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Ab initio molecular orbital study of the C2H4+Cl2→C2H4Cl2 reaction
Journal of Molecular Structure (Theochem) 503 (2000) 231–240 www.elsevier.nl/locate/theochem
Ab initio molecular orbital study of the C2 H4 ⫹ Cl2 ! C2H4Cl2 reaction Yuzuru Kurosaki* Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan Received 25 June 1999; received in revised form 16 August 1999; accepted 31 August 1999
Abstract A new mechanism of the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction in gas phase has been theoretically proposed using ab initio molecular orbital methods; Cl is abstracted from Cl2 by C2H4, which leads first to the production of C2 H4 Cl ⫹ Cl radicals and then to immediate recombination to form C2H4Cl2. It was predicted that this abstraction reaction, C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl; is 25.1 kcal mol ⫺1 endothermic with no transition state at the PMP4(SDTQ,full)/6-311⫹⫹G(d,p)//MP2(fc)/6-31⫹G(d,p) level of theory. The previously proposed mechanism, direct Cl2 addition to C2H4 to produce C2H4Cl2, has also been examined and an energy barrier of 36.3 kcal mol ⫺1 was obtained at the same level of theory. Therefore one concludes that the new mechanism is energetically more feasible than the direct Cl2 addition to C2H4 for the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction in the gas phase. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Alkene halogenation; Gas-phase reaction; Ab initio molecular orbital calculation; Intrinsic reaction coordinate; RHF–UHF instability
1. Introduction Although alkene halogenations, C2 H4 ⫹ X2 ! CH2 XCH2 X (X F; Cl, or Br), have been quite familiar to organic chemists for many years, it seems that there still remain open questions about the reaction mechanisms. Since the early work [1– 3] in 1930s, it has been widely accepted that alkene halogenations occur via formation of a charge-separated species [4–8]: a cyclic halogenium cation (C2H4X ⫹) plus halogen anion (X ⫺). It may be true that in polar solvents the charge-separated species
* Present address: Advanced Photon Research Center, Japan Atomic Research Institute, Umemidai 8–1, Kizu-cho, Soraku-gun, Kyoto 619–0215, Japan. Tel.: ⫹81-77-471-3371; fax: ⫹81-77-4713316. E-mail address: [email protected]. (Y. Kurosaki).
can be stabilized by solvation and the halogenation can occur via formation of a cyclic halogenium cation plus halogen anion. In the gas phase, however, the potential energy surface correlated to the chargeseparated asymptote should correspond to an electronic-excited potential surface of the C2 H4 ⫹ X2 system; hence it is unlikely that the mechanism via charge-separated species dominates the halogenation. One can thus roughly understand the reaction mechanism; however, detailed information for geometries and energetics including transition state (TS) for both reactions in the gas phase and in polar solvents is still unavailable. Compared to experimental studies, there have been a limited number of theoretical studies for alkene halogenations. Results of the theoretical studies to date are briefly reviewed here. Jaszunski and Kochanski [9] examined the C2 H4 ⫹ Cl2 reaction at
0166-1280/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00317-6
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Y. Kurosaki / Journal of Molecular Structure (Theochem) 503 (2000) 231–240
the Hartree–Fock (HF) level. They concluded that this system can produce a C2H4…Cl2 complex in the first step and that the energy of the C2 H4 Cl⫹ ⫹ Cl⫺ asymptote is too high for the intermediate state of halogenation. They then speculated that a solvent can stabilize this charge-separated intermediate state, thereby allowing the reaction. However, they considered only the C2v reaction pathway where the Cl2 axis is perpendicular to the CyC bond of C2H4. Yamabe et al. [10] optimized the geometries of TSs for the C2 H4 ⫹ F2 ; C2 H4 ⫹ Cl2 ; and C2 H4 ⫹ Br2 reactions at the HF/3-21G level of theory and found that fluorination of C2H4 occurs via a four-centered TS while both chlorination and bromination occur via three-centered TSs. However, they did not determine the reaction pathways for any of these reactions. As far as we are aware, Iwaoka et al. [11] were the first to calculate the gas-phase reaction pathway for the C2 H4 ⫹ F2 reaction. They determined the intrinsic reaction coordinate (IRC) for this reaction at the second-order Møller–Plesset (MP2) level of theory with the 6-31⫹G basis set and confirmed that a C2H4…F2 complex connects with the final syn addition product via a rhombic-type TS. Several years ago, Cossi et al. [12] studied the C2 H4 ⫹ Br2 reaction in solvents using a continuum solvation model. They obtained the first theoretical results for this reaction in solvents; however, optimizations for most geometries of minima were done only partially and the TS geometry was completely unidentified. Recently, Rivail and co-workers [13,14] have theoretically investigated the solvent effect on the C2 H4 ⫹ Br2 reaction using discrete and continuum models for solvents [13] and using a molecular dynamics method [14]. They found a marked difference between the reaction mechanisms in the gas phase and in polar solvents; the TS was predicted to have Cs symmetry in the gas phase, while C2v symmetry in polar solvents [13]. Also they found that dynamic solvent effects play an important role for the reaction mechanism [14]. Very recently, Koerner et al. [15] have examined the deuterium kinetic isotope effect (KIE) for the C2 H4 ⫹ Br2 reaction in methanol and dichloroethane
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using both experimental and theoretical techniques. They experimentally observed inverse KIEs for reactions in both the solvents and then explained these effects using theoretical methods based on density functional theory. The theoretical studies of these authors have elucidated several aspects of the alkene-halogenation mechanism; it seems, however, that detailed information about the mechanism is still lacking for reactions in the gas-phase as well as those in solvents. For example, other reaction pathways in the gas phase that are different from those of Yamabe et al. [10] and Iwaoka et al. [11] have not been investigated and an overall reaction pathway in solvents has not been determined. Although the alkene-halogenation mechanism in solvents attracts our interest, in this paper we focus our attention on the gas-phase mechanism for the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction since even the gasphase mechanism has not been entirely understood. We examine the following two reaction pathways: Cl2 addition to C2H4, which directly leads to the production of 1,2-dichloroethane C2H4Cl2; and Cl abstraction from Cl2 by C2H4, which leads first to the production of C2 H4 Cl ⫹ Cl radicals and then to the immediate recombination to form C2H4Cl2. The former reaction pathway was previously proposed [10,11], while the latter is first examined in this work. We will find that the latter reaction pathway is energetically more feasible than the former.
2. Methods of calculation All ab initio molecular orbital (MO) calculations were carried out using the gaussian 94 package program [16]. For direct Cl2 addition to C2H4, geometries of stationary points were optimized at the MP2 perturbation [17–19] level with the 6-31⫹G(d,p) basis set under the frozen-core (fc) approximation. Harmonic vibrational frequencies were computed analytically at the same level in order to characterize the optimized
Fig. 1. Optimized geometries for TS2 at the CASSCF(4,4)/6-31⫹G(d,p) level and other species at the MP2(fc)/6-31⫹G(d,p) level. In parentheses for the C2H4…Cl2 complex are given the geometrical values for the isolated C2H4 and Cl2 molecules. Bond lengths and angles ˚ and degree, respectively. are given in A
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geometries as potential minima or saddle points. Single-point energy calculations for the MP2(fc)/631⫹G(d,p) geometries were also carried out at the fourth-order MP (MP4) level including single, double, triple and quadruple (SDTQ) substitutions of all electrons (full) [20,21] with the 6-311⫹⫹G(d,p) basis set. Basis-set superposition error (BSSE) was estimated using the counterpoise method [22] for the van der Waals (vdW) complex produced in the reactant region. The IRC [23–25] was also calculated at the MP2(fc)/6-31⫹G(d,p) level with the step size being 0.1 amu 1/2 bohr. For Cl abstraction from Cl2 by C2H4, due to a high muticonfiguration character, geometries were optimized at the complete-active-space self-consistentfield (CASSCF) level [26], where four electrons are distributed in four active orbitals (CASSCF(4,4)), with the 6-31⫹G(d,p) basis set. The active space includes ClCl s and s ⴱ orbitals and CC p and p ⴱ orbitals. The IRC was calculated at the CASSCF(4,4)/6-31⫹G(d,p) level with the step size being 0.1 amu 1/2 bohr. Since the CASSCF level of theory does not take dynamical electron correlation
effects into account, single-point energies on the calculated IRC were obtained at other levels of theory. At every 0.2 amu 1/2 bohr point on the calculated IRC, single-point energies at the restricted HF (RHF), unrestricted HF (UHF), RMP2(fc), UMP2(fc) and spin-projected UMP4(SDTQ,fc) (PMP4(SDTQ,fc)) levels with the 6-31⫹G(d,p) basis set were calculated.
