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Relative reactivity and regioselectivity of halogen-substituted ethenes and propene toward addition of an OH radical or O (3P) atom: An ab initio study
Journal of Molecular Structure: THEOCHEM 770 (2006) 59–65 www.elsevier.com/locate/theochem
Relative reactivity and regioselectivity of halogen-substituted ethenes and propene toward addition of an OH radical or O (3P) atom: An ab initio study Ahmed M. El-Nahas a,1, Tadafumi Uchimaru a,b,*, Masaaki Sugie a, Kazuaki Tokuhashi a, Akira Sekiya a a
Research Institute for Innovation in Sustainable Chemistry, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan b Research Institute of Computational Sciences (RICS), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Received 27 March 2006; received in revised form 11 May 2006; accepted 17 May 2006 Available online 3 June 2006
Abstract This paper describes the results of ab initio investigations on the reactions of OH radical/O (3P) atom addition to halogen-substituted ethenes (CH2aCHX, CH2aCX2; XZF, Cl, Br) and propene. Two reaction pathways, addition to the substituted carbon atom (a-site) and addition to the non-substituted carbon atom (b-site), have been examined. The energetic of each reaction coordinate has been evaluated at the computational level of PMP2/aug-cc-pVTZ//MP2/6-311CG(2d,p). Our calculations suggested that the reactions of OH radical addition should be more exothermic than those of the O (3P) atom addition and that the a-addition products should be lower in energy than the corresponding b-addition products. Relative stabilities of the transition states for the a- and b-addition channels can be discussed in terms of the exothermicities of the reaction channels and the relative spin densities in the 3pp* states of the reactant ethene molecules. For the reactions of the chloro- and bromosubstituted ethenes, the transition states for the a-addition were found to be higher in energy than those for the b-addition, but for the reactions of the fluoro-substituted ethenes and propene, the differences in energy between the transition states for the a- and b-addition channels were found to be rather small. q 2006 Elsevier B.V. All rights reserved. Keywords: Ab initio calculations; Regioselectivity ; Halogen-substituted ethenes; Propene; OH radicals; O (3P) atoms
1. Introduction Unsaturated compounds possessing a carbon–carbon double bond react with various active species in the atmosphere, such as OH and NO3 radicals, O3 molecule, and Cl, Br, and O (3P) atoms. From the standpoint of atmospheric chemistry, the most important reaction is addition of an OH radical to a carbon–carbon double bond, and OH radical addition is a key step for atmospheric
* Corresponding author. Address: Research Institute of Computational Sciences (RICS), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan. Tel.: C81 29 861 4800; fax: C81 29 851 5426. E-mail address: [email protected] (T. Uchimaru). 1 Permanent address: Chemistry Department, Faculty of Science, El-Menoufia University, Shebin El-Kom, Egypt.
0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.05.036
degradation of unsaturated compounds. Furthermore, to accurately model the early stages of smog formation in urban areas and to model smog chamber experiments, reactions of O (3P) atoms with unsaturated compounds are also needed to be taken into account [1–5]. In this work, we have examined reactions of OH radicals and O ( 3P) atoms with mono- and 1,1-dihaloethenes (CH2aCHX/CH2aCX2, XZF, Cl, Br), as well as with propene (CH2aCH–CH3). These alkene molecules are all unsymmetrical and two reaction pathways can be distinguished: addition to the substituted (a) carbon atom of the double bond and addition to non-substituted CH2 (b) carbon atom. A number of theoretical and experimental studies have been reported on the radical addition to unsymmetrical substituted alkenes. In general, the normal pathway is the attack at the b carbon atoms, but addition at the a position is also experimentally observed [6–8]. We have carried out ab initio molecular orbital calculations on the OH radical addition channels (1) through (3), as well as the O (3P)
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atom addition channels (4) through (6) (XZF, Cl, Br):
3. Results and discussion
CH2 Z CHX C OH/ CH2 KCðOHÞHX
(1a)
CH2 Z CHX C OH/ HOCH2 KCHX
(1b)
CH2 Z CX2 C OH/ CH2 KCðOHÞX2
(2a)
CH2 Z CX2 C OH/ HOCH2 KCX2
(2b)
CH2 Z CHKCH3 C OH/ CH2 KCHðOHÞKCH3
(3a)
CH2 Z CHKCH3 C OH/ HOCH2 KCHKCH3
(3b)
CH2 Z CHX C O/ CH2 KCðOÞHX
(4a)
CH2 Z CHX C O/ OCH2 KCHX
(4b)
CH2 Z CX2 C O/ CH2 KCðOÞX2
(5a)
CH2 Z CX2 C O/ OCH2 KCX2
(5b)
CH2 Z CHKCH3 C O/ CH2 KCHðOÞKCH3
(6a)
CH2 Z CHKCH3 C O/ OCH2 KCHKCH3
(6b)
Table 1 gives the MP2/6-311CG(2d,p)-optimized geometrical parameters of the reactants, the transition states, and the product radicals for the reactions of OH radical/O (3P) atom addition to the substituted ethenes [the reactions (1) through (6)]. The structures of the transition states and the radical products are not very sensitive to the halogen substituents, and we thus give typical structures of the stationary points, i.e. the transition states and the product radicals for the reactions of CH2aCHCl, CH2aCCl2, and CH2aCH–CH3 in Figs. 1–3, respectively. Relative energies of the transition states and the product radicals are given in Table 2. The total energies and the zero-point energies (ZPEs) are summarized in supplementary information. 3.1. Structures and relative stabilities of the radical products
We have also examined the difference in reactivity between an OH radical and O (3P) atom, as well as factors controlling the regioselectivity, i.e. a-addition versus b-addition, in these reactions.
2. Computational details Ab initio calculations were carried out with the Gaussian 98 and Gaussian 03 suites of programs [9,10]. Using frozen-core Møller Plesset perturbation theory truncated at the secondorder (MP2ZFC) [11] in conjunction with the 6-311CG(2d,p) basis set, we performed full geometry optimizations for the reactants, products, and transition states for the addition of OH radical/O (3P) atom to the ethene molecules. Restricted (RMP2) and unrestricted (UMP2) methods were used for the closed- and open-shell systems, respectively. Spin contamination of the open-shell systems in this study was small. For the doublet radicals and the triplet biradicals, the expectation values of the total spin hS2i were less than 0.76 and 2.01, respectively, after spin annihilations. For the transition states, spin contamination was slightly larger than in the stable radicals; however, all values of hS2i were less than 0.76 and 2.01 after spin annihilations. For each stationary point, we carried out vibrational frequency calculation and examined the vibrational modes by using the Molekel program [12]. In addition, MP2 single-point energy calculations were carried out using the aug-cc-pVTZ basis set. We refined the relative energies of the stationary points as the projected energies [13] at the MP2/aug-cc-pVTZ level of theory based on the structures optimized at the MP2/6311CG(2d,p) level, i.e. PMP2/aug-cc-pVTZ//MP2/6-311C G(2d,p) level.
