A Computational Study of the Mechanisms of the Photoisomerization

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A Computational Study of the Mechanisms of the Photoisomerization Reactions of Monocyclic and Bicyclic Olefins Ming-Der Su* Department of Applied Chemistry, National Chiayi University, Chiayi 60004, Taiwan

bS Supporting Information ABSTRACT: The mechanisms of the photochemical isomerization reactions were investigated theoretically using a model system of cyclohexene (1), cycloheptene (2), norbornene (3), and two bicyclic olefins (4 and 5) using the CASSCF (six-electron/six-orbital active space) and MP2-CAS methods with the 6-311(d,p) basis set. The structures of the conical intersections, which play a decisive role in such photoisomerizations, were obtained. The intermediates and transition structures of the ground state were also calculated to assist in providing a qualitative explanation of the reaction pathways. Two photoreaction pathways were examined in the present work. The first can produce a photoproduct with an extra ring. The other can yield a photoproduct with a smaller ring with an external double bond. Both pathways involve cyclic carbene intermediates. Also, our model investigations suggest that both reaction pathways follow a similar photochemical pattern as follows: reactant f Franck
Condon region f conical intersection f cyclic carbene intermediate f transition state f photoproduct. Moreover, these two reaction pathways can compete with each other since the energetics of their conical intersection points are quite similar. Our present theoretical results agree with the available experimental observations.

I. INTRODUCTION The photochemistry of alkenes has been the subject of extensive experimental as well as theoretical studies over the past 50 years.1 From the large body of experimental evidence, it is clear that the photoisomerization of simple alkenes upon direct excitation is often a complex process. For instance, cis
trans isomerization,1b [1,3]-hydrogen migration,1b unimolecular dehydrogenation,2 and hydrogen atom abstraction3 are common alkene photoreactions that have been identified as π, π* reactions. In 1978, Srinivasan and Brown observed that the photochemistry of cycloalkene in solution illustrates the general photochemical behavior of cyclic alkenes as well as the nature of the carbene or carbene-like intermediates that are involved;4 see Table 1. That is, the simple cyclic alkenes display a competing type of behavior as exemplified by the isomerization of cyclic olefin to a mixture of multicycloalkane and positional isomer with an external double bond. It is these fascinating experimental results that have inspired this study. As far as we are aware, no theoretical study of such photoisomerization reactions involving disubstituted cyclic olefins has yet been reported. Since the photoreactions of cyclic olefins are both novel and useful, a detailed understanding of their reaction mechanisms would allow more control over their reactivity. In fact, a detailed understanding of disubstituted cycloalkene reaction mechanisms is of r 2011 American Chemical Society

interest not only for the advancement of basic science but also for the continued development of their synthetic chemistry. We have thus undertaken an investigation of the potential energy surfaces of disubstituted cycloalkene systems. It is surprising how little is known about the mechanisms of photoisomerizations of cyclic olefins considering the importance of alkenes in synthetic chemistry and the extensive research activity on the alkene species.1
4 A theoretical study of the photoisomerizations of both monocyclic (1 and 2) and bicyclic (3
5) olefins was thus undertaken. These were chosen as model systems because experimental studies were available for comparison.4 In the following sections, we describe the method and present the results for the phototransposition reactions of such cyclic alkenes in detail. Conical intersection (CI) regions 5 on the potential surface, where decay to the ground-state surface can occur, have been located, and ground-state reaction paths leading from these conical intersections to a variety of products have been identified. On the basis of this information, the reaction process is explained. It will be shown below that the conical intersections 5 play a crucial role in the photoisomerization reactions of disubstituted cycloalkenes. 6,7 Received: October 5, 2010 Revised: March 30, 2011 Published: May 03, 2011 5157

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The Journal of Physical Chemistry A Table 1. Photochemical Reactants (1
5) and Products (φ = Quantum Yields) from Some Cyclicolefins at 185 nma

a

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Scheme 1

See ref 4.