3. Results and discussion 3.1. Direct Cl2 addition to C2H4 Mechanism of Cl2 addition to C2H4 in the gas phase, which directly leads to production of 1,2-dichloroethane C2H4Cl2, is discussed here. Although this mechanism was previously proposed [10,11], here we confirm again that this direct reaction pathway for the present reaction really exists, using the IRC method. It was found that the vdW complex C2H4…Cl2 is produced in the reactant region. As shown in Fig. 1,
Table 1 Harmonic vibrational frequencies calculated at the MP2(fc)/6-31⫹G(d,p) level for the optimized geometries Sym
Frequencies (cm ⫺1)
Cl2 C2H4
D∞h C2h
C2H4Cl
Cs
C2H4Cl ⫹
C2v
C2H4…Cl2
C2v
trans-C2H4Cl2
C2h
gauche-C2H4Cl2
C2
TS1
Cs
TS2 a
Cs
542 846 3230 208 1339 579 1276 10I 992 3326 125 1188 3248 123 1204 3234 452i 1049 3334 351i 1081 3404
a
At the CASSCF(4,4)/6-31⫹G(d,p) level.
913 3247 317 1518 604 1524 61 1070 3350 222 1320 3268 269 1272 3245 106 1166 3417 67 1170 3438
984 3324 625 1548 867 1569 63 1264
1071 3349 712 3183 1007 3238 79 1401
1262
1404
1514
1709
805 3257 1013 3240 105 1514
1119 3265 1167 3358 509 1701
1124 3387 1211 3368 847 3230
1306
930 3246
313 1332
780 1411
801 1534
825 1534
1064 3179
1106 3187
423 1385
708 1403
736 1509
935 1514
1005 3161
1095 3166
132 1235
323 1267
676 1504
718 1561
852 3227
957 3292
71 1259
171 1348
313 1588
435 1651
807 3319
854 3328
1248
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Table 2 Total energies and ZPEs for the MP2(fc)/6-31⫹G(d,p) geometries (hartree)
Cl Cl ⫺ Cl2 C2H4 C2H4Cl C2H4Cl ⫹ C2H4…Cl2 trans-C2H4Cl2 gauche-C2H4Cl2 TS1 TS2 b a b
MP2(fc)/6-31⫹G(d,p) a
MP4(SDTQ,full)/6-311⫹⫹G(d,p)
⫺459.55409 ⫺459.67115 ⫺919.17502 ⫺78.32320 ⫺537.90235 ⫺537.62391 ⫺997.50227 ⫺997.58922 ⫺997.58692 ⫺997.44009 ⫺996.96278
⫺459.65339 ⫺459.76720 ⫺919.37348 ⫺78.42369 ⫺538.10449 ⫺537.82483 ⫺997.80161 ⫺997.88940 ⫺997.88706 ⫺997.74259
(0.00123) (0.05207) (0.05402) (0.05757) (0.05397) (0.06023) (0.06011) (0.05653) (0.05537)
In parentheses are given ZPEs. At the CASSCF(4,4)/6-31⫹G(d,p) level.
this vdW complex was assumed to have C2v symmetry; the Cl2 molecule is perpendicularly bound to the C2H4 molecular plane. Although this C2v vdW complex was calculated to have a very small imaginary frequency at the present MP2(fc)/6-31⫹G(d,p) level (see Tables 1 and 2), further optimization was not done in this work. BSSE should often be taken into account for weakly bound systems such as vdW complexes. In Table 3 are given the results of the BSSE correction with the counterpoise method for the vdW complex and BSSE was predicted to be about 0.002 hartree. In Table 4 are summarized geometrical parameters and stabilization energies (relative to the C2 H4 ⫹ Cl2 asymptote) for this vdW complex, including the results of other authors. It is seen that the X–Cl distance (X is the midpoint of the CyC bond of C2H4) calculated at the MP2 level of theory agrees fairly well with the experimental value ˚ . The calculated stabilization energy of [31], 3.128 A this vdW complex seems sensitive to both the method and basis set. The present MP2(fc)/6-31⫹G(d,p) and MP4(SDTQ,full)/6-311⫹⫹G(d,p) levels give slightly smaller values than the experimental one [32], 1.7– 2.4 kcal mol ⫺1. In Fig. 2 the stabilization energies obtained in this work are also shown. Optimized geometry for the TS of the present Cl2 addition reaction (TS1) is depicted in Fig. 1. Harmonic vibrational analyses predicted that TS1 has one imaginary frequency mode of 452i cm ⫺1 (see Table 1), confirming that TS1 is located at the saddle point of the potential energy surface. Yamabe et al. [10]
also obtained the same TS at the HF/3-21G level. It is seen that the internuclear distance between Cl ˚ larger atoms in the present TS1 geometry is 0.3–0.4 A than the HF value while that between Cl and C atoms ˚ smaller than the HF value (see Ref. are 0.1–0.2 A [10]). As shown in Fig. 2, the relative energy of TS1 with respect to the C2 H4 ⫹ Cl2 asymptote was calculated to be 36.3 kcal mol ⫺1 at the MP4(SDTQ,full)/6311⫹⫹G(d,p)//MP2(fc)/6-31⫹G(d,p) level, where zero-point vibrational energy (ZPE) was taken into account. It is therefore concluded that this reaction does not occur under normal conditions in the gas phase because of the large activation barrier. In Table 5 are shown the calculated dipole moments for TS1 and other neutral molecules. It is seen that the dipole moment of TS1 was predicted to be considerably larger than the dipole moments of other neutral molecules. This suggests that polar solvents can significantly stabilize TS1 and can totally change the reaction energetics. It is anticipated that RHF– UHF instability usually occurs for RHF wavefunctions when a chemical bond is stretched. We tried to obtain a UHF wavefunction for TS1 in order to check if RHF–UHF instability occurs; however, a UHF wavefunction for which the total energy is lower than that for the RHF wavefunction was not obtained, implying that the RHF wavefunction well describes the electronic structure of TS1. Moreover, we re-optimized the TS1 geometry at the CASSCF(4,4)/631⫹G(d,p) level in order to make sure this prediction is true. Consequently, essentially the same geometry
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Table 3 BSSE for the C2H4…Cl2 complex (hartree) C2H4
MP2(fc)/6-31⫹G(d,p) DE a BSSE b MP4(SDTQ,full)/6311⫹⫹G(d,p) c DE BSSE
Cl2
Uncounterpoise
Counterpoise
Uncounterpoise
Counterpoise
⫺78.32319 0.00083 0.00210 ⫺78.42s372
⫺78.32402
⫺919.17494 0.00127
⫺919.17621
⫺78.42441
⫺919.37367
⫺919.37587
0.00069 0.00289
0.00220
DE E uncounterpoise ⫺ E counterpoise: BSSE DE C2 H4 ⫹ DE Cl2 : c For the MP2(fc)/6-31⫹G(d,p) geometry. a
b