Addition of an OH radical or O (3P) atom to the carbon– carbon double bond results in change in the hybridization of the carbon atoms in the parent molecule; the sp2 hybrid double bond carbon atoms are converted to the sp3 hybrid carbon atom and the radical center carbon atom. On going from the parent ethene molecules to the product radicals, the bond order between the carbon atoms is decreased and, correspondingly, the carbon–carbon bonds are longer for the product radicals than for the parent ethenes (Table 1). For example, OH radical addition to CH2aCHF molecule lengthens the carbon–carbon ˚ in the parent CH2aCHF molecule to 1.484 bond from 1.325 A ˚ and 1.479 A in the a- and b-addition product radicals, respectively. The corresponding carbon–carbon bond lengthening for O (3P) atom addition is still slightly larger; the carbon–carbon bond lengths in the a- and b-addition product radicals are 1.491 ˚ , respectively. and 1.484 A Table 2 indicates that the OH radical addition and the O (3P) atom addition are both highly exothermic; the exothermicities of the reactions amount to 17–46 kcal/mol. Furthermore, it should be noted that the OH radical addition reactions are always more exothermic than the corresponding O (3P) atom addition reactions. The exothermicities for the OH radical addition reactions range from 30 to 46 kcal/mol, while the exothermicities for the O (3P) atom addition range from 17 to 32 kcal/mol. Comparison between the a- and b-addition product radicals is quite interesting. For both OH radical addition and O (3P) atom addition reactions, the C–X and C–X 0 bonds are longer and, conversely, the C–O bonds are shorter, for the a-addition products than for the b-addition products (see Table 1). For the OH radical addition to CH2aCHF, the C–F bond lengths in the ˚ , respectively, a- and b-addition products are 1.399 and 1.356 A while the C–O bond lengths in the a- and b-addition products ˚ . For the O (3P) atom addition to are 1.388 and 1.437 A ˚ , and CH2aCHF, the C–F bond lengths are 1.397 and 1.343 A ˚ , respectively, for the C–O bond lengths are 1.336 and 1.407 A the a- and b-addition products. For the OH radical addition to ˚ , and CH2aCHBr, the C–Br bond lengths are 2.049 and 1.871 A ˚ , respectively, for the C–O bond lengths are 1.379 and 1.434 A the a- and b-addition products. For O (3P) atom addition to
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Table 1 ˚ ) in the reactants, transition states, and products for the reactions of OH radical/O (3P) atom addition to the substituted alkenes Bond lengths (A Substituted alkene
Substrate
Transition state
CH2aCHF (XZF)
CH2aCF2 (XZF)
CH2aCHCl (XZCl)
CH2aCCl2 (XZCl)
CH2aCHBr (XZBr)
CH2aCBr2a (XZBr)
CH2aCH–CH3 (XZCH3)
C–C C–F C–O C–C C–F, C–F 0 C–O C–C C–Cl C–O C–C C–Cl, C–Cl 0 C–O C–C C–Br C–O C–C C–Br, C–Br 0 C–O C–C C–Me C–O
1.325 1.350 1.322 1.323
1.329 1.742 1.330 1.733
1.329 1.892 1.331 1.889
1.336 1.499
O (3P) atom addition
OH radical addition Product
Transition state
Product
a-Addition
b-Addition
a-Addition
b-Addition
a-Addition
b-Addition
a-Addition
b-Addition
1.326 1.335 2.046 1.327 1.304, 1.310 2.011 1.328 1.738 2.020 1.327 1.727, 1736 1.985 1.327 1.890 2.015 1.326 1.887, 1895 1.987 1.334 1.496 2.075
1.322 1.345 2.048 1.321 1.311, 1.318 2.018 1.324 1.736 2.059 1.322 1.724, 1.730 2.062 1.324 1.885 2.056 1.322 1.879, 1884 2.057 1.331 1.494 2.073
1.484 1.399 1.388 1.483 1.358, 1.372 1.371 1.482 1.826 1.399 1.473 1.902, 1.821 1.381 1.459 2.049 1.379 1.465 1.971, 1.990 1.380 1.488 1.523 1.436
1.479 1.356 1.437 1.494 1.343, 1.331 1.424 1.483 1.725 1.435 1.490 1.717, 1.729 1.427 1.484 1.871 1.434 1.492 1.869, 1.881 1.425 1.487 1.490 1.449
1.337 1.338 1.947 1.335 1.311, 1.311 1.931 1.341 1.741 1.935 1.340 1.735, 1.735 1.923 1.339 1.894 1.935 1.338 1.894, 1.894 1.926 1.345 1.500 1.976
1.334 1.338 1.959 1.337 1.313, 1.313 1.920 1.335 1.725 1.972 1.332 1.720, 1.720 1.972 1.335 1.874 1.968 1.333 1.874, 1.874 1.975 1.343 1.492 1.971
1.491 1.397 1.336 1.486 1.367, 1.367 1.350 1.486 1.840 1.341 1.463 1.801, 1.857 1.339 1.475 2.040 1.337 – – – – 1.485 1.553 1.386
1.484 1.343 1.407 1.493 1.331, 1.331 1.406 1.483 1.716 1.394 1.492 1.714, 1.714 1.406 1.490 1.855 1.405 1.492 1.869, 1.869 1.386 1.488 1.489 1.392
Geometries were optimized at the computational level of MP2/6-311CG(2d,p). a We could not attain complete geometry optimization of the a-addition product for the reaction of CH2aCBr2 with O (3P) atom.
˚ , and CH2aCHBr, the C–Br bond lengths are 2.040 and 1.855 A ˚ the C–O bond lengths are 1.337 and 1.405 A, respectively, for the a- and b-addition products. Exactly the same trends can be seen for the C–CH3 and C–O bond lengths in the radical products resulting from CH2aCH–CH3, but the differences in the bond lengths between the a- and b-addition products are much less remarkable as compared with the halogen-substituted ethenes. The above-mentioned differences in C–X/C–X 0 and C–O bond lengths between the a- and b-addition products are attributable to the hyperconjugative interaction in the a-addition products. The oxygen atom of the OH radical/O (3P) atom attacks at the carbon atom bearing substituent X in the a-addition, and hence, the lone pair electrons on the oxygen atom can be delocalized into the antibonding orbital of the C–X/C–X 0 bond in the addition product, i.e. Eq. (7), resulting in the C–O bond shortening and the C–X bond lengthening concomitantly.
(7)
Such hyperconjugative interactions are clearly shown in the natural bond orbital (NBO) analyses [14–16]; the second-order stabilization caused by the interactions between the lone pair on the oxygen atom and the antibonding orbital of the C–X bond was calculated to be more than 20 kcal/mol for the a-addition products of the OH radical reactions (Table 3). For the b-addition products, on the other hand, hyperconjugative
orbital interactions will not occur between the oxygen lone pair and the C–X antibonding orbital. It should be noted that the a-addition products are always lower in energy than the corresponding b-addition products. The differences in energy between the a- and b-addition products are quite large for the fluoro-substituted ethenes: for CH2aCHF and CH2aCF2 reactions with OH radical/O (3P) atom, the a-addition products are lower in energy by more than 10 kcal/mol than the b-addition products (Table 2). For chloroand bromo-substituted ethenes, the differences in energy between the a- and b-addition products are less remarkable. For CH2aCH–CH3, the differences in energy between the aand b-addition products are still smaller, less than 1 kcal/mol; the exothermicities are 31.64 and 30.05 kcal/mol for the a- and b-addition of an OH radical to CH2aCH–CH3, respectively, while the exothermicities are 23.56 and 23.11 kcal/mol for O (3P) atom addition to CH2aCH–CH3 (Table 2). 3.2. Structures and relative stabilities of the transition states for the addition reactions As mentioned in Section 3.1, the exothermicity of the reaction is larger for the OH addition reactions than for the O (3P) addition reactions. Correspondingly, the transition states appear to be more reactant-like for the OH addition reactions than for the O (3P) addition reactions (see Table 1). In the transition states for the OH radical addition reactions, the C–C bond lengths remain almost unchanged as compared with those in the parent molecules, while the C–C bonds are elongated by
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Fig. 1. MP2/6-311CG(2d,p)-optimized structures of the transition states and the product adducts for the reactions of CH2aCHCl.