II. METHOLOGY All geometries were fully optimized without imposing any symmetry constraints, although in some instances, the resulting structures show various elements of symmetry. The CASSCF calculations were performed using the MCSCF program released in GAUSSIAN 03.8 The active space for describing the photorearrangements of cyclic alkenes comprises six electrons in six orbitals, that is, two p
π orbitals plus two σ(C
C) and σ*(C
C) orbitals. The CASSCF method was used with the 6-311G(d) basis sets for geometry optimization (vide infra). The optimization of conical intersections was achieved in the (f-2)-dimensional intersection space using the method of Bearpark et al.9 implemented in the GAUSSIAN 03 program. Every stationary point was characterized by its harmonic frequencies computed analytidcally at the CASSCF level. Localization of the minima, transition states, and conical intersection minima has been performed using Cartesian coordinates; therefore, the results are independent of any specific choice of internal variables. To correct the energetics for dynamic electron correlation, we have used the multireference Møller
Plesset algorithm10 as implemented in the program package GAUSSIAN 03. Unless otherwise noted, the relative energies given in the text are those determined at the MP2-CAS-(6,6)/6-311G(d,p) level using the CAS(6,6)/6-311G(d) (hereafter designed MP2-CAS and CASSCF, respectively) geometry. III. GENERAL CONSIDERATIONS Since the photoisomerization process is general for most disubstituted cycloalkenes on direct irradiation as demonstrated

in Table 1, it is thus possible to construct a certain consistency in these reactions, which at least serves as a basis for discussion. In this section, we describe possible excited-state reaction paths that lead to conical intersections. A schematic representation of the relationships between the intersections and possible reaction routes is shown in Scheme 1. As one can see in Scheme 1, in the case of the singlet photochemistry of disubstituted cyclic olefin (Table 1), 4 the most reasonable pathways for the conversion of reactant to multicycloalkane (Pro-A) and to isomer (Pro-B) are route A and route B, respectively. That is to say, route A involves ring-closure of the disubstituted cyclic alkene to form a cyclocarbene intermediate (Int-A) followed by hydrogen migration (TS-A) to form the multicycloalkane species (Pro-A). In this route, a cyclic photoproduct with an added hydrocarbon ring is formed; see route A in Scheme 1. On the other hand, the experimental facts strongly imply the existence of another cyclocarbene intermediate (Int-B), which is formed by an initial migration of an intramolecular C
C bond followed by the migration of a C
H bond (TS-B) to yield a cycloalkene with an external double bond (Pro-B). In this route, the cyclic photoproduct formed contains ones less carbon atom than the reactant; see route B in Scheme 1. We shall use the above mechanisms to help locate the funnel from the excited-state surface to the ground-state 5158

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Figure 1. Energy profiles for the photoisomerization modes of cyclohexene (1). The abbreviations FC and CI stand for Frank
Condon and conical intersection, respectively. The relative energies were obtained at the MP2-CAS-(6,6)/6-311G(d,p)//CAS(6,6)/6-311G(d) and CAS(6,6)/6-311G(d) (in parentheses) levels of theory. All energies (in kcal/mol) are given with respect to the reactant (1). For the CASSCF optimized structures of the crucial points, see Figure 2. For more information, see the text.

