ) bp1y + a(p2y cos R + p2z sin R + p3y) (17) Simiarly, substituting eq 16 and eq 17 into eq 2, for the x component of the SO coupling matrix element, we have
case B: -ip2 K 2 σ [b (V12 + Vπ12) + 4abVπ23] sin R (18) 4x2 Thus, the SO coupling matrix element of case B varies proportionally to the sine of the rotation angle. Then, it is apparent that eq 18 reaches a maximum at R ) 90°, where it becomes 〈H ˆ SO〉x )
case B (R ) 90°): 〈H ˆ SO〉x,max )
is used to indicate directional changes following distortion. The dotted lines indicate bonds to be formed. Since this mechanism requires 45° rotations, it may lead to two isomeric structures resulting in stereochemical retention and inversion conformations as illustrated in 7. Conversely, since the SO coupling expression associated with case A(ii) (R ) 90°) (eq 15) contains only intermolecular contributions, it is obvious that case A(ii) will prefer the “tight” (product-like) geometry. Similarly, as seen in eq 15, since the coefficients of those intermolecular terms are only b2, its SO coupling matrix element will rise as polarity increases (b > a). Hence, case A(ii) will be favorable in a polar solvent and the
-ip2 K 2 σ [b (V12 + Vπ12) + 4abVπ23] 4x2
(19)
It should be qualified that due to the requirement for ionicity of the singlet diradical, which can facilitate the SO coupling and therefore enhance the intersystem crossing, the optimum angle (R), in practice, will be less than 90°.26 Since the SO coupling matrix element of case B (eq 19) is quite similar to that of case A(i) (eq 14), the considerations for the latter are also applicable to the former. We thus anticipate that case B will take place preferentially in a “loose” (reactant-like) geometry and will be encouraged in a nonpolar solvent. Furthermore, this monorotation mechanism may be loosely termed a perpendicular diradicaloid, after which the system either inverts a spin and relaxes to the ground-state reactant or rearranges to a singlet product. It must be noted that if case B is performed all the stereochemical information contained in the reactants is lost in the final products. In addition to cyclopropanes, this mechanism will afford other products typical of diradicals such as abstraction, insertion, and polymerization, etc. The MO description for this is illustrated in 10. The dotted line indicates the bond to be formed. We shall see some experimental evidence for such predictions in the next section.
Triplet Carbenic Addition Chemistry
J. Phys. Chem., Vol. 100, No. 11, 1996 4343 and (ii) γ ) 90°. That is
case C (β ) 19.47°, γ ) 0°): 〈H ˆ SO〉2 ) Before further discussion, it has to be mentioned that the monocentric term (carbene) arisen from consideration of the HOMO and LUMO expressions as in eqs 11 and 12 would not change the conclusions of both case A and case B owing to the zero value in its x component of the SO coupling term. (ii) Stereoselection Rules (Qy) for T1y. For the y component situation, it has been proved previously that the system will adopt an A′′ type motion in the Cs symmetry, and so this is not considered here. In summary, the reason for this behavior is that the y component path is unable to lead to the experimentallyexisting molecular conformations as well as create an efficient SO coupling interaction. (iii) Stereoselection Rules (Qz) for T1z. As discussed earlier, the z component of T1 will be coupled to S0 by an A′ type motion in the Cs symmetry. This is a totally symmetric motion which preserves the symmetry of the complex. Nevertheless, in order to be efficient it must generate an x, y perpendicular AO relationship. Two kinds of motions which satisfy conditions are shown in 11 and 12. These are called case C and case D, respectively.
Case C involves a conrotation of the π bond and a distortion of the carbene. The HOMO and the LUMO can be expressed as a function of the rotation angle γ (carbene) and the pyramidalization angle β (π bond) as shown in 11. That is
HOMO ) a(p1x cos γ + p1y sin γ) - b(p2y cos β + p2x sin β - p3y cos β + p3x sin β) (20) LUMO ) b(p1y cos γ - p1x sin γ) + a(p2y cos β + p2x sin β + p3y cos β - p3x sin β) (21) Then, using eq 2, the z component of the SO coupling matrix element takes the form
-ip2 K [(0.33b2 - 0.94a2)(Vσ12 + Vπ12) + 2 0.63ab(Vσ23 + Vπ23)] (24)
case C (β ) 19.47°, γ ) 90°): -ip2 K (25) [0.63ab(Vσ23 + Vπ23)] 2 For case C(i), eq 24 contains intermolecular (Vσ12 + Vπ12) and intramolecular (Vσ23 + Vπ23) terms, both of whose values are negative owing to eq 5. Thus, eq 24 may reach an extreme when the following conditions apply: 1 > b g 1.7a (which forces those two terms in eq 24 to be additive) and decreasing intermolecular distances. In such situations, case C(i) will occur preferentially in a “tight” (product-like) conformation. Nevertheless, high polarity will in turn reduce the magnitude of the second term in eq 24, in which it is weighted by 0.63ab,33 so that the SO coupling expression will slowly increase as polarity increases. Moreover, this mechanism will preserve the geometric integrity of the olefin as shown by dotted lines in 13, denoting the bonds which are to be formed. 〈H ˆ SO〉z )
Alternatively, as discussed previously, the case C(ii) mechanism (eq 25) will be favorable in a nonpolar (b ≈ a) solvent since its SO coupling expression only contains the coefficient ab.33 It has to be pointed out that, in principle, the case C(ii) is a σ approach (least motion), resulting in a geometric retention conformer, i.e., the cyclopropane with the corresponding geometry of the starting olefin. A distortion complex corresponding to such a σ-attack process is pictorially illustrated in 14, where we use the coloring convention of the p AOs to indicate the directional changes following distortion. The dotted lines indicate the bonds to be formed.
