Mechanism of addition-fragmentation reaction of thiocarbonyls compounds in free radical polymerization. A DFT study

Computational and Theoretical Chemistry 1027 (2014) 39–45

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Mechanism of addition-fragmentation reaction of thiocarbonyls compounds in free radical polymerization. A DFT study Nadjia Latelli a,b, Nadia Ouddai b, Michel Arotçaréna c, Philippe Chaumont c, Pierre Mignon d, Henry Chermette d,⇑ a

Faculté des sciences, département de chimie, Université de Msila, BP 166 Ichbilia, 28000 M’sila, Algeria Laboratoire chimie des matériaux et des vivants: activité, réactivité, Université El-Hadj Lakhdar, Batna, Algeria Université de Lyon, Université Lyon 1(UCBL) et UMR CNRS 5223, Ingénierie des Matériaux Polymères, F-69622 Villeurbanne Cedex, France d Université de Lyon, Université Lyon 1 et CNRS UMR 5280, Institut des Sciences Analytiques, 43 bd du 11 novembre 1918, 69622 Villeurbanne Cedex, France b c

a r t i c l e

i n f o

Article history: Received 3 September 2013 Received in revised form 15 October 2013 Accepted 18 October 2013 Available online 30 October 2013 Keywords: DFT calculation Thiocarbonyl compounds RAFT agents

a b s t r a c t In the present study we analyze the reaction mechanisms involved by Xanthates (SA(C@S)AO) and Thiocarbonates (OA(C@S)AO) compounds in a reversible addition fragmentation chain transfer (RAFT) polymerization. For the purpose, theoretical calculations have been performed by means of density functional theory (DFT), using the B3LYP, M06, CAM-B3LYP, LC-xPBE exchange correlation functionals and 6-31G⁄ basis sets. Thanks to the transition state theory, the rates of addition and fragmentation reactions were obtained. It is shown that, for these systems, the fragmentation step is more selective than the addition step, and that the range-separated functionals give results close to the experimental trends. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Interest in organic radical reactions for synthesis has rapidly increased over the past several years due to the development of new synthetic methods and an increased understanding of radical kinetics. Techniques for controlling free-radical polymerization, including nitroxide-mediated polymerization (NMP) [1], atom transfer polymerization (ATRP) [2], reversible addition fragmentation chain transfer (RAFT) polymerization [3], thioketone mediated polymerization (TKMP) [4,5] and cobalt-mediated polymerization (CMP) [6] are an important new development as they allow for the production of polymers with narrow molecular weight distributions, designed end-groups, and controlled architectures, such as star polymers, graft polymers and block polymers. The RAFT process, first developed by Rizzardo et al. [3] uses the small-radical chemistry of Zard and co-workers [7], i.e. the thiocarbonyl compounds 2 (known as RAFT agents), which reversibly react with the growing polymeric radical 1 via the chain transfer reaction shown in Scheme 1, producing a polymeric thiocarbonyl compound 4 as the inactive species. Both the reactive double bond C@S and the simple weak S–R bond are the structural keys of RAFT transfer agents based on thiocarbonyl compounds. Thus, by changing Z and/or R groups it

⇑ Corresponding author. E-mail address: [email protected] (H. Chermette). 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.10.018

is possible to modify the addition and fragmentation rate and, therefore, the activity of the RAFT agent [8,9]. In the present study, we focus on thionocarbonates, and dithiocarbonates (xanthates) which have been synthesized by some of us [10]. In order to get a better insight of the fragmentation of the O–C bond, we first choose the O-benzyl S-methyl xanthate CAF1 (see Fig. 1). In this molecule, the fragmentation of the S–C bond releases a methyl radical, strongly unstable whereas the fragmentation of the O–C bond forms a more stable benzyl radical. In the case of CAF3 (Fig. 1) we investigate the effect of changing the SCH3 group in CAF1 by a OPh group. Recently some theoretical studies related to chain transfer agents used in RAFT polymerization have shown how quantumchemical calculations can now efficiently be used in a practical fashion to study free-radical polymerization processes [11–15]. In the present work, molecular orbital calculations are used to understand the reactivity and kinetics for three RAFT reactions: (O-benzyl S-methyl xanthate (CAF1), 1,2-diphenyl-1,2-éthane pyrothiono carbonate (CAF2) and O-benzyl O-phenyl thiocarbonate (CAF3). (See Fig. 1). It is known that standard DFT calculations (e.g. B3LYP) perform poorly for the description of radicals [16] and the origin of the failure is traditionally assigned to the overestimation of the electronic delocalization, leading to significant selfinteraction energy errors [14,17,18]. In order to circumvent that, exchange–correlation functionals with long-range separation have recently been developed, and two of them, namely the CAM-B3LYP, LC-xPBE functionals are tested in the present work. Finally, for

40

N. Latelli et al. / Computational and Theoretical Chemistry 1027 (2014) 39–45

Scheme 1. Simplified reversible addition-fragmentation chain transfer (RAFT) polymerization scheme.