surface that corresponds to a conical intersection in the following section.7,11

IV. RESULTS AND DISCUSSION As mentioned previously (see Scheme 1), two minimumenergy pathways on the singlet excited potential energy surface of the disubstituted cyclic olefin were characterized by optimizing the geometries along the C
H coordinate (route A) and the C
C coordinate (route B) leading to the photoproducts Pro-A (multicycloalkane) and Pro-B (a cyclic olefin), respectively, as stated in Scheme 1. To understand the difference between the two reaction paths (routes A and B), it is best to start the discussion with the reaction profiles as summarized in Figure 1, which also contains the relative energies of the crucial points with respect to the groundstate minimum cyclohexene (1). Selected optimized geometrical parameters for the stationary points and conical intersections are collected in Figure 2, and their corresponding energies are given in Table 2. Nevertheless, because of the similarities of the photoreaction pathways in the chosen reactant species (1
5), we shall only discuss the photoreaction mechanisms of cyclohexene (1). The other potential energy surfaces for reactants 2
5 are represented in Figures 3
10. Their corresponding energetics and the Cartesian coordinates calculated at the CASSCF/6-311G(d) level are collected in the Supporting Information.

Figure 2. The CAS(6,6)/6-311G(d) geometries (in Å and deg) for path 1 and path 2 of cyclohexene (1), conical intersection (CI), intermediate (Int), transition state (TS), and isomer products. The derivative coupling and gradient difference vectors, those which lift the degeneracy, are computed with CASSCF at the conical intersections CI-1 and CI-2. The corresponding CASSCF vectors are shown inset. Also, the heavy arrows indicate the main atomic motions in the transition-state eigenvector. For more information, see the Supporting Information.

In the first step, the reactant (cyclohexene) is promoted to its excited singlet state by a vertical excitation as shown in the left-hand side of Figure 1. After the vertical excitation process, the molecule is situated on the excited singlet surface but still possesses the S0 (ground-state) geometry.12 From the point reached by the vertical excitation (FC-1), the molecule relaxes to reach an S1/S0 CI where the photoexcited system decays nonradiatively to S0. Namely, the photochemically active relaxation path starting from the S1 1(π1 f π2*) excited state of cyclohexene leads either to S1/S0 CI-1 (path 1) or CI2 (path 2) both of which are shown in Figure 2. Remarkably, the computed vertical excitation energy (156 kcal/mol) to the lowest excited π* state of 1 is in good agreement with the experimental irradiation of 185 nm (=155 kcal/mol) light to 1. Accordingly, our computational results confirm the experimental observations4 that the only excited state involved in the photorearrangement of cyclohexene (1) is the singlet (π, π*). 5159

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Table 2. Energies (in kcal/mol) of 1 for the Critical Points Located along Paths 1 and 2 at the MP2-CAS(6,6)/6-311G(d, p)//CASSCF(6,6)/6-311G(d) and CASSCF(6,6)/6-311G(d) (in Parentheses) Levels a structure

a

state

ΔErelb

1

S0

0.0 (0.0)

FC-1

S1

155.6 (172.8)

CI-1

S1/S0

122.3 (119.0)

Int-1

S0

73.01 (70.19)

TS-1

S0

97.54 (93.18)

TS-10

S0

93.57 (95.22)

Pro-1 CI-2

S0 S1/S0

Int-2

S0

TS-2

S0

TS-20

S0

Pro-2

S0

13.28 (19.68) 121.3 (118.1) 85.46 (80.75) 100.9 (87.04) 99.72 (96.74) 3.251 (4.670)

See Figures 1 and 2. b Energy relative to 1.

Figure 4. The CAS(6,6)/6-311G(d) geometries (in Å and deg) for path 3 and path 4 of cycloheptene (2), conical intersection (CI), intermediate (Int), transition state (TS), and isomer products. The derivative coupling and gradient difference vectors, those which lift the degeneracy, computed with CASSCF at the conical intersections CI-3 and CI-4. The corresponding CASSCF vectors are shown the inset. Also, the heavy arrows indicate the main atomic motions in the transition-state eigenvector. For more information, see the Supporting Information.

Figure 3. Energy profiles for the photoisomerization modes of cycloheptene (2). The abbreviations FC and CI stand for Frank
Condon and conical intersection, respectively. The relative energies were obtained at the MP2-CAS-(6,6)/6-311G(d,p)//CAS(6,6)/6-311G(d) and CAS(6,6)/6-311G(d) (in parentheses) levels of theory. All energies (in kcal/mol) are given with respect to the reactant (2). For the CASSCF optimized structures of the crucial points, see Figure 4. For more information, see the text.