˚ in the transition states for the O (3P) atom addition. w0.01 A Furthermore, the forming C–O bonds are longer in the transition states for the OH radical addition than in those for O (3P) atom addition. Except for the transition states for the fluoro-substituted ethenes, the lengths of C–X/C–X 0 bonds, as well as the lengths of the forming C–O bonds, in the transition states suggest the same tendencies as observed for the product radicals; C–X/ C–X 0 bonds are longer and the forming C–O bonds are shorter in the a-addition transition states than in the b-addition transition states (Table 1). For instance, in the transition states for OH radical addition to the a- and b-sites of CH2aCHBr molecule, the C–Br bond lengths are 1.890 and ˚ , respectively, while the C–O bond lengths are 2.015 1.885 A ˚ . For O (3P) atom addition, the C–Br bond lengths and 2.056 A ˚ in the a- and b-addition transition states, are 1.894 and 1.874 A ˚. respectively, and the C–O bond lengths are 1.935 and 1.968 A These differences in bond lengths between the a- and b-addition transition states are much less remarkable than between the a- and b-addition products, but suggest that the transition state for the a-addition should undergo orbital interaction similar to that observed for the product radicals, i.e. the hyperconjugative interactions between the oxygen lone pair orbital and the antibonding s* orbitals of C–X/C–X 0 bonds (Eq. (7)).
Fig. 2. MP2/6-311CG(2d,p)-optimized structures of the transition states and the product adducts for the reactions of CH2aCCl2.
Relative stabilities of the transition states for the a- and b-addition channels can be discussed in terms of two factors. The first factor is the thermodynamic effect, i.e. the difference in exothermicity between the a- and b-addition reaction channels [17]. The thermodynamic effect, which directly corresponds to the relative strengths of the C–O bonds in the a- and b-addition product radicals, should be related with the hyperconjugative interactions between the oxygen lone pair orbital and the s* orbitals of C–X/C–X 0 bonds (Eq. (7)). The contribution of this type of hyperconjugative interaction should be smaller in the transition states than in the products radicals, but such orbital interactions will partially occur even in the transition states. The second factor is the relative spin density at the a- and b-sites in the 3 pp* triplet state of the ethene molecules [17–20]. The importance of the relative spin densities in the triplet state in directing the regiochemistry for radical addition is rationalized considering the state correlation diagram (SCD) model that belongs to the general approach of curve crossing diagrams [18]. The main electronic interactions during radical addition to a double bond can be described as the spin density interactions between the radical and the alkene molecules. For the parent ethene molecule, the triplet 3pp* state is described with one unpaired electron on each carbon atom. Substitution in the ethene molecule disturbs the symmetry of the electronic spin density and a carbon atom with higher spin density will be more reactive for radical addition.
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vrððr Þ f ððr Þ Z vN
nððr Þ
63
:
(8)
In a finite-difference approach, Yang and Mortier [24] gave expressions for the ‘condensed’ fukui functions (Eqs. (9)–(11)) [25] for nucleophilic attack
fiC Z qi ðN 0 ÞKqi ðN 0 C 1Þ
(9)
for electrophilic attack
fiK Z qi ðN 0 K1ÞKqi ðN 0 Þ
(10)
½qi ðN 0 K1ÞKqi ðN 0 C 1Þ 2
(11)
for radical attack
Fig. 3. MP2/6-311CG(2d,p)-optimized structures of the transition states and the product adducts for the reactions of CH2aCH–CH3.
According to the frontier molecular orbital (FMO) picture, the major orbital interactions in the transition states will occur between the p and p* orbitals (the HOMO and LUMO) of the ethene molecule and the SOMO of the OH radical/O (3P) atom. In addition, regiochemistry should also be rationalized with the Fukui functions proposed by Parr and Yang in 1984 [21–23]. The Fukui function describes the local changes in the electron density ðrððr ÞÞ due to the change in the global number of electrons of the system (N) (Eq. (8)):
fi0 Z
N0 denotes the number of electrons for the neutral system and qi(N) represents the charges for atom i in the system with N electrons. Values of fiC; fiK and fi0 describe the reactivity toward nucleophilic, electropohilic, and radical attack, respectively: larger value represents higher reactivity. If the orbital relaxation due to addition or removal of an electron is neglected, fiC and fiK correspond to the LUMO and HOMO densities, respectively, and fi0 corresponds to the average of the densities of the HOMO and LUMO. The p and p* orbitals are both singly occupied in the triplet 3 pp* state, and thus the relative spin densities in the 3pp* state are closely related with the Fukui functions (Eqs. (9)– (11)), as well as the densities of the HOMO and LUMO. We thus calculated both the spin densities in the triplet 3pp* states and values of the Fukui functions for the ethene molecules (Table 4). Table 2 indicates that the a-addition products are lower in energy than the b-addition products, while Table 4 shows that the spin density in the triplet 3pp* state of the ethene molecules is higher at the b-site than at the a-site. The thermodynamic effect and the relative spin density effect, thus, oppose each other. Correspondingly to the values for the relative spin densities, the Fukui function f 0, which indicates the reactivity toward radical attack, is larger at the b-site than at the a-site for all ethene molecules studied in this work (Table 4). For the chloro- and bromo-substituted ethenes, the transition states for the a-addition of OH radical/O (3P) atom are higher
Table 2 Energies (in kcal/mol) of the transition states and products for the reactions of OH radical/O (3P) atom addition to substituted alkenes Substrate
Transition state
CH2aCHF CH2aCF2 CH2aCHCl CH2aCCl2 CH2aCHBr CH2aCBr2 CH2aCH– CH3
Addition reaction of O (3P) atom
Addition reaction of OH radical Product
Transition state
Product
a-Addition
b-Addition
a-Addition
b-Addition
a-Addition
b-Addition
a-Addition
b-Addition
K0.34 0.09 0.91 3.88 0.74 3.54 K1.31
K0.09 0.84 K0.71 K0.68 K1.06 K1.17 K1.08
K39.03 K46.24 K34.15 K35.31 K36.60 K35.56 K31.64
K29.51 K31.19 K32.35 K34.68 K32.59 K34.83 K30.05
5.14 4.79 6.06 8.31 5.64 11.83 3.31
4.25 6.53 3.94 3.90 3.88 4.88 2.81
K31.37 K32.02 K25.98 K25.40 K26.76 – K23.56
K16.79 K16.77 K23.91 K20.76 K19.59 K19.67 K23.11
Calculated energies of the transition states and products relative to the reactants are given. Calculations were carried out at the level of PMP2/aug-cc-pVTZ//MP2/6311CG(2d,p)CDZPE.
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Table 3 Second-order stabilization energies (DEnKs*(C–X) and DEnKs*(C–X 0 ) in kcal/mol) corresponding to the hyperconjugative interactions between the lone pair on the oxygen atoms and the antibonding orbitals of the C–X bonds in the a-addition products of the OH radical reactions Species
DEnKs*(C–X)
CH2–CHF(OH) CH2–CF2(OH) CH2–CHCl(OH) CH2–CCl2(OH) CH2–CHBr(OH) CH2–CBr2(OH)
24.83 23.26 23.31 23.15 27.11 24.56
DEnKs*(C–X 0 ) 6.65 2.66 2.08
The NBO analyses were carried out for the UHF/6-311CG(2d,p) densities. The sums of the second-order stabilization energies in the a and b orbitals are given.
