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Theoretical studies on the substituent effect of the thermal cycloaddition of ethylene and formaldehyde
THEO CHEM Journal
of Molecular
Structure
(Theochem)
336 (1995) 9 l-100
Theoretical studies on the substituent effect of the thermal cycloaddition of ethylene and formaldehyde Guang-Ju
Chen, Xiao-Yuan
Fu*
Chemistry Department, Beijing Normal Universit.y, Beijing 100875, People’s Republic of China Received
23 November
1993; accepted
17 November
1994
Abstract Ab initio HF molecular orbital calculations using 3-21G and 6-31G* basis sets and including electron correlation (MP2 to MP4) have been applied to investigate the concerted supra-antara [2s + 2a] thermal cycloaddition reaction of some substituted ethylenes and formaldehyde. The stepwise reaction paths have also been studied for one of the reactions by using UHF/3-21G and MP2/3-21G. The calculated results indicate that although the presence of some particular substituents can decrease the activation barriers obviously, the title reaction is difficult to carry out via the supra-antara [2s + 2a] thermal cycloaddition pathway under moderate conditions. However, the reactions are probably carried out via stepwise pathways when there are strong electron-withdrawing groups in formaldehyde and/or electron-releasing groups in ethylene.
1. Introduction The gas-phase decomposition of oxetane to form ethylene and formaldehyde has been studied by Zalotal and co-workers [1,2] and others [3,4] and the reverse reaction, the [2+2] gas-phase cycloaddi-
tion reaction, has not been found experimentally. The transition state structures of the concerted supra-antara ([2s+2a]) and stepwise cycloaddition reaction of ethylene and formaldehyde have been optimized by us previously at the HF/3-21G and MP2/3-21G levels [5,6]. Because the activation barrier is high and the activation entropy negative, this cycloaddition reaction proceeds with difficulty. The question is whether, if some proper substituents are added to ethylene and formaldehyde respectively, these cycloaddition reactions can be made to occur. * Corresponding 0166-1280/95/$09.50
author. 0
1995
SSDI 0166-1280(94)04039-7
On the basis of this consideration, some electronwithdrawing groups have been added to the formaldehyde molecule and on electron-releasing group to ethylene, and the effect of substituents on the reaction barriers is investigated. In this work we have studied the following type of reaction theoretically (the subscripts in Scheme 1 comprise the numbering system of the products and the transition states structures): Reaction x Y z
(1) H HH H
(2) NH2 H
(3) H HH F
(4) NH2 F
(5) H HH CF3
(6) NH2 CF,
(7) H FF CF,
(8) NH2 CF,
Firstly, we have fully optimized the geometries of the [2s+2a] transition states for all these reactions and confirmed them by vibrational frequency analysis. Secondly, the stepwise reaction paths have also been studied for reaction (8) to compare with the concerted one. The electron correlation and the
Elsevier Science B.V. All rights reserved
92
G.-J. Chen, X.-Y. Fu/Journal
of MolecularStructure
(Theochem)
336 (1995) 91-100
TS l
Scheme
effects of the basis sets have also been explored. The role of activation entropies is discussed.
I
time, UHF was also used for investigating the stationary points of the [2s+2a] reaction path for comparison with the RHF calculation. The results show that they are consistent with that of RHF.
2. Method of calculation 3. Results and discussion All the calculations based on Hartree-Fock formulation were performed by using the GAUSSIAN 86 program packages [7] at a Vax-4000 workstation. For the [2s+2a] reaction pathway, the full geometry optimization was carried out at the Hartree-Fock level with analytical first and second energy derivatives without any symmetry restriction. The basis set used for the optimizations was 3-21G [8]. To confirm the transition state structure, we computed the second derivative matrix analytically. The electron correlation was taken into account using the second-order Maller-Plesset (MP2) [9] for all reactions and MP4 [lo] for the first four reactions at the 3-21G HF optimized geometries. In order to account for the effect of the basis sets, MP2/6-31G* [l l] calculations were performed for reactions (l)-(4) using 3-21G HF optimized geometries. The transition states of reactions (l)-(4) were further calculated by 2 x 2 MCSCF using GAUSSIAN 92[121to confirm the reliability of the results obtained using single configuration calculations (MP4, MP2/6-31G* and 2 x 2 MCSCF calculations have not been carried out for reactions (.5)-(8) because the atoms involved in these reactions are rather large). The activation entropy of each reaction was calculated by using the calculated vibrational frequencies and a statistical method. The stepwise processes for reaction (8) were studied using the unrestricted Hartree-Fock (UHF) at the level of the 3-21G basis set. MP2 single point calculations on 3-21G geometries of some stationary points were also carried out. In order to obtain the spin population, the “mix” option was used to mix the frontier molecular orbitals. At the same
3.1. Reactants
and products
3.1.1. The frontier molecular orbitals of the reactant
We optimized the geometries of the reactant by using an energy gradient technique at the 3-21G level and obtained their geometries and molecular orbitals. Upon adding a substituent to ethylene or formaldehyde its C=C or C=O double bond, respectively, is shortened, but the frontier molecular orbitals (FMO) of H2C=CHNH2 are still a 7rcI) orbital (HOMO) and a 7rilJorbital (LUMO), i.e. its FM0 are similar to those of ethylene. At the same time, the 7rc2)molecular orbital is NHOMO and 7rfZj LUMO for substituted formaldehyde (i.e. their FM0 are also similar to those of formaldehyde). Although the types of FM0 are not changed, their relative energies are different. There are two types of FM0 interactions between the reactants: the HOMO (7rc1))of (substituted) ethylene and the LUMO (7ri2) of (substituted) formaldeTable 1 Energy gaps of FM0 of the substituted Reaction
(1) (2) (3) (4) (5) (6) (7) (8)
ethylene and formaldehyde
Energy gap of FMO/eV
@?I,-$,I
-e(2)
14.34 14.03 14.42 14.11 12.79 12.48 12.77 12.45
19.41 19.60 19.86 20.05 20.74 20.93 21.01 21.20
-$)I
G.-J. Chen. X.-Y. FulJournal of Molecular Structure (Theochem) Table 2 The main geometric Parameter
parameters
c2-03 c4-03 L”3c2c, !C403C2 LC403C2C,
(bond lengths in A, bond angles in deg)
Reaction
(1) cl-c2
of all products
93
336 (1995) 91-100
.5578 1.4757
I
1.4757
90.95 91.00 0.00
(2) 1.5539 1.4756 1.4758 91.09 91.51 5.68
(3)
(4)
1.5578 1.4828 1.4328 89.40 92.79 0.59
1.4337 89.81 92.30 3.00
hyde; the NHOMO (7r& of (substituted) formaldehyde and the LUMO (7rit,) of (substituted) ethylene. However, the energy gap between the former is much smaller than the latter as shown in Table 1. Therefore, in terms of frontier orbital theory, if the above reaction proceeds via the supra-antara [2s+2a] reaction path, the interactions of FM0 are mainly 7rc1)molecular orbitals of HlC=CHz or H2C=CHNH2 with 7rTZ,of the formaldehyde or substituted formaldehyde. 3.1.2. Structures of the products We also obtained the geometries of the products by using an energy gradient technique at the 3-21G level. The main geometric parameters of the products are given in Table 2 with the numbering system shown in Scheme 1 and the energies E (a.u.) are shown in Table 3. It can be seen from Table 2 that the substituent slightly affects the molecular skeleton. For example, C2-0s is lengthened and C2-0s shortened with addition of the substituent, and these molecules are puckered rings with twisted angles. Table 3 Energy E (a.u.) of the products mized geometries