We next investigate the relaxation on the excited-state potential surface. On the basis of the earlier prediction, we

searched for a conical crossing point between S0 and S1 surfaces for the two reaction pathways (path 1 and path 2). For path 1, the geometry at the conical intersection S1/S0 CI-1 of C1 symmetry is given in Figure 2. Our theoretical findings suggest that S1/S0 CI-1 is 34 kcal/mol lower in energy than FC-1 at the MP2-CAS level of theory. The main difference between cyclohexene (1) and S1/S0 CI-1, apart from the nonplanar conformation, is found to be the C1dC2 distance which is shorter in cyclohexene (1.339 Å) compared to 1.441 Å in S1/S0 CI-1. In Figure 2, we also give the directions of the derivative coupling and gradient difference vectors for the S1/S0 CI-1 conical intersection. As a result, funneling through the S1/S0 CI-1 conical intersection may lead to two different ground-state reaction pathways via either the derivative coupling vector or the gradient difference vector direction.5 Any linear combination of these vectors causes the degeneracy to be lifted, and therefore, these vectors give an indication of possible reaction pathways available on the ground-state surface after decay. As demonstrated in Figure 2, 5160

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Figure 5. Energy profiles for the photoisomerization modes of norbornene (3). The abbreviations FC and CI stand for Frank
Condon and conical intersection, respectively. The relative energies were obtained at the MP2-CAS-(6,6)/6-311G(d,p)//CAS(6,6)/6-311G(d) and CAS(6,6)/6-311G(d) (in parentheses) levels of theory. All energies (in kcal/mol) are given with respect to the reactant (3). For the CASSCF optimized structures of the crucial points, see Figure 6. For more information, see the text.

the major contribution of the derivative coupling vector involves the C1dC2 double bond expanding, while the gradient difference vector corresponds to the concerted C
H bond-stretching motion. Following the gradient difference vector from S1/S0 CI-1 (Figure 2) is the formation of a carbene-like isomer Int-1. This intermediate is nonplanar with the C1—C2 and C2—C3 bonds being 1.501 and 1.501 Å long, respectively. Then, a [1,3] hydrogen migration with formation of an intramolecular C1—C3 bond can take place via transition state (TS-1) to give the photoproduct Pro-1. Also, this ground-state Int-1 species can revert to the starting molecule 1 via the transition state (TS-10 ) in a thermal process as illustrated in Figure 1. The optimized transition-state structure (TS-1) along with the calculated transition vectors are shown in Figure 2. The heavy arrows in this figure indicate the directions in which the atoms move in the normal coordinate corresponding to the imaginary frequency. Examination of the single imaginary frequency for this transition state (811i cm
1) provides excellent confirmation of the above reaction processes. Moreover, as one may see in Figure 2, this Pro-1 molecule has a nonplanar bicyclic conformation, and its energy lies above the corresponding reactant by 13 kcal/mol. On the other hand, the dark reaction on the ground-state potential energy surface is also examined. Although photoexcitation raises cyclohexene (1) into an excited electronic state, the products of the photochemical process are

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Figure 6. The CAS(6,6)/6-311G(d) geometries (in Å and deg) for path 5 and path 6 of norbornene (3), conical intersection (CI), intermediate (Int), transition state (TS), and isomer products. The derivative coupling and gradient difference vectors, those which lift the degeneracy, computed with CASSCF at the conical intersections CI-5 and CI-6. The corresponding CASSCF vectors are shown inset. Also, the heavy arrows indicate the main atomic motions in the transition-state eigenvector. For more information, see the Supporting Information.