by more than 1 kcal/mol in energy than that for the b-addition, i.e. addition to the b-site is energetically preferable over that to the a-site (Table 2). The regioselectivity for addition to the chloro- and bromo-substituted ethenes is thus considered to be controlled not by the thermodynamic effect, but by the relative spin density effect in the 3pp* triplet state: the relative spin densities in the 3pp* states, as well as values of the Fukui finctions fC, f K, and f 0, are larger at the b-site than at the a-site for the chloro- and bromo-substituted ethenes (Table 4). As compared with the addition to the chloro- and bromosubstituted ethenes, the thermodynamic effect is larger for the addition to the fluoro-substituted ethenes. For fluoro-substituted ethenes, the differences in energy between a-addition and b-addition product radicals are more than 10 kcal/mol (Table 2), and the a-addition product radicals are highly stable as compared with the b-addition product radicals. The thermodynamic effect and the spin density effect will thus almost cancel each other for the addition to the fluorosubstituted ethenes. For the addition of an OH radical/O (3P) atom to CH2aCHF, as well as for the addition of an OH radical to CH2aCF2, the differences in energy between the a- and
b-addition transition states are less than 1 kcal/mol; the a-addition transition states for the reactions of CH2aCHF and CH2aCF2 with the OH radical were calculated to be slightly lower than the corresponding b-addition transition states, and, conversely, the b-addition transition state for the reaction of CH2aCHF with the O (3P) atom was calculated to be slightly lower than the a-addition transition state (Table 2). For the addition of O (3P) atom to CH2aCF2, however, our calculations suggested that the thermodynamic effect should direct the regiochemistry; the addition to the a-site might be the major reaction channel for this reaction. For radical addition to CH2aCH–CH3, the thermodynamic effects are quite small; Table 2 indicates that the differences in energy between the a- and b-addition product radicals are less than 1.5 kcal/mol for the OH radical/O (3P) atom reactions. The differences in energy between the transition states for the a- and b-addition are still smaller, less than 0.5 kcal/mol (Table 2). In accord with the previously reported computational results [26–28], our calculations suggested that OH radical addition to the a-site should be favorable over that to the b-site both kinetically (0.3 kcal/mol) and thermodynamically (1.5 kcal/mol). For O (3P) atom addition to CH2aCH–CH3, on the other hand, our calculations suggested that the a-addition should be slightly favorable thermodynamically and that the b-addition channel should be slightly favorable kinetically: the energy differences in the transition states and the product radicals between the a- and b-addition channels were calculated to be w0.5 kcal/mol. Similarly to the halogen substituted ethenes, the spin density in the 3pp* state is significantly larger at the b-site than at the a-site for the CH2aCH–CH3 molecule, as well (Table 4). Furthermore, values of the Fukui functions are also larger at the b-site than at the a-site. Considering the above-mentioned results, neither the relative spin densities in the 3pp* state nor the Fukui function f0 will be the major factor in controlling the regioselectivity for radical addition to the CH2aCH–CH3 molecule.
Table 4 Relative spin densities in the 3pp* state and values for the fukui functions for the ethene molecules 3
Molecule CH2aCHF CH2aCF2 CH2aCHCl CH2aCCl2 CH2aCHBr CH2aCBr2 CH2aCHCH3
C(a) C(b) C(a) C(b) C(a) C(b) C(a) C(b) C(a) C(b) C(a) C(b) C(a) C(b)
pp* State
Fukui function
Spin density
fC
fK
f0
1.0276 1.2130 0.9303 1.2450 0.9583 1.2196 0.7891 1.2943 0.9673 1.2087 0.6761 1.2375 1.0034 1.2311
0.5014 0.4854 0.4964 0.4699 0.4553 0.5252 0.3988 0.5487 0.4529 0.5281 0.4021 0.5530 0.4604 0.4735
0.4013 0.5166 0.3321 0.5435 0.2915 0.4026 0.2390 0.3986 0.2121 0.3270 0.1836 0.3359 0.4141 0.5070
0.4514 0.5010 0.4143 0.5067 0.3734 0.4639 0.3189 0.4736 0.3325 0.4275 0.2928 0.4444 0.4373 0.4902
Relative spin densities and values for the fukui functions were both calculated at the MP2/6-311CG(2d,p)-optimized singlet state geometries. UMP2/6-311C G(2d,p) and (U)HF/6-311G wave functions were employed for calculating relative spin densities and values for the fukui functions, respectively. Details for the procedure for calculating values of the Fukui functions are given in Ref. [24].
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4. Conclusion
References
We have carried out ab initio investigations on the reactions of OH radical/O (3P) atom addition to halogen-substituted ethenes (CH2aCHX, CH2aCX2; XZF, Cl, Br) and propene (CH2aCH–CH3). Two reaction pathways, i.e. addition to the substituted carbon atom (a-site) and addition to the nonsubstituted carbon atom (b-site), have been examined. The energetic of each reaction coordinate has been evaluated at the computational level of PMP2/aug-cc-pVTZ//MP2/6-311C G(2d,p). We have mainly examined the relative reactivity and regioselectivity of the reactions and have obtained the following findings. For both a- and b-addition channels, the addition reactions of OH radicals are more exothermic (30–46 kcal/mol) than those of O (3P) atoms (17–32 kcal/mol). Correspondingly, the transition states for the OH radical addition reactions appear to be more reactant-like than those for the O (3P) atom addition reactions. The a-addition product radicals are more stable than the b-addition product radicals for both the reactions of OH radicals and those of O (3P) atoms. The differences in energy between the a- and b- addition products are more than 10 kcal/mol for fluoro-substituted ethenes, and the differences are less remarkable for chloro- and bromo-substituted ethenes. For CH2aCH– CH3, the differences in energy between the a- and b-addition products are quite small, less than 1 kcal/mol. The differences in C–O and C–X bond lengths between the a- and b-addition product radicals suggest the hyperconjugative orbital interactions between the lone pair orbital on the oxygen atom and the antibonding s* C–X orbital in the a-addition products. Relative stabilities of the transition states for the a- and b-addition channels can be discussed in terms of the thermodynamic effect and the relative spin densities at the a- and b- sites in the 3pp* states of the reactant ethene molecules. The former refers to the difference in stability between the a- and b- addition product radicals, and the latter is closely related to the state correlation diagram (SCD) model [18], as well as the picture of the frontier molecular orbital (FMO) theory and the Fukui functions [21–25]. These two factors oppose each other for OH radical/O (3P) atom addition reactions studied in the present work. Our results suggest that the regioselectivity for OH radical/O (3P) atom addition to the chloro- and bromo-substituted ethenes should be controlled not by the thermodynamic effect, but by the relative spin densities at the a- and b-sites in the 3pp* states. For fluoro-substituted ethenes, the thermodynamic effect and the spin density effect will probably cancel out each other. For addition to CH2aCH–CH3, neither the spin density in the 3pp* state nor the Fukui function f0 may be the major factor in controlling the regioselectivity. Our results suggest that the regioselectivity for the addition to the fluoro-substituted ethenes and the addition to CH2aCH–CH3 will be relatively low.