at the level of HF/3-21G
Reaction
E(HF/3-21G)
E(MP2/3-2lG)
(1) (2) (3) (4) (5) (6) (7) (8)
-190.83891 -245.55160 -289.17207 -343.88615 -524.65862 -579.37185 -622.98476 -677.70375
-191.22264 -246.03918 -289.66999 -344.48725 -525.47688 -580.29355 -623.91951 -678.74176
1.5542 1.4813
opti-
(5)
(6)
(7)
1.5574 1.4858 1.458 1 90.13 91.51 8.19
1.5539 1.4817 1.4570 90.66 91.36 6.13
1.5563 1.4919 1.4205 89.07 91.89 7.07
3.2. Concerted supra-antara 3.2.1. Optimized
(8) 1.5560 1.4917
1.4107 89.28 92.85 3.85
[2s+2a] cycloaddition
geometries
The [2s+2a] reaction paths of all reactions are assumed to involve singlet states because the cycloaddition reaction takes place under thermal conditions. The geometric parameters corresponding to the transition states for each reaction are given in Table 4 with the numbering system shown in Scheme 1. There is some regularity in the change of the developing bonds C2-0s and Ci-C4 with reactions (l)-(8), i.e. C2-O3 is lengthened and Ci -Cd is shortened from reactions (1) to (8). This indicates that the substituents may increase the non-synchronism of the reaction; the larger the substituent, the more obvious is this effect. The bond angles of the molecular skeleton also vary with the substituents, i.e. 103C2C1 decreases and LC4C1C2 increases. The changes in the other bond lengths and angles are small. From data for the main dihedral angle 103C2C4C1, it can be realized that the four-membered ring of the TS is somewhat twisted. Each transition state was confirmed to have only one imaginary vibration frequency f in the normal coordinate analysis based on the analytical second derivatives of energy. Values off (cm-‘) are 1433.8i, 1402.51, 1337.31, 1295.61, 1299.71, 1253.11, 1074.Oi and 1031.9i for reactions (l)-(8) respectively. The vibrational frequencies are gradually reduced from reactions (1) to (8). This sequence is in accord with the sequence of the charge transfer between the two reactants and the activation energy of the reactions (see below). For these transition states, the major contribution of the
94
G.-J. Chen, X.-Y. Fu/Journal
Table 4 The geometric Parameter
parameters
of all transition
of Molecular Structure (Theochem)
336 (1995)
91ClOO
states (bond lengths in A; bond angles in deg)
Reaction 1
2
3
4
5
6
7
8
-
1.4004
cl-c2 03 -c2 Cl --c4 x5-c, H6-Cl H7-C2 Y9&4 zIorc4 icI
c203
LC4ClC2 ix5c1c2 ~H6ClG ~H7GG
iY9C403 ~ZIOC403 103c2c4cI fx5~1~2~3 iH6CIC203 iH7C2CIC4 iH8C2CIC4 iy9c403c2 iz10c403c2 HII-N5 ~HIINs% iH12N503 IHIINsCIC~ ~HI~NsCIC~
2.0279 2.0040
1.4006 2.0398 1.9768
1.0725 1.0727
1.4427 1.0777
1.0674 1.0817 1.0810 98.74 78.46 118.71 118.23 121.58 120.64 120.29 169.46 109.25 -99.75 98.72 -92.95 116.02 -96.14
1.0662 1.0847 1.0815 89.11 78.18 117.14 117.22 121.64 120.32 120.13 164.52 110.62 -96.63 98.40 -92.90 123.10 -89.31 1.0043 115.46 114.60 93.65 -135.35
1.4052 2.0435 1.9385 1.0737 1.0729 1.0671 1.3600 1.0756 92.25 81.90 118.39 117.71 121.94 118.69 122.19 158.87 116.47 -95.09 99.45 -89.83 129.81 -90.57
1.4057 2.0586 1.9063 1.4453
1.0772 1.0660 1.3666 1.0771 91.85 81.49 116.22 117.05 122.06 118.36 122.39 156.57 115.04 -93.87 98.68 -90.23 133.60 -86.73 1.0045 115.25 113.56 87.48 -143.12
1.0686 1.5120 1.0836 91.87 83.16 117.54 118.49 120.72 116.23 121.67 196.47 96.46 -115.80 88.14 -93.16 97.41 -125.91
1.3530
CIO-F13
1.3530 1.3451 111.90 112.36 109.82 185.02 120.73 -119.22
CIO-FI, CIOCFI~ ~F13GoC4 ~F14GoC4 ~FIsCIOC~ ~F13C1oC403 ~F14GoC403 ~F15C1oC403
imaginary vibrational mode contains the formation of C2-0s and C-C, bonds and the lengthening of C2-C1 and Os-C4 bonds. Besides, the bending vibrations of the group (CH,) located at C4 and the rotation of the groups (CH,) located at Ci, C2 and C4 are also important contributions. 3.2.2. Electron densities The overlap populations involved in the molecular
1.3977 2.1633 1.9033 1.0733 1.0708
between heavy atoms skeletons of the transi-
1.4007 2.1563 1.8694 1.4403
I .4043 2.2208 1.8131 1.0738
1.0772
1.0723
1.0656 1.5090 1.0821 92.02 81.55 117.05 116.23 121.69 118.20 121.19 157.75 116.15 -92.81 93.16 -89.88 129.45 -91.94 1.0046 114.91 112.53 87.78 -143.51 1.3613 1.3457 1.3457 109.94 112.62 111.25 186.86 119.48 -118.83
1.0691 1.5228 1.3755 84.57 87.75 116.86 118.19 120.90 117.55 119.07 203.56 92.85 -122.34 88.19 -90.51 97.30 -133.78
1.3459 1.3541 1.3390 112.61 109.78 110.74 183.32 119.31 -121.48
1.4066 2.2354 1.8281 1.4369 1.0762 1.0686 1.5204 1.3874 85.82 86.42 115.32 116.68 121.35 118.00 118.84 201.38 96.03 -118.06 83.56 -94.28 100.33 -130.68 1.0015 115.52 113.24 106.94 -119.67 1.3459 1.3558 1.3381 112.64 109.23 111.20 180.41 118.89 -121.94
tion states of reactions (l)-(S) are summarized in Table 5. In each transition state, the overlap population data indicate that the chemical bonds in C, C4 and C2-0s are developing. There are large populations in Cd-O3 and Ci-C2 which indicate that there are still chemical bonds between them. All the other bond overlap populations between non-neighbouring atoms are negative, indicating a repulsive interaction. The amount of the charge transfer (CT) can be calculated by means of atomic charges obtained by
G.-J. Chen, X.-Y. FujJournal of Molecular Structure (Theochem) Table 5 Bond overlap
populations
Reaction (1)
(2) (3) (4) (5) (6) (7) (8)
at the HF/3-21G
optimized
cl-c2
cl-03
cl-c4
CZ-03
c2-c4
03-c4
0.2366 0.2313 0.2239 0.2101 0.1780 0.1752 0.1550 0.1373
-0.0797 -0.0830 -0.1022 ~0.1054 -0.0858 -0.088 1 -0.1063 -0.1013
0.0373 0.0406 0.0689 0.0574 0.0363 0.0111 0.0555 0.0484
0.0791 0.0804 0.0761 0.0784 0.0554 0.0546 0.0490 0.0505
-0.0098 -0.0178 -0.0352 -0.0399 -0.0309 -0.0170 -0.0463 PO.0599
0.3303 0.3309 0.3414 0.3396 0.3353 0.3522 0.3538 0.3708
states and the activation barrier AE, (kJmol_‘) of the reactions at the HF/3-21G levels are shown in Table 6 (AEb is the activation barrier of the reverse reaction). It can be seen that the activation barriers of the reactions decrease from reactions (1) to (8), indicating that all the substituents selected would make this reaction proceed more easily. In order to improve the energetics, the MP2 procedure was used to rectify the barriers for all the reactions in this work; the values of MP2 energy of each species for all the reactions are shown in Table 6. It can also be seen that the regularities
3.2.3. Energy barrier and activation entropies The energies E (a.u.) of the transition barrier Table 6 Energy E (a.u.) values of the transition using HF/3-21G optimized geometries
E (HF/3-21G) A& A& E (MP2/3-21G) A-& A& E (MP2/6-3 1G*) A&
states and the activation
barriers
AE, (kJ mol-‘)
of the reactions
Reaction
(1)
(2)
(3)
-190.71050 294.8 337.1 -191.09819 311.9 330.6 -192.34348 282.0
-245.42428 294.9 334.3 -245.91855 298.5 316.7 -247.52887 273.3
-289.06127 289.2 290.9 -289.57053 297.5 261.6 -291.39939 271.4
(4) -343.77763 282.5 284.9 -344.39254 279.8 248.7 -346.58619 258.9
Reaction (5) E (HF/3-21G) A.% A& E (MP2/3-21G) AE, A&
-524.52845 251.8 341.8 -525.35087 295.7 330.8
(6) -579.24426 246.5 335.0 -580.17383 275.4 314.3
95
TS geometries
using Mulliken population analysis. The (CT) values from substituted ethylene to the substituted formaldehyde are -0.1871 e, -0.2030 e, -0.2056 e, -0.2188 e, -0.3496 e, -0.3583 e, -0.3876 e and -0.3959 e for reactions (l)-(8) respectively. Thus, the amount of CT increases from reactions (1) to (8) similarly to the decreasing trend of the activation barrier.