controlled by the ground-state (thermal) potential energy surface.5 We also successfully searched for a transition state (TS-10 .) on the S0 surface located near the structure CI-1. As shown in Figure 1, the energy of TS-10 connecting 1 and Int-1 on the S0 surface lies 28 kcal/mol below the energy of S1/S0 CI-1. Therefore, the new ground-state Int-1 species can revert to the starting molecule 1 in a thermal process on the ground state as given in Figure 1. In consequence, our computational results suggest that the mechanism for path 1 should proceed as follows:

The photoisomerization of cyclohexene (1) as described in path 2 is also examined. From Figure 2, one may foresee that the other carbene-like species (Int-2) should play a key role in the photorearrangement reactions of 1. Indeed, along the 5161

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Figure 7. Energy profiles for the photoisomerization modes of bicyclic olefin (4). The abbreviations FC and CI stand for Frank
Condon and conical intersection, respectively. The relative energies were obtained at the MP2-CAS-(6,6)/6-311G(d,p)//CAS(6,6)/6-311G(d) and CAS(6,6)/6-311G(d) (in parentheses) levels of theory. All energies (in kcal/mol) are given with respect to the reactant (4). For the CASSCF optimized structures of the crucial points, see Figure 8. For more information, see the text.

C2---C3 stretching reaction path, a conical intersection, S1/S0 CI-2, is obtained at the — C2C1C3 bond angle of 116. Our computational results predict that the energy of CI-2 lies 121 kcal/mol above 1 and 35 kcal/mol below FC-1. Funneling through the conical intersection, different reaction pathways on the ground-state surface may be predicted by following the derivative coupling vector or the gradient difference vector direction.5 According to the results demonstrated in Figure 2, examination of these two vectors for CI-2 provides important information about the photoisomerization process (path 2) of 1: the derivative coupling vector is mainly related to the C2--C3 stretching mode that gives a carbene-like intermediate (Int-2) on the S0 surface, whereas the gradient difference vector relates to the asymmetric C1C2H bending motion that leads to a vibrationally hot 1-S0 species. From Int-2, isomerization can take place in two directions: either via a C
H bond insertion to produce the five-membered ring photoproduct Pro-2 via transition-state TS-2 or by reverting to the initial reactant (1) via another transition state (TS-20 ). Our calculations indicate that the transition-state TS-2 is characterized by one imaginary frequency of 1183i cm
1. The normal coordinate corresponding to the imaginary frequency is primarily located at the C
H bond cleavage. Accordingly, our

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Figure 8. The CAS(6,6)/6-311G(d) geometries (in Å and deg) for path 7 and path 8 of bicyclic olefin (4), conical intersection (CI), intermediate (Int), transition state (TS), and isomer products. The derivative coupling and gradient difference vectors, those which lift the degeneracy, computed with CASSCF at the conical intersections CI-7 and CI-8. The corresponding CASSCF vectors are shown inset. Also, the heavy arrows indicate the main atomic motions in the transition-state eigenvector. For more information, see the Supporting Information.

theoretical investigations suggest that path 2 can proceed as follows:

Besides this, as can be seen in Figure 1 and Table 2, the theoretical results indicate that the relative energetics of the critical points of path 1 are 156, 122, 73.0, 97.5, 93.6, and 13.3 kcal/mol for FC-1, S1/S0 CI-1, Int-1, TS-1, TS-10 , and Pro-1, respectively, with respect to 1. Similarly, the relative energetics of the critical points of path 2 are 156, 121, 85.5, 101, 99.7, and 3.25 kcal/mol for FC-1, S1/S0 CI-2, Int-2, TS-2, TS-20 , and Pro-2, respectively, with respect to 1. Furthermore, our CAS-MP2 calculations demonstrate that the isomerization barriers for paths 1 and 2 are about 24.5 and 15.5 kcal/mol higher in energy than the intermediates Int-1 and Int-2. Accordingly, because of the high excess energy of 34 and 35 kcal/mol resulting from the relaxation from FC-1 to CI-1 and to CI-2, the barrier 5162