as the MP2(fc)/6-31⫹G(d,p) one was obtained and the weight for a HF configuration was found to be 0.975. This means that the present MP2 method based on the RHF wavefunction gives a reliable result for geometry and energy for TS1. Optimized geometries for trans- and gaucheC2H4Cl2 are also shown in Fig. 1. These geometries were confirmed to be located at the minima of potential energy surface by harmonic vibrational analyses (see Table 1). As shown in Fig. 2, relative energies of trans- and gauche-C2H4Cl2 with respect to the C2H4⫹Cl2 asymptote were predicted to be ⫺53.5 and ⫺52.1 kcal mol ⫺1, respectively, Table 4 ˚ ) and stabilization energies DE (kcal Geometrical parameters (A mol ⫺1) for the C2H4…Cl2 complex (all calculated values are BSSE corrected) Method
X–Cl a
Cl–Cl
DE
References
HF/MIDI4 HHLYP b/6-311G(d,p) MP2/6-311G(d,p) B3LYP/6-311G(d) MP2/6-311G(d) MP2(fc)/6-31⫹G(d,p) MP4(SDTQ,full)/6311⫹⫹G(d,p) c Experiment Experiment
3.337 3.055 3.003 2.81 2.98 3.065
2.195 2.038 2.044
0.5 2.1 1.6 3.3 1.7 0.8 0.6
[27] [28,29] [28,29] [30] [30] This work This work
1.7–2.7
[31] [32]
a
2.043
3.128
X is the midpoint of the CyC bond of C2H4. DFT using the Becke half-and-half functional. c For the MP2(fc)/6-31⫹G(d,p) geometry. b
at the MP4(SDTQ,full)/6-311⫹⫹G(d,p)//MP2(fc)/ 6-31⫹G(d,p) level. An available experimental value [3] for the exothermic energy is 43.7 kcal mol ⫺1, which is slightly smaller than the present values. It is considered that a TS with a small activation barrier exists for the trans–gauche rotation; however, the TS was not optimized in this work. Several authors [33– 40] have already calculated the geometry, energy difference and rotational barrier for trans- and gauche-C2H4Cl2. Although not given explicitly in this paper, the present results for geometry and energetics for trans- and gauche- C2H4Cl2 agree quite well with the previous calculations. In order to verify that TS1 is located at the saddle point of the reaction pathway for direct Cl2 addition to C2H4, the IRC was calculated at the MP2(fc)/631⫹G(d,p) level. In Fig. 3 is shown the potential energy profile along the IRC; the absolute value of s given in amu 1/2 bohr is the arc length of the IRC from the TS and s ⬍ 0; s 0 and 0 ⬍ s correspond to the reactant C2 H4 ⫹ Cl2 region, TS, and the product (C2H4Cl2) region, respectively. The zero point of energy is set to be the total energy of the C2H4…Cl2 complex. Since the imaginary frequency mode of TS1 has the Cs symmetry, the geometry maintains the Cs symmetry at every point on the IRC. Therefore, synC2H4Cl2 (where dihedral angle F (ClCCCl) is 0.0⬚) is produced along the IRC in the product region. This C2H4Cl2 should be a TS for intramolecular rotation and hence instability of the IRC is considered to occur in the product region, which means that potential energy decreases along a direction
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Fig. 2. Potential energy diagram for the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction at the PMP4(SDTQ,full)/6-311⫹⫹G(d,p)//MP2(fc)/631⫹G(d,p) ⫹ ZPE level. In a parenthesis for the C2H4…Cl2 complex are given the BSSE corrected energy value. The unit is kcal mol ⫺1.
orthogonal to the IRC. It is seen in Fig. 3 that the C2H4…Cl2 complex is located where s ⬍ ⫺20 amu 1/ 2 bohr, while the product is located around s 8 amu1=2 bohr: Since IRC adopts the mass-scaled coordinate, the shape of the potential energy curve along the IRC depends on atomic masses. Fig. 3 suggests that motions of Cl atoms are more significant in the reactant region rather than the product region. Examining geometrical changes along the IRC revealed that TS1 connects with both the C2H4…Cl2 complex and syn-C2H4Cl2. This means that TS1 is located at the saddle point on the reaction pathway of direct Cl2 addition to C2H4. 3.2. Cl abstraction from Cl2 by C2H4 In this subsection mechanism of Cl abstraction from Cl2 by C2H4 in the gas phase, which leads first to the production of C2 H4 Cl ⫹ Cl radicals and then to Table 5 Dipole moments estimated at the MP2(fc)/6-31⫹G(d,p) level (debye) TS1 C2H4…Cl2 Gauche-C2H4Cl2 C2H4Cl
11.46 0.74 2.83 1.96
the immediate recombination to form 1,2-dichloroethane C2H4Cl2, is discussed and compared to the direct Cl2 addition to C2H4. It is evident that the wavefunction of TS for the C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl reaction (TS2) has a high multiconfiguration character. Therefore the CASSCF(4,4)/6-31⫹G(d,p) level of theory was employed for the TS2 geometry optimization. Also given in Fig. 1 is the optimized geometry for TS2, which has Cs symmetry. It was confirmed that TS2 has one imaginary frequency mode of 351i cm ⫺1 (see Table 1). The barrier height and reaction energy for the C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl reaction were calculated to be 28.6 and 25.8 kcal mol ⫺1 (without ZPE correction) at the CASSCF(4,4)/6-31⫹G(d,p) level. The present CASSCF(4,4) calculation predicted that the highest weight of HF configuration for the TS2 wavefunction is 0.700, which is considerably smaller than 1.0. This means that computational methods based on the single-determinant HF theory are inappropriate for theoretical analyses of the present reaction. It is worth noting that Resende et al. [41] have recently found a similar TS for the reaction at the C2 H2 ⫹ Cl2 ! C2 H2 Cl ⫹ Cl CASSCF(6,6)/6-31G(d,p) level. The IRC for the C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl reaction was calculated at the CASSCF(4,4)/6-31⫹G(d,p)
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Fig. 3. Potential energy profile along the IRC for the C2 H4 ⫹ Cl2 ! TS1 ! C2 H4 Cl2 reaction in the gas phase at the MP2(fc)/6-31⫹G(d,p) level; s ⬍ 0; s 0 and 0 ⬍ s correspond to the reactant C2 H4 ⫹ Cl2 region, TS1, and product (C2H4Cl2) region, respectively, and the zero point of energy is set to be the total energy of the C2H4…Cl2 complex.
Fig. 4. Potential energy profiles along the IRC for the C2 H4 ⫹ Cl2 ! TS2 ! C2 H4 Cl ⫹ Cl reaction in the gas phase; the IRC was calculated at the CASSCF(4,4)/6-31⫹G(d,p) level and single-point energies were obtained at the RHF, UHF, RMP2(fc), UMP2(fc), and PMP4(SDTQ,fc) levels with the 6-31⫹G(d,p) basis set along the CASSCF(4,4)/6-31⫹G(d,p) IRC. The zero point of relative energy is set to be the total energy of the C2 H4 ⫹ Cl2 asymptote for each level of theory.