[1] R. Atkinson, J. Phys. Chem. Ref. Data 26 (1997) 215. [2] R. Atkinson, J. Arey, Chem. Rev. 103 (2003) 4605. [3] R.P. Wayne, Chemistry of Atmospheres, 3rd ed. Oxford University Press, Oxford, 2000. [4] J.P. Killus, Z. Whitten, Environ. Sci. Technol. 18 (1984) 142. [5] P.E. Paulson, H. Seinfeld, J. Geophys. Res. 97 (1992) 20703. [6] J.M. Tedder, C. Walton, Tetrahedron 36 (1980) 701. [7] J.M. Tedder, Angew. Chem. Int. Ed. Engl. 21 (1982) 401. [8] B. Giese, Angew. Chem. Int. Ed. Engl. 22 (1983) 753. [9] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, GAUSSIAN 98, Revision A.9, GAUSSIAN, Inc., Pittsburgh, PA, 1998. [10] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, GAUSSIAN 03, Revision B.05, GAUSSIAN, Inc., Pittsburgh PA, 2003. [11] C. Møller, D. Plesset, Phys. Rev. 46 (1934) 618. [12] . MOLEKEL 4.3, P. Flu¨kiger, H.P. Lu¨thi, S. Portmann, J. Weber, Swiss Center for Scientific Computing, Manno (Switzerland), 2000–2000. [13] H.B. Schlegel, J. Phys. Chem. 92 (1988) 3075. [14] NBO Version 3.1, E.D. Glendening, A.E. Reed, J.E. Carpenter, F. Weinhold. [15] A.E. Reed, L.A. Curtiss, F. Weinhold, Chem. Rev. 88 (1988) 899. [16] J.E. Carpenter, F. Weinhold, J. Mol. Struct. (THEOCHEM) 169 (1988) 41. [17] S. Sekusˇak, K.R. Liedl, A. Sabljic´, J. Phys. Chem. A 102 (1998) 1583. [18] S.S. Shaik, E. Canadell, J. Am. Chem. Soc. 112 (1990) 1446. [19] R. Arnaud, V. Vetere, V. Barone, Chem. Phys. Lett. 293 (1998) 295. [20] R. Arnaud, V. Vetere, V. Barone, J. Comput. Chem. 21 (2000) 675. [21] R.G. Parr, W. Yang, J. Am. Chem. Soc. 106 (1984) 4049. [22] R.G. Pearson, Chemical Hardness, Wiley–VCH Verlag GmbH Pappelallee 3, D-69469 Weinheim, Germany, 1997. [23] R.F. Nalewajski, J. Korchowiec, Charge Sensitivity Approach to Electronic Structure and Chemical Reactivity, in: Cheuk-Yu Ng (Ed.), Advanced Series in Physical Chemistry, vol. 8, World Scientific, Singapore, 1997. [24] W. Yang, W.J. Mortier, J. Am. Chem. Soc. 108 (1986) 5708. [25] J. Korchowiec, T. Uchimaru, J. Phys. Chem. A 102 (1998) 10167. [26] J.R. Alvarez-Idaboy, I. Dı´az-Acosta, A. Vivier-Bunge, J. Comput. Chem. 19 (1998) 811. [27] I. Dı´az-Acosta, J.R. Alvarez-Idaboy, A. Vivier-Bunge, Int. J. Chem. Kinet. 31 (1999) 29. [28] C. Selc¸uki, V. Aviyente, J. Mol. Model. 7 (2001) 398.
Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.theochem.2006. 05.036.
Relative reactivity and regioselectivity of halogen-substituted ethenes and propene toward addition of an OH radical or O (3P) atom: An ab initio study Ahmed M. El-Nahas a,1, Tadafumi Uchimaru a,b,*, Masaaki Sugie a, Kazuaki Tokuhashi a, Akira Sekiya a a
Research Institute for Innovation in Sustainable Chemistry, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan b Research Institute of Computational Sciences (RICS), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Received 27 March 2006; received in revised form 11 May 2006; accepted 17 May 2006 Available online 3 June 2006
Abstract This paper describes the results of ab initio investigations on the reactions of OH radical/O (3P) atom addition to halogen-substituted ethenes (CH2aCHX, CH2aCX2; XZF, Cl, Br) and propene. Two reaction pathways, addition to the substituted carbon atom (a-site) and addition to the non-substituted carbon atom (b-site), have been examined. The energetic of each reaction coordinate has been evaluated at the computational level of PMP2/aug-cc-pVTZ//MP2/6-311CG(2d,p). Our calculations suggested that the reactions of OH radical addition should be more exothermic than those of the O (3P) atom addition and that the a-addition products should be lower in energy than the corresponding b-addition products. Relative stabilities of the transition states for the a- and b-addition channels can be discussed in terms of the exothermicities of the reaction channels and the relative spin densities in the 3pp* states of the reactant ethene molecules. For the reactions of the chloro- and bromosubstituted ethenes, the transition states for the a-addition were found to be higher in energy than those for the b-addition, but for the reactions of the fluoro-substituted ethenes and propene, the differences in energy between the transition states for the a- and b-addition channels were found to be rather small. q 2006 Elsevier B.V. All rights reserved. Keywords: Ab initio calculations; Regioselectivity ; Halogen-substituted ethenes; Propene; OH radicals; O (3P) atoms
1. Introduction Unsaturated compounds possessing a carbon–carbon double bond react with various active species in the atmosphere, such as OH and NO3 radicals, O3 molecule, and Cl, Br, and O (3P) atoms. From the standpoint of atmospheric chemistry, the most important reaction is addition of an OH radical to a carbon–carbon double bond, and OH radical addition is a key step for atmospheric
* Corresponding author. Address: Research Institute of Computational Sciences (RICS), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan. Tel.: C81 29 861 4800; fax: C81 29 851 5426. E-mail address: [email protected] (T. Uchimaru). 1 Permanent address: Chemistry Department, Faculty of Science, El-Menoufia University, Shebin El-Kom, Egypt.
0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.05.036
degradation of unsaturated compounds. Furthermore, to accurately model the early stages of smog formation in urban areas and to model smog chamber experiments, reactions of O (3P) atoms with unsaturated compounds are also needed to be taken into account [1–5]. In this work, we have examined reactions of OH radicals and O ( 3P) atoms with mono- and 1,1-dihaloethenes (CH2aCHX/CH2aCX2, XZF, Cl, Br), as well as with propene (CH2aCH–CH3). These alkene molecules are all unsymmetrical and two reaction pathways can be distinguished: addition to the substituted (a) carbon atom of the double bond and addition to non-substituted CH2 (b) carbon atom. A number of theoretical and experimental studies have been reported on the radical addition to unsymmetrical substituted alkenes. In general, the normal pathway is the attack at the b carbon atoms, but addition at the a position is also experimentally observed [6–8]. We have carried out ab initio molecular orbital calculations on the OH radical addition channels (1) through (3), as well as the O (3P)
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atom addition channels (4) through (6) (XZF, Cl, Br):
3. Results and discussion
CH2 Z CHX C OH/ CH2 KCðOHÞHX
(1a)
CH2 Z CHX C OH/ HOCH2 KCHX
(1b)
CH2 Z CX2 C OH/ CH2 KCðOHÞX2
(2a)
CH2 Z CX2 C OH/ HOCH2 KCX2
(2b)
CH2 Z CHKCH3 C OH/ CH2 KCHðOHÞKCH3
(3a)
CH2 Z CHKCH3 C OH/ HOCH2 KCHKCH3
(3b)
CH2 Z CHX C O/ CH2 KCðOÞHX
(4a)
CH2 Z CHX C O/ OCH2 KCHX
(4b)
CH2 Z CX2 C O/ CH2 KCðOÞX2
(5a)
CH2 Z CX2 C O/ OCH2 KCX2
(5b)
CH2 Z CHKCH3 C O/ CH2 KCHðOÞKCH3
(6a)
CH2 Z CHKCH3 C O/ OCH2 KCHKCH3
(6b)
Table 1 gives the MP2/6-311CG(2d,p)-optimized geometrical parameters of the reactants, the transition states, and the product radicals for the reactions of OH radical/O (3P) atom addition to the substituted ethenes [the reactions (1) through (6)]. The structures of the transition states and the radical products are not very sensitive to the halogen substituents, and we thus give typical structures of the stationary points, i.e. the transition states and the product radicals for the reactions of CH2aCHCl, CH2aCCl2, and CH2aCH–CH3 in Figs. 1–3, respectively. Relative energies of the transition states and the product radicals are given in Table 2. The total energies and the zero-point energies (ZPEs) are summarized in supplementary information. 3.1. Structures and relative stabilities of the radical products
We have also examined the difference in reactivity between an OH radical and O (3P) atom, as well as factors controlling the regioselectivity, i.e. a-addition versus b-addition, in these reactions.
2. Computational details Ab initio calculations were carried out with the Gaussian 98 and Gaussian 03 suites of programs [9,10]. Using frozen-core Møller Plesset perturbation theory truncated at the secondorder (MP2ZFC) [11] in conjunction with the 6-311CG(2d,p) basis set, we performed full geometry optimizations for the reactants, products, and transition states for the addition of OH radical/O (3P) atom to the ethene molecules. Restricted (RMP2) and unrestricted (UMP2) methods were used for the closed- and open-shell systems, respectively. Spin contamination of the open-shell systems in this study was small. For the doublet radicals and the triplet biradicals, the expectation values of the total spin hS2i were less than 0.76 and 2.01, respectively, after spin annihilations. For the transition states, spin contamination was slightly larger than in the stable radicals; however, all values of hS2i were less than 0.76 and 2.01 after spin annihilations. For each stationary point, we carried out vibrational frequency calculation and examined the vibrational modes by using the Molekel program [12]. In addition, MP2 single-point energy calculations were carried out using the aug-cc-pVTZ basis set. We refined the relative energies of the stationary points as the projected energies [13] at the MP2/aug-cc-pVTZ level of theory based on the structures optimized at the MP2/6311CG(2d,p) level, i.e. PMP2/aug-cc-pVTZ//MP2/6-311C G(2d,p) level.