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Figure 9. Energy profiles for the photoisomerization modes of bicyclic olefin (5). The abbreviations FC and CI stand for Frank
Condon and conical intersection, respectively. The relative energies were obtained at the MP2-CAS-(6,6)/6-311G(d,p)//CAS(6,6)/6-311G(d) and CAS(6,6)/6-311G(d) (in parentheses) levels of theory. All energies (in kcal/mol) are given with respect to the reactant (5). For the CASSCF optimized structures of the crucial points, see Figure 10. For more information, see the text.

heights of TS-1 (or TS-10 ) and TS-2 (or TS-20 ) can easily be overcome. This strongly implies that both cyclic carbene intermediates (Int-1 and Int-2) are kinetically unstable and will rearrange spontaneously to give the more stable photoisomers Pro-1 and Pro-2 as well as the initial reactant 1.5 This is what we observed in the cyclohexene (1) system, which is in good agreement with the experimental observations as illustrated in Table 1.4 As mentioned earlier, the other reactant species (2
5) also adopt the same two photoreaction pathways. Namely, one is the formation of a cyclic carbene which subsequently rearranges by a hydrogen migration to produce a photoproduct with an extra ring (i.e., route A). The other is formation of a cyclic carbene, which subsequently isomerizes by a hydrogen shift to yield a photoproduct with a smaller ring and a double bond external to this ring (i.e., route B). Their photochemically potential energy surfaces and optimized geometrical structures are given in Figures 3
10. Also, the corresponding energetics are depicted in Tables 3
6 in the Supporting Information, respectively. As can be seen in Figures 3
10, they all have similar photoisomerization reaction patterns. Again, as shown in the figures and tables, all these theoretical findings are in accordance with the experimental observations.4

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Figure 10. The CAS(6,6)/6-311G(d) geometries (in Å and deg) for path 9 and path 10 of bicyclic olefin (5), conical intersection (CI), intermediate (Int), transition state (TS), and isomer products. The derivative coupling and gradient difference vectors, those which lift the degeneracy, computed with CASSCF at the conical intersections CI-9 and CI-10. The corresponding CASSCF vectors are shown inset. Also, the heavy arrows indicate the main atomic motions in the transition-state eigenvector. For more information, see the Supporting Information.

VI. CONCLUSION The photochemical reaction pathways of cyclic olefin species (1
5) were investigated by ab initio calculations at the CAS(6,6)/6-311G(d) and MP2-CAS(6,6)/6-311G(d,p)//CAS(6,6)/ 6-311G(d) levels of theory. In the present work, two reaction pathways, route A and route B, were also examined theoretically. Taking all the systems studied in this paper together, one can draw the following conclusions: (1) Our theoretical investigations present the first theoretical evidence that the photoisomerization reactions of such monocyclic and bicyclic olefins undergo the conical intersection mechanisms. Knowledge of the conical intersection of the cyclic alkene species is of great importance in understanding its reaction mechanism since it can affect the driving force for photochemistry. For instance, cyclohexene (1) is vertically excited to the S1 state. Then, radiationless decay from S1 to S0 occurs via two conical intersections (CI-1 and CI-2), which results in cyclic carbene intermediates (Int-1 and Int-2, respectively). 5163