Y. Kurosaki / Journal of Molecular Structure (Theochem) 503 (2000) 231–240
level. It was confirmed that TS2 connects with both the C2H4…Cl2 complex and C2 H4 Cl ⫹ Cl products by examining the geometrical change along the IRC. Potential energy profiles at the RHF, UHF, RMP2(fc), UMP2(fc), PMP4(SDTQ,fc) and CASSCF(4,4) levels with the 6-31⫹G(d,p) basis set along the CASSCF(4,4)/6-31⫹G(d,p) IRC are shown in Fig. 4. The reactant C2 H4 ⫹ Cl2 region, the TS, and the product C2 H4 Cl ⫹ Cl region correspond to s ⬍ 0; s 0 and 0 ⬍ s; respectively. The zero point of relative energy is set to be the total energy of the C2 H4 ⫹ Cl2 asymptote for each level of theory. It is seen that the RHF and UHF levels give the same energy value at the initial stage; however, around s ⫺5 the RHF–UHF instability emerges and the RHF ⫺ curve correlates to the ionic C2 H⫹ 5 ⫹ Cl asymptote and the UHF one to the neutral C2 H4 Cl ⫹ Cl asymptote. Although the UHF curve shows qualitatively correct behavior in the product C2 H4 Cl ⫹ Cl region, the spin state is largely contaminated by higher spin states and the expectation value for spin operator S 2 (具S 2典) significantly deviates from the singlet true value of 0; 具S 2典 becomes almost 1 around the C2 H4 Cl ⫹ Cl asymptotic region, where it is thought that singlet and triplet states are equally mixed. The RMP2(fc) and UMP2(fc) curves exhibit qualitatively the same behaviors as the RHF and UHF ones. The PMP4(SDTQ,fc) curve shows a similar behavior to the CASSCF(4,4) one. It should be noted, however, that the potential barrier from the C2 H4 Cl ⫹ Cl products was predicted to disappear at the PMP4(SDTQ,fc)/6-31⫹G(d,p) level. According to Schlegel [42], the PMP4 method describes the asymptotic behavior of chemical-bond dissociation well and gives good agreement with full CI results. We can therefore consider that reaction pathway for Cl abstraction from Cl2 by C2H4 to form C2 H4 Cl ⫹ Cl has no TS. Since the reaction pathway for Cl abstraction from Cl2 by C2H4, i.e. C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl ! C2 H4 Cl2 was predicted to have no TS, it is clearly seen from Fig. 2 that this reaction pathway is energetically more feasible than that for direct Cl2 addition to C2H4, i.e. C2 H4 ⫹ Cl2 ! TS1 ! C2 H4 Cl2 ; described in Section 3.1. At the MP4(SDTQ,full)/6311⫹⫹G(d,p)//MP2(fc)/6-31⫹G(d,p) level, it was calculated that direct Cl2 addition requires an energy of 36.3 kcal mol ⫺1 to surmount the barrier, while Cl abstraction requires energy of 25.1 kcal mol ⫺1.
239
In Fig. 2 the relative energy value for the chargeseparated C2 H5 Cl⫹ ⫹ Cl⫺ asymptote, which was calculated to be quite large, is also given. The optimized geometry for C2H4Cl ⫹ is also illustrated in Fig.1, which was predicted to have C2v symmetry. The obtained high-energy value for the C2 H4 Cl⫹ ⫹ Cl⫺ asymptote suggests that this asymptote correlates with an electronic excited state of the present system and the charge-separated species are not important under normal conditions in the gas phase. It is expected, however, that the charge-separated species is greatly stabilized in polar solvents and plays an important role in the alkene-halogenation mechanism in solvents. Although the investigation of solvent effects on the present reaction is beyond the scope of this work, this must be a subject of great interest in future work. Actually, a few theoretical studies for alkene halogenation C2 H4 ⫹ Br2 in solvents have been recently reported [12–15] and several aspects of the solvent effects have been gradually revealed.
4. Conclusions In this work, two reaction pathways for the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction in the gas phase, i.e. direct Cl2 addition to C2H4 and Cl abstraction from Cl2 by C2H4, have been theoretically examined and compared using ab initio MO methods. The former reaction pathway was previously proposed, while the latter has been first examined in this work. Reaction pathway for direct Cl2 addition to C2H4 was predicted to have a TS (TS1) that is 36.3 kcal mol ⫺1 higher in energy than the C2H4⫹Cl2 reactants at the PMP4(SDTQ,full)/6311⫹⫹G(d,p)//MP2(fc)/6-31⫹G(d,p) level. Reaction pathway for Cl abstraction from Cl2 was predicted to have a TS at the CASSCF(4,4)/631⫹G(d,p) level; however, the single-point energy calculations along the CASSCF(4,4) IRC at the PMP4(SDTQ,fc)/6-31⫹G(d,p) level revealed that this pathway leads to the C2 H4 Cl ⫹ Cl asymptote without undergoing a TS. Since the C2 H4 Cl ⫹ Cl asymptote was calculated to be 25.1 kcal mol ⫺1 higher in energy than the C2 H4 ⫹ Cl2 reactants at the PMP4(SDTQ,full)/6-311⫹⫹G(d,p)//MP2(fc)/631⫹G(d,p) level, one concludes that in the gas
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phase the C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl ! C2 H4 Cl2 pathway is energetically more feasible than the C2 H4 ⫹ Cl2 ! TS1 ! C2 H4 Cl2 pathway. Although solvent effects were not discussed in this work, they must be an important issue for the present reaction since it is widely known among organic chemists that alkene halogenation occurs only in polar solvents under normal conditions. Recently, a few authors have reported the theoretical results for alkene halogenation C2 H4 ⫹ Br2 in solvents and some roles of solvents have been elucidated; it is still unlikely, however, that solvent effects on alkene halogenation are completely understood. It is desirable in the future that solvent effects on alkene halogenation will be extensively studied using sophisticated theoretical techniques.
Acknowledgements The author is grateful to Dr. Yoichi Matsuzaki and Dr. Atsushi Nogami at Advanced Technology Research Laboratories, Nippon Steel Corporation, for stimulating suggestion and discussion. The author also thanks Dr. Toshiyuki Takayanagi for critical reading of this manuscript and helpful comments.
