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A theoretical study on the mechanism of cycloaddition reaction between vinylidene and acetone
Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44 www.elsevier.com/locate/theochem
A theoretical study on the mechanism of cycloaddition reaction between vinylidene and acetone Xiuhui Lu*, Weirong Wu, Haibin Yu, Xiuli Yang, Yuehua Xu School of Chemistry and Chemical Engineering, Jinan University, Jinan, Shandong 250022, People’s Republic of China Received 8 April 2005; revised 23 July 2005; accepted 23 July 2005 Available online 10 October 2005
Abstract Mechanisms of cycloaddition reaction between singlet vinylidene and acetone have been investigated with MP2/6-31G* method. Energies for the involved conformations are further improved using CCSD(T)//MP2/6-31G* and MP2/6-311G**//6-31G* for the geometries optimized with MP2/6-31G* method. On the basis of the potential energy surface profile, it can be predicted that the dominant reaction pathway for the reaction consists of three steps: (1) the two reactants firstly form an active four-membered ring intermediate, INT2, which is a barrier-free exothermic reaction, DEZK81.6 kJ/mol (K95.0 kJ/mol, MP2/6-311G**//6-31G*); (2) the intermediate INT2 further reacts with acetone to form a polycyclic intermediate, INT3, through a barrier-free exothermic reaction, DEZK31.0 kJ/mol (K32.3 kJ/mol, MP2/6-311G**//6-31G*); (3) INT3 isomerizes to a polycyclic product P3 via a transition state TS3 with an energy barrier of 25.1 kJ/mol (21.2 kJ/mol, MP2/6-311G**//6-31G*). q 2005 Elsevier B.V. All rights reserved. Keywords: Vinylidene; Cycloaddition reaction; Potential energy surface; CCSD(T)//MP2/6-31G* method
1. Introduction Since unsaturated carbenes were recognized as active intermediates in 1960s, they have not only attracted much attention from theoretical chemist, also been practically applied to organic chemistry [1,2]. For example, they provide simple and direct synthesis for small-ring, highly strained compounds, as well as those that are hardly synthesized through conventional ways [2–5]. Apeloig and Fox et al. [6,7] have studied the stereoselectivity of substituting group in the products of the vinylidene addition to olefins using experimental and theoretical methods, as well as the rearrangement reaction of vinylidene [8,9]. We have investigated mechanisms of cycloaddition reaction between dichloro-vinylidene and ethylene [10]. But, compared with the study on saturated carbenes, the study on unsaturated carbene has just begun and is a new branch of carbene chemistry. For mechanisms * Corresponding author. Tel.: C86 5312 769853; fax: C86 5312 769853. E-mail address: [email protected] (X. Lu).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.07.019
of cycloaddition reaction, which are quite difficult to investigate directly using experimental methods due to the active character of unsaturated carbene, the theoretical study is proved to be very useful. In order to explore the rules of cycloaddition reaction between unsaturated carbene and the asymmetric p-bonded compound, vinylidene and acetone were selected as model molecules. The cycloaddition reaction mechanism was investigated and analyzed theoretically. The results show that the cycloaddition reaction between vinylidene and acetone proceeds in the following three possible pathways:
ð1Þ
ð2Þ
ð3Þ
40
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44
2. Calculation methods MP2/6-31G* [11] implemented in the Gaussion98 package is employed to locate all the stationary points along the reaction pathways. Full optimization and vibrational analysis are done for the stationary points on the reaction profile. Zero point energy, CCSD(T)//MP2/6-31G* and MP2/ 6-311G**//6-31G* corrections are included for the energy calculations. In order to explicitly establish the relevant species, the intrinsic reaction coordinate (IRC) [12,13] is also carried out for all the transition states appearing on the cycloaddition energy surface profile. 3. Results and discussions 3.1. Reaction 1: the pathways forming the three-membered ring product Theoretical calculations indicate that the ground state of vinylidene is a singlet [14] state. The geometric parameters
for the intermediates (INT1a, INT1b), transition states (TS1a, TS1b) and product P1 are given in Fig. 1. The energies of the different conformations are listed in Table 1. The potential energy surfaces for the reaction path are given in Fig. 2. The unique imaginary frequencies of the transition states TS1a and TS1b are 385.1i and 524.6i, respectively. IRC calculations of TS1a and TS1b, indicate that TS1a connects INT1a with P1, and that TS1b connects INT1b with P1. According to Fig. 2, it can be directly seen that reaction 1 has two path ways, a and b, each of which consists of two steps: the first one is that the two reactants (R1, R2) form the intermediates INT1a and INT1b, respectively, in which the two reactions are both barrier-free exothermic reactions with energy decreases of 15.6 and 16.9 kJ/mol (16.2 and 17.7 kJ/mol, MP2/6-311G**//6-31G*), respectively; the intermediates INT1a and INT1b then isomerize to the three-membered ring product P1 via transition states TS1a and TS1b, in which energy barriers are 32.7 H(1)