case C: -ip2 K 2 {[b sin(β + Y) - a2 sin(β + γ)](Vσ12 + 4 Vπ12) + [b2 sin(β - γ) - a2 cos(β - γ)](Vσ13 + Vπ13) +
〈H ˆ SO〉z )
2ab(Vσ23 + Vπ23) sin(2β)} (22) Taking into account the relationships Vσ12 + Vπ12 ) Vσ13 + Vπ13 and β ≈ 19.47° (which completes a tetrahedral angle34, one obtains
case C: -ip2 K 〈H ˆ SO〉z ) [(0.33b2 - 0.94a2)(Vσ12 + Vπ12) cos γ + 2 0.63ab(Vσ23 + Vπ23)] (23) Hence, eq 23 may reach two possible extremes at (i) γ ) 0°
On the other hand, the case D mechanism which also maximizes 〈H ˆ SO〉z describes a mixture of three motions: a distortion of the carbene about the z axis (γ), a pyramidalization of the py AO at C-2 about the z axis (β), and a rotation of the py AO at C-3 about the x axis (R). The valence MOs of the complex, after rotation by γ, β, and R in the direction shown in 12, are then expressed in the equations
HOMO ) a(p1x cos γ + p1y sin γ) - b(p2y cos β + p2x sin β - p3y cos R + p3x sin R) (26) LUMO ) b(p1y cos γ - p1x sin γ) + a(p2y cos β + p2x sin β + p3y cos R - p3z sin R) (27)
4344 J. Phys. Chem., Vol. 100, No. 11, 1996
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Substituting into eq 2 leads to
case D: -ip2 K 2 {[b sin(β + γ) - a2 cos(β + γ)](Vσ12 + 4 Vπ12) - [b2 sin γ + a2 cos γ](Vσ13 + Vπ13) cos R + 2ab(Vσ23 +
〈HSO〉z )
Vπ23) sin β cos R} (28) Using eq 5, it is easy to see that the second term in eq 28 is no additive since those values of (Vσ + Vπ) are negative. If we consider the relationship Vσ12 + Vπ12 ) Vσ13 + Vπ13, then two extremes can be easily distinguished, i.e., (i) β ) 19.47°, R ) γ ) 90° and (ii) β ) 19.47°, R ) γ ) 0°. Substituting into eq 28, one may obtain the SO matrix elements for those pathways as follows:
case D (β ) 19.47°, R ) γ ) 90°): 〈H ˆ SO〉z )
-ip2 K [(0.94b2 + 0.33a2)(Vσ12 + Vπ12)] (29) 4
case D (β ) 19.47°, R ) γ ) 0°): 〈H ˆ SO〉z )
-ip2 K [(0.33b2 - 1.94a2)(Vσ12 + Vπ12) + 4 0.66ab (Vσ23 + Vπ23)] (30)
In the case D(i) mechanism, there is an initial formation of a new bond between the carbene and one carbon moiety of the olefin as a result of a favorable initial overlap between them (see 15). The resulting singlet species, after spin inversion, can
either relax its geometry and then fall apart or yield a geometric inversion cycloproduct via a ring closure. Furthermore, the SO coupling matrix element for case D(i) (eq 29) only contains intermolecular contributions so that this mechanism will prefer a “tight” (product-like) geometry. Additionally, since the multiplier of (Vσ12 + Vπ12) is (0.94b2 + 0.33a2) which will increases as polarity increases (b > a), we thus anticipate that the case D(i) will be favorable in highly polar conditions. Three intriguing points are noteworthy. Firstly, in principle, the case D(i) pathway is by nature a σ approach as shown in 15. Secondly, one may argue that the case D(i) route does not involve a totally symmetric A′ mechanism in the Cs symmetry. In fact, since the case D(i) pathway is recognized as a σ approach, which adopts the C2V symmetry, it is easy to show that for a C2V symmetry the z component of T1 will be coupled to S0 by a B2-type motion. In such a case, therefore, in order to maximize the z component of a two-center SO coupling interaction the case D(i) mechanism must generate the requisite x, y perpendicular AO relationship to create an efficient SO coupling interaction as illustrated in 15. Thirdly, the case D(i) mechanism is intrinsically different from the case B mechanism. The former leads to the cyclopropane with geometric inversion through the σ approach while the latter results in stereorandomization through the π approach. The case D(i) can be easily understood pictorially from 16, in which we make use of valence-bond mechanism showing the relationships of coupling
between the carbene and the olefin. In other words, during the case D(i) cycloaddition, the rotation transition of the AOs would give rise to a probability of obtaining wave functions with singlet ionic characters, which can induce the spin flipping as well as facilitate the SO coupling.35 Then, both the nσ and nπ orbitals of the carbene will have more or less overlaps with the pπ orbitals of the olefin, which ultimately gives only the cyclopropane with the geometric inversion. However, this is not the case in case B mechanism since it produces the diradical (coValent) system as in 10, yielding stereorandom products. In contrast, for case D(ii), since eq 30 is similar to eq 24, the considerations for the latter also apply to the former. Namely, the intermolecular distance and high polarity may have opposing effects on the magnitude of the SO coupling expression. In addition, with such angular characteristics, case D(ii) is reduced to a pyramidalization mechanism involving only one carbon moiety. Therefore, this route is expected to be inefficient and will be neglected in future discussions. Before further discussion, since the free carbene has a monocentric SO coupling of an estimated 38 cm-126a,39a which is larger than the bicentric terms mentioned above, it is necessary to examine the possibility of singlet participation. Namely, the triplet-singlet crossing already occurs in the carbene fragment. However, such an intramolecular intersystem crossing before attacking olefins may be improbable because it would require a fortuitous near-degeneracy of at least one pair of vibrationrotation energy levels of the singlet and triplet states.39b Indeed, one recent ab initio study done by Reuter et al.23c supports this point of view. Nevertheless, it is believed that the result of the monocentric term arisen from carbene (for instance, see eqs 20, 21 and 26, 27) will basically reinforce the yield of stereorention adducts, if the carbene’s energy difference between the two lowest vibrational levels of the singlet and the triplet state is fairly small. Furthermore, it is worthwhile for us to reexamine the SO matrix expressions for the above mechanisms. Comparing eqs 14, 15, 19, 24, 25, and 29 and taking into account the relationship |Vσ23| > |Vσ12| > Vπ23 > Vπ12 (due to eq 5), it is easy to prove that
|(eq 25)2| > |(eq15)2| g |(eq 29)2| > |(eq 19)2| g |(eq 14)2| > |(eq 24)2| Consequently, we come to the conclusion that for the triplet carbonic addition to the olefin, the cyclopropane with geometric retention should be the most faVorable product (i.e., a stereospecific addition), because of a larger SO coupling matrix element as well as a less conformational change. This conclusion, which should be applicable to the gas phase reaction, is based on the model we used here as well as on the assumption that other controlling factors are constant. Additionally, the above result implies that the σ approach would be preferred in the triplet addition, which has been confirmed by some ab initio studies.23c It is notable that, on the other hand, the formation of stereoinVersion adducts would be comparable to that of stereoretention adducts as intermolecular distance decreases (see eqs 25, 15, and 29). According to Skell-Woodworth’s hypothesis, as stated earlier, one would expect that an entirely nonstereospecific carbene addition is to yield identical product mixtures from cis,trans pairs of alkene. However, if different