Addition of an OH radical or O (3P) atom to the carbon– carbon double bond results in change in the hybridization of the carbon atoms in the parent molecule; the sp2 hybrid double bond carbon atoms are converted to the sp3 hybrid carbon atom and the radical center carbon atom. On going from the parent ethene molecules to the product radicals, the bond order between the carbon atoms is decreased and, correspondingly, the carbon–carbon bonds are longer for the product radicals than for the parent ethenes (Table 1). For example, OH radical addition to CH2aCHF molecule lengthens the carbon–carbon ˚ in the parent CH2aCHF molecule to 1.484 bond from 1.325 A ˚ and 1.479 A in the a- and b-addition product radicals, respectively. The corresponding carbon–carbon bond lengthening for O (3P) atom addition is still slightly larger; the carbon–carbon bond lengths in the a- and b-addition product radicals are 1.491 ˚ , respectively. and 1.484 A Table 2 indicates that the OH radical addition and the O (3P) atom addition are both highly exothermic; the exothermicities of the reactions amount to 17–46 kcal/mol. Furthermore, it should be noted that the OH radical addition reactions are always more exothermic than the corresponding O (3P) atom addition reactions. The exothermicities for the OH radical addition reactions range from 30 to 46 kcal/mol, while the exothermicities for the O (3P) atom addition range from 17 to 32 kcal/mol. Comparison between the a- and b-addition product radicals is quite interesting. For both OH radical addition and O (3P) atom addition reactions, the C–X and C–X 0 bonds are longer and, conversely, the C–O bonds are shorter, for the a-addition products than for the b-addition products (see Table 1). For the OH radical addition to CH2aCHF, the C–F bond lengths in the ˚ , respectively, a- and b-addition products are 1.399 and 1.356 A while the C–O bond lengths in the a- and b-addition products ˚ . For the O (3P) atom addition to are 1.388 and 1.437 A ˚ , and CH2aCHF, the C–F bond lengths are 1.397 and 1.343 A ˚ , respectively, for the C–O bond lengths are 1.336 and 1.407 A the a- and b-addition products. For the OH radical addition to ˚ , and CH2aCHBr, the C–Br bond lengths are 2.049 and 1.871 A ˚ , respectively, for the C–O bond lengths are 1.379 and 1.434 A the a- and b-addition products. For O (3P) atom addition to
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61
Table 1 ˚ ) in the reactants, transition states, and products for the reactions of OH radical/O (3P) atom addition to the substituted alkenes Bond lengths (A Substituted alkene
Substrate
Transition state
CH2aCHF (XZF)
CH2aCF2 (XZF)
CH2aCHCl (XZCl)
CH2aCCl2 (XZCl)
CH2aCHBr (XZBr)
CH2aCBr2a (XZBr)
CH2aCH–CH3 (XZCH3)
C–C C–F C–O C–C C–F, C–F 0 C–O C–C C–Cl C–O C–C C–Cl, C–Cl 0 C–O C–C C–Br C–O C–C C–Br, C–Br 0 C–O C–C C–Me C–O
1.325 1.350 1.322 1.323
1.329 1.742 1.330 1.733
1.329 1.892 1.331 1.889
1.336 1.499
O (3P) atom addition
OH radical addition Product
Transition state
Product
a-Addition
b-Addition
a-Addition
b-Addition
a-Addition
b-Addition
a-Addition
b-Addition
1.326 1.335 2.046 1.327 1.304, 1.310 2.011 1.328 1.738 2.020 1.327 1.727, 1736 1.985 1.327 1.890 2.015 1.326 1.887, 1895 1.987 1.334 1.496 2.075
1.322 1.345 2.048 1.321 1.311, 1.318 2.018 1.324 1.736 2.059 1.322 1.724, 1.730 2.062 1.324 1.885 2.056 1.322 1.879, 1884 2.057 1.331 1.494 2.073
1.484 1.399 1.388 1.483 1.358, 1.372 1.371 1.482 1.826 1.399 1.473 1.902, 1.821 1.381 1.459 2.049 1.379 1.465 1.971, 1.990 1.380 1.488 1.523 1.436
1.479 1.356 1.437 1.494 1.343, 1.331 1.424 1.483 1.725 1.435 1.490 1.717, 1.729 1.427 1.484 1.871 1.434 1.492 1.869, 1.881 1.425 1.487 1.490 1.449
1.337 1.338 1.947 1.335 1.311, 1.311 1.931 1.341 1.741 1.935 1.340 1.735, 1.735 1.923 1.339 1.894 1.935 1.338 1.894, 1.894 1.926 1.345 1.500 1.976
1.334 1.338 1.959 1.337 1.313, 1.313 1.920 1.335 1.725 1.972 1.332 1.720, 1.720 1.972 1.335 1.874 1.968 1.333 1.874, 1.874 1.975 1.343 1.492 1.971
1.491 1.397 1.336 1.486 1.367, 1.367 1.350 1.486 1.840 1.341 1.463 1.801, 1.857 1.339 1.475 2.040 1.337 – – – – 1.485 1.553 1.386
1.484 1.343 1.407 1.493 1.331, 1.331 1.406 1.483 1.716 1.394 1.492 1.714, 1.714 1.406 1.490 1.855 1.405 1.492 1.869, 1.869 1.386 1.488 1.489 1.392
Geometries were optimized at the computational level of MP2/6-311CG(2d,p). a We could not attain complete geometry optimization of the a-addition product for the reaction of CH2aCBr2 with O (3P) atom.
˚ , and CH2aCHBr, the C–Br bond lengths are 2.040 and 1.855 A ˚ the C–O bond lengths are 1.337 and 1.405 A, respectively, for the a- and b-addition products. Exactly the same trends can be seen for the C–CH3 and C–O bond lengths in the radical products resulting from CH2aCH–CH3, but the differences in the bond lengths between the a- and b-addition products are much less remarkable as compared with the halogen-substituted ethenes. The above-mentioned differences in C–X/C–X 0 and C–O bond lengths between the a- and b-addition products are attributable to the hyperconjugative interaction in the a-addition products. The oxygen atom of the OH radical/O (3P) atom attacks at the carbon atom bearing substituent X in the a-addition, and hence, the lone pair electrons on the oxygen atom can be delocalized into the antibonding orbital of the C–X/C–X 0 bond in the addition product, i.e. Eq. (7), resulting in the C–O bond shortening and the C–X bond lengthening concomitantly.