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[14] M. Strnad, M.T.C. Martins-Costa, C. Millot, I. Tun˜o´n, M.F. Ruiz-Lo´pez, J.L. Rivail, J. Chem. Phys. 106 (1997) 3643. [15] T. Koerner, R.S. Brown, J.L. Gainsforth, M. Klobukowski, J. Am. Chem. Soc. 120 (1998) 5628. [16] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, gaussian 94, Revision D.3 (Gaussian, Inc., Pittsburgh, PA, 1995). [17] M. Head-Gordon, J.A. Pople, M.J. Frisch, Chem. Phys. Lett. 153 (1988) 503. [18] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166 (1990) 275. [19] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166 (1990) 281. [20] R. Krishnan, J.A. Pople, Int. J. Quantum Chem. 14 (1978) 91. [21] R. Krishnan, M.J. Frisch, J.A. Pople, J. Chem. Phys. 72 (1980) 4244. [22] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [23] K. Fukui, J. Phys. Chem. 74 (1970) 4161. [24] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [25] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523. [26] D. Hegarty, M.A. Robb, Mol. Phys. 38 (1979) 1795. [27] H. Matsuzawa, S. Iwata, Chem. Phys. 163 (1992) 297. [28] E. Ruiz, D.R. Salahub, A. Vela, J. Am. Chem. Soc. 117 (1995) 1141. [29] E. Ruiz, D. Salahub, A. Vela, J. Phys. Chem. 100 (1996) 12265. [30] H.C. Kang, Chem. Phys. Lett. 254 (1996) 135. [31] H.I. Bloemink, K. Hinds, A.C. Legon, J.C. Thorn, Chem. Phys. Lett. 223 (1994) 162. [32] G.A. Bowmaker, P.D.W. Boyd, J. Chem. Soc. Faraday Trans. 83 (1987) 2211. [33] K.B. Wiberg, M.A. Murcko, J. Phys. Chem. 91 (1987) 3616. [34] M.W. Wong, M.J. Frisch, K.B. Wiberg, J. Am. Chem. Soc. 113 (1991) 4776. [35] D.A. Dixon, N. Matsuzawa, S.C. Walker, J. Phys. Chem. 96 (1992) 10 740. [36] A. Chung-Phillps, J. Mol. Struct. (Theochem) 89 (1992) 417. [37] H. Cardy, C. Larrieu, M. Chaillet, J. Ollivier, Chem. Phys. 169 (1993) 305. [38] G.M. Kuramshina, F. Weinhold, Y.A. Pentin, Russ. J. Phys. Chem. 68 (1994) 1828. [39] W.L. Jorgensen, N.A. McDonald, M. Selmi, P.R. Rablen, J. Am. Chem. Soc. 117 (1995) 11809. [40] K.B. Wiberg, T.A. Keith, M.J. Frisch, M. Murcko, J. Phys. Chem. 99 (1995) 9072. [41] S.M. Resende, J.R. Pliego Jr., W.B. De Almeida, J. Chem. Soc. Faraday Trans. 94 (1998) 2895. [42] H.B. Schlegel, J. Chem. Phys. 84 (1986) 4530.
Ab initio molecular orbital study of the C2 H4 ⫹ Cl2 ! C2H4Cl2 reaction Yuzuru Kurosaki* Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan Received 25 June 1999; received in revised form 16 August 1999; accepted 31 August 1999
Abstract A new mechanism of the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction in gas phase has been theoretically proposed using ab initio molecular orbital methods; Cl is abstracted from Cl2 by C2H4, which leads first to the production of C2 H4 Cl ⫹ Cl radicals and then to immediate recombination to form C2H4Cl2. It was predicted that this abstraction reaction, C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl; is 25.1 kcal mol ⫺1 endothermic with no transition state at the PMP4(SDTQ,full)/6-311⫹⫹G(d,p)//MP2(fc)/6-31⫹G(d,p) level of theory. The previously proposed mechanism, direct Cl2 addition to C2H4 to produce C2H4Cl2, has also been examined and an energy barrier of 36.3 kcal mol ⫺1 was obtained at the same level of theory. Therefore one concludes that the new mechanism is energetically more feasible than the direct Cl2 addition to C2H4 for the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction in the gas phase. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Alkene halogenation; Gas-phase reaction; Ab initio molecular orbital calculation; Intrinsic reaction coordinate; RHF–UHF instability
1. Introduction Although alkene halogenations, C2 H4 ⫹ X2 ! CH2 XCH2 X (X F; Cl, or Br), have been quite familiar to organic chemists for many years, it seems that there still remain open questions about the reaction mechanisms. Since the early work [1– 3] in 1930s, it has been widely accepted that alkene halogenations occur via formation of a charge-separated species [4–8]: a cyclic halogenium cation (C2H4X ⫹) plus halogen anion (X ⫺). It may be true that in polar solvents the charge-separated species
* Present address: Advanced Photon Research Center, Japan Atomic Research Institute, Umemidai 8–1, Kizu-cho, Soraku-gun, Kyoto 619–0215, Japan. Tel.: ⫹81-77-471-3371; fax: ⫹81-77-4713316. E-mail address: [email protected]. (Y. Kurosaki).
can be stabilized by solvation and the halogenation can occur via formation of a cyclic halogenium cation plus halogen anion. In the gas phase, however, the potential energy surface correlated to the chargeseparated asymptote should correspond to an electronic-excited potential surface of the C2 H4 ⫹ X2 system; hence it is unlikely that the mechanism via charge-separated species dominates the halogenation. One can thus roughly understand the reaction mechanism; however, detailed information for geometries and energetics including transition state (TS) for both reactions in the gas phase and in polar solvents is still unavailable. Compared to experimental studies, there have been a limited number of theoretical studies for alkene halogenations. Results of the theoretical studies to date are briefly reviewed here. Jaszunski and Kochanski [9] examined the C2 H4 ⫹ Cl2 reaction at
0166-1280/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00317-6
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the Hartree–Fock (HF) level. They concluded that this system can produce a C2H4…Cl2 complex in the first step and that the energy of the C2 H4 Cl⫹ ⫹ Cl⫺ asymptote is too high for the intermediate state of halogenation. They then speculated that a solvent can stabilize this charge-separated intermediate state, thereby allowing the reaction. However, they considered only the C2v reaction pathway where the Cl2 axis is perpendicular to the CyC bond of C2H4. Yamabe et al. [10] optimized the geometries of TSs for the C2 H4 ⫹ F2 ; C2 H4 ⫹ Cl2 ; and C2 H4 ⫹ Br2 reactions at the HF/3-21G level of theory and found that fluorination of C2H4 occurs via a four-centered TS while both chlorination and bromination occur via three-centered TSs. However, they did not determine the reaction pathways for any of these reactions. As far as we are aware, Iwaoka et al. [11] were the first to calculate the gas-phase reaction pathway for the C2 H4 ⫹ F2 reaction. They determined the intrinsic reaction coordinate (IRC) for this reaction at the second-order Møller–Plesset (MP2) level of theory with the 6-31⫹G basis set and confirmed that a C2H4…F2 complex connects with the final syn addition product via a rhombic-type TS. Several years ago, Cossi et al. [12] studied the C2 H4 ⫹ Br2 reaction in solvents using a continuum solvation model. They obtained the first theoretical results for this reaction in solvents; however, optimizations for most geometries of minima were done only partially and the TS geometry was completely unidentified. Recently, Rivail and co-workers [13,14] have theoretically investigated the solvent effect on the C2 H4 ⫹ Br2 reaction using discrete and continuum models for solvents [13] and using a molecular dynamics method [14]. They found a marked difference between the reaction mechanisms in the gas phase and in polar solvents; the TS was predicted to have Cs symmetry in the gas phase, while C2v symmetry in polar solvents [13]. Also they found that dynamic solvent effects play an important role for the reaction mechanism [14]. Very recently, Koerner et al. [15] have examined the deuterium kinetic isotope effect (KIE) for the C2 H4 ⫹ Br2 reaction in methanol and dichloroethane
233
using both experimental and theoretical techniques. They experimentally observed inverse KIEs for reactions in both the solvents and then explained these effects using theoretical methods based on density functional theory. The theoretical studies of these authors have elucidated several aspects of the alkene-halogenation mechanism; it seems, however, that detailed information about the mechanism is still lacking for reactions in the gas-phase as well as those in solvents. For example, other reaction pathways in the gas phase that are different from those of Yamabe et al. [10] and Iwaoka et al. [11] have not been investigated and an overall reaction pathway in solvents has not been determined. Although the alkene-halogenation mechanism in solvents attracts our interest, in this paper we focus our attention on the gas-phase mechanism for the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction since even the gasphase mechanism has not been entirely understood. We examine the following two reaction pathways: Cl2 addition to C2H4, which directly leads to the production of 1,2-dichloroethane C2H4Cl2; and Cl abstraction from Cl2 by C2H4, which leads first to the production of C2 H4 Cl ⫹ Cl radicals and then to the immediate recombination to form C2H4Cl2. The former reaction pathway was previously proposed [10,11], while the latter is first examined in this work. We will find that the latter reaction pathway is energetically more feasible than the former.