CAF1

CAF3

CAF2 Fig. 1. Schematic representation of RAFT agents.

sake of comparison, the more recently developed M06 functional is also tested. Besides, the post Hartree–Fock MP2 [19–21] model is used to assess the effect of the inclusion of the dispersion energy. It is known that accurate calculations of the energetics of such RAFT reactions require very high level of theory, which indeed can be afforded only for very small systems. Coote [15] suggested the ‘‘W1 theory or better’’. W1 theory approximates CCSD (T) calculations by basis set extrapolation and is not really tractable for systems containing more than five non-hydrogen atoms. In the present work, more approximate methods are used, in order to investigate bigger systems, to the detriment of the accuracy, which can be estimated here to a few kcal mol1 instead of one or two kJ mol1 which would represent the chemical accuracy needed for these systems. The aims of the research are 2-fold: First in order to better understand the reactivity in the addition – fragmentation reactions within the RAFT process, the magnitude of the calculated thermodynamic quantities at 298.15 K are examined at three modern levels of theory. Second, the individual rate coefficients for addition and fragmentation for the different RAFT agents are compared at the same three levels of theories. As such, it is hoped to get a deeper understanding of the effects of substituents in these reactions.

MP2/cc-PVTZ and MP2/6-31G+(d) energy barriers were compared to the barriers of reactions calculated within the DFT formalism. To understand the reactivity of the three RAFT agents, global reactivity descriptors, such as electronic chemical potential and chemical hardness have been determined by ionization potential and electronic affinity calculations [31,32]. The vertical ionization potentials (IP) and electron affinities (EA) were computed as differences in total energies of the native systems and their corresponding cation or anion, respectively: IP = E(N  1)  E(N); EA = E(N)  E(N + 1), N being the total number of electron of the native system, at its geometrical structure [33]. The electronic chemical potential (l) and the chemical hardness (g) of each system were next derived from the ionization potentials and electron affinities as:

2. Computational procedures

kðTÞ ¼ jðTÞ

All calculations have been carried out at DFT level using the GAUSSIAN09 program package [22]. Functionals B3LYP [23], M06 [24], CAM-B3LYP [25], and LC-xPBE [26–29] were used throughout. An all electron valence double-zeta basis augmented with one polarization function (6-31G (d)) has been retained for all atoms other than hydrogen [30]. All transition states have been characterized, corresponding to first order saddle points, i.e. with only one imaginary frequency. All calculations bearing on radicals were performed within the spin-unrestricted formalism. Using the B3LYP/6-31G(d) optimized structures, we calculated energies at the MP2 level of theory, with four basis sets, in order to estimate the importance of this parameter for the accuracy of the method, since it is known that, like all post-Hartree–Fock methods, MP2 is sensitive to the extent of the basis set. On the contrary, DFT methods, which involve functionals including fitted parameters obtained through calculations performed with moderate basis sets, are much less sensitive, so that a systematic increase of the basis set does not lead to better performances contrary to post-HF methods. The MP2/6-31G(d), MP2/6-311G(d),

where kB and h are Boltzmann’s and Planck’s constants respectively, R the ideal gas constant, m the molecularity of the reaction and DG– is the activation free energy of the considered reaction. c° is the standard unit of concentration (mol L1). The value of c° depends on the standard-state concentration assumed in calculating the thermodynamic quantities. In the present work, these quantities were calculated for 1 mol of an ideal gas at 298.15 K and 1 atm, and hence, c° = 0.04087 mol L1. j(T) is the tunneling coefficient which corrects for quantum effects in motion along the reaction path [35,36]. It can be assumed to be negligible (i.e., k(T)  1) for the addition of carbon-centered radicals to thiocarbonyl compounds.

l¼

IP þ EA 2

g ¼ IP  EA

ð1Þ ð2Þ

From the determined accurate geometries, frequencies and energies, gas-phase rate coefficients are obtained using the standard textbook formulae [34]:

ðDRTG– Þ kB T  0 1me C h

ð3Þ

3. Results and discussion The ionization potential (IP), electron affinity (EA), electronic chemical potential (l), chemical hardness (g) are collected in Table S1. First of all, qualitatively we can notice that all computed chemical potentials of thiocarbonyl compounds (3.51 to

N. Latelli et al. / Computational and Theoretical Chemistry 1027 (2014) 39–45

separated DFT methods still remain low in comparison to MP2, by about 34 to 40 kJ/mol. One may keep in mind that the MP2 level is known to overestimate the dispersion energy for only a few kJ/ mol, which might artificially and marginally increase the DFT/ MP2 discrepancy [37]. In addition, when the activation energies computed for CAF1 and CAF3 are compared, the latter values are always higher, thus suggesting a slower kinetics for the CAF3, which can also be observed through the calculations of the rate coefficients (See Table 2). It is important to remark that the activation energies are almost the same for CAF1 and CAF2 when they are computed at the B3LYP and CAM-B3LYP levels. However at LC-xPBE and MP2 levels the difference is more pronounced and CAF1 shows a smaller barrier than CAF2. The exchange range separation works differently on the reaction energy (DE), the reaction becomes more exothermic when range separation is included as compared to B3LYP (from 16 to