(7)
Such hyperconjugative interactions are clearly shown in the natural bond orbital (NBO) analyses [14–16]; the second-order stabilization caused by the interactions between the lone pair on the oxygen atom and the antibonding orbital of the C–X bond was calculated to be more than 20 kcal/mol for the a-addition products of the OH radical reactions (Table 3). For the b-addition products, on the other hand, hyperconjugative
orbital interactions will not occur between the oxygen lone pair and the C–X antibonding orbital. It should be noted that the a-addition products are always lower in energy than the corresponding b-addition products. The differences in energy between the a- and b-addition products are quite large for the fluoro-substituted ethenes: for CH2aCHF and CH2aCF2 reactions with OH radical/O (3P) atom, the a-addition products are lower in energy by more than 10 kcal/mol than the b-addition products (Table 2). For chloroand bromo-substituted ethenes, the differences in energy between the a- and b-addition products are less remarkable. For CH2aCH–CH3, the differences in energy between the aand b-addition products are still smaller, less than 1 kcal/mol; the exothermicities are 31.64 and 30.05 kcal/mol for the a- and b-addition of an OH radical to CH2aCH–CH3, respectively, while the exothermicities are 23.56 and 23.11 kcal/mol for O (3P) atom addition to CH2aCH–CH3 (Table 2). 3.2. Structures and relative stabilities of the transition states for the addition reactions As mentioned in Section 3.1, the exothermicity of the reaction is larger for the OH addition reactions than for the O (3P) addition reactions. Correspondingly, the transition states appear to be more reactant-like for the OH addition reactions than for the O (3P) addition reactions (see Table 1). In the transition states for the OH radical addition reactions, the C–C bond lengths remain almost unchanged as compared with those in the parent molecules, while the C–C bonds are elongated by
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Fig. 1. MP2/6-311CG(2d,p)-optimized structures of the transition states and the product adducts for the reactions of CH2aCHCl.
˚ in the transition states for the O (3P) atom addition. w0.01 A Furthermore, the forming C–O bonds are longer in the transition states for the OH radical addition than in those for O (3P) atom addition. Except for the transition states for the fluoro-substituted ethenes, the lengths of C–X/C–X 0 bonds, as well as the lengths of the forming C–O bonds, in the transition states suggest the same tendencies as observed for the product radicals; C–X/ C–X 0 bonds are longer and the forming C–O bonds are shorter in the a-addition transition states than in the b-addition transition states (Table 1). For instance, in the transition states for OH radical addition to the a- and b-sites of CH2aCHBr molecule, the C–Br bond lengths are 1.890 and ˚ , respectively, while the C–O bond lengths are 2.015 1.885 A ˚ . For O (3P) atom addition, the C–Br bond lengths and 2.056 A ˚ in the a- and b-addition transition states, are 1.894 and 1.874 A ˚. respectively, and the C–O bond lengths are 1.935 and 1.968 A These differences in bond lengths between the a- and b-addition transition states are much less remarkable than between the a- and b-addition products, but suggest that the transition state for the a-addition should undergo orbital interaction similar to that observed for the product radicals, i.e. the hyperconjugative interactions between the oxygen lone pair orbital and the antibonding s* orbitals of C–X/C–X 0 bonds (Eq. (7)).
Fig. 2. MP2/6-311CG(2d,p)-optimized structures of the transition states and the product adducts for the reactions of CH2aCCl2.
Relative stabilities of the transition states for the a- and b-addition channels can be discussed in terms of two factors. The first factor is the thermodynamic effect, i.e. the difference in exothermicity between the a- and b-addition reaction channels [17]. The thermodynamic effect, which directly corresponds to the relative strengths of the C–O bonds in the a- and b-addition product radicals, should be related with the hyperconjugative interactions between the oxygen lone pair orbital and the s* orbitals of C–X/C–X 0 bonds (Eq. (7)). The contribution of this type of hyperconjugative interaction should be smaller in the transition states than in the products radicals, but such orbital interactions will partially occur even in the transition states. The second factor is the relative spin density at the a- and b-sites in the 3 pp* triplet state of the ethene molecules [17–20]. The importance of the relative spin densities in the triplet state in directing the regiochemistry for radical addition is rationalized considering the state correlation diagram (SCD) model that belongs to the general approach of curve crossing diagrams [18]. The main electronic interactions during radical addition to a double bond can be described as the spin density interactions between the radical and the alkene molecules. For the parent ethene molecule, the triplet 3pp* state is described with one unpaired electron on each carbon atom. Substitution in the ethene molecule disturbs the symmetry of the electronic spin density and a carbon atom with higher spin density will be more reactive for radical addition.
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vrððr Þ f ððr Þ Z vN
nððr Þ
63
:
(8)
In a finite-difference approach, Yang and Mortier [24] gave expressions for the ‘condensed’ fukui functions (Eqs. (9)–(11)) [25] for nucleophilic attack
fiC Z qi ðN 0 ÞKqi ðN 0 C 1Þ
(9)
for electrophilic attack
fiK Z qi ðN 0 K1ÞKqi ðN 0 Þ
(10)
½qi ðN 0 K1ÞKqi ðN 0 C 1Þ 2
(11)
for radical attack
Fig. 3. MP2/6-311CG(2d,p)-optimized structures of the transition states and the product adducts for the reactions of CH2aCH–CH3.
According to the frontier molecular orbital (FMO) picture, the major orbital interactions in the transition states will occur between the p and p* orbitals (the HOMO and LUMO) of the ethene molecule and the SOMO of the OH radical/O (3P) atom. In addition, regiochemistry should also be rationalized with the Fukui functions proposed by Parr and Yang in 1984 [21–23]. The Fukui function describes the local changes in the electron density ðrððr ÞÞ due to the change in the global number of electrons of the system (N) (Eq. (8)):
fi0 Z
N0 denotes the number of electrons for the neutral system and qi(N) represents the charges for atom i in the system with N electrons. Values of fiC; fiK and fi0 describe the reactivity toward nucleophilic, electropohilic, and radical attack, respectively: larger value represents higher reactivity. If the orbital relaxation due to addition or removal of an electron is neglected, fiC and fiK correspond to the LUMO and HOMO densities, respectively, and fi0 corresponds to the average of the densities of the HOMO and LUMO. The p and p* orbitals are both singly occupied in the triplet 3 pp* state, and thus the relative spin densities in the 3pp* state are closely related with the Fukui functions (Eqs. (9)– (11)), as well as the densities of the HOMO and LUMO. We thus calculated both the spin densities in the triplet 3pp* states and values of the Fukui functions for the ethene molecules (Table 4). Table 2 indicates that the a-addition products are lower in energy than the b-addition products, while Table 4 shows that the spin density in the triplet 3pp* state of the ethene molecules is higher at the b-site than at the a-site. The thermodynamic effect and the relative spin density effect, thus, oppose each other. Correspondingly to the values for the relative spin densities, the Fukui function f 0, which indicates the reactivity toward radical attack, is larger at the b-site than at the a-site for all ethene molecules studied in this work (Table 4). For the chloro- and bromo-substituted ethenes, the transition states for the a-addition of OH radical/O (3P) atom are higher
Table 2 Energies (in kcal/mol) of the transition states and products for the reactions of OH radical/O (3P) atom addition to substituted alkenes Substrate
Transition state
CH2aCHF CH2aCF2 CH2aCHCl CH2aCCl2 CH2aCHBr CH2aCBr2 CH2aCH– CH3
Addition reaction of O (3P) atom
Addition reaction of OH radical Product
Transition state
Product
a-Addition
b-Addition
a-Addition
b-Addition
a-Addition
b-Addition
a-Addition
b-Addition
K0.34 0.09 0.91 3.88 0.74 3.54 K1.31
K0.09 0.84 K0.71 K0.68 K1.06 K1.17 K1.08
K39.03 K46.24 K34.15 K35.31 K36.60 K35.56 K31.64
K29.51 K31.19 K32.35 K34.68 K32.59 K34.83 K30.05
5.14 4.79 6.06 8.31 5.64 11.83 3.31
4.25 6.53 3.94 3.90 3.88 4.88 2.81
K31.37 K32.02 K25.98 K25.40 K26.76 – K23.56
K16.79 K16.77 K23.91 K20.76 K19.59 K19.67 K23.11
Calculated energies of the transition states and products relative to the reactants are given. Calculations were carried out at the level of PMP2/aug-cc-pVTZ//MP2/6311CG(2d,p)CDZPE.