H(1) 1.088 120.5 C(1) 1.308 C(2) 119.5 1.087 89.7 H(2)
H(1)
1.092 C(1)
111.7
129.5
1.319 C(2)
H(2) 1.0822 C(1) 1.0834 119.9 120.9 1.327
1.081 H(2)
95.0
C(2) 138.7 2.900
2.218
121.6 1.510 C(3) 79.9 Me(2) O 121.6 1.231 Me(1) 1.510 C(1)C(2)OC(3)= 179.9 H(1)C(1)C(2)O= -180. 0 H(2)C(1)C(2)O= 0.0 Me(1)C(3)OC(2)= - 88.9 Me(2)C(3)OC(2)= 88.9
120.5 C(3) 66.6 O 1.256 1.511 120.6 Me(2) Me(1) 1.511 C(1)C(2)OC(3)=180.0 H(1)C(1)C(2)O= -180.0 H(2)C(1)C(2)O= 0.0 Me(1)C(3)OC(2)= -9 8.8 Me(2)C(3)OC(2)=98.9
INT1a
1.371
1.505 Me(2) Me(1)
113.5 1.505
1.101 H(1)
P1 H(2) 1.089
1.088 C(1) 108.6 H(1) 137.1 1.348 123.6
H(1)
1.088 120.5 1.309 C(1)
H(2)
R1 1.676
102.8 C(3) 1.231 O 121.0 1.512 C(1)C(2)OC(3)= -0 .2 Me(1) H(1)C(1)C(2)O= 0.0 H(2)C(1)C(2)O= -18 0.0 Me(1)C(3)OC(2)=179 .6 Me(2)C(3)OC(2)= -0 .4
INT1b
C(2)
C(2)
3.734 Me(2) 1.511 122.4
O
1.512
C(1)C(2)OC(3)=180.0 H(1)C(1)C(2)O=180.0 H(2)C(1)C(2)O=0.1 Me(1)C(3)OC(2)= -111.6 Me(2)C(3)OC(2)=111.6
TS1a C(2) 1.302 H(2) 130.1 1.083 76.5 109.7 C(1)
59.6
113.5 C(3)
94.1 120.1 C(3) 1.493 O 1.282 Me(2) 120.1 Me(1) 1.493 C(1)C(2)OC(3)= 0.0 H(1)C(1)C(2)O= 0.0 H(2)C(1)C(2)O= -180.0 Me(1)C(3)OC(2)= -92.5 Me(2)C(3)OC(2)=92.5
TS1b
Me(2) 1.514 121.7 1.228 C(3)
O
Me(1)
R2
˚ and angles are in degree. Fig. 1. The geometrical parameters for the species in cycloaddition reaction 1 at MP2/6-31G* level. Lengths are in A
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44
41
Table 1 Total energies ET (a.u.) and relative energies ER (kJ molK1) for the species from a various theoretical methods Reaction
Species
MP2/6-31G* ET
Reaction 1 Reaction 2
Reaction 3
a b
R1CR2 INT1a TS1a(INT1a-P1) P1 INT1b TS1b(INT1b-P1) INT2 TS2(INT2-P2) P2 INT2CR2 INT3 TS3 P3
a
K269.39939 K269.40617 K269.39552 K269.49225 K269.40659 K269.37232 K269.43676 K269.38554 K269.49548 K461.87477 K461.88759 K461.87973 K461.96131
CCSD(T)//MP2/6-31G*
MP2/6-311G**//6-31G*
ERb
ET
ER
ET
ER
0.0 K17.8 10.2 K243.8 K18.9 71.1 K98.1 36.4 K252.3 0.0 K33.7 K13.0 K227.2
K269.49258 K269.49851 K269.48608 K269.57160 K269.49901 K269.46229 K269.52368 K269.46858 K269.57453 K462.01586 K462.02767 K462.01811 K462.09065
0.0 K15.6 17.1 K207.5 K16.9 79.5 K81.6 63.0 K215.2 0.0 K31.0 K5.9 K196.4
K269.56634 K269.57250 K269.56170 K269.65595 K269.57307 K269.53998 K269.60252 K269.55511 K269.66014 K462.16436 K462.17665 K462.16858 K462.24744
0.0 K16.2 12.2 K235.3 K17.7 69.2 K95.0 29.5 K246.3 0.0 K32.3 K11.1 K218.1
ETZE(Species)CZPE. ERZETKE(R1CR2) and ERZETKE(INT2CR2).
and 96.4 kJ/mol (28.4 and 86.9 kJ/mol, MP2/6-311G**// 6-31G*), respectively. In the first steps of paths a and b, the energy difference between INT1a and INT1b is only 1.3 kJ/ mol (1.5 kJ/mol, MP2/6-311G**//6-31G*). Thus, the probability to form the both is similar. However, the energy barrier of path b is 63.7 kJ/mol (58.5 kJ/mol, MP2/ 6-311G**//6-31G*) higher than that of path a in their isomerization to P1. Therefore, path a will be a dominant reaction channel of reaction 1. 3.2. Reaction 2: the channels forming the four-membered ring products Geometric parameters for the intermediate INT2, transition state TS2 and product P2 appearing in reaction 2 (69.2) 79.5 TS1b
100
50
∆E/(KJ · mol-1)
0.0
-50 -100
between vinylidene (R1) and acetone (R2) are given in Fig. 3. The energies of the different conformations are listed in Table 1. The potential energy surface for the reaction 2 is illustrated in Fig. 2. The unique imaginary frequency of the transition state TS2 is 1527.8i. IRC of TS2 indicates that it connects INT2 and P2. Fig. 2 shows that reaction 2 also consists of two steps: the first one is that the two reactants (R1, R2) form a four-membered ring intermediate INT2, in which the reaction is a barrier-free exothermic reaction with an energy decrease of 81.6 kJ/mol (95.0 kJ/mol, MP2/6-311G**//6-31G*), INT2 then takes place a hydrogen transfer to form product P2 via transition state TS2 with a barrier of 144.6 kJ/mol (124.5 kJ/mol, MP2/6-311G**//6-31G*).
R1+R2 0.0
(-16.2) -15.6 INT1a
TS2 63.0 (29.5) TS1a 17.1 (12.2)
INT1b -16.9 (-17.7) INT2 -81.6 (-95.0)
(-11.1) -5.9 TS3
INT2+R2 0.0 INT3 -31.0 (-32.3)
b a
-150
-200
-250
P2 -215.7 (-246.3)
Reaction (2)
P1 -207.5 (-235.3)
Reaction (1)
P3 -196.4 (-218.1)
Reaction (3)
Fig. 2. The potential energy surface for the cycloaddition reaction of vinylidene and acetone at CCSD(T)//MP2/6-31G* and MP2/6-311G**//6-31G* level. MP2/6-311G**//6-31G* relative energies were in parentheses.