Triplet Carbenic Addition Chemistry product distributions are observed, the reaction exhibits some degree of stereospecificity. Referring to many experimental observations,1,7,19,36 one finds that actually an entirely nonstereospecific triplet carbene is very hard to obtain (so preserving some degree of stereospecificity). In other words, loss of stereochemistry is not complete in triplet additions. Most triplet carbene additions produced a majority of products with stereoretention as well as a minority of products with stereoinversion, though sometimes both yields were comparable. For instance, the vapor phase photolysis of 2,2,2-trifluorodiazoethane in the presence of cis-2-butene led to 60% nonstereospecific addition of CF3HC:.36a Bis(trifluoromethyl)carbene, produced by pyrolysis of the corresponding diazirine, yielded 17% of trans adduct in its reaction with cis-2-butene.36b Likewise, diphenylcarbene reacts with cis-2-butene to produce 13% of trans1,2-dimethyl-3,3-diphenylcyclopropane and 87% of the cisisomer.19f It was found that the spectroscopically observed ground state of the above three carbenes is triplet. Hence, our above model prediction is strongly supported by experiments.37 Moreover, the case B mechanism, as studied early (eq 19), would produce 1,3-diradical species (such as trimethylene diradical in CH2 + ethylene reaction) as intermediates or transition structures in the triplet additions. This might then yield either cyclopropanes after an intersystem crossing or some other products typical of diradicals, whose conformations are different from cyclopropanes. Since the magnitude of the matrix element of the case B mechanism is small compared to other possible mechanisms and its yielded diradicals are known as unstable species, it is reasonable to conclude that the case B approach should not dominate in the triplet additions and the yields of its products would be small, which can be seen as side products. This is in agreement with the experimental observations.19,36 It has to be mentioned that, according to some sophisticated calculations,38c,e the trimethylene diradical is found to have a rather low SO coupling constant (0-2.5 cm-1), which is very sensitive to rotation of the terminal methylenes but relatively insensitive to the CCC angle. Indeed, according to one recent ab initio study,23c it was found that energetically favorable conversion from the triplet to the singlet surface can only happen at large CH2-C2H4 separations (i.e., in the region of weak carbene-olefin interaction). This implies that the intersystem crossing in the triplet additions would probably occur before trimethylene diradicals are formed. Thus, the role of the trimethylene diradical in the triplet addition reaction is still uncertain23c and requires special computational studies as well as available experimental evidences if experiments exist. Such studies, however, are beyond the scope of the present work. Nevertheless, as stated previously, the probability of a spin inversion process occurring is proportional to the SO coupling matrix element. Hence, in general, this effect should be reflected by the quantum yield of the addition reaction, if the energy gap separating the S0 and T1 states is assumed to be constant. Comparing SO coupling expressions for these mechanisms, it is evident that the difference between their absolute values is small. This implies that competing reaction mechanisms exist in the triplet carbenic addition chemistry. Thus, the reason for the nonstereospecificity of the addition of triplet carbene to olefins is presumably because the combination of its stereochemically different spin-inVersion mechanism, caused by the different symmetries of the triplet subleVels (T1x, T1y, T1z), could result in a nonstereospecific appearance. This is in accordance with the experimental observations.1,6-19 A summary of the mechanisms of cycloadditions which result from spin inversion in a triplet carbene-olefin complex is given in Scheme 1. In each case, only the final products are indicated.
J. Phys. Chem., Vol. 100, No. 11, 1996 4345 SCHEME 1
Also, from our previous proofs, we summarize the features of the above mechanisms (such as the character of attacking pathway, the stereochemistry of adducts, preferred intermolecular distances, polarity, and the order of the magnitude of the SO coupling expressions, etc.) in Table 1. The rules embodied in this scheme and table are, of course, very approximate, but they can hopefully provide the basis for constructive experimentation. What is more important is that some of the mechanisms proposed in the Scheme 1 and Table 1 (for instance, case C) can perform intersystem crossing without passing through a rotatory and a fast equilibrium diradical. In addition, those mechanisms as shown in Scheme 1 and Table 1 are found to be identical with the orbitalsymmetry-allowed pathway either [π2a + σ2a] or [π2s + σ2s],39c except for the case A(ii) route. Therefore, it is believed that the triplet carbene addition reaction should be a case where orbital-symmetry and spin-inversion requirements conspire to yield the same product.39d It should be notable that our stereoselection mechanisms (see 6-10) and associated mechanistic interpretations for triplet carbenic additions are strongly analogous to those found in the work of Shaik and Epiotis.27b,c In addition to the above SO coupling matrix considerations, certain other effects peculiar to triplet cycloadditions will be discussed in the following section. 2. Other Controlling Factors. (a) The Solvent Effect. In this section we shall see that the polarity of the solution environments plays a significant role in determining the final stereochemistry of the cycloaddition. As seen from Table 1, three mechanisms are suitable for nonpolar cases, i.e., case A(i) (eq 14), case B (eq 19), and case C(ii) (eq 25). Comparing their SO coupling expressions, as proved previously, one can easily obtain |(eq 25)2| > |(eq 19)2| g |(eq 14)2|. It is therefore anticipated that nonpolar enViron-
4346 J. Phys. Chem., Vol. 100, No. 11, 1996
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TABLE 1: Effects of Intermolecular Distances, Stereochemistry, and Polarity on the SO Coupling Matrix Elements of the Triplet Carbenic Addition to the cis-Olefina
a
For details, see the text. b In absolute values. c Loose indicates “reactant-like” geometry. d Tight indicates “product-like” geometry.