Energy
336 (1995) 91-100
(7) -622.87450 224.9 289.5 -623.81848 239.8 265.3
(8) -677.59208 215.1 293.2 -678.63971 224.2 267.9
at different
levels of theory
96
G.-J. Chen, X.-Y. FujJournal of Molecular Structure (Theochem)
Table 7 Energy E (a.u.) values optimized geometries
of the transition
-6 AK (1) TS2 A&
(2)
TS, A-%
(3)
TS4 G
(4)
states and the activation
E [MP3]
E [MP4
-191.11286 317.7 -289.57509 307.4 -245.93487 302.2 -344.39902 286.8
-191.12511 322.3 -289.58886 310.8 -245.94948 305.5 -344.41509 289.4
E [MP4 PQN
@‘I
~191.12170 324.1 -289.58543 313.4 -245.94540 307.8 ~344.41100 292.1
displaying the activation barriers are not changed after MP2 calculations. The transition states of reactions (l)-(4) (concerted paths) are further calculated by single point 2 x 2 MCSCF. The results indicate that the weighted coefficients of the reference ground state configuration are 0.992, 0.985, 0.992 and 0.992 respectively. Obviously, the calculated results obtained by HF are basically correct. In addition to MP2/3-2 1G calculations, MP2/631G* and MP4/3-21G based on the HF/3-21G optimized geometries were also used for calculating the barriers of reactions (l)-(4). The activation barriers of the reactions are reduced significantly (about 20 kJmoll*) relative to MP2/3-21G (see Table 6). The MP results are lowered by 6.7, 2.8 and 14.8 kJ mol-‘, respectively, for reactions (2)(4) in the case of MP4 (SDTQ) calculations. Obviously, the drop is the biggest when there are substituents in both reactants (see Table 7). By comparing Tables 6 and 7 it can be seen that the activation barriers of these cycloaddition reacTable 8 Entropy s values of the transition states and activation Asi of reactions (l)-(8) in J mol-’ K-’ Reaction (1) (2) (3) (4) (5) (6) (7) (8)
s 285.6 306.4 299.2 323.0 351.2 376.4 364.6 386.6
barriers
AE,
(kJmol-‘)
336 (1995) 91LlOO
at different
E WP4 (SDQ)l -191.13084 315.2 -289.59838 301.9 -245.95640 297.4 -344.42532 280.6
MP levels using HF/3-21G
E [MP4 (SDTQ)] -191.14694 304.2 -289.61912 288.2 -245.97616 .286.4 -344.44902 267.7
tions are still high even though the electron correlation and the effect of the basis set are considered, and the activation entropy of each reaction is negative. The entropies and the activation entropies obtained by using the calculated vibrational frequencies and a statistical method are given in Table 8 with the values of exp (As’/R). As is shown in Table 8, the activation entropies of these cycloaddition reactions are negative. The values of exp (As#/R) indicate that the rate of the reactions will also be decreased by the activation entropy. Thus, in the light of conventional transition state theory, the ratio of the reaction rates of reactions (8) and (1) is 6.90 x lOI at the MP2/3-2 1G level at room temperature. Therefore, although the barrier of reaction (8) is much lowered by substituents in the reactants, the rate of reaction (8) is still very low (about 1O-37s-‘). Even though at high temperature (such as 600K) its reaction rate (the change of the activation barrier and entropy with temperature were not taken into account) is about 1.6 x 10-17, the reactions we have studied proceed only with difficulty via the [2s+2a] reaction path.
entropies
3.3. Cycloaddition by a stepwise process
A,#
exp(As#/R)
- 150.2 -164.5 -164.4 -175.8 -181.8 -191.7 -185.7 -198.7
1.4 2.6 2.6 6.6 3.2 9.7 2.0 4.2
x x x x x x x x
10-8 1O-9 1O-9 lo-‘0 IO-” lo-” lo-‘0 IO-”
From the above discussion, it can be seen that the activation barriers of the [2s+2a] reaction paths calculated are rather high, even though the electron correlation and the effect of the basis set are accounted for. Besides, the activation entropies of these cycloaddition reactions are negative values. This shows that the reactions we have studied proceed with difficulty via [2s+2a] reaction paths.
G.-J. Chen. X.-Y. Fu/Journal of Molecular Structure (Theochem)
91
differences between their activation barriers are not large after the electron correlation had been taken into account, using the second-order Moller-Plesset perturbation method (MP2). This shows that these two paths can compete with each other. The activation barriers (about 187kJmoll’) of stepwise reaction pathways are much smaller than that of the [2s+2a] reaction path (about 224 kJ mall’) (UMP2/3-21G), and
Therefore, stepwise reaction paths must be investigated. Obviously, for the stepwise reaction mechanism, there are at least two possible reaction paths, namely, to form the C-C or the C-O bond first. For simplicity, only reaction (8) is studied, i.e. the following process is investigated (the atomic subscripts at INTl and INT2 of Scheme 2 comprise the numbering system of the intermediate and the transition structures): 46 r\ Be C, TSI
336 (1995) 91blOO
F+ C, fi
\ yj;
1:
II,Hs
/
y-y0
INTi CHa=CH!% + O=CFCF3
/-CFCFS 11, !; Iis
o,,
NHk
1'
\_
INTZ Scheme 2.