2. Methods of calculation All ab initio molecular orbital (MO) calculations were carried out using the gaussian 94 package program [16]. For direct Cl2 addition to C2H4, geometries of stationary points were optimized at the MP2 perturbation [17–19] level with the 6-31⫹G(d,p) basis set under the frozen-core (fc) approximation. Harmonic vibrational frequencies were computed analytically at the same level in order to characterize the optimized
Fig. 1. Optimized geometries for TS2 at the CASSCF(4,4)/6-31⫹G(d,p) level and other species at the MP2(fc)/6-31⫹G(d,p) level. In parentheses for the C2H4…Cl2 complex are given the geometrical values for the isolated C2H4 and Cl2 molecules. Bond lengths and angles ˚ and degree, respectively. are given in A
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geometries as potential minima or saddle points. Single-point energy calculations for the MP2(fc)/631⫹G(d,p) geometries were also carried out at the fourth-order MP (MP4) level including single, double, triple and quadruple (SDTQ) substitutions of all electrons (full) [20,21] with the 6-311⫹⫹G(d,p) basis set. Basis-set superposition error (BSSE) was estimated using the counterpoise method [22] for the van der Waals (vdW) complex produced in the reactant region. The IRC [23–25] was also calculated at the MP2(fc)/6-31⫹G(d,p) level with the step size being 0.1 amu 1/2 bohr. For Cl abstraction from Cl2 by C2H4, due to a high muticonfiguration character, geometries were optimized at the complete-active-space self-consistentfield (CASSCF) level [26], where four electrons are distributed in four active orbitals (CASSCF(4,4)), with the 6-31⫹G(d,p) basis set. The active space includes ClCl s and s ⴱ orbitals and CC p and p ⴱ orbitals. The IRC was calculated at the CASSCF(4,4)/6-31⫹G(d,p) level with the step size being 0.1 amu 1/2 bohr. Since the CASSCF level of theory does not take dynamical electron correlation
effects into account, single-point energies on the calculated IRC were obtained at other levels of theory. At every 0.2 amu 1/2 bohr point on the calculated IRC, single-point energies at the restricted HF (RHF), unrestricted HF (UHF), RMP2(fc), UMP2(fc) and spin-projected UMP4(SDTQ,fc) (PMP4(SDTQ,fc)) levels with the 6-31⫹G(d,p) basis set were calculated.
3. Results and discussion 3.1. Direct Cl2 addition to C2H4 Mechanism of Cl2 addition to C2H4 in the gas phase, which directly leads to production of 1,2-dichloroethane C2H4Cl2, is discussed here. Although this mechanism was previously proposed [10,11], here we confirm again that this direct reaction pathway for the present reaction really exists, using the IRC method. It was found that the vdW complex C2H4…Cl2 is produced in the reactant region. As shown in Fig. 1,
Table 1 Harmonic vibrational frequencies calculated at the MP2(fc)/6-31⫹G(d,p) level for the optimized geometries Sym
Frequencies (cm ⫺1)
Cl2 C2H4
D∞h C2h
C2H4Cl
Cs
C2H4Cl ⫹
C2v
C2H4…Cl2
C2v
trans-C2H4Cl2
C2h
gauche-C2H4Cl2
C2
TS1
Cs
TS2 a
Cs
542 846 3230 208 1339 579 1276 10I 992 3326 125 1188 3248 123 1204 3234 452i 1049 3334 351i 1081 3404
a
At the CASSCF(4,4)/6-31⫹G(d,p) level.
913 3247 317 1518 604 1524 61 1070 3350 222 1320 3268 269 1272 3245 106 1166 3417 67 1170 3438
984 3324 625 1548 867 1569 63 1264
1071 3349 712 3183 1007 3238 79 1401
1262
1404
1514
1709
805 3257 1013 3240 105 1514
1119 3265 1167 3358 509 1701
1124 3387 1211 3368 847 3230
1306
930 3246
313 1332
780 1411
801 1534
825 1534
1064 3179
1106 3187
423 1385
708 1403
736 1509
935 1514
1005 3161
1095 3166
132 1235
323 1267
676 1504
718 1561
852 3227
957 3292
71 1259
171 1348
313 1588
435 1651
807 3319
854 3328
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Table 2 Total energies and ZPEs for the MP2(fc)/6-31⫹G(d,p) geometries (hartree)
Cl Cl ⫺ Cl2 C2H4 C2H4Cl C2H4Cl ⫹ C2H4…Cl2 trans-C2H4Cl2 gauche-C2H4Cl2 TS1 TS2 b a b
MP2(fc)/6-31⫹G(d,p) a
MP4(SDTQ,full)/6-311⫹⫹G(d,p)
⫺459.55409 ⫺459.67115 ⫺919.17502 ⫺78.32320 ⫺537.90235 ⫺537.62391 ⫺997.50227 ⫺997.58922 ⫺997.58692 ⫺997.44009 ⫺996.96278
⫺459.65339 ⫺459.76720 ⫺919.37348 ⫺78.42369 ⫺538.10449 ⫺537.82483 ⫺997.80161 ⫺997.88940 ⫺997.88706 ⫺997.74259
(0.00123) (0.05207) (0.05402) (0.05757) (0.05397) (0.06023) (0.06011) (0.05653) (0.05537)
In parentheses are given ZPEs. At the CASSCF(4,4)/6-31⫹G(d,p) level.