ments may result in the stereospecific addition of the triplet carbene to olefins. Nevertheless, this prediction has to be used with caution since the latter two pathways (cases B and C) may lead to stereorandom products, increasing the nonstereospecificity. For instance, the largely stereospecific addition of cyclopentadienylidene failed to respond to dilution with hexfluorobenzene, and the stereospecificity of addition to cis-2butene dropped only from about 99% to 97% on 24-fold dilution.40d However, Jones and co-workers succeeded in altering the stereospecificity of addition of diphenylmethylene to cis-β-deuteriostyrene, a substrate favorable to triplet addition.40a The product ratio is changed from 65% cis, 35% trans with no C6F6 present to 56% cis, 44% trans at 0.95 mole fraction C6F6. This dilution effect may result from a delicate balance of a number of opposing mechanisms as discussed previously (cases A, B, and C). Some intriguing examples can be found in ref 40. On the other hand, as in Table 1, three mechanisms are also suitable for polar conditions, i.e., case A(ii) (eq 15), case C(i) (eq 24), and case D(i) (eq 29); the latter two cases are especially favorable in highly polar solvents. Comparing their SO coupling expressions, as proved earlier, one can easily obtain |(eq 15)2| g |(eq 29)2| > |(eq 24)2|. It is therefore predicted that the cycloaddition of triplet carbenes to olefins in polar conditions will preferentially result in products haVing stereoinVersion. Unfortunately, due to a lack of available experimental data on this topic, this prediction remains to be proved or disproved by future experiments. (b) The Substituent Effect. One striking substituent effect, which was usually ignored, on the addition of the triplet carbene to the olefin is that the nature of substituents on the olefin may affect the stereochemistry of cyclopropane. It was suggested that when π donors and π acceptors are substituted as in 17a, the charge distribution of the CdC bond is strongly polarized.41
Hence, π bonding is weak in the planar structure of 17a, while the zwitterionic state of the perpendicular structure 17b is stabilized significantly by the π acceptors at the anion site and by the π donors at the cation site. For the perpendicular structure of 17b, the zwitterionic site becomes more stable than its alternative, diradical state. According to Salem and Rowland’s work,26 as mentioned earlier, such singlet ionic MOs can facilitate the SO coupling and therefore enhance the intersystem crossing. Moreover, this zwitterionic species (17b) will be increasingly stabilized as the polarity increases. Consequently, using the results in Table 1, one may predict that the addition of the triplet carbene to the olefin, which has π donor and π acceptor substituents as in 17a, will preferentially lead to a stereoinVersion product, especially in a highly polar solVent.42 It must be pointed out that this prediction is based on the assumption that other controlling factors are equal. Unfortunately, to our knowledge, there are no relevant experimental studies which have tested this prediction. It is well known that steric effects play an important role in the determination of stereochemistry. This effect is also expected to exist along the pathway of addition of the triplet carbene to the olefin, but it is still a fact not generally appreciated. Considering the attacking pathway and the intermolecular distance during the cycloaddition, as seen in Table 1, one may conclude that the π approach (3) would be faVored in producing stereoretention products, whereas the σ approach (4) would be efficient in yielding stereoinVersion adducts. These conclusions are reasonable from the stereochemical hindrance viewpoint. Furthermore, because of steric effects the stereoretention cyclopropane is expected to predominate when the carbene XYC: bears substituents which are bulky.43,44 Likewise, when the substituents of the olefin are bulky groups as in 18, the yields of the stereoretention product would dominate.
Triplet Carbenic Addition Chemistry Although stereochemical data for studying such steric effects in triplet carbene addition reactions are not well established, some confirming examples (such as carbenes with bulky substituents) can be found in refs 9-13 and 36. Also, as a result of the nonbonded interactions (steric effects) between the two alkyl groups bonded to the two cis-olefinic carbon atoms, the triplet carbenic reaction with cis-olefin might be considerably less stereospecific than with the trans-olefin, the latter producing mainly stereoretention product.19j,k In summary, steric configuration is predominantly (but not completely) retained in carbene addition to olefins. Experimental observations are in good agreement with this conclusion.1m,o,19,36 Furthermore, two different adducts may be obtained from the stereospecific reaction of a monosubstituted carbene or carbenoid with olefins lacking both a center of symmetry and a 2-fold symmetry axis along the CdC bond (e.g., cis-2-butene). The isomeric adducts are designated as syn/anti or endo/exo pairs, the syn or endo configuration being assigned to the cyclopropane in which the carbene substituent has a cis relationship to the larger number of alkyl groups.1c,d Experimentally, it was found that carbene and carbenoid addition reactions show a preference for the formation of the presumably thermodynamically less stable syn(endo) isomers, suggesting a transition state with attractive interactions between the carbene substituent and the alkyl groups. The nature of such attractive forces is unknow at present, although these results may be explained by assuming strong London interactions between the polarizable carbene substituent and the alkyl groups. This question is beyond the scope of the present work and will not be discussed here.45 (c) The Heavy Atom Effect. As we see from eq 1, the