The reaction in Scheme 2 yields two intermediates (INTl or INT2) via transition states TSl or TS3, followed by ring closure to form the product via transition states TS2 or TS4. The geometries of all stationary points on the potential energy surface were fully optimized using the unrestricted Hartree-Fock (UHF) at the 3-21G basis set. MP2 single point calculations on 3-21G geometries of some stationary points were also carried out. The optimized geometric parameters of the intermediates and the transition states in these pathways are given in Table 9. The corresponding energies and the activation barrier AE, of the forward reactions and AE, of the reverse reactions are also shown in Table 10. As shown in Table 9, there are some differences between the geometric parameters in these two stepwise paths. For example, the geometries of the molecular skeletons are different; their main dihedral angles are 46.71”and 68.19” in TSl and TS3 respectively. But from Table 10, the
the activation entropy of stepwise reactions (ratedetermining step) is calculated to be about 170.0 J mol-’ K-l. Therefore, in terms of conventional transition state theory, the ratio of the reaction rates of the stepwise process and the [2s+2a] path of reaction (8) is 1.04 x lo* at the MP2/3-21 level at room temperature. Hence the stepwise process predominates. However, relative to the stepwise process for reaction (l), the activation barrier of the stepwise process for reaction (8) is low (about 80 kJ mall’ [6]), although it is well known that there are some spin contaminations in the results of UHF calculations. We have estimated the approximate energy of the projections of the UMP2 singlet state (PUMP2) on the basis of the scheme developed by Yamaguchi et al. [13(a)] and Skancke et al. [13(b)]. The values obtained are also given in Table 10. It can be found that the activation barriers of reaction (8) are about 70 kJ mall’ after elimination of spin contamination. Therefore, reaction (8) can probably be carried out even if
98 Table 9 Geometric Parameter
G.-J. Chen. X.-Y. FulJournal of Molecular Structure (Theochem)
parameters
of all stationary TSI
c1orc4
1.4014 1.8139 1.2916 1.3704 1.0696 1.0717 1.0706 1.3625 1.4840
CIO-FI~
1.3406
cl-c2 c2-03 03-c4 N5-c1 H6-Cl H7-G Ha-C5 F9&4
CtorF14 GO-FE HII-N5
1.3635 1.3427 0.9968 110.45 115.53 123.41 119.66 93.74 98.61
117.93 120.20 111.97 111.21 110.44 120.83 46.71 83.20 -87.49 168.83 -75.54 -74.91 64.30 170.12 119.94 -121.69 1.61
points of the stepwise paths for reaction
INTl 1.4942 1.4783 1.3482 1.3946 1.0726 1.0800 1.0774 1.3497 1.4841 1.3439 1.3500 1.3475 0.9993 109.49 116.76 115.61 118.21 102.95 108.63 114.45 115.97 110.87 108.5 113.56 117.32 61.99 52.62 -161.39 182.62 -60.39 -128.68 97.78 188.08 119.07 -121.41 -33.00
TS2 1.5058 1.4742 1.3619 1.3911 1.0719 1.0778 1.0754
1.3498 1.4834 1.3448 1.3505 1.3482 1.0996 107.16 109.82 116.92 119.24 106.17 108.20 114.21 115.99 110.90 108.81 113.69 118.51 27.37 83.84 -128.00 148.64 -92.61 -135.23 90.43 188.28 119.06 -121.32 -34.03
there are unfavourable activation entropies in the cycloaddition reaction. The reaction rate is about 1.3 x 10e2 at 600 K (the change of the activation barrier and entropy with temperature are not taken into account). Obviously, if the hydrogens of formaldehyde are substituted by stronger electronwithdrawing groups than F and CFs and/or the hydrogens on ethylene, are substituted by stronger electron-releasing groups than NH2, the cycloaddition reactions would be expected to proceed even at room temperature. In fact, when hydrogens
336 (1995) 91-100
(8) (bond lengths in A; bond angles in deg)
Parameter
TS3
CIO-F13
1.4402 1.9107 1.2782 1.3961 1.0728 1.0714 1.0708 1.3785 I .5087 1.3454
C10rF14
1.3533
Cl
-c2
Cl
--c4
c4c03 NS+I H6-Cl H7-C2 K-C2 F9&4 clod4
CIO-FIS H11rN5 IC4CI
c2
jO3C4CI INsCIC~
iH6CIC403 fH7C2C,C4 iH8C2C,C4 fF9C4G
C2
1.3423 0.9983 101.66 106.64 108.11 97.53 120.28 119.25 101.74 103.93 111.79 110.22 111.99 118.53 68.19 -168.07 -50.51 100.97 -64.57 -55.75 -168.30 197.70 118.99 -121.18 41.52
INT2 1.5030 1.5516 1.3857 1.4505 1.0815 1.0702 1.0712 1.3809 1.5124 1.3420 1.3464 1.3459 1.0028 109.93 108.49 111.49 106.19 116.99 121.39 109.25 112.32 111.61 109.44 111.52 113.30 52.10 173.31 -67.90 155.52 -35.44 -70.34 171.20 187.33 119.91 -120.97 59.66
TS4 1s220 1.5256 1.4050 1.4403 1.0778 1.0720 1.0704 1.3803 1.4987 1.3401 1.3457 1.3504
1.0029 98.99 100.67 115.84 108.21 117.76 120.46 111.17 114.33 113.42 109.76 108.84 113.72 25.02 147.11 -88.84 77.78 -123.41 -93.83 144.34 181.44 121.59 -120.82 60.11
on formaldehyde are substituted by -CN and P-N02C5H4, respectively, 3,3,4,4-tetralkoxyoxetane-Zcarbonitriles are formed in excellent yields at room temperature [14]. In order to confirm the characteristics of these reaction paths, the gross atomic spin densities and charge populations were calculated and the values of some atoms are listed in Table 11. From Table 11, it can be confirmed that these stepwise reaction pathways are mainly of a diradicaloid nature.
G.-J. Chen. X.-Y. Fu/Journal of Molecular Structure (Theochem)
Table 10 Energy E (a.u.) values of all the stationary points, the activation barrier AE (kJmol_‘) values (J mol-’ K-i) of reaction (8) at different levels of theory using HF/3-21G optimized geometries TSl
Energy E (UHF/3-21G) A& A& E (UMP2/3-21G) A& A& E (PUMP2/3-21G) A& A& ASi Table 11 The Mulliken Atom
Cl CZ 03 c4
INTl
-677.63590 100.0
-677.63858
177.7 -678.64557
-677.66032
677.65446 129.4 -678.65655 223.7 -678.68715
-678.69976 67.6
143.4
196.3 -180.6
-165.4
atomic
spin densities
(SD) and charge
INTl
TSI
As+
TS4
-678.65351 189.0
252.5 -678.66701
678.69793 72.4
entropies
INT2
-677.64683 71.3
-677.63605
-678.65444 186.6
and the activation
TS3
TS2
99
336 (1995) 91-100
populations
TS2
Atom
SD
CP
SD
CP
SD
CP
-0.77 0.41 -0.43 0.91
0.07 -0.38 -0.54 0.70
-1.01 0.14 -0.01 0.98
0.01 -0.15 -0.69 0.69
-0.95 0.13 -0.04 0.95
-0.02 -0.14 -0.68 0.68
4. Conclusions
TS3 SD
c2 c, c4 o3
PI.20 0.55 -0.45 0.82
INT2
TS4 _____
CP
SD
CP
SD
CP
-0.33 -0.07 0.58 -0.43
-1.30 0.26 -0.17 1.02
-0.33 -0.17 0.51 -0.33
-1.14 0.20 PO.14 0.92
-0.3 1 -0.18 0.54 -0.36
References
On the basis of the above results and discussion, the following conclusions can be drawn. (a) Some substituents can reduce the activation barriers of the title reaction. The stronger are the electron-withdrawing groups in formaldehyde and/ or the electron-releasing group in ethylene, the smaller are the activation barriers of the cycloaddition reactions. (b) The cycloaddition reactions we studied proceed with difficulty via the [2s+2a] reaction path owing to the high activation barrier and unfavourable activation entropies. However, the reactions are probably carried out via stepwise pathways when the strong electron-withdrawing groups are in formaldehyde and/or the electron-releasing group is in ethylene. Acknowledgements This project was supported by the Foundation the National Natural Science Fund of China.
(CP) (3-21G) on four atoms
of
PI L. Zalotal,
Zs. Hunyadi-Zoltan, T. Berces and F. Marta, Int. J. Chem. Kinet., 15 (1983) 505. L. Zalotal, T. Berces and F. Marta, PI Zs. Hunyadi-Zoltan, Acta Chim. Acad. Sci. Hung., 15 (1983) 505. and R.A. Scott, J. Chem. Sot., Faraday 131K.A. Holbrook Trans. 1, 71 (1975) 1849. [41D.A. Bittker and W.D. Walters, J. Am. Chem. Sot., 77 (1955) 2326. [51G.J. Chen, DC. Fang and X.Y. Fu, Int. J. Quantum Chem., 23 (1989) 501. P-YG.J. Chen and X.Y. Fu. J. Mol. Sci. (China), 9 (1993) 6. [71M.J. Frisch, J.A. Binkley, H.B. Schlegel, K. Raghavachari, C.F. Melius, R.L. Martin, J.J.P. Stewart, F.W. Bobrowicz, C.M. Rohlfing, L.R. Kahn, D.J. Defrees, R. Seeger, R.A. Whiteside, D.J. Fox, E.M. Fleuder and J.A. Pople, GAUSSIAN 86, Carnegie Mellon Chemistry Publishing Unit.. Pittsburgh, PA, 1984. PI M.S. Gordon, J.S. Binkley, J.A. Pople, W.J. Pietro and W.J. Hehre, J. Am. Chem. Sot., 104 (1982) 2797. [91C. Meller and M.S. Plesset, Phys. Rev., 46 (1934) 618. DOI (a) R. Krishnan and J.A. Pople, Int. J. Quantum Chem., 14 (1978) 91. (b) R. Krishnan, M.J. Frisch and J.A. Pople, J. Chem. Phys., 72 (1980) 4244.