this vdW complex was assumed to have C2v symmetry; the Cl2 molecule is perpendicularly bound to the C2H4 molecular plane. Although this C2v vdW complex was calculated to have a very small imaginary frequency at the present MP2(fc)/6-31⫹G(d,p) level (see Tables 1 and 2), further optimization was not done in this work. BSSE should often be taken into account for weakly bound systems such as vdW complexes. In Table 3 are given the results of the BSSE correction with the counterpoise method for the vdW complex and BSSE was predicted to be about 0.002 hartree. In Table 4 are summarized geometrical parameters and stabilization energies (relative to the C2 H4 ⫹ Cl2 asymptote) for this vdW complex, including the results of other authors. It is seen that the X–Cl distance (X is the midpoint of the CyC bond of C2H4) calculated at the MP2 level of theory agrees fairly well with the experimental value ˚ . The calculated stabilization energy of [31], 3.128 A this vdW complex seems sensitive to both the method and basis set. The present MP2(fc)/6-31⫹G(d,p) and MP4(SDTQ,full)/6-311⫹⫹G(d,p) levels give slightly smaller values than the experimental one [32], 1.7– 2.4 kcal mol ⫺1. In Fig. 2 the stabilization energies obtained in this work are also shown. Optimized geometry for the TS of the present Cl2 addition reaction (TS1) is depicted in Fig. 1. Harmonic vibrational analyses predicted that TS1 has one imaginary frequency mode of 452i cm ⫺1 (see Table 1), confirming that TS1 is located at the saddle point of the potential energy surface. Yamabe et al. [10]
also obtained the same TS at the HF/3-21G level. It is seen that the internuclear distance between Cl ˚ larger atoms in the present TS1 geometry is 0.3–0.4 A than the HF value while that between Cl and C atoms ˚ smaller than the HF value (see Ref. are 0.1–0.2 A [10]). As shown in Fig. 2, the relative energy of TS1 with respect to the C2 H4 ⫹ Cl2 asymptote was calculated to be 36.3 kcal mol ⫺1 at the MP4(SDTQ,full)/6311⫹⫹G(d,p)//MP2(fc)/6-31⫹G(d,p) level, where zero-point vibrational energy (ZPE) was taken into account. It is therefore concluded that this reaction does not occur under normal conditions in the gas phase because of the large activation barrier. In Table 5 are shown the calculated dipole moments for TS1 and other neutral molecules. It is seen that the dipole moment of TS1 was predicted to be considerably larger than the dipole moments of other neutral molecules. This suggests that polar solvents can significantly stabilize TS1 and can totally change the reaction energetics. It is anticipated that RHF– UHF instability usually occurs for RHF wavefunctions when a chemical bond is stretched. We tried to obtain a UHF wavefunction for TS1 in order to check if RHF–UHF instability occurs; however, a UHF wavefunction for which the total energy is lower than that for the RHF wavefunction was not obtained, implying that the RHF wavefunction well describes the electronic structure of TS1. Moreover, we re-optimized the TS1 geometry at the CASSCF(4,4)/631⫹G(d,p) level in order to make sure this prediction is true. Consequently, essentially the same geometry
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Table 3 BSSE for the C2H4…Cl2 complex (hartree) C2H4
MP2(fc)/6-31⫹G(d,p) DE a BSSE b MP4(SDTQ,full)/6311⫹⫹G(d,p) c DE BSSE
Cl2
Uncounterpoise
Counterpoise
Uncounterpoise
Counterpoise
⫺78.32319 0.00083 0.00210 ⫺78.42s372
⫺78.32402
⫺919.17494 0.00127
⫺919.17621
⫺78.42441
⫺919.37367
⫺919.37587
0.00069 0.00289
0.00220
DE E uncounterpoise ⫺ E counterpoise: BSSE DE C2 H4 ⫹ DE Cl2 : c For the MP2(fc)/6-31⫹G(d,p) geometry. a
b
as the MP2(fc)/6-31⫹G(d,p) one was obtained and the weight for a HF configuration was found to be 0.975. This means that the present MP2 method based on the RHF wavefunction gives a reliable result for geometry and energy for TS1. Optimized geometries for trans- and gaucheC2H4Cl2 are also shown in Fig. 1. These geometries were confirmed to be located at the minima of potential energy surface by harmonic vibrational analyses (see Table 1). As shown in Fig. 2, relative energies of trans- and gauche-C2H4Cl2 with respect to the C2H4⫹Cl2 asymptote were predicted to be ⫺53.5 and ⫺52.1 kcal mol ⫺1, respectively, Table 4 ˚ ) and stabilization energies DE (kcal Geometrical parameters (A mol ⫺1) for the C2H4…Cl2 complex (all calculated values are BSSE corrected) Method
X–Cl a
Cl–Cl
DE
References
HF/MIDI4 HHLYP b/6-311G(d,p) MP2/6-311G(d,p) B3LYP/6-311G(d) MP2/6-311G(d) MP2(fc)/6-31⫹G(d,p) MP4(SDTQ,full)/6311⫹⫹G(d,p) c Experiment Experiment
3.337 3.055 3.003 2.81 2.98 3.065
2.195 2.038 2.044
0.5 2.1 1.6 3.3 1.7 0.8 0.6
[27] [28,29] [28,29] [30] [30] This work This work
1.7–2.7
[31] [32]
a
2.043
3.128
X is the midpoint of the CyC bond of C2H4. DFT using the Becke half-and-half functional. c For the MP2(fc)/6-31⫹G(d,p) geometry. b
at the MP4(SDTQ,full)/6-311⫹⫹G(d,p)//MP2(fc)/ 6-31⫹G(d,p) level. An available experimental value [3] for the exothermic energy is 43.7 kcal mol ⫺1, which is slightly smaller than the present values. It is considered that a TS with a small activation barrier exists for the trans–gauche rotation; however, the TS was not optimized in this work. Several authors [33– 40] have already calculated the geometry, energy difference and rotational barrier for trans- and gauche-C2H4Cl2. Although not given explicitly in this paper, the present results for geometry and energetics for trans- and gauche- C2H4Cl2 agree quite well with the previous calculations. In order to verify that TS1 is located at the saddle point of the reaction pathway for direct Cl2 addition to C2H4, the IRC was calculated at the MP2(fc)/631⫹G(d,p) level. In Fig. 3 is shown the potential energy profile along the IRC; the absolute value of s given in amu 1/2 bohr is the arc length of the IRC from the TS and s ⬍ 0; s 0 and 0 ⬍ s correspond to the reactant C2 H4 ⫹ Cl2 region, TS, and the product (C2H4Cl2) region, respectively. The zero point of energy is set to be the total energy of the C2H4…Cl2 complex. Since the imaginary frequency mode of TS1 has the Cs symmetry, the geometry maintains the Cs symmetry at every point on the IRC. Therefore, synC2H4Cl2 (where dihedral angle F (ClCCCl) is 0.0⬚) is produced along the IRC in the product region. This C2H4Cl2 should be a TS for intramolecular rotation and hence instability of the IRC is considered to occur in the product region, which means that potential energy decreases along a direction
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Fig. 2. Potential energy diagram for the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction at the PMP4(SDTQ,full)/6-311⫹⫹G(d,p)//MP2(fc)/631⫹G(d,p) ⫹ ZPE level. In a parenthesis for the C2H4…Cl2 complex are given the BSSE corrected energy value. The unit is kcal mol ⫺1.
orthogonal to the IRC. It is seen in Fig. 3 that the C2H4…Cl2 complex is located where s ⬍ ⫺20 amu 1/ 2 bohr, while the product is located around s 8 amu1=2 bohr: Since IRC adopts the mass-scaled coordinate, the shape of the potential energy curve along the IRC depends on atomic masses. Fig. 3 suggests that motions of Cl atoms are more significant in the reactant region rather than the product region. Examining geometrical changes along the IRC revealed that TS1 connects with both the C2H4…Cl2 complex and syn-C2H4Cl2. This means that TS1 is located at the saddle point on the reaction pathway of direct Cl2 addition to C2H4. 3.2. Cl abstraction from Cl2 by C2H4 In this subsection mechanism of Cl abstraction from Cl2 by C2H4 in the gas phase, which leads first to the production of C2 H4 Cl ⫹ Cl radicals and then to Table 5 Dipole moments estimated at the MP2(fc)/6-31⫹G(d,p) level (debye) TS1 C2H4…Cl2 Gauche-C2H4Cl2 C2H4Cl
11.46 0.74 2.83 1.96
the immediate recombination to form 1,2-dichloroethane C2H4Cl2, is discussed and compared to the direct Cl2 addition to C2H4. It is evident that the wavefunction of TS for the C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl reaction (TS2) has a high multiconfiguration character. Therefore the CASSCF(4,4)/6-31⫹G(d,p) level of theory was employed for the TS2 geometry optimization. Also given in Fig. 1 is the optimized geometry for TS2, which has Cs symmetry. It was confirmed that TS2 has one imaginary frequency mode of 351i cm ⫺1 (see Table 1). The barrier height and reaction energy for the C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl reaction were calculated to be 28.6 and 25.8 kcal mol ⫺1 (without ZPE correction) at the CASSCF(4,4)/6-31⫹G(d,p) level. The present CASSCF(4,4) calculation predicted that the highest weight of HF configuration for the TS2 wavefunction is 0.700, which is considerably smaller than 1.0. This means that computational methods based on the single-determinant HF theory are inappropriate for theoretical analyses of the present reaction. It is worth noting that Resende et al. [41] have recently found a similar TS for the reaction at the C2 H2 ⫹ Cl2 ! C2 H2 Cl ⫹ Cl CASSCF(6,6)/6-31G(d,p) level. The IRC for the C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl reaction was calculated at the CASSCF(4,4)/6-31⫹G(d,p)
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Fig. 3. Potential energy profile along the IRC for the C2 H4 ⫹ Cl2 ! TS1 ! C2 H4 Cl2 reaction in the gas phase at the MP2(fc)/6-31⫹G(d,p) level; s ⬍ 0; s 0 and 0 ⬍ s correspond to the reactant C2 H4 ⫹ Cl2 region, TS1, and product (C2H4Cl2) region, respectively, and the zero point of energy is set to be the total energy of the C2H4…Cl2 complex.