42
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44 H(1) H(2) 1.0952 1.0952
H(1) H(2) 1.397 1.087 132.6 52.5 C(1)
113.9 1.5392
C(1)
H(1) 1.080 137.3 C(1) 1.344
1.414 C(2) 92.0 1.417
91.7 C(2)
99.6
109.8 C(3)
91.3 1.482 O
108.9
C(2)
85.7
C(3)
O 1.505 108.9 1.512 Me(2) 1.512 Me(1) C(1)C(2)OC(3)= 0.0 H(1)C(1)C(2)O= 179.9 H(2)C(1)C(2)O= -179.9 Me(1)C(3)OC(2)= -117.4 Me(2)C(3)OC(2)=117.5
1.514 110.9 Me(2) 1.515 Me(1) C(1)C(2)OC(3)= -2.9 H(1)C(1)C(2)O= 175.5 H(2)C(1)C(2)O= -111.2 Me(1)C(3)OC(2)= -112.4 Me(2)C(3)OC(2)=121.0
P2
TS2
INT2
1.085
1.390
1.340 95.7 109.6 C(3) 1.494 O 1.510 109.6 Me(2) 1.510 Me(1) C(1)C(2)OC(3)= 0.0 H(1)C(1)C(2)O= 117.3 H(2)C(1)C(2)O= -117.2 Me(1)C(3)OC(2)= -117.3 Me(2)C(3)OC(2)=117.4
H(2)
140.0
˚ and angles Fig. 3. The geometrical parameters of INT2, TS2, P2 and the atomic numbering for cycloaddition reaction 2 at MP2/6-31G* level. Length are in A are in degree.
According to Fig. 2, reaction 2 and path a of reaction 1 compete each other. For their first step, the energy of INT2 is 66.0 kJ/mol (78.8 kJ/mol, MP2/6-311G**//6-31G*) lower than that of INT1a. Thus, the reaction to form INT2 will be a favorable reaction pathway of the two reactants (R1, R2). For their second step, the energy barrier of the former is 111.9 kJ/mol (96.1 kJ/mol, MP2/6-311G**//631G*) higher than that of the latter. Therefore, reaction 2 will be difficult to proceed, and it may end in INT2 when path a of reaction 1 exists. INT2 can be considered as the product of the [2C2] cyloaddition action of the bonding p-orbitals of the two reactants (R1, R2). Since the s lone
O(2)
1.233 121.4 1.509 Me(4) 1.509 121.9 Me(3)
73.1 C(6)
electron pair and the 2p unoccupied orbital of C(2) in INT2 do not participate in the bond formation, INT2 is still an active intermediate as shown in Fig. 5. It may further react with acetone to form polycyclic compounds. 3.3. Reaction (3): the channels forming the polycyclic compounds In cycloaddition reaction 3, the active four-membered ring intermediate, INT2, further reacts with acetone to form a polycyclic compound, P3. The geometric parameters for the intermediate INT3, transition state TS3 and product P3
O(2)
1.25 6 59 .7
3.077
2.45 2
11 9.7 1.51 5 Me(4) C(6) 1.51 6 12 0.0 Me(3) O(2)
H(1) 1.094 113.0 82.5 Me(1) 1.532 C(2) C(1) 114.1 92.3 1.510 1.095 109.4 95.3 1.337 H(2) C(3) O(1) 1.501 109.4 C(1)C(2)O(1)C(3)= -0.5 1.510 Me(1)C(3)O(1)C(2)= -116.6 Me(2) Me(2)C(3)O(1)C(2)= 117.8 H(1)C(1)C(2)O(1)= 117.3 H(2)C(1)C(2)O(1)= -116.7 O(2)C(2)C(1)C(3)= -95.7 C(6)O(2)C(2)O(1)= 106.4 Me(3)C(6)O(2)C(2)= -86.8 Me(4)C(6)O(2)C(2)= 92.2
INT3
H(1) 1.093 113.8
H(1) 90 .6 1.09 1 11 5.9 1.52 9 Me(1) C(2) C(1) 93 .5 11 1.5 1.50 9 10 8.2 1.09 6 94 .2 1.33 1 H(2) C(3) O(1) 1.50 7 10 9.9 1.50 8 C(1)C(2)O(1)C(3)= -5.0 Me(1)C(3)O(1)C(2)= -110.6 Me(2) Me(2)C(3)O(1)C(2)= 123.5 H(1)C(1)C(2)O(1)= 123.4 H(2)C(1)C(2)O(1)= -109.4 O(2)C(2)C(1)C(3)= -95.8 C(6)O(2)C(2)O(1)= 106.5 Me(3)C(6)O(2)C(2)= -86.8 Me(4)C(6)O(2)C(2)= 92.2
TS3
1.411 124.1
60.6
1.482
113.9 1.505 Me(4) C(2) 94.2 C(6) 115.6 113.9 1.513 109.6 1.094 1.418 1.504 Me(3) 90.5 H(2) C(3) O(1) 1.479 109.6 1.513 C(1)C(2)O(1)C(3)= -0.7 Me(1)C(3)O(1)C(2)= -116.7 Me(2) Me(2)C(3)O(1)C(2)= 118.4 H(1)C(1)C(2)O(1)= 116.2 H(2)C(1)C(2)O(1)= -115.0 O(2)C(2)C(1)C(3)= -128.8 C(6)O(2)C(2)O(1)= 114.8 Me(3)C(6)O(2)C(2)= -109.8 Me(4)C(6)O(2)C(2)= 112.2 Me(1)
C(1)
1.514
P3
˚ and angles Fig. 4. The geometrical parameters of INT3, TS3, P3 and the atomic numbering for cycloaddition reaction (3) at MP2/6-31G*level. Length are in A are in degree.