SO coupling matrix element is directly proportional to the atomic number of an atom.28,46,47 Thus, whenever a reactant contains a heavy atom center which is not necessarily directly involved in the reaction, a strong SO coupling may be obtained. In other words, the system, via the agency of the heavy atom, can enhance the probability of spin-forbidden transition through coupling of spin and orbital angular momenta. This, in turn, can provide the necessary orthogonal AO interactions without any need for distortions. Unfortunately, very few data of triplet carbenic addition reactions have been reported for the heavy atom effect, but the few available results are in agreement with this prediction. Some supporting evidence comes from the fact that ground sulfur atom (in the 3P state), whose valence shell is isoelectronic with methylene, adds largely stereospecifically to cis-2-butene.48-51 On the other hand, it was found that triplet nitrene (NH)52 and triplet oxygen atom (in the 3P state),53 which are isoelectronic to the carbene (CH2), always added in a nonstereospecific manner. The reason for this is presumably because the heavy atom effect is relatively unimportant in the first low elements. One may therefore predict that triplet P-R, As-R, Sb-R, and Bi-R (R ) H or alkyl group) should add stereospecifically to ethylenes. Furthermore, Mcbee and Sienkowski reported that triplet tetrabromocyclopentadienylidene added to the trans-olefin olefin led to only the trans addition product, due to the heavy atom effect of four bromine atoms on the reaction of the carbene.54 Many other intriguing experimental results may perhaps be related to the heavy atom effect.55-57 For instance, photolysis of methylene iodide dissolved in olefins gives cyclopropanes in modest yield. Within the limit of detection (5%), this reaction was found to be stereospecific.55,58 Additionally, the SimmonSmith reaction is an example of a variety of R-eliminations which transfer methylene to a double bond via an organometallic
J. Phys. Chem., Vol. 100, No. 11, 1996 4347 reagent. In all cases cyclopropanes are formed with complete stereospecificity.57 To account for the high specificity of these reactions, two mechanisms involving organometallic intermediates have been proposed.56 Nevertheless, from our study it is believed that a concerted process due to the effect of heavy atoms should play a decisive role in the stereochemistry of the formation of cyclopropanes. III. Conclusion This work represents an attempt to apply group theory to discover the motions which lead to spin inversion and then to evaluate their relative efficiency using delocalized MOs as a semiquantitative tool. We have assumed that spin inversion plays a central role in triplet carbene cycloaddition and concentrated on evaluating the chemical implications of the inter- and intramolecular components of the crucial SO coupling matrix element. The emerging picture from the present study provides a set of stereoselection rules which can be used to analyze reactivity patterns in triplet carbene addition reactions. Indeed, each spin inversion mechanism has its own stereochemical consequences. Hence, stereospecificity in chemical reactions need not arise exclusively from the electronic features of singlet carbene addition reactions; it may also follow from the SO coupling properties of reactions in triplet states. It has to be emphasized that the approach proposed in this study has been proven to be a good alternative to the commonly accepted explanation, the Skell-Woodworth mechanism. In spite of its simplicity and some mathematical approximations in cases, our approach proves to be rather effective. It is unrivaled at providing insights into the stereochemical behavior of triplet carbene addition reactions (see our conclusions in Scheme 1 and Table 1). We have found that the agreement with available experimental results is very encouraging.59 The understanding obtained from our model permits us to suggest a number of specific predictions which in the future may be confirmed or refuted by experiments or more rigorous theory. It is hoped that our study will stimulate for further research into the subject. Acknowledgment. I wish to thank Professor Michael A. Robb (King’s College, University of London, U.K.) for his encouragement and support. I gratefully acknowledge the hospitality of Dr. Paul Sherwood at the DRAL Daresbury Laboratory in U.K., where this paper was prepared. I am also grateful to Professor Sason Shaik (The Hebrew University, Israel) for critical comments of and helpful corrections to the manuscript. References and Notes (1) For reviews, see: (a) Hine, J. DiValent Carbon; Academic Press: New York, 1964. (b) Krimes, W. Carbene Chemistry, 1st ed.; Academic Press: New York, 1964; Chapter 1. (c) Bethell, D. AdV. Phys. Org. Chem. 1969, 7, 153-209. (d) Moss, R. A. In SelectiVe Organic Transformations; Thyagarajan, B. S., Ed.; Wiley: New York, 1970; pp 35-88. (e) Krimes, W. Carbene Chemistry, 2nd ed.; Academic Press: New York, 1971; Chapter 8. (f) Moss, R. A.; Jones, M., Jr. Carbenes; Wiley: New York, 1973; Vol. 1. (g) Jones, M., Jr.; Moss, R. A. Carbenes; Wiley: New York, 1975; Vol. 2. (h) Moss, R. A.; Jones, M., Jr. ReactiVe Intermediates; Wiley: New York, 1978; Vol. 1. (i) Moss, R. A.; Jones, M., Jr. ReactiVe Intermediates; Wiley: New York, 1981; Vol. 2, Chapter 3. (j) Moss, R. A.; Jones, M., Jr. ReactiVe Intermediates; Wiley: New York, 1985; Vol. 3, Chapter 3. (k) Abramovitch, R. A. ReactiVe Intermediates; Plenum: New York, 1980; Vol. 1. (l) Platz, M. S. Kinetics And Spectroscopy of Carbenes And Biradicals; Plenum: New York, 1990. (m) DeMore, W. B.; Benson, S. W. AdV. Photochem. 1964, 2, 219-261. (n) Tomioka, H. Res. Chem. Intermed. 1994, 20, 605-634. (o) Closs, G. L. In Topics in Stereochemistry; Eliel, E. L., Allinger, N. L., Eds.; Interscience: New York, 1968; Vol. 3, pp 193-235.