100 [ll]
G.-J. Chen, X.-Y. FujJournal of Molecular Structure (Theochem)
(a) W.J. Hehre, R. Ditchfield and J.A. Pople, J. Chem. Phys., 56 (1972) 2257. (b) A. Szabo and N.S. Osthmd, Modern Quantum Chemistry; Introduction to Advanced Electronic Structure, Macmillan, New York, 1982. [12] M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, ES. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin,
336 (199.5) 91-100
D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart and J.A. Pople, GAUSSIAN 92, Revision A, Gaussian Inc., Pittsburgh, PA, 1992. [13] (a) K. Yamaguchi, Y. Takahara, T. Fueno and K.N. Houk, Theor. Chim. Acta, 73 (1988) 337. (b) P.N. Skancke, N. Koga and K. Morokuma, J. Am. Chem. Sot., 111 (1989) 1559. [14] P.H.J. Ooms, J.W. Scheeren and R.J.F. Nivard, J. Chem. Sot. Perkin Trans. 1 (1976) 1048.
of Molecular
Structure
(Theochem)
336 (1995) 9 l-100
Theoretical studies on the substituent effect of the thermal cycloaddition of ethylene and formaldehyde Guang-Ju
Chen, Xiao-Yuan
Fu*
Chemistry Department, Beijing Normal Universit.y, Beijing 100875, People’s Republic of China Received
23 November
1993; accepted
17 November
1994
Abstract Ab initio HF molecular orbital calculations using 3-21G and 6-31G* basis sets and including electron correlation (MP2 to MP4) have been applied to investigate the concerted supra-antara [2s + 2a] thermal cycloaddition reaction of some substituted ethylenes and formaldehyde. The stepwise reaction paths have also been studied for one of the reactions by using UHF/3-21G and MP2/3-21G. The calculated results indicate that although the presence of some particular substituents can decrease the activation barriers obviously, the title reaction is difficult to carry out via the supra-antara [2s + 2a] thermal cycloaddition pathway under moderate conditions. However, the reactions are probably carried out via stepwise pathways when there are strong electron-withdrawing groups in formaldehyde and/or electron-releasing groups in ethylene.
1. Introduction The gas-phase decomposition of oxetane to form ethylene and formaldehyde has been studied by Zalotal and co-workers [1,2] and others [3,4] and the reverse reaction, the [2+2] gas-phase cycloaddi-
tion reaction, has not been found experimentally. The transition state structures of the concerted supra-antara ([2s+2a]) and stepwise cycloaddition reaction of ethylene and formaldehyde have been optimized by us previously at the HF/3-21G and MP2/3-21G levels [5,6]. Because the activation barrier is high and the activation entropy negative, this cycloaddition reaction proceeds with difficulty. The question is whether, if some proper substituents are added to ethylene and formaldehyde respectively, these cycloaddition reactions can be made to occur. * Corresponding 0166-1280/95/$09.50
author. 0
1995
SSDI 0166-1280(94)04039-7
On the basis of this consideration, some electronwithdrawing groups have been added to the formaldehyde molecule and on electron-releasing group to ethylene, and the effect of substituents on the reaction barriers is investigated. In this work we have studied the following type of reaction theoretically (the subscripts in Scheme 1 comprise the numbering system of the products and the transition states structures): Reaction x Y z
(1) H HH H
(2) NH2 H
(3) H HH F
(4) NH2 F
(5) H HH CF3
(6) NH2 CF,
(7) H FF CF,
(8) NH2 CF,
Firstly, we have fully optimized the geometries of the [2s+2a] transition states for all these reactions and confirmed them by vibrational frequency analysis. Secondly, the stepwise reaction paths have also been studied for reaction (8) to compare with the concerted one. The electron correlation and the
Elsevier Science B.V. All rights reserved
92
G.-J. Chen, X.-Y. Fu/Journal
of MolecularStructure
(Theochem)
336 (1995) 91-100
TS l
Scheme
effects of the basis sets have also been explored. The role of activation entropies is discussed.
I
time, UHF was also used for investigating the stationary points of the [2s+2a] reaction path for comparison with the RHF calculation. The results show that they are consistent with that of RHF.
2. Method of calculation 3. Results and discussion All the calculations based on Hartree-Fock formulation were performed by using the GAUSSIAN 86 program packages [7] at a Vax-4000 workstation. For the [2s+2a] reaction pathway, the full geometry optimization was carried out at the Hartree-Fock level with analytical first and second energy derivatives without any symmetry restriction. The basis set used for the optimizations was 3-21G [8]. To confirm the transition state structure, we computed the second derivative matrix analytically. The electron correlation was taken into account using the second-order Maller-Plesset (MP2) [9] for all reactions and MP4 [lo] for the first four reactions at the 3-21G HF optimized geometries. In order to account for the effect of the basis sets, MP2/6-31G* [l l] calculations were performed for reactions (l)-(4) using 3-21G HF optimized geometries. The transition states of reactions (l)-(4) were further calculated by 2 x 2 MCSCF using GAUSSIAN 92[121to confirm the reliability of the results obtained using single configuration calculations (MP4, MP2/6-31G* and 2 x 2 MCSCF calculations have not been carried out for reactions (.5)-(8) because the atoms involved in these reactions are rather large). The activation entropy of each reaction was calculated by using the calculated vibrational frequencies and a statistical method. The stepwise processes for reaction (8) were studied using the unrestricted Hartree-Fock (UHF) at the level of the 3-21G basis set. MP2 single point calculations on 3-21G geometries of some stationary points were also carried out. In order to obtain the spin population, the “mix” option was used to mix the frontier molecular orbitals. At the same
3.1. Reactants
and products
3.1.1. The frontier molecular orbitals of the reactant
We optimized the geometries of the reactant by using an energy gradient technique at the 3-21G level and obtained their geometries and molecular orbitals. Upon adding a substituent to ethylene or formaldehyde its C=C or C=O double bond, respectively, is shortened, but the frontier molecular orbitals (FMO) of H2C=CHNH2 are still a 7rcI) orbital (HOMO) and a 7rilJorbital (LUMO), i.e. its FM0 are similar to those of ethylene. At the same time, the 7rc2)molecular orbital is NHOMO and 7rfZj LUMO for substituted formaldehyde (i.e. their FM0 are also similar to those of formaldehyde). Although the types of FM0 are not changed, their relative energies are different. There are two types of FM0 interactions between the reactants: the HOMO (7rc1))of (substituted) ethylene and the LUMO (7ri2) of (substituted) formaldeTable 1 Energy gaps of FM0 of the substituted Reaction
(1) (2) (3) (4) (5) (6) (7) (8)
ethylene and formaldehyde
Energy gap of FMO/eV
@?I,-$,I
-e(2)
14.34 14.03 14.42 14.11 12.79 12.48 12.77 12.45
19.41 19.60 19.86 20.05 20.74 20.93 21.01 21.20
-$)I
G.-J. Chen. X.-Y. FulJournal of Molecular Structure (Theochem) Table 2 The main geometric Parameter
parameters
c2-03 c4-03 L”3c2c, !C403C2 LC403C2C,
(bond lengths in A, bond angles in deg)
Reaction
(1) cl-c2
of all products
93
336 (1995) 91-100
.5578 1.4757
I
1.4757
90.95 91.00 0.00
(2) 1.5539 1.4756 1.4758 91.09 91.51 5.68
(3)
(4)
1.5578 1.4828 1.4328 89.40 92.79 0.59
1.4337 89.81 92.30 3.00