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44
are shown in Fig. 4. The energies of the different conformations are listed in Table 1. The potential energy surface for reaction 3 is also illustrated in Fig. 2. The unique imaginary frequency of transition state TS3 is 303.1i. IRC of TS3 shows that TS3 connects INT3 with P3. According to Fig. 2, reaction 3 is completed by two steps. The first step is that INT2 reacts with acetone to form the intermediate INT3, which is a barrier-free exothermic reaction with an energy decrease of 31.0 kJ/mol (32.3 kJ/ mol, MP2/6-311G**//6-31G*). The second step is that the intermediate INT3 isomerizes to the polycyclic product P3 via transition state TS3 with a barrier of 25.1 kJ/mol (21.2 kJ/mol, MP2/6-311G**//6-31G*). Fig. 2 shows that the second step (INT1a/TS1a/P1) of path a in reaction 1 is the rate-determining step for reaction 1, and that the second step (INT3/TS3/P3) of reaction 3 is the rate-determining step for reaction 3. With the energy barrier of path a in reaction 1 being 7.6 kJ/mol (7.2 kJ/mol, MP2/6-311G**//6-31G*) higher than that of reaction 3, reaction 3 will be the dominant reaction pathway. On the basis of the above analysis, the leading reaction channel for cycloaddition reaction between singlet vinylidene and acetone is shown below: Reactionð2Þ
R1 C R2 / INT2
CR2 Reactionð3Þ
/
TS3
INT3 / P3
The mechanism of cyloaddition reaction could be explained with the molecular orbital diagram (Fig. 5). According to MO symmetry-adaption rule, as vinylidene initially interacts with acetone, the [2C2] cyloaddition of the bonding p-orbitals in vinylidene and acetone firstly results in four-membered ring intermediate INT2. Since s lone electron pair and the 2p unoccupied orbital on C(2) do not participate in the bond formation, INT2 is quite active and tends to further react with acetone. During the reaction, the insertion of the unoccupied 2p orbital of C(2) in INT2 into the p-orbital of acetone first
43
¦Ð* 2p HOMO ¦Ò ¦Ð HOMO INT2
(H3C)2C=O
Fig. 6. A schematic interaction diagram for the frontier orbitals of INT2 and (H3C)2CaO
and the p electrons transfer then to the unoccupied 2p orbital give a p/p donor–acceptor bond, consequently forming the intermediate INT3. With the reaction going, the intermediate INT3, by gradually increasing :C(1)C(2)O(2) (INT3: 82.58, TS3: 90.68, P3: 124.18), ˚, stretching the bond between C(6)-O(2) (INT3: 1.233 A ˚ ˚ TS3: 1.256 A, P3: 1.482 A) and decreasing the bond ˚ , TS3: 2.452 A ˚ , P3 : between C(2)-O(2) (INT3: 3.077 A ˚ 1.411 A ), finally transforms into the more stable polycyclic product P3 via transition state TS3. In the conformation of P3, s lone electron pair and the p unoccupied orbital on C(2) have formed circular donor– acceptor bonds of s/p* and p/p with the antibonding p* unoccupied orbital on C(6), and the p electron localize at the O(2) end. According to the molecular orbital theory, this kind of bonding effect is shown in Fig. 6. In the conformation of P3, there are no longer any s lone pair electrons and the 2p unoccupied orbital on C(2), which is the main reason that the conformation of P3 is more stable and is also the driving force that changes INT3 into P3.
4. Conclusion + O(2) –
–
– Me(4) C(6) R2 + Me(3)
+
¦Ð
¦Ð* ¡¡
H(1)
2p
+ Me(1) C(1)
¦Ò
C(2) –
C(3)
INT2
O(1)
Me(2) Fig. 5. MO symmetry-adaption Of INT2 and (H3C)2CaO
On the basis of the potential energy surface profile obtained with CCSD(T)//MP2/6-31G* and MP2/6311G**//6-31G* methods for the cycloaddition reaction between singlet vinylidene and acetone, it can be predicted that the dominant reaction pathway for the reaction consists of three steps: (1) the two reactants firstly form an active four-membered ring intermediate INT2, which is a barrierfree exothermic reaction with an energy decrease of 81.6 kJ/mol (95.0 kJ/mol, MP2/6-311G**//6-31G*); (2) the intermediate INT2 further reacts with acetone to form a polycyclic intermediate, INT3, through a barrier-free exothermic reaction with an energy decrease of 31.0 kJ/mol (K32.3 kJ/mol, MP2/6-311G**//6-31G*); (3) INT3 isomerizes to a polycyclic product P3 via a transition state TS3 with an energy barrier of 25.1 kJ/mol (21.2 kJ/mol, MP2/6311G**//6-31G*).
44
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44
Acknowledgements This project was supported by the Natural Science Foundation of Shandong Province, the People’s Republic of China (No. Y2002B07).
[4] [5] [6] [7] [8] [9]
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P.J. Stang, J. Organomet. Chem. 46 (1981) 4585. P.J. Stang, J.A. Bjork, Chem. Commun. (1978) 1057. R. Krishnan, M.J. Frisch, J.A. Pople, Chem. Phys. Lett. 79 (1981) 408. M.J. Frisch, R. Krishnan, J.A. Pople, Chem. Phys. Lett. 81 (1981) 421. Y. Apeloig, M. Karni, S.P.J. tang, D.P. Fox, J. Am. Chem. Soc. 105 (1983) 4781. D.P. Fox, S.P.J. tang, Y. Apeloig, M. Karni, J. Am. Chem. Soc. 108 (1986) 750. X.H. Lu, Y.X. Wang, J. Mol. Struct. (Theochem) 686 (2004) 207. L.A. Curtis, K. Raghavachari, J.A. Pople, J. Chem. Phys. 98 (1993) 1293. K. Fukui, J. Phys. Chem. 74 (1970) 4161. K. Ishida, K. Morokuma, A. Komornicki, J. Chem. Phys. 66 (1981) 2153. P.J. Stang, M.G. Mangum, J. Am. Chem. Soc. 97 (1975) 1459.