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Table 3 Second-order stabilization energies (DEnKs*(C–X) and DEnKs*(C–X 0 ) in kcal/mol) corresponding to the hyperconjugative interactions between the lone pair on the oxygen atoms and the antibonding orbitals of the C–X bonds in the a-addition products of the OH radical reactions Species
DEnKs*(C–X)
CH2–CHF(OH) CH2–CF2(OH) CH2–CHCl(OH) CH2–CCl2(OH) CH2–CHBr(OH) CH2–CBr2(OH)
24.83 23.26 23.31 23.15 27.11 24.56
DEnKs*(C–X 0 ) 6.65 2.66 2.08
The NBO analyses were carried out for the UHF/6-311CG(2d,p) densities. The sums of the second-order stabilization energies in the a and b orbitals are given.
by more than 1 kcal/mol in energy than that for the b-addition, i.e. addition to the b-site is energetically preferable over that to the a-site (Table 2). The regioselectivity for addition to the chloro- and bromo-substituted ethenes is thus considered to be controlled not by the thermodynamic effect, but by the relative spin density effect in the 3pp* triplet state: the relative spin densities in the 3pp* states, as well as values of the Fukui finctions fC, f K, and f 0, are larger at the b-site than at the a-site for the chloro- and bromo-substituted ethenes (Table 4). As compared with the addition to the chloro- and bromosubstituted ethenes, the thermodynamic effect is larger for the addition to the fluoro-substituted ethenes. For fluoro-substituted ethenes, the differences in energy between a-addition and b-addition product radicals are more than 10 kcal/mol (Table 2), and the a-addition product radicals are highly stable as compared with the b-addition product radicals. The thermodynamic effect and the spin density effect will thus almost cancel each other for the addition to the fluorosubstituted ethenes. For the addition of an OH radical/O (3P) atom to CH2aCHF, as well as for the addition of an OH radical to CH2aCF2, the differences in energy between the a- and
b-addition transition states are less than 1 kcal/mol; the a-addition transition states for the reactions of CH2aCHF and CH2aCF2 with the OH radical were calculated to be slightly lower than the corresponding b-addition transition states, and, conversely, the b-addition transition state for the reaction of CH2aCHF with the O (3P) atom was calculated to be slightly lower than the a-addition transition state (Table 2). For the addition of O (3P) atom to CH2aCF2, however, our calculations suggested that the thermodynamic effect should direct the regiochemistry; the addition to the a-site might be the major reaction channel for this reaction. For radical addition to CH2aCH–CH3, the thermodynamic effects are quite small; Table 2 indicates that the differences in energy between the a- and b-addition product radicals are less than 1.5 kcal/mol for the OH radical/O (3P) atom reactions. The differences in energy between the transition states for the a- and b-addition are still smaller, less than 0.5 kcal/mol (Table 2). In accord with the previously reported computational results [26–28], our calculations suggested that OH radical addition to the a-site should be favorable over that to the b-site both kinetically (0.3 kcal/mol) and thermodynamically (1.5 kcal/mol). For O (3P) atom addition to CH2aCH–CH3, on the other hand, our calculations suggested that the a-addition should be slightly favorable thermodynamically and that the b-addition channel should be slightly favorable kinetically: the energy differences in the transition states and the product radicals between the a- and b-addition channels were calculated to be w0.5 kcal/mol. Similarly to the halogen substituted ethenes, the spin density in the 3pp* state is significantly larger at the b-site than at the a-site for the CH2aCH–CH3 molecule, as well (Table 4). Furthermore, values of the Fukui functions are also larger at the b-site than at the a-site. Considering the above-mentioned results, neither the relative spin densities in the 3pp* state nor the Fukui function f0 will be the major factor in controlling the regioselectivity for radical addition to the CH2aCH–CH3 molecule.
Table 4 Relative spin densities in the 3pp* state and values for the fukui functions for the ethene molecules 3
Molecule CH2aCHF CH2aCF2 CH2aCHCl CH2aCCl2 CH2aCHBr CH2aCBr2 CH2aCHCH3
C(a) C(b) C(a) C(b) C(a) C(b) C(a) C(b) C(a) C(b) C(a) C(b) C(a) C(b)
pp* State
Fukui function
Spin density
fC
fK
f0
1.0276 1.2130 0.9303 1.2450 0.9583 1.2196 0.7891 1.2943 0.9673 1.2087 0.6761 1.2375 1.0034 1.2311
0.5014 0.4854 0.4964 0.4699 0.4553 0.5252 0.3988 0.5487 0.4529 0.5281 0.4021 0.5530 0.4604 0.4735
0.4013 0.5166 0.3321 0.5435 0.2915 0.4026 0.2390 0.3986 0.2121 0.3270 0.1836 0.3359 0.4141 0.5070
0.4514 0.5010 0.4143 0.5067 0.3734 0.4639 0.3189 0.4736 0.3325 0.4275 0.2928 0.4444 0.4373 0.4902
Relative spin densities and values for the fukui functions were both calculated at the MP2/6-311CG(2d,p)-optimized singlet state geometries. UMP2/6-311C G(2d,p) and (U)HF/6-311G wave functions were employed for calculating relative spin densities and values for the fukui functions, respectively. Details for the procedure for calculating values of the Fukui functions are given in Ref. [24].
A.M. El-Nahas et al. / Journal of Molecular Structure: THEOCHEM 770 (2006) 59–65
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4. Conclusion
References
We have carried out ab initio investigations on the reactions of OH radical/O (3P) atom addition to halogen-substituted ethenes (CH2aCHX, CH2aCX2; XZF, Cl, Br) and propene (CH2aCH–CH3). Two reaction pathways, i.e. addition to the substituted carbon atom (a-site) and addition to the nonsubstituted carbon atom (b-site), have been examined. The energetic of each reaction coordinate has been evaluated at the computational level of PMP2/aug-cc-pVTZ//MP2/6-311C G(2d,p). We have mainly examined the relative reactivity and regioselectivity of the reactions and have obtained the following findings. For both a- and b-addition channels, the addition reactions of OH radicals are more exothermic (30–46 kcal/mol) than those of O (3P) atoms (17–32 kcal/mol). Correspondingly, the transition states for the OH radical addition reactions appear to be more reactant-like than those for the O (3P) atom addition reactions. The a-addition product radicals are more stable than the b-addition product radicals for both the reactions of OH radicals and those of O (3P) atoms. The differences in energy between the a- and b- addition products are more than 10 kcal/mol for fluoro-substituted ethenes, and the differences are less remarkable for chloro- and bromo-substituted ethenes. For CH2aCH– CH3, the differences in energy between the a- and b-addition products are quite small, less than 1 kcal/mol. The differences in C–O and C–X bond lengths between the a- and b-addition product radicals suggest the hyperconjugative orbital interactions between the lone pair orbital on the oxygen atom and the antibonding s* C–X orbital in the a-addition products. Relative stabilities of the transition states for the a- and b-addition channels can be discussed in terms of the thermodynamic effect and the relative spin densities at the a- and b- sites in the 3pp* states of the reactant ethene molecules. The former refers to the difference in stability between the a- and b- addition product radicals, and the latter is closely related to the state correlation diagram (SCD) model [18], as well as the picture of the frontier molecular orbital (FMO) theory and the Fukui functions [21–25]. These two factors oppose each other for OH radical/O (3P) atom addition reactions studied in the present work. Our results suggest that the regioselectivity for OH radical/O (3P) atom addition to the chloro- and bromo-substituted ethenes should be controlled not by the thermodynamic effect, but by the relative spin densities at the a- and b-sites in the 3pp* states. For fluoro-substituted ethenes, the thermodynamic effect and the spin density effect will probably cancel out each other. For addition to CH2aCH–CH3, neither the spin density in the 3pp* state nor the Fukui function f0 may be the major factor in controlling the regioselectivity. Our results suggest that the regioselectivity for the addition to the fluoro-substituted ethenes and the addition to CH2aCH–CH3 will be relatively low.
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Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.theochem.2006. 05.036.