hyde; the NHOMO (7r& of (substituted) formaldehyde and the LUMO (7rit,) of (substituted) ethylene. However, the energy gap between the former is much smaller than the latter as shown in Table 1. Therefore, in terms of frontier orbital theory, if the above reaction proceeds via the supra-antara [2s+2a] reaction path, the interactions of FM0 are mainly 7rc1)molecular orbitals of HlC=CHz or H2C=CHNH2 with 7rTZ,of the formaldehyde or substituted formaldehyde. 3.1.2. Structures of the products We also obtained the geometries of the products by using an energy gradient technique at the 3-21G level. The main geometric parameters of the products are given in Table 2 with the numbering system shown in Scheme 1 and the energies E (a.u.) are shown in Table 3. It can be seen from Table 2 that the substituent slightly affects the molecular skeleton. For example, C2-0s is lengthened and C2-0s shortened with addition of the substituent, and these molecules are puckered rings with twisted angles. Table 3 Energy E (a.u.) of the products mized geometries
at the level of HF/3-21G
Reaction
E(HF/3-21G)
E(MP2/3-2lG)
(1) (2) (3) (4) (5) (6) (7) (8)
-190.83891 -245.55160 -289.17207 -343.88615 -524.65862 -579.37185 -622.98476 -677.70375
-191.22264 -246.03918 -289.66999 -344.48725 -525.47688 -580.29355 -623.91951 -678.74176
1.5542 1.4813
opti-
(5)
(6)
(7)
1.5574 1.4858 1.458 1 90.13 91.51 8.19
1.5539 1.4817 1.4570 90.66 91.36 6.13
1.5563 1.4919 1.4205 89.07 91.89 7.07
3.2. Concerted supra-antara 3.2.1. Optimized
(8) 1.5560 1.4917
1.4107 89.28 92.85 3.85
[2s+2a] cycloaddition
geometries
The [2s+2a] reaction paths of all reactions are assumed to involve singlet states because the cycloaddition reaction takes place under thermal conditions. The geometric parameters corresponding to the transition states for each reaction are given in Table 4 with the numbering system shown in Scheme 1. There is some regularity in the change of the developing bonds C2-0s and Ci-C4 with reactions (l)-(8), i.e. C2-O3 is lengthened and Ci -Cd is shortened from reactions (1) to (8). This indicates that the substituents may increase the non-synchronism of the reaction; the larger the substituent, the more obvious is this effect. The bond angles of the molecular skeleton also vary with the substituents, i.e. 103C2C1 decreases and LC4C1C2 increases. The changes in the other bond lengths and angles are small. From data for the main dihedral angle 103C2C4C1, it can be realized that the four-membered ring of the TS is somewhat twisted. Each transition state was confirmed to have only one imaginary vibration frequency f in the normal coordinate analysis based on the analytical second derivatives of energy. Values off (cm-‘) are 1433.8i, 1402.51, 1337.31, 1295.61, 1299.71, 1253.11, 1074.Oi and 1031.9i for reactions (l)-(8) respectively. The vibrational frequencies are gradually reduced from reactions (1) to (8). This sequence is in accord with the sequence of the charge transfer between the two reactants and the activation energy of the reactions (see below). For these transition states, the major contribution of the
94
G.-J. Chen, X.-Y. Fu/Journal
Table 4 The geometric Parameter
parameters
of all transition
of Molecular Structure (Theochem)
336 (1995)
91ClOO
states (bond lengths in A; bond angles in deg)
Reaction 1
2
3
4
5
6
7
8
-
1.4004
cl-c2 03 -c2 Cl --c4 x5-c, H6-Cl H7-C2 Y9&4 zIorc4 icI
c203
LC4ClC2 ix5c1c2 ~H6ClG ~H7GG
iY9C403 ~ZIOC403 103c2c4cI fx5~1~2~3 iH6CIC203 iH7C2CIC4 iH8C2CIC4 iy9c403c2 iz10c403c2 HII-N5 ~HIINs% iH12N503 IHIINsCIC~ ~HI~NsCIC~
2.0279 2.0040
1.4006 2.0398 1.9768
1.0725 1.0727
1.4427 1.0777
1.0674 1.0817 1.0810 98.74 78.46 118.71 118.23 121.58 120.64 120.29 169.46 109.25 -99.75 98.72 -92.95 116.02 -96.14
1.0662 1.0847 1.0815 89.11 78.18 117.14 117.22 121.64 120.32 120.13 164.52 110.62 -96.63 98.40 -92.90 123.10 -89.31 1.0043 115.46 114.60 93.65 -135.35
1.4052 2.0435 1.9385 1.0737 1.0729 1.0671 1.3600 1.0756 92.25 81.90 118.39 117.71 121.94 118.69 122.19 158.87 116.47 -95.09 99.45 -89.83 129.81 -90.57
1.4057 2.0586 1.9063 1.4453
1.0772 1.0660 1.3666 1.0771 91.85 81.49 116.22 117.05 122.06 118.36 122.39 156.57 115.04 -93.87 98.68 -90.23 133.60 -86.73 1.0045 115.25 113.56 87.48 -143.12
1.0686 1.5120 1.0836 91.87 83.16 117.54 118.49 120.72 116.23 121.67 196.47 96.46 -115.80 88.14 -93.16 97.41 -125.91
1.3530
CIO-F13
1.3530 1.3451 111.90 112.36 109.82 185.02 120.73 -119.22
CIO-FI, CIOCFI~ ~F13GoC4 ~F14GoC4 ~FIsCIOC~ ~F13C1oC403 ~F14GoC403 ~F15C1oC403
imaginary vibrational mode contains the formation of C2-0s and C-C, bonds and the lengthening of C2-C1 and Os-C4 bonds. Besides, the bending vibrations of the group (CH,) located at C4 and the rotation of the groups (CH,) located at Ci, C2 and C4 are also important contributions. 3.2.2. Electron densities The overlap populations involved in the molecular
1.3977 2.1633 1.9033 1.0733 1.0708
between heavy atoms skeletons of the transi-
1.4007 2.1563 1.8694 1.4403
I .4043 2.2208 1.8131 1.0738
1.0772
1.0723
1.0656 1.5090 1.0821 92.02 81.55 117.05 116.23 121.69 118.20 121.19 157.75 116.15 -92.81 93.16 -89.88 129.45 -91.94 1.0046 114.91 112.53 87.78 -143.51 1.3613 1.3457 1.3457 109.94 112.62 111.25 186.86 119.48 -118.83
1.0691 1.5228 1.3755 84.57 87.75 116.86 118.19 120.90 117.55 119.07 203.56 92.85 -122.34 88.19 -90.51 97.30 -133.78
1.3459 1.3541 1.3390 112.61 109.78 110.74 183.32 119.31 -121.48
1.4066 2.2354 1.8281 1.4369 1.0762 1.0686 1.5204 1.3874 85.82 86.42 115.32 116.68 121.35 118.00 118.84 201.38 96.03 -118.06 83.56 -94.28 100.33 -130.68 1.0015 115.52 113.24 106.94 -119.67 1.3459 1.3558 1.3381 112.64 109.23 111.20 180.41 118.89 -121.94
tion states of reactions (l)-(S) are summarized in Table 5. In each transition state, the overlap population data indicate that the chemical bonds in C, C4 and C2-0s are developing. There are large populations in Cd-O3 and Ci-C2 which indicate that there are still chemical bonds between them. All the other bond overlap populations between non-neighbouring atoms are negative, indicating a repulsive interaction. The amount of the charge transfer (CT) can be calculated by means of atomic charges obtained by
G.-J. Chen, X.-Y. FujJournal of Molecular Structure (Theochem) Table 5 Bond overlap
populations
Reaction (1)
(2) (3) (4) (5) (6) (7) (8)
at the HF/3-21G
optimized
cl-c2
cl-03
cl-c4
CZ-03
c2-c4
03-c4
0.2366 0.2313 0.2239 0.2101 0.1780 0.1752 0.1550 0.1373
-0.0797 -0.0830 -0.1022 ~0.1054 -0.0858 -0.088 1 -0.1063 -0.1013
0.0373 0.0406 0.0689 0.0574 0.0363 0.0111 0.0555 0.0484
0.0791 0.0804 0.0761 0.0784 0.0554 0.0546 0.0490 0.0505
-0.0098 -0.0178 -0.0352 -0.0399 -0.0309 -0.0170 -0.0463 PO.0599
0.3303 0.3309 0.3414 0.3396 0.3353 0.3522 0.3538 0.3708
states and the activation barrier AE, (kJmol_‘) of the reactions at the HF/3-21G levels are shown in Table 6 (AEb is the activation barrier of the reverse reaction). It can be seen that the activation barriers of the reactions decrease from reactions (1) to (8), indicating that all the substituents selected would make this reaction proceed more easily. In order to improve the energetics, the MP2 procedure was used to rectify the barriers for all the reactions in this work; the values of MP2 energy of each species for all the reactions are shown in Table 6. It can also be seen that the regularities
3.2.3. Energy barrier and activation entropies The energies E (a.u.) of the transition barrier Table 6 Energy E (a.u.) values of the transition using HF/3-21G optimized geometries
E (HF/3-21G) A& A& E (MP2/3-21G) A-& A& E (MP2/6-3 1G*) A&
states and the activation
barriers
AE, (kJ mol-‘)
of the reactions
Reaction
(1)
(2)
(3)
-190.71050 294.8 337.1 -191.09819 311.9 330.6 -192.34348 282.0
-245.42428 294.9 334.3 -245.91855 298.5 316.7 -247.52887 273.3
-289.06127 289.2 290.9 -289.57053 297.5 261.6 -291.39939 271.4
(4) -343.77763 282.5 284.9 -344.39254 279.8 248.7 -346.58619 258.9
Reaction (5) E (HF/3-21G) A.% A& E (MP2/3-21G) AE, A&
-524.52845 251.8 341.8 -525.35087 295.7 330.8
(6) -579.24426 246.5 335.0 -580.17383 275.4 314.3
95
TS geometries
using Mulliken population analysis. The (CT) values from substituted ethylene to the substituted formaldehyde are -0.1871 e, -0.2030 e, -0.2056 e, -0.2188 e, -0.3496 e, -0.3583 e, -0.3876 e and -0.3959 e for reactions (l)-(8) respectively. Thus, the amount of CT increases from reactions (1) to (8) similarly to the decreasing trend of the activation barrier.