A theoretical study on the mechanism of cycloaddition reaction between vinylidene and acetone Xiuhui Lu*, Weirong Wu, Haibin Yu, Xiuli Yang, Yuehua Xu School of Chemistry and Chemical Engineering, Jinan University, Jinan, Shandong 250022, People’s Republic of China Received 8 April 2005; revised 23 July 2005; accepted 23 July 2005 Available online 10 October 2005
Abstract Mechanisms of cycloaddition reaction between singlet vinylidene and acetone have been investigated with MP2/6-31G* method. Energies for the involved conformations are further improved using CCSD(T)//MP2/6-31G* and MP2/6-311G**//6-31G* for the geometries optimized with MP2/6-31G* method. On the basis of the potential energy surface profile, it can be predicted that the dominant reaction pathway for the reaction consists of three steps: (1) the two reactants firstly form an active four-membered ring intermediate, INT2, which is a barrier-free exothermic reaction, DEZK81.6 kJ/mol (K95.0 kJ/mol, MP2/6-311G**//6-31G*); (2) the intermediate INT2 further reacts with acetone to form a polycyclic intermediate, INT3, through a barrier-free exothermic reaction, DEZK31.0 kJ/mol (K32.3 kJ/mol, MP2/6-311G**//6-31G*); (3) INT3 isomerizes to a polycyclic product P3 via a transition state TS3 with an energy barrier of 25.1 kJ/mol (21.2 kJ/mol, MP2/6-311G**//6-31G*). q 2005 Elsevier B.V. All rights reserved. Keywords: Vinylidene; Cycloaddition reaction; Potential energy surface; CCSD(T)//MP2/6-31G* method
1. Introduction Since unsaturated carbenes were recognized as active intermediates in 1960s, they have not only attracted much attention from theoretical chemist, also been practically applied to organic chemistry [1,2]. For example, they provide simple and direct synthesis for small-ring, highly strained compounds, as well as those that are hardly synthesized through conventional ways [2–5]. Apeloig and Fox et al. [6,7] have studied the stereoselectivity of substituting group in the products of the vinylidene addition to olefins using experimental and theoretical methods, as well as the rearrangement reaction of vinylidene [8,9]. We have investigated mechanisms of cycloaddition reaction between dichloro-vinylidene and ethylene [10]. But, compared with the study on saturated carbenes, the study on unsaturated carbene has just begun and is a new branch of carbene chemistry. For mechanisms * Corresponding author. Tel.: C86 5312 769853; fax: C86 5312 769853. E-mail address: [email protected] (X. Lu).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.07.019
of cycloaddition reaction, which are quite difficult to investigate directly using experimental methods due to the active character of unsaturated carbene, the theoretical study is proved to be very useful. In order to explore the rules of cycloaddition reaction between unsaturated carbene and the asymmetric p-bonded compound, vinylidene and acetone were selected as model molecules. The cycloaddition reaction mechanism was investigated and analyzed theoretically. The results show that the cycloaddition reaction between vinylidene and acetone proceeds in the following three possible pathways:
ð1Þ
ð2Þ
ð3Þ
40
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44
2. Calculation methods MP2/6-31G* [11] implemented in the Gaussion98 package is employed to locate all the stationary points along the reaction pathways. Full optimization and vibrational analysis are done for the stationary points on the reaction profile. Zero point energy, CCSD(T)//MP2/6-31G* and MP2/ 6-311G**//6-31G* corrections are included for the energy calculations. In order to explicitly establish the relevant species, the intrinsic reaction coordinate (IRC) [12,13] is also carried out for all the transition states appearing on the cycloaddition energy surface profile. 3. Results and discussions 3.1. Reaction 1: the pathways forming the three-membered ring product Theoretical calculations indicate that the ground state of vinylidene is a singlet [14] state. The geometric parameters