4348 J. Phys. Chem., Vol. 100, No. 11, 1996 (2) (a) Samder, W.; Bucher, G.; Wierlacher, S. Chem. ReV. 1993, 93, 1583-1621. (b) Trozzole, A. M.; Wasserman, E. In Reference 1f, Chapter 5. (c) For one related ab initio study see: Yamamoto, N.; Bernardi, F.; Bottoni, A.; Olivucci, M.; Robb, M. A.; Wilsey, S. J. Am. Chem. Soc. 1994, 116, 2064-2074. (3) (a) Turro, N. J. Modern Molecular Photochemistry; University Science Books: Milly Valley, CA, 1991; pp 551-552. (b) Gilbert, A.; Baggott. 1991; pp 450-455. (c) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic Chemistry, 3rd ed.; Harperdson: New York, 1987; pp 556-562. (d) Gilchrist, T. L.; Storr, R. C. Organic Reactions and Orbital Symmetry, 2nd ed.; Cambridge University Press: Cambridge, England, 1979; pp 212-215. (e) Gill, G. B.; Willis, M. R. Pericyclic Reactions; Chapman and Hall: London, 1974; pp 92-94. (4) (a) Skell, P. S.; Woodworth, R. C. J. Am. Chem. Soc. 1956, 78, 4496-4497; (b) 1959, 81, 3383-3386. (5) Namely, it is widely accepted that stereospecific addition to cisand trans-butene implies a singlet carbene, whereas the absence of stereochemical specificity is considered to imply a triplet carbene. (6) (a) Hartzler, H. D. J. Am. Chem. Soc. 1961, 83, 4997-4999. (b) Jones, W. M.; Grasley, M. H.; Brey, W. S. J. Am. Chem. Soc. 1953, 85, 2754-2759. (c) Funakubo, E.; Moritani, I.; Nagai, T.; Nishida, S.; Murahashi, S. Tetrahedron Lett. 1963, 1069-1071. (d) Mitsch, R. A. J. Am. Chem. Soc. 1965, 87, 758-761. (e) Wescott, L. D.; Skell, P. S. J. Am. Chem. Soc. 1965, 87, 1721-1724. (f) Blomstrom, D. C.; Herbig, K.; Simmons, H. E. J. Org. Chem. 1965, 30, 959-964. (g) Closs, G. L.; Moss, R. A.; Coyle, J. J. J. Am. Chem. Soc. 1962, 84, 4985-4986. (h) Bader, R. F.; Generosa, J. I. Can. J. Chem. 1965, 43, 1631-1644. (i) Doering, W. v. E.; Mole, T. Tetrahedron 1960, 10, 65-69. (j) Skell, P. S.; Klebe, J. J. Am. Chem. Soc. 1960, 82, 247-248. (k) Doering, W. v. E.; Jones, M., Jr. Tetrahedron Lett. 1963, 791-794. (l) Duncan, F. J.; Cvetanovic, R. J. J. Am. Chem. Soc. 1962, 84, 3593-3594. (m) Jones, M., Jr.; Ando, W.; Kulczycki, A. Tetrahedron Lett. 1967, 3191-3195. (7) (a) Gasper, P. P.; Hammond, G. S. Carbene Chemistry; Academic Press: New York, 1964; Chapter 12. (b) Gaspar, P. P.; Hammond, G. S. In Carbene Chemistry; Moss, R. A., Jones, M., Jr. Eds.; Wiley: New York, 1975; Vol. 2, Chapter 6. (c) Closs, G. L.; Moss, R. A. J. Am. Chem. Soc. 1964, 86, 4042-4052. (8) Jones, G. W.; Chang, K. T.; Munjal, R.; Shechter, H. J. Am. Chem. Soc. 1978, 100, 2922-2923. (9) Murahashi, S.-I.; Moritani, I.; Nishino, M. J. Am. Chem. Soc. 1967, 89, 1257-1259. (10) (a) Moss, R. A.; Dolling, U.-H. J. Am. Chem. Soc. 1971, 93, 954960. (b) Baron, W. J.; DeCamp, M. R.; Hendrick, M. E.; Jones, M., Jr.; Levine, R. H.; Sohn, M. B. In Carbenes; Moss, R. A., Jones, M., Jr., Eds.; Wiley: New York, 1973; Vol. 1; Chapter 1 and see references therein. (c) Reference 1k, Chapter 6. (d) On the other hand, however, a conventional interpretation of such stereospecific additions is that the chemistry of phenylcarbene involves a very low-lying, thermally accessible, and highly reactive singlet and a much less reactive ground triplet state (see ref 8c,e). We do not agree with this point of view and assume that spin-orbit coupling should play an important role in determining the stereospecificity of the triplet carbenes, which is extensively studied in the present work. (e) In terms of the “reactivity” aspect, in Su’s work it was found that the singlet carbene (whose ground state is triplet) is much more reactive in carbenic chemistry than the triplet carbene due to the energy difference between those two states of a carbene (i.e., ∆ESt ) Etriplet - Esinglet). See: Su, M.-D. Inorg. Chem. 1995, 34, 3829-3831. (11) Closs, G. L.; Closs, L. E. Angew. Chem., Int. Ed. Engl. 1962, 1, 334-335. (12) (a) Ciganek, E. J. Am. Chem. Soc. 1966, 88, 1979-1984. (b) Closs, G. L.; Moss, R. A. J. Am. Chem. Soc. 1964, 86, 4042-4052. (13) Gasper, P. P.; Lin, C.-T.; Dunbar, B. L. W.; Mack, D. P.; Balasubrmanian, P. J. Am. Chem. Soc. 1984, 106, 2128-2139. (14) Grasse, P. B.; Brauer, B.-E.; Zupancic, J. J.; Kaufamnn, K. J.; Schuster, G. B. J. Am. Chem. Soc. 1983, 105, 6833-6845. (15) (a) Jones, W. M.; Hamon, B. N.; Joines, R. C.; Ennis, C. L. Tetrahedron Lett. 1969, 3909-3912. (b) Although Jones et al. presumably concluded that a singlet cycloheptatrienylidene might determine its stereospecific addition to olefin, we doubt such a point of view and suggest that a triplet cycloheptatrienylidene should play a decisive role in this stereochemical addition. (16) Analogously related examples whose explanations use singlet carbenes are questionable and should be reconsidered with triplet carbenes playing a key role; see also: (a) Moritani, I.; Yamamoto, Y.; Murahashi, S.-I. Tetrahedron Lett. 1968, 5755-5758. (b) Gasper, P. P.; Whitsel, B. L.; Jones, M., Jr.; Lambert, J. B. J. Am. Chem. Soc. 1980, 102, 61086113. (c) Moss, R. A.; Joyce, M. A. J. Am. Chem. Soc. 1977, 100, 44754480. (d) Jones, M., Jr.; Harrison, A. M.; Rettig, K. R. J. Am. Chem. Soc. 1969, 91, 7462-7466. (e) Jones, W. M.; Grasley, M. H.; Bery, W. S., Jr. J. Am. Chem. Soc. 1963, 85, 2754-2759. (f) Moss, R. A.; Przybyla, J. R. J. Org. Chem. 1968, 33, 3816-3821. (g) Jones, M., Jr.; Ando, W.; Kulczycki, A. Tetrahedron Lett. 1967, 1391-1396. (17) Kopecky, K. R.; Hammond, G. S.; Leermakers, P. A. J. Am. Chem. Soc. 1961, 83, 2397-2398.