Energy
336 (1995) 91-100
(7) -622.87450 224.9 289.5 -623.81848 239.8 265.3
(8) -677.59208 215.1 293.2 -678.63971 224.2 267.9
at different
levels of theory
96
G.-J. Chen, X.-Y. FujJournal of Molecular Structure (Theochem)
Table 7 Energy E (a.u.) values optimized geometries
of the transition
-6 AK (1) TS2 A&
(2)
TS, A-%
(3)
TS4 G
(4)
states and the activation
E [MP3]
E [MP4
-191.11286 317.7 -289.57509 307.4 -245.93487 302.2 -344.39902 286.8
-191.12511 322.3 -289.58886 310.8 -245.94948 305.5 -344.41509 289.4
E [MP4 PQN
@‘I
~191.12170 324.1 -289.58543 313.4 -245.94540 307.8 ~344.41100 292.1
displaying the activation barriers are not changed after MP2 calculations. The transition states of reactions (l)-(4) (concerted paths) are further calculated by single point 2 x 2 MCSCF. The results indicate that the weighted coefficients of the reference ground state configuration are 0.992, 0.985, 0.992 and 0.992 respectively. Obviously, the calculated results obtained by HF are basically correct. In addition to MP2/3-2 1G calculations, MP2/631G* and MP4/3-21G based on the HF/3-21G optimized geometries were also used for calculating the barriers of reactions (l)-(4). The activation barriers of the reactions are reduced significantly (about 20 kJmoll*) relative to MP2/3-21G (see Table 6). The MP results are lowered by 6.7, 2.8 and 14.8 kJ mol-‘, respectively, for reactions (2)(4) in the case of MP4 (SDTQ) calculations. Obviously, the drop is the biggest when there are substituents in both reactants (see Table 7). By comparing Tables 6 and 7 it can be seen that the activation barriers of these cycloaddition reacTable 8 Entropy s values of the transition states and activation Asi of reactions (l)-(8) in J mol-’ K-’ Reaction (1) (2) (3) (4) (5) (6) (7) (8)
s 285.6 306.4 299.2 323.0 351.2 376.4 364.6 386.6
barriers
AE,
(kJmol-‘)
336 (1995) 91LlOO
at different
E WP4 (SDQ)l -191.13084 315.2 -289.59838 301.9 -245.95640 297.4 -344.42532 280.6
MP levels using HF/3-21G
E [MP4 (SDTQ)] -191.14694 304.2 -289.61912 288.2 -245.97616 .286.4 -344.44902 267.7
tions are still high even though the electron correlation and the effect of the basis set are considered, and the activation entropy of each reaction is negative. The entropies and the activation entropies obtained by using the calculated vibrational frequencies and a statistical method are given in Table 8 with the values of exp (As’/R). As is shown in Table 8, the activation entropies of these cycloaddition reactions are negative. The values of exp (As#/R) indicate that the rate of the reactions will also be decreased by the activation entropy. Thus, in the light of conventional transition state theory, the ratio of the reaction rates of reactions (8) and (1) is 6.90 x lOI at the MP2/3-2 1G level at room temperature. Therefore, although the barrier of reaction (8) is much lowered by substituents in the reactants, the rate of reaction (8) is still very low (about 1O-37s-‘). Even though at high temperature (such as 600K) its reaction rate (the change of the activation barrier and entropy with temperature were not taken into account) is about 1.6 x 10-17, the reactions we have studied proceed only with difficulty via the [2s+2a] reaction path.
entropies
3.3. Cycloaddition by a stepwise process
A,#
exp(As#/R)
- 150.2 -164.5 -164.4 -175.8 -181.8 -191.7 -185.7 -198.7
1.4 2.6 2.6 6.6 3.2 9.7 2.0 4.2
x x x x x x x x
10-8 1O-9 1O-9 lo-‘0 IO-” lo-” lo-‘0 IO-”
From the above discussion, it can be seen that the activation barriers of the [2s+2a] reaction paths calculated are rather high, even though the electron correlation and the effect of the basis set are accounted for. Besides, the activation entropies of these cycloaddition reactions are negative values. This shows that the reactions we have studied proceed with difficulty via [2s+2a] reaction paths.
G.-J. Chen. X.-Y. Fu/Journal of Molecular Structure (Theochem)
91
differences between their activation barriers are not large after the electron correlation had been taken into account, using the second-order Moller-Plesset perturbation method (MP2). This shows that these two paths can compete with each other. The activation barriers (about 187kJmoll’) of stepwise reaction pathways are much smaller than that of the [2s+2a] reaction path (about 224 kJ mall’) (UMP2/3-21G), and
Therefore, stepwise reaction paths must be investigated. Obviously, for the stepwise reaction mechanism, there are at least two possible reaction paths, namely, to form the C-C or the C-O bond first. For simplicity, only reaction (8) is studied, i.e. the following process is investigated (the atomic subscripts at INTl and INT2 of Scheme 2 comprise the numbering system of the intermediate and the transition structures): 46 r\ Be C, TSI
336 (1995) 91blOO
F+ C, fi
\ yj;
1:
II,Hs
/
y-y0
INTi CHa=CH!% + O=CFCF3
/-CFCFS 11, !; Iis
o,,
NHk
1'
\_
INTZ Scheme 2.