for the intermediates (INT1a, INT1b), transition states (TS1a, TS1b) and product P1 are given in Fig. 1. The energies of the different conformations are listed in Table 1. The potential energy surfaces for the reaction path are given in Fig. 2. The unique imaginary frequencies of the transition states TS1a and TS1b are 385.1i and 524.6i, respectively. IRC calculations of TS1a and TS1b, indicate that TS1a connects INT1a with P1, and that TS1b connects INT1b with P1. According to Fig. 2, it can be directly seen that reaction 1 has two path ways, a and b, each of which consists of two steps: the first one is that the two reactants (R1, R2) form the intermediates INT1a and INT1b, respectively, in which the two reactions are both barrier-free exothermic reactions with energy decreases of 15.6 and 16.9 kJ/mol (16.2 and 17.7 kJ/mol, MP2/6-311G**//6-31G*), respectively; the intermediates INT1a and INT1b then isomerize to the three-membered ring product P1 via transition states TS1a and TS1b, in which energy barriers are 32.7 H(1)
H(1) 1.088 120.5 C(1) 1.308 C(2) 119.5 1.087 89.7 H(2)
H(1)
1.092 C(1)
111.7
129.5
1.319 C(2)
H(2) 1.0822 C(1) 1.0834 119.9 120.9 1.327
1.081 H(2)
95.0
C(2) 138.7 2.900
2.218
121.6 1.510 C(3) 79.9 Me(2) O 121.6 1.231 Me(1) 1.510 C(1)C(2)OC(3)= 179.9 H(1)C(1)C(2)O= -180. 0 H(2)C(1)C(2)O= 0.0 Me(1)C(3)OC(2)= - 88.9 Me(2)C(3)OC(2)= 88.9
120.5 C(3) 66.6 O 1.256 1.511 120.6 Me(2) Me(1) 1.511 C(1)C(2)OC(3)=180.0 H(1)C(1)C(2)O= -180.0 H(2)C(1)C(2)O= 0.0 Me(1)C(3)OC(2)= -9 8.8 Me(2)C(3)OC(2)=98.9
INT1a
1.371
1.505 Me(2) Me(1)
113.5 1.505
1.101 H(1)
P1 H(2) 1.089
1.088 C(1) 108.6 H(1) 137.1 1.348 123.6
H(1)
1.088 120.5 1.309 C(1)
H(2)
R1 1.676
102.8 C(3) 1.231 O 121.0 1.512 C(1)C(2)OC(3)= -0 .2 Me(1) H(1)C(1)C(2)O= 0.0 H(2)C(1)C(2)O= -18 0.0 Me(1)C(3)OC(2)=179 .6 Me(2)C(3)OC(2)= -0 .4
INT1b
C(2)
C(2)
3.734 Me(2) 1.511 122.4
O
1.512
C(1)C(2)OC(3)=180.0 H(1)C(1)C(2)O=180.0 H(2)C(1)C(2)O=0.1 Me(1)C(3)OC(2)= -111.6 Me(2)C(3)OC(2)=111.6
TS1a C(2) 1.302 H(2) 130.1 1.083 76.5 109.7 C(1)
59.6
113.5 C(3)
94.1 120.1 C(3) 1.493 O 1.282 Me(2) 120.1 Me(1) 1.493 C(1)C(2)OC(3)= 0.0 H(1)C(1)C(2)O= 0.0 H(2)C(1)C(2)O= -180.0 Me(1)C(3)OC(2)= -92.5 Me(2)C(3)OC(2)=92.5
TS1b
Me(2) 1.514 121.7 1.228 C(3)
O
Me(1)
R2
˚ and angles are in degree. Fig. 1. The geometrical parameters for the species in cycloaddition reaction 1 at MP2/6-31G* level. Lengths are in A
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44
41
Table 1 Total energies ET (a.u.) and relative energies ER (kJ molK1) for the species from a various theoretical methods Reaction
Species
MP2/6-31G* ET
Reaction 1 Reaction 2
Reaction 3
a b
R1CR2 INT1a TS1a(INT1a-P1) P1 INT1b TS1b(INT1b-P1) INT2 TS2(INT2-P2) P2 INT2CR2 INT3 TS3 P3
a
K269.39939 K269.40617 K269.39552 K269.49225 K269.40659 K269.37232 K269.43676 K269.38554 K269.49548 K461.87477 K461.88759 K461.87973 K461.96131
CCSD(T)//MP2/6-31G*
MP2/6-311G**//6-31G*
ERb
ET
ER
ET
ER
0.0 K17.8 10.2 K243.8 K18.9 71.1 K98.1 36.4 K252.3 0.0 K33.7 K13.0 K227.2
K269.49258 K269.49851 K269.48608 K269.57160 K269.49901 K269.46229 K269.52368 K269.46858 K269.57453 K462.01586 K462.02767 K462.01811 K462.09065
0.0 K15.6 17.1 K207.5 K16.9 79.5 K81.6 63.0 K215.2 0.0 K31.0 K5.9 K196.4
K269.56634 K269.57250 K269.56170 K269.65595 K269.57307 K269.53998 K269.60252 K269.55511 K269.66014 K462.16436 K462.17665 K462.16858 K462.24744
0.0 K16.2 12.2 K235.3 K17.7 69.2 K95.0 29.5 K246.3 0.0 K32.3 K11.1 K218.1
ETZE(Species)CZPE. ERZETKE(R1CR2) and ERZETKE(INT2CR2).
and 96.4 kJ/mol (28.4 and 86.9 kJ/mol, MP2/6-311G**// 6-31G*), respectively. In the first steps of paths a and b, the energy difference between INT1a and INT1b is only 1.3 kJ/ mol (1.5 kJ/mol, MP2/6-311G**//6-31G*). Thus, the probability to form the both is similar. However, the energy barrier of path b is 63.7 kJ/mol (58.5 kJ/mol, MP2/ 6-311G**//6-31G*) higher than that of path a in their isomerization to P1. Therefore, path a will be a dominant reaction channel of reaction 1. 3.2. Reaction 2: the channels forming the four-membered ring products Geometric parameters for the intermediate INT2, transition state TS2 and product P2 appearing in reaction 2 (69.2) 79.5 TS1b
100
50
∆E/(KJ · mol-1)
0.0
-50 -100
between vinylidene (R1) and acetone (R2) are given in Fig. 3. The energies of the different conformations are listed in Table 1. The potential energy surface for the reaction 2 is illustrated in Fig. 2. The unique imaginary frequency of the transition state TS2 is 1527.8i. IRC of TS2 indicates that it connects INT2 and P2. Fig. 2 shows that reaction 2 also consists of two steps: the first one is that the two reactants (R1, R2) form a four-membered ring intermediate INT2, in which the reaction is a barrier-free exothermic reaction with an energy decrease of 81.6 kJ/mol (95.0 kJ/mol, MP2/6-311G**//6-31G*), INT2 then takes place a hydrogen transfer to form product P2 via transition state TS2 with a barrier of 144.6 kJ/mol (124.5 kJ/mol, MP2/6-311G**//6-31G*).