Fig. 4. Potential energy profiles along the IRC for the C2 H4 ⫹ Cl2 ! TS2 ! C2 H4 Cl ⫹ Cl reaction in the gas phase; the IRC was calculated at the CASSCF(4,4)/6-31⫹G(d,p) level and single-point energies were obtained at the RHF, UHF, RMP2(fc), UMP2(fc), and PMP4(SDTQ,fc) levels with the 6-31⫹G(d,p) basis set along the CASSCF(4,4)/6-31⫹G(d,p) IRC. The zero point of relative energy is set to be the total energy of the C2 H4 ⫹ Cl2 asymptote for each level of theory.
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level. It was confirmed that TS2 connects with both the C2H4…Cl2 complex and C2 H4 Cl ⫹ Cl products by examining the geometrical change along the IRC. Potential energy profiles at the RHF, UHF, RMP2(fc), UMP2(fc), PMP4(SDTQ,fc) and CASSCF(4,4) levels with the 6-31⫹G(d,p) basis set along the CASSCF(4,4)/6-31⫹G(d,p) IRC are shown in Fig. 4. The reactant C2 H4 ⫹ Cl2 region, the TS, and the product C2 H4 Cl ⫹ Cl region correspond to s ⬍ 0; s 0 and 0 ⬍ s; respectively. The zero point of relative energy is set to be the total energy of the C2 H4 ⫹ Cl2 asymptote for each level of theory. It is seen that the RHF and UHF levels give the same energy value at the initial stage; however, around s ⫺5 the RHF–UHF instability emerges and the RHF ⫺ curve correlates to the ionic C2 H⫹ 5 ⫹ Cl asymptote and the UHF one to the neutral C2 H4 Cl ⫹ Cl asymptote. Although the UHF curve shows qualitatively correct behavior in the product C2 H4 Cl ⫹ Cl region, the spin state is largely contaminated by higher spin states and the expectation value for spin operator S 2 (具S 2典) significantly deviates from the singlet true value of 0; 具S 2典 becomes almost 1 around the C2 H4 Cl ⫹ Cl asymptotic region, where it is thought that singlet and triplet states are equally mixed. The RMP2(fc) and UMP2(fc) curves exhibit qualitatively the same behaviors as the RHF and UHF ones. The PMP4(SDTQ,fc) curve shows a similar behavior to the CASSCF(4,4) one. It should be noted, however, that the potential barrier from the C2 H4 Cl ⫹ Cl products was predicted to disappear at the PMP4(SDTQ,fc)/6-31⫹G(d,p) level. According to Schlegel [42], the PMP4 method describes the asymptotic behavior of chemical-bond dissociation well and gives good agreement with full CI results. We can therefore consider that reaction pathway for Cl abstraction from Cl2 by C2H4 to form C2 H4 Cl ⫹ Cl has no TS. Since the reaction pathway for Cl abstraction from Cl2 by C2H4, i.e. C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl ! C2 H4 Cl2 was predicted to have no TS, it is clearly seen from Fig. 2 that this reaction pathway is energetically more feasible than that for direct Cl2 addition to C2H4, i.e. C2 H4 ⫹ Cl2 ! TS1 ! C2 H4 Cl2 ; described in Section 3.1. At the MP4(SDTQ,full)/6311⫹⫹G(d,p)//MP2(fc)/6-31⫹G(d,p) level, it was calculated that direct Cl2 addition requires an energy of 36.3 kcal mol ⫺1 to surmount the barrier, while Cl abstraction requires energy of 25.1 kcal mol ⫺1.
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In Fig. 2 the relative energy value for the chargeseparated C2 H5 Cl⫹ ⫹ Cl⫺ asymptote, which was calculated to be quite large, is also given. The optimized geometry for C2H4Cl ⫹ is also illustrated in Fig.1, which was predicted to have C2v symmetry. The obtained high-energy value for the C2 H4 Cl⫹ ⫹ Cl⫺ asymptote suggests that this asymptote correlates with an electronic excited state of the present system and the charge-separated species are not important under normal conditions in the gas phase. It is expected, however, that the charge-separated species is greatly stabilized in polar solvents and plays an important role in the alkene-halogenation mechanism in solvents. Although the investigation of solvent effects on the present reaction is beyond the scope of this work, this must be a subject of great interest in future work. Actually, a few theoretical studies for alkene halogenation C2 H4 ⫹ Br2 in solvents have been recently reported [12–15] and several aspects of the solvent effects have been gradually revealed.
4. Conclusions In this work, two reaction pathways for the C2 H4 ⫹ Cl2 ! C2 H4 Cl2 reaction in the gas phase, i.e. direct Cl2 addition to C2H4 and Cl abstraction from Cl2 by C2H4, have been theoretically examined and compared using ab initio MO methods. The former reaction pathway was previously proposed, while the latter has been first examined in this work. Reaction pathway for direct Cl2 addition to C2H4 was predicted to have a TS (TS1) that is 36.3 kcal mol ⫺1 higher in energy than the C2H4⫹Cl2 reactants at the PMP4(SDTQ,full)/6311⫹⫹G(d,p)//MP2(fc)/6-31⫹G(d,p) level. Reaction pathway for Cl abstraction from Cl2 was predicted to have a TS at the CASSCF(4,4)/631⫹G(d,p) level; however, the single-point energy calculations along the CASSCF(4,4) IRC at the PMP4(SDTQ,fc)/6-31⫹G(d,p) level revealed that this pathway leads to the C2 H4 Cl ⫹ Cl asymptote without undergoing a TS. Since the C2 H4 Cl ⫹ Cl asymptote was calculated to be 25.1 kcal mol ⫺1 higher in energy than the C2 H4 ⫹ Cl2 reactants at the PMP4(SDTQ,full)/6-311⫹⫹G(d,p)//MP2(fc)/631⫹G(d,p) level, one concludes that in the gas
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phase the C2 H4 ⫹ Cl2 ! C2 H4 Cl ⫹ Cl ! C2 H4 Cl2 pathway is energetically more feasible than the C2 H4 ⫹ Cl2 ! TS1 ! C2 H4 Cl2 pathway. Although solvent effects were not discussed in this work, they must be an important issue for the present reaction since it is widely known among organic chemists that alkene halogenation occurs only in polar solvents under normal conditions. Recently, a few authors have reported the theoretical results for alkene halogenation C2 H4 ⫹ Br2 in solvents and some roles of solvents have been elucidated; it is still unlikely, however, that solvent effects on alkene halogenation are completely understood. It is desirable in the future that solvent effects on alkene halogenation will be extensively studied using sophisticated theoretical techniques.
Acknowledgements The author is grateful to Dr. Yoichi Matsuzaki and Dr. Atsushi Nogami at Advanced Technology Research Laboratories, Nippon Steel Corporation, for stimulating suggestion and discussion. The author also thanks Dr. Toshiyuki Takayanagi for critical reading of this manuscript and helpful comments.
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