The reaction in Scheme 2 yields two intermediates (INTl or INT2) via transition states TSl or TS3, followed by ring closure to form the product via transition states TS2 or TS4. The geometries of all stationary points on the potential energy surface were fully optimized using the unrestricted Hartree-Fock (UHF) at the 3-21G basis set. MP2 single point calculations on 3-21G geometries of some stationary points were also carried out. The optimized geometric parameters of the intermediates and the transition states in these pathways are given in Table 9. The corresponding energies and the activation barrier AE, of the forward reactions and AE, of the reverse reactions are also shown in Table 10. As shown in Table 9, there are some differences between the geometric parameters in these two stepwise paths. For example, the geometries of the molecular skeletons are different; their main dihedral angles are 46.71”and 68.19” in TSl and TS3 respectively. But from Table 10, the
the activation entropy of stepwise reactions (ratedetermining step) is calculated to be about 170.0 J mol-’ K-l. Therefore, in terms of conventional transition state theory, the ratio of the reaction rates of the stepwise process and the [2s+2a] path of reaction (8) is 1.04 x lo* at the MP2/3-21 level at room temperature. Hence the stepwise process predominates. However, relative to the stepwise process for reaction (l), the activation barrier of the stepwise process for reaction (8) is low (about 80 kJ mall’ [6]), although it is well known that there are some spin contaminations in the results of UHF calculations. We have estimated the approximate energy of the projections of the UMP2 singlet state (PUMP2) on the basis of the scheme developed by Yamaguchi et al. [13(a)] and Skancke et al. [13(b)]. The values obtained are also given in Table 10. It can be found that the activation barriers of reaction (8) are about 70 kJ mall’ after elimination of spin contamination. Therefore, reaction (8) can probably be carried out even if
98 Table 9 Geometric Parameter
G.-J. Chen. X.-Y. FulJournal of Molecular Structure (Theochem)
parameters
of all stationary TSI
c1orc4
1.4014 1.8139 1.2916 1.3704 1.0696 1.0717 1.0706 1.3625 1.4840
CIO-FI~
1.3406
cl-c2 c2-03 03-c4 N5-c1 H6-Cl H7-G Ha-C5 F9&4
CtorF14 GO-FE HII-N5
1.3635 1.3427 0.9968 110.45 115.53 123.41 119.66 93.74 98.61
117.93 120.20 111.97 111.21 110.44 120.83 46.71 83.20 -87.49 168.83 -75.54 -74.91 64.30 170.12 119.94 -121.69 1.61
points of the stepwise paths for reaction
INTl 1.4942 1.4783 1.3482 1.3946 1.0726 1.0800 1.0774 1.3497 1.4841 1.3439 1.3500 1.3475 0.9993 109.49 116.76 115.61 118.21 102.95 108.63 114.45 115.97 110.87 108.5 113.56 117.32 61.99 52.62 -161.39 182.62 -60.39 -128.68 97.78 188.08 119.07 -121.41 -33.00
TS2 1.5058 1.4742 1.3619 1.3911 1.0719 1.0778 1.0754
1.3498 1.4834 1.3448 1.3505 1.3482 1.0996 107.16 109.82 116.92 119.24 106.17 108.20 114.21 115.99 110.90 108.81 113.69 118.51 27.37 83.84 -128.00 148.64 -92.61 -135.23 90.43 188.28 119.06 -121.32 -34.03
there are unfavourable activation entropies in the cycloaddition reaction. The reaction rate is about 1.3 x 10e2 at 600 K (the change of the activation barrier and entropy with temperature are not taken into account). Obviously, if the hydrogens of formaldehyde are substituted by stronger electronwithdrawing groups than F and CFs and/or the hydrogens on ethylene, are substituted by stronger electron-releasing groups than NH2, the cycloaddition reactions would be expected to proceed even at room temperature. In fact, when hydrogens
336 (1995) 91-100
(8) (bond lengths in A; bond angles in deg)
Parameter
TS3
CIO-F13
1.4402 1.9107 1.2782 1.3961 1.0728 1.0714 1.0708 1.3785 I .5087 1.3454
C10rF14
1.3533
Cl
-c2
Cl
--c4
c4c03 NS+I H6-Cl H7-C2 K-C2 F9&4 clod4
CIO-FIS H11rN5 IC4CI
c2
jO3C4CI INsCIC~
iH6CIC403 fH7C2C,C4 iH8C2C,C4 fF9C4G
C2
1.3423 0.9983 101.66 106.64 108.11 97.53 120.28 119.25 101.74 103.93 111.79 110.22 111.99 118.53 68.19 -168.07 -50.51 100.97 -64.57 -55.75 -168.30 197.70 118.99 -121.18 41.52
INT2 1.5030 1.5516 1.3857 1.4505 1.0815 1.0702 1.0712 1.3809 1.5124 1.3420 1.3464 1.3459 1.0028 109.93 108.49 111.49 106.19 116.99 121.39 109.25 112.32 111.61 109.44 111.52 113.30 52.10 173.31 -67.90 155.52 -35.44 -70.34 171.20 187.33 119.91 -120.97 59.66
TS4 1s220 1.5256 1.4050 1.4403 1.0778 1.0720 1.0704 1.3803 1.4987 1.3401 1.3457 1.3504
1.0029 98.99 100.67 115.84 108.21 117.76 120.46 111.17 114.33 113.42 109.76 108.84 113.72 25.02 147.11 -88.84 77.78 -123.41 -93.83 144.34 181.44 121.59 -120.82 60.11
on formaldehyde are substituted by -CN and P-N02C5H4, respectively, 3,3,4,4-tetralkoxyoxetane-Zcarbonitriles are formed in excellent yields at room temperature [14]. In order to confirm the characteristics of these reaction paths, the gross atomic spin densities and charge populations were calculated and the values of some atoms are listed in Table 11. From Table 11, it can be confirmed that these stepwise reaction pathways are mainly of a diradicaloid nature.
G.-J. Chen. X.-Y. Fu/Journal of Molecular Structure (Theochem)
Table 10 Energy E (a.u.) values of all the stationary points, the activation barrier AE (kJmol_‘) values (J mol-’ K-i) of reaction (8) at different levels of theory using HF/3-21G optimized geometries TSl
Energy E (UHF/3-21G) A& A& E (UMP2/3-21G) A& A& E (PUMP2/3-21G) A& A& ASi Table 11 The Mulliken Atom
Cl CZ 03 c4
INTl
-677.63590 100.0
-677.63858
177.7 -678.64557
-677.66032
677.65446 129.4 -678.65655 223.7 -678.68715
-678.69976 67.6
143.4
196.3 -180.6
-165.4
atomic
spin densities
(SD) and charge
INTl
TSI
As+
TS4
-678.65351 189.0
252.5 -678.66701
678.69793 72.4
entropies
INT2
-677.64683 71.3
-677.63605
-678.65444 186.6
and the activation
TS3
TS2
99
336 (1995) 91-100
populations
TS2
Atom
SD
CP
SD
CP
SD
CP
-0.77 0.41 -0.43 0.91
0.07 -0.38 -0.54 0.70
-1.01 0.14 -0.01 0.98
0.01 -0.15 -0.69 0.69
-0.95 0.13 -0.04 0.95
-0.02 -0.14 -0.68 0.68
4. Conclusions
TS3 SD
c2 c, c4 o3
PI.20 0.55 -0.45 0.82
INT2
TS4 _____
CP
SD
CP
SD
CP
-0.33 -0.07 0.58 -0.43
-1.30 0.26 -0.17 1.02
-0.33 -0.17 0.51 -0.33
-1.14 0.20 PO.14 0.92
-0.3 1 -0.18 0.54 -0.36
References
On the basis of the above results and discussion, the following conclusions can be drawn. (a) Some substituents can reduce the activation barriers of the title reaction. The stronger are the electron-withdrawing groups in formaldehyde and/ or the electron-releasing group in ethylene, the smaller are the activation barriers of the cycloaddition reactions. (b) The cycloaddition reactions we studied proceed with difficulty via the [2s+2a] reaction path owing to the high activation barrier and unfavourable activation entropies. However, the reactions are probably carried out via stepwise pathways when the strong electron-withdrawing groups are in formaldehyde and/or the electron-releasing group is in ethylene. Acknowledgements This project was supported by the Foundation the National Natural Science Fund of China.
(CP) (3-21G) on four atoms
of
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G.-J. Chen, X.-Y. FujJournal of Molecular Structure (Theochem)
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