R1+R2 0.0
(-16.2) -15.6 INT1a
TS2 63.0 (29.5) TS1a 17.1 (12.2)
INT1b -16.9 (-17.7) INT2 -81.6 (-95.0)
(-11.1) -5.9 TS3
INT2+R2 0.0 INT3 -31.0 (-32.3)
b a
-150
-200
-250
P2 -215.7 (-246.3)
Reaction (2)
P1 -207.5 (-235.3)
Reaction (1)
P3 -196.4 (-218.1)
Reaction (3)
Fig. 2. The potential energy surface for the cycloaddition reaction of vinylidene and acetone at CCSD(T)//MP2/6-31G* and MP2/6-311G**//6-31G* level. MP2/6-311G**//6-31G* relative energies were in parentheses.
42
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44 H(1) H(2) 1.0952 1.0952
H(1) H(2) 1.397 1.087 132.6 52.5 C(1)
113.9 1.5392
C(1)
H(1) 1.080 137.3 C(1) 1.344
1.414 C(2) 92.0 1.417
91.7 C(2)
99.6
109.8 C(3)
91.3 1.482 O
108.9
C(2)
85.7
C(3)
O 1.505 108.9 1.512 Me(2) 1.512 Me(1) C(1)C(2)OC(3)= 0.0 H(1)C(1)C(2)O= 179.9 H(2)C(1)C(2)O= -179.9 Me(1)C(3)OC(2)= -117.4 Me(2)C(3)OC(2)=117.5
1.514 110.9 Me(2) 1.515 Me(1) C(1)C(2)OC(3)= -2.9 H(1)C(1)C(2)O= 175.5 H(2)C(1)C(2)O= -111.2 Me(1)C(3)OC(2)= -112.4 Me(2)C(3)OC(2)=121.0
P2
TS2
INT2
1.085
1.390
1.340 95.7 109.6 C(3) 1.494 O 1.510 109.6 Me(2) 1.510 Me(1) C(1)C(2)OC(3)= 0.0 H(1)C(1)C(2)O= 117.3 H(2)C(1)C(2)O= -117.2 Me(1)C(3)OC(2)= -117.3 Me(2)C(3)OC(2)=117.4
H(2)
140.0
˚ and angles Fig. 3. The geometrical parameters of INT2, TS2, P2 and the atomic numbering for cycloaddition reaction 2 at MP2/6-31G* level. Length are in A are in degree.
According to Fig. 2, reaction 2 and path a of reaction 1 compete each other. For their first step, the energy of INT2 is 66.0 kJ/mol (78.8 kJ/mol, MP2/6-311G**//6-31G*) lower than that of INT1a. Thus, the reaction to form INT2 will be a favorable reaction pathway of the two reactants (R1, R2). For their second step, the energy barrier of the former is 111.9 kJ/mol (96.1 kJ/mol, MP2/6-311G**//631G*) higher than that of the latter. Therefore, reaction 2 will be difficult to proceed, and it may end in INT2 when path a of reaction 1 exists. INT2 can be considered as the product of the [2C2] cyloaddition action of the bonding p-orbitals of the two reactants (R1, R2). Since the s lone
O(2)
1.233 121.4 1.509 Me(4) 1.509 121.9 Me(3)
73.1 C(6)
electron pair and the 2p unoccupied orbital of C(2) in INT2 do not participate in the bond formation, INT2 is still an active intermediate as shown in Fig. 5. It may further react with acetone to form polycyclic compounds. 3.3. Reaction (3): the channels forming the polycyclic compounds In cycloaddition reaction 3, the active four-membered ring intermediate, INT2, further reacts with acetone to form a polycyclic compound, P3. The geometric parameters for the intermediate INT3, transition state TS3 and product P3
O(2)
1.25 6 59 .7
3.077
2.45 2
11 9.7 1.51 5 Me(4) C(6) 1.51 6 12 0.0 Me(3) O(2)
H(1) 1.094 113.0 82.5 Me(1) 1.532 C(2) C(1) 114.1 92.3 1.510 1.095 109.4 95.3 1.337 H(2) C(3) O(1) 1.501 109.4 C(1)C(2)O(1)C(3)= -0.5 1.510 Me(1)C(3)O(1)C(2)= -116.6 Me(2) Me(2)C(3)O(1)C(2)= 117.8 H(1)C(1)C(2)O(1)= 117.3 H(2)C(1)C(2)O(1)= -116.7 O(2)C(2)C(1)C(3)= -95.7 C(6)O(2)C(2)O(1)= 106.4 Me(3)C(6)O(2)C(2)= -86.8 Me(4)C(6)O(2)C(2)= 92.2
INT3
H(1) 1.093 113.8
H(1) 90 .6 1.09 1 11 5.9 1.52 9 Me(1) C(2) C(1) 93 .5 11 1.5 1.50 9 10 8.2 1.09 6 94 .2 1.33 1 H(2) C(3) O(1) 1.50 7 10 9.9 1.50 8 C(1)C(2)O(1)C(3)= -5.0 Me(1)C(3)O(1)C(2)= -110.6 Me(2) Me(2)C(3)O(1)C(2)= 123.5 H(1)C(1)C(2)O(1)= 123.4 H(2)C(1)C(2)O(1)= -109.4 O(2)C(2)C(1)C(3)= -95.8 C(6)O(2)C(2)O(1)= 106.5 Me(3)C(6)O(2)C(2)= -86.8 Me(4)C(6)O(2)C(2)= 92.2
TS3
1.411 124.1
60.6
1.482
113.9 1.505 Me(4) C(2) 94.2 C(6) 115.6 113.9 1.513 109.6 1.094 1.418 1.504 Me(3) 90.5 H(2) C(3) O(1) 1.479 109.6 1.513 C(1)C(2)O(1)C(3)= -0.7 Me(1)C(3)O(1)C(2)= -116.7 Me(2) Me(2)C(3)O(1)C(2)= 118.4 H(1)C(1)C(2)O(1)= 116.2 H(2)C(1)C(2)O(1)= -115.0 O(2)C(2)C(1)C(3)= -128.8 C(6)O(2)C(2)O(1)= 114.8 Me(3)C(6)O(2)C(2)= -109.8 Me(4)C(6)O(2)C(2)= 112.2 Me(1)
C(1)
1.514
P3
˚ and angles Fig. 4. The geometrical parameters of INT3, TS3, P3 and the atomic numbering for cycloaddition reaction (3) at MP2/6-31G*level. Length are in A are in degree.