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The Journal of Physical Chemistry A Starting from these conical intersections, the products of the photoisomerizations as well as the initial reactant can be reached on barrierless relaxation paths. As a result, these findings, on the basis of the conical intersection viewpoint, have helped us to better understand the photochemical reactions and to support the experimental observations.4 (2) It has been generally assumed in the past that the photoisomerizations of cyclic olefins have involved cyclic carbene intermediates.4 Our theoretical calculations demonstrate that these carbene mechanisms all involve a chemical bond migration (either C
H bond or C
C bond) to form the cyclic carbene intermediates. They are then followed by a [1,3] or [1,2] hydrogen shift to reach the final photoproducts (Pro-1 or Pro-2) Again, our model investigations confirm the photoreaction patterns proposed previously.4 Moreover, our theoretical investigations suggest that for cyclic olefin species (1
5) these two reaction pathways should compete with each other since the energetics for both conical intersection points (CI-A and CI
B) are quite similar.13 After this paper had been submitted, one reviewer suggested that relative yields of various products could be computed using a Rice
Ramsperger
Kassel
Marcus (RRKM)-type statistical theory approach. Thus, the RRKM and microcanonical vibrational transition-state theories14 have been applied to study the present systems. However, because of a multideterminant character of the wave functions, it is impossible to obtain the reaction rates of conical intersections at present theoretical level of theory. Nevertheless, the photoexcited reactants can go through the conical intersections to obtain the final photoisomerization products, which can be reached on ground-state pathways. As discussed previously, for example, the critical transition states on 1 are TS-1 (path 1) and TS-2 (Path 2). Rate constants corresponding to these transition states are 5.3  105 and 3.1  105 s
1 in the forward directions and 3.7  104 and 2.2  104 s
1 in the reverse directions, respectively. As a result, the total rate constants of cyclohexene (1) isomerization reaction are 8.4  105 and 5.9  104 s
1 in the forward and reverse directions, respectively. According to these results, the major isomerization channel is path 1 that provides φ = 0.07 product Pro-1. These theoretical results are in reasonable agreement with available experimental observations as already shown in Table 1.4 Again, these theoretical findings suggest that the conical intersections play a crucial role in such photochemical isomerization reactions. It is hoped that the present work will stimulate a further research into this subject.

’ ASSOCIATED CONTENT

bS

Supporting Information. The CAS(6,6)/6-311G(d) optimized geometries and MP2-CAS-(6,6)/6-311G(d,p)//CAS(6,6)/6-311G(d) energies. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The author is grateful to the National Center for HighPerformance Computing of Taiwan for generous amounts of

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computing time and the National Science Council of Taiwan for the financial support. The author also wishes to thank Professor Michael A. Robb, Dr. S. Wilsey, Dr. Michael J. Bearpark (University of London), and Professor Massimo Olivucci (Universita degli Studi di Siena, Italy) for their encouragement and support during his stay in London. The author would like to thank Dr. J.-H. Sheu for the computer assistance. Special thanks are also due to referees 1 and 2 for very helpful suggestions and comments.