Su (18) Indeed, it has been pointed out that all nonstereospecific additions need not be due to triplets and that all triplets need not add in a nonstereospecific manner; see: (a) DeMore, W. B.; Benson, S. W. AdV. Photochem. 1964, 2, 219-261. (b) Kirmse, W. Carbene Chemistry; Academic Press: New York, 1964; Chapter 12. (c) Reference 7. What is more important is that some of the mechanisms proposed in this work can perform intersystem crossing without passing through a rotatory and a fast equilibrium diradical as traditionally explained; see the text. (19) For instance, see: (a) Etter, R. M.; Skovronek, H. S.; Skell, P. S. J. Am. Chem. Soc. 1959, 81, 1008-1009. (b) Skell, P. S.; Klebe, J. J. Am. Chem. Soc. 1960, 82, 247-248. (c) Frey, H. M. J. Am. Chem. Soc. 1960, 82, 5947-5948. (d) Durr, H.; Bujnoch, W. Tetrahedron Lett. 1973, 14331436. (e) Eder, T. W.; Carr, R. W. J. Phys. Chem. 1969, 73, 2074-2076. (f) Baron, W. J.; Hendrick, M. E.; Jones, M., Jr. J. Am. Chem. Soc. 1973, 95, 6286-6292. (g) Ring, D. F.; Rabinovitch, B. S. J. Phys. Chem. 1968, 72, 191-195. (h) Atherton, J. H.; Fields, R. J. Chem. Soc. C 1968, 22762283. (i) Kirmse, W. Carbene Chemistry; Academic Press: New York, 1964; Chapter 5, see references therein. (j) Moritani, I.; Yamamoto, Y.; Murahashi, S. Tetrahedron Lett. 1968, 5697-5701. (k) Jones, M., Jr.; Ando, W. J. Am. Chem. Soc. 1968, 90, 2200-2201. (20) Hoffmann, R. J. Am. Chem. Soc. 1968, 90, 1475-1485. (21) Broder, N.; Dewar, M. J. S.; Wasson, J. S. J. Am. Chem. Soc. 1972, 94, 9095-9102. (22) (a) Halevi, E. A.; Trindle, C. Isr. J. Chem. 1977, 16, 283-290. (b) In Halevi and Trindle’s work, they considered it possible that “rapid spin-inversion” might occur sufficiently early in the approach of the reactants to one another than C2V symmetry is never lost. (23) For ab initio studies, see: (a) Moreno, M.; Lluch, J. M.; Oliva, A.; Bertran, J. THEOCHEM 1988, 164, 17-24. (b) Homberger, G.; Dorigo, A. E.; Kirmse, W.; Houk, K. N. J. Am. Chem. Soc. 1989, 111, 475-477. (c) Reuter, W.; Engels, B.; Peyerimhoff, S. D. J. Phys. Chem. 1992, 96, 6221-6232. (24) However, Halvei and Trindle used SO coupling effect only on a complex at a strict geometry (C2V symmetry), which definitely produces a single product, without considering other possible mechanisms as studied in the present work. (25) Lin, S. H. J. Chem. Phys. 1966, 44, 3759-3765. (26) (a) Salem, L.; Rowland, C. Angew. Chem., Int. Ed. Engl. 1972, 11, 92-11. (b) Salem, L. Pure Appl. Chem. 1973, 33, 317-328. (27) (a) Shaik, S.; Epiotis, N. D. J. Am. Chem. Soc. 1978, 100, 18-29. (b) Shaik, S. J. Am. Chem. Soc. 1979, 101, 3184-3196. (c) Shaik, S.; Epiotis, N. D. J. Am. Chem. Soc. 1980, 102, 122-131. (d) Shaik, S. J. Am. Chem. Soc. 1979, 101, 2736-2738. (28) (a) McGlynn, S. P.; Azumi, T.; Kinoshita, M. The Triplet State; Prentice-Hall: New York, 1969; pp 190-198. (b) McGlynn, S. P.; Vanquickenborne, L. G.; Kinoshita, M.; Carroll, D. G. Introduction to Applied Quantum Chemistry; Holt, Rinehart and Winston: New York, 1972; Chapter 11. (29) For instance, consider a SO matrix element connecting a singlet state S0 with a triplet state T1, where S0 is derived from a configuration [ ]a2 and where T1 is derived from a configuration [ ]a1b1. The brackets denote filled MOs and a and b are valence MOs. In this case, one can obtain 〈S0|HSO|T1〉 ) N〈aβ|hˆ SO|bR〉 where hˆ SO is the one-electron SO operator and N is a constant. R and β stand for spin-up and spin-down, respectively. From this simple result, one can see that S0 and T1 configurations must differ in the occupancy number of not more than one molecular orbital. (30) For π approach, the triplet excited state [ ]ψ1aψ1b is (A′)(A′)(A′) ) A′ where the bracket ([ ]) denotes filled MOs and ψa and ψb are valence MOs. (31) Both HOMO and LUMO can be expressed as a function of the rotation and bending angles; see also ref 27 and: Trindle, C.; Pamuk, H. O. Tetrahedron 1978, 34, 747-752. (32) It must be noted that since any contributions from s orbitals on the nucleus will be annihilated by the ˆl part of the operator,28 we will therefore consider only the action on p orbitals in future. (33) Strictly speaking, in the extreme case, the MO polarization should make 2ab zero while (a2 + b2) should approach unity. Therefore, as polarity increases (a2 + b2) becomes larger than 2ab. See ref 27b,c. (34) Theoretically, this SO expression (eq 22) may reach an extreme at β ) 45°. But actually, β is geometrically constrained to ∼19.47° in order to satisfy the tetrahedral angle requirement; see ref 27b. (35) According to Salem’s work, the intersystem crossing via SO coupling is controlled both by an “ionic” factor and by an “orientational” factor. For details see ref 26. (36) (a) Atherton, R. N.; Speight, J. G. J. Chem. Soc. C 1967, 14501458. (b) Gale, D. M.; Middleton, W. J.; Krespan, C. G. J. Am. Chem. Soc. 1966, 88, 3617-3623. (c) Kopecky, K. R.; Hammond, G. S.; Leermaker. J. Am. Chem. Soc. 1962, 84, 1015-1019. (d) Ref 17. (e) Cowan, D. O.; Couch, M. M.; Kopecky, K. R.; Hammond, G. S. J. Org. Chem. 1964, 29, 1922-1925.
Triplet Carbenic Addition Chemistry (37) Our prediction for the stereospecific trapping of 3CH2 by ethylene was also supported by Halevi and Trindle’s work using the “orbital correspondence analysis in maximum symmetry” theory; see refs 22 and 24. (38) For ab initio studies of trimethylene diradical in its triplet electronic state, see: (a) Doubleday, C., Jr.; McIver, J. W., Jr.; Page, M. J. Am. Chem. Soc. 1982, 104, 6533-6542. (b) Yamaguchi, Y.; Schaefer, H. F. J. Am. Chem. Soc. 1984, 106, 5115-5118. (c) Furlani, T. R.; King, H. F. J. Phys. Chem. 1985, 82, 5577-5583. (d) Yamaguchi, Y.; Osamura, Y.; Schaefer, H. F. J. Am. Chem. Soc. 1983, 105, 7506-7511. (e) Carlacci, L.; Doubleday, C., Jr.; Furlani, T. R.; King, H. F.; McIver, J. W., Jr. J. Am. Chem. Soc. 1987, 109, 5323-5329. (f) Doubleday, C., Jr.; McIver, J. W., Jr.; Page, M. J. Phys. Chem. 1988, 92, 4367-4371. (39) (a) However, according to one recent ab initio study, it was found that the SO coupling constant for CH2 is calculated to be ∼10 cm-1 using the 4s3p2d1f basis set at the MCSCF level. See: Vahtras, O.; A° gren, H.; Jorgensen, P.; Jensen, H. J. Aa.; Helgaker, T.; Olsen, J. J. Chem. Phys. 1992, 96, 2118-2126. (b) Eder, T. W.; Carr, R. W. J. Chem. Phys. 1970, 53, 2258-2266. (c) Woodward, R. B.; Hoffmann, R. The