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44
are shown in Fig. 4. The energies of the different conformations are listed in Table 1. The potential energy surface for reaction 3 is also illustrated in Fig. 2. The unique imaginary frequency of transition state TS3 is 303.1i. IRC of TS3 shows that TS3 connects INT3 with P3. According to Fig. 2, reaction 3 is completed by two steps. The first step is that INT2 reacts with acetone to form the intermediate INT3, which is a barrier-free exothermic reaction with an energy decrease of 31.0 kJ/mol (32.3 kJ/ mol, MP2/6-311G**//6-31G*). The second step is that the intermediate INT3 isomerizes to the polycyclic product P3 via transition state TS3 with a barrier of 25.1 kJ/mol (21.2 kJ/mol, MP2/6-311G**//6-31G*). Fig. 2 shows that the second step (INT1a/TS1a/P1) of path a in reaction 1 is the rate-determining step for reaction 1, and that the second step (INT3/TS3/P3) of reaction 3 is the rate-determining step for reaction 3. With the energy barrier of path a in reaction 1 being 7.6 kJ/mol (7.2 kJ/mol, MP2/6-311G**//6-31G*) higher than that of reaction 3, reaction 3 will be the dominant reaction pathway. On the basis of the above analysis, the leading reaction channel for cycloaddition reaction between singlet vinylidene and acetone is shown below: Reactionð2Þ
R1 C R2 / INT2
CR2 Reactionð3Þ
/
TS3
INT3 / P3
The mechanism of cyloaddition reaction could be explained with the molecular orbital diagram (Fig. 5). According to MO symmetry-adaption rule, as vinylidene initially interacts with acetone, the [2C2] cyloaddition of the bonding p-orbitals in vinylidene and acetone firstly results in four-membered ring intermediate INT2. Since s lone electron pair and the 2p unoccupied orbital on C(2) do not participate in the bond formation, INT2 is quite active and tends to further react with acetone. During the reaction, the insertion of the unoccupied 2p orbital of C(2) in INT2 into the p-orbital of acetone first
43
¦Ð* 2p HOMO ¦Ò ¦Ð HOMO INT2
(H3C)2C=O
Fig. 6. A schematic interaction diagram for the frontier orbitals of INT2 and (H3C)2CaO
and the p electrons transfer then to the unoccupied 2p orbital give a p/p donor–acceptor bond, consequently forming the intermediate INT3. With the reaction going, the intermediate INT3, by gradually increasing :C(1)C(2)O(2) (INT3: 82.58, TS3: 90.68, P3: 124.18), ˚, stretching the bond between C(6)-O(2) (INT3: 1.233 A ˚ ˚ TS3: 1.256 A, P3: 1.482 A) and decreasing the bond ˚ , TS3: 2.452 A ˚ , P3 : between C(2)-O(2) (INT3: 3.077 A ˚ 1.411 A ), finally transforms into the more stable polycyclic product P3 via transition state TS3. In the conformation of P3, s lone electron pair and the p unoccupied orbital on C(2) have formed circular donor– acceptor bonds of s/p* and p/p with the antibonding p* unoccupied orbital on C(6), and the p electron localize at the O(2) end. According to the molecular orbital theory, this kind of bonding effect is shown in Fig. 6. In the conformation of P3, there are no longer any s lone pair electrons and the 2p unoccupied orbital on C(2), which is the main reason that the conformation of P3 is more stable and is also the driving force that changes INT3 into P3.
4. Conclusion + O(2) –
–
– Me(4) C(6) R2 + Me(3)
+
¦Ð
¦Ð* ¡¡
H(1)
2p
+ Me(1) C(1)
¦Ò
C(2) –
C(3)
INT2
O(1)
Me(2) Fig. 5. MO symmetry-adaption Of INT2 and (H3C)2CaO
On the basis of the potential energy surface profile obtained with CCSD(T)//MP2/6-31G* and MP2/6311G**//6-31G* methods for the cycloaddition reaction between singlet vinylidene and acetone, it can be predicted that the dominant reaction pathway for the reaction consists of three steps: (1) the two reactants firstly form an active four-membered ring intermediate INT2, which is a barrierfree exothermic reaction with an energy decrease of 81.6 kJ/mol (95.0 kJ/mol, MP2/6-311G**//6-31G*); (2) the intermediate INT2 further reacts with acetone to form a polycyclic intermediate, INT3, through a barrier-free exothermic reaction with an energy decrease of 31.0 kJ/mol (K32.3 kJ/mol, MP2/6-311G**//6-31G*); (3) INT3 isomerizes to a polycyclic product P3 via a transition state TS3 with an energy barrier of 25.1 kJ/mol (21.2 kJ/mol, MP2/6311G**//6-31G*).
44
X. Lu et al. / Journal of Molecular Structure: THEOCHEM 755 (2005) 39–44
Acknowledgements This project was supported by the Natural Science Foundation of Shandong Province, the People’s Republic of China (No. Y2002B07).
[4] [5] [6] [7] [8] [9]
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