’ REFERENCES (1) For reviews, see (a) Griffin, G. W. Angew. Chem., Int. Ed. Engl. 1971, 10, 537. (b) Kropp, P. J. In Organic Photochemistry; Padwa, A., Ed.; Marcel Dekker: New York, 1979; Vol. 4, p 1. (c) Hixson, S. S. In Organic Photochemistry; Padwa, A., Ed.; Marcel Dekker: New York, 1979; Vol. 4, p 191. (d) Leigh, W. J.; Srinivasan, R. Acc. Chem. Res. 1987 , 20, 107 and references therein. (e) Arai, T.; Tokumaru, K. Chem. Rev. 1993, 93, 23. (f) Leigh, W. J. Chem. Rev. 1993, 93, 487 and references therein. (g) Flynn, A. B.; Ogilvie, W. Chem. Rev. 2007, 107, 4698. (2) Leigh, W. J.; Srinivasan, R. J. Am. Chem. Soc. 1987, 104, 4424. (3) Inoue, Y.; Mukai, T.; Hakushi, T. Chem. Lett. 1982, 1045. (4) Srinivasan, R.; Brown, K. H. J. Am. Chem. Soc. 1978, 100, 4602. (5) (a) Bernardi, F.; Olivucci, M.; Robb, M. A. Isr. J. Chem. 1993, 265. (b) Klessinger, M. Angew. Chem., Int. Ed. Engl. 1995, 34, 549. (c) Bernardi, F.; Olivucci, M.; Robb, M. A. Chem. Soc. Rev. 1996, 321. (d) Bernardi, F.; Olivucci, M.; Robb, M. A. J. Photochem. Photobiol., A: Chem. 1997, 105, 365. (e) Klessinger, M. Pure Appl. Chem. 1997, 69, 773. (f) Klessinger, M.; Michl, J. In Excited States and Photochemistry of Organic Molecules; VCH Publishers: New York, 1995. (6) For recently related studies on the photoisomerization of cyclohexene, see Wilsey, S.; Houk, K. N. J. Am. Chem. Soc. 2002, 124, 11182. (7) Recently, it has been shown clearly that the stereochemical outcome of the photoreactions cannot be interpreted in terms of bicyclic minima and excimer minima and the barriers between them. Instead, the main feature of many photoreactions is the existence of a real conical intersection. That is to say, most photochemical reactions of molecules start on an excited electronic potential surface but cross over to a lower potential energy surface somewhere along the reaction pathway. They finally reach the ground-state surface by a sequence of radiationless transitions (i.e., conical intersections) and move on the ground-state surface toward the product. This mechanism is not controlled by the avoided surface crossing and the resulting energy gap between ground and excited state but rather by the presence of minima and transition states on ground- and excited-state surfaces themselves. Furthermore, the existence of a conical intersection region provides access to many ground-state pathways that can lead to different photoproducts. This has already been both experimentally and theoretically proved to be a general feature of the excited states relevant to photochemical reactions. For details, see refs 5 and 6. (8) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, , G.; Liashenko, , A.; Piskorz, A.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S. Pople, J. A. Gaussian, Inc.: Pittsburgh, PA, 2003. (9) Bearpark, M. J.; Robb, M. A.; Schlegel, H. B. Chem. Phys. Lett. 1994, 223, 269. (10) McDouall, J. J. W.; Peasley, K.; Robb, M. A. Chem. Phys. Lett. 1988, 148, 183. 5164

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(11) We thank one reviewer for suggesting a reference book, see Kirmse, W. Carbene Chemistry; Academic Press: New York, 1964; p 56. (12) (a) The S1 excited state created by direct excitation of a cyclohexene is a vertical state with the same geometry as the groundstate (S0) molecule. (b) An excited state with geometry identical to the ground state is sometimes called a Franck
Condon (FC) state. (13) One reviewer pointed out that the photochemical mechanisms we found theoretically could be somewhat different from those proposed by the available experimental work. However, the experimental group assumed two hypothetical mechanisms (Schemes I and II in ref 4) to explain their findings without further experimental detections and data. That is, the experimentalists did not have solid supporting evidence for these proposed mechanisms. The mechanisms they proposed could be inaccurate (ref 4) considering the great technical difficulties involved in making such a measurement for photochemically labile molecules and should be reexamined carefully and thoroughly. Moreover, the dynamic factor will be considered to determine how the efficiency of two reactions associated with wavelengths of excitation (such as one-photo vs two-photo process) is different. It is quite dangerous to draw a final conclusion on the basis of so far available experimental findings. We thus use the conical intersection mechanisms to interpret and rationalize such experimental results in this work. At least, our approach can provide chemists with important insights into the mechanisms controlling these photochemical reactions and thus permit them to predict the results of some unknown both monocyclic and bicyclic olefin species. The predictions may be useful as a guide to future synthetic efforts and to indicate problems that merit further study by both theory and experiment. (14) (a) Eyring, H.; Lin, S. H.; Lin, S. M. Basic Chemical Kinetics; Wiley: New York, 1980. (b) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics; Prentice Hall: Upper Saddle River, NJ, 1999. (c) Kislov, V. V.; Nguyen, T. L.; Mebel, A. M.; Lin, S. H.; Smith, S. C. J. Chem. Phys. 2004, 120, 7008.

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