ConserVation of Orbital Symmetry; Verlag Chemie: Weinheim, 1970. (d) According to a theoretical study (see ref 27d), it was proved that whenever both orbitalsymmetry and spin-inversion requirements are met along the same reaction coordinate, the reaction can be stereospecific. (40) For nonpolar solvent cases see: (a) Reference 10a. (b) Reference 12a. (c) Reference 19f. (d) Reference 16h. (e) Jones, M., Jr.; Rettig, K. R. J. Am. Chem. Soc. 1965, 87, 4013-4015. (f) Jones, M., Jr.; Kulczycki, A., Jr.; Hummel, K. F. Tetrahedron Lett. 1967, 183-187. (g) Moss, R. A.; Young, C. M. J. Am. Chem. Soc. 1983, 105, 5859-5865. (h) Jones, M., Jr.; Harrison, A. M.; Rettig, K. R. J. Am. Chem. Soc. 1969, 91, 74627466. (i) Pirkle, W. H.; Koser, G. F. Tetrahedron Lett. 1968, 3959-3962. (41) For details, see: (a) Salem, L. Acc. Chem. Res. 1979, 12, 87-92. (b) Albright, T. A.; Burdett, J. K.; Whangbo, W.-H. Orbital Interactions in Chemistry; John Wiley and Sons: New York, 1985; Chapter 10. (42) Experimentally, it is reported that a triplet ground state carbene is largely susceptible to solvent polarity, and the results are consistent with stabilization of the zwitterionic singlet state in solvents of high polarity. See: Garcia-Garibay, M. A.; Theroff, C.; Shin, S. H.; Jernelius, J. Tetrahedron Lett. 1993, 34, 8415-8418. (43) In addition, it was suggested that the triplet ground state of carbene XYC: is expected for substituents which are electropositive (with respect to carbon) and/or are bulky. This, in turn, can enhance the formation of stereoretention cyclopropanes. See: (a) Muller, P. H.; Rondan, N. G.; Houk, K. N.; Harrison, J. F.; Hooper, D.; Willen, B. H.; Liebman, J. F. J. Am. Chem. Soc. 1981, 103, 5049-5052. (b) Carter, E. A.; Goddard, W. A., III. J. Chem. Phys. 1988, 88, 1752-1763. (44) Furthermore, according to one recent ab initio study (see ref 23a), it was suggested that the triplet addition reaction would become more unfavorable as the electron-releasing character of substituents of the carbene is increased. (45) Nevertheless, there is a related theoretical study using the extended Huckel method to interpret such phenomena; see: Hoffmann, R.; Levin, C. C.; Moss, R. A. J. Am. Chem. Soc. 1973, 95, 629-631. (46) For the heavy atom effect, see: (a) Turro, N. J. Modern Molecular Photochemistry; The Benjamin/Cummings Co.: Menlo Park, CA, 1978; Chapter 6. (b) El-Sayed, M. A. Acc. Chem. Res. 1968, 1, 8-16; (c) J. Chem. Phys. 1963, 38, 2834-2838.
J. Phys. Chem., Vol. 100, No. 11, 1996 4349 (47) Other factors which are known to affect singlet-triplet intersystem crossing include the following: (1) the magnitude of the singlet-triplet energy difference between the two states; (2) the configuration of the initial and of the final states; and (3) vibronic or Franck-Condon factors. See: (a) Reference 26a. (b) Robinson, G. W.; Frosch, R. P. J. Chem. Phys. 1962, 37, 1962-1973; (c) J. Chem. Phys. 1963, 38, 1187-1203. (d) Borkman, R. F. Mol. Photochem. 1972, 4, 453-471. (48) (a) Gunning, H. E.; Strausz, O. P. AdV. Photochem. 1966, 4, 143194. (b) Sandhu, H. S.; Lown, E. M.; Strausz, O. P.; Gunning, H. E. J. Am. Chem. Soc. 1966, 88, 254-263. (c) Lown, E. M.; Dedio, E. L. J. Am. Chem. Soc. 1967, 89, 1056-1062. (49) (a) However, extended Huckel calculations suggested that triplet sulfur addition reactions are stereospecific because the reactants correlate with an excited state of the product thiirane which retains CC bonding. See: Hoffmann, R.; Wan, C. C.; Neagu, V. Mol. Phys. 1970, 19, 113120. (b) For a similar explanation based on orbital correlation diagrams and ab initio SCF study refer to refs 50 and 51, respectively. (50) Leppin, E.; Gollnick, K. Tetrahedron Lett. 1969, 3819-3824. (51) Strausz, O. P.; Gunning, H. E.; Denes, A. S.; Csizmadia, I. G. J. Am. Chem. Soc. 1972, 94, 8317-8321. (52) (a) McConaghy, J. S.; Lwowski, W. J. Am. Chem. Soc. 1967, 89, 2357-2364; (b) J. Am. Chem. Soc. 1967, 89, 4450-4456. (c) For the ab initio study, see: Fueno, T.; Bonacic-Koutecky, V.; Koutecky, J. J. Am. Chem. Soc. 1983, 105, 5547-5557. (53) (a) Cvetanovic, R. J. AdV. Photochem. 1963, 1, 115-145. (b) Cvetanovic, R. J. Phys. Chem. 1970, 74, 2730-2732. (c) Scheer, M. D.; Klein, R. J. Phys. Chem. 1970, 74, 2732-2733. (d) Huie, R. E.; Herron, J. T. Prog. React. Kinet. 1975, 8, 1-17. (54) Mcbee, E. T.; Sienkowski, K. J. J. Org. Chem. 1973, 38, 13401344. (55) (a) Blomstrom, D. C.; Herbig, K.; Simmons, H. E. J. Org. Chem. 1965, 30, 959-964. (b) Kopecky, K. R.; Hammond, G. S.; Leermaakers, P. A. J. Am. Chem. Soc. 1962, 84, 1015-1019. (c) Wittig, G.; Wingler, F. Chem. Ber. 1964, 97, 2139-2145; (d) 1964, 97, 2146-2164. (56) (a) Simmons, H. E.; Smith, R. D. J. Am. Chem. Soc. 1958, 80, 5323-5324; (b) 1959, 81, 4256-4264. (c) Blanchard, E. P.; Simmons, H. E. J. Am. Chem. Soc. 1964, 86, 1337-1346. (d) Simmons, H. E.; Blanchard, E. P.; Smith, R. D. J. Am. Chem. Soc. 1964, 86, 1347-1356. (e) Skell, P. S.; Valenty, S. J.; Humer, P. W. J. Am. Chem. Soc. 1973, 95, 5041-5043. (57) (a) Friedman, L.; Berger, J. D. J. Am. Chem. Soc. 1961, 83, 492493. (b) Doering, W. v. E.; Roth, W. Tetrahedron 1963, 19, 715-723. (c) Reference 1c, p 184. (58) However, there are some questions as to whether the cyclopropanes are formed by addition of free methylene or whether some other intermediates, such as an excited methylene iodide or iodomethyl radical, is involved in the methylene transfer reaction. Nevertheless, one may expect that the presence of methylene iodide and iodine in solution would considerably enhance spin relaxation (heavy atom effect). (59) It must be emphasized that those spin-inversion mechanisms suggested in this work (case A-case D) and their associated interpretations were derived first and justified by Shaik and Epiotis in ref 27b,c. The author wishes to thank professor Sason Shaik for pointing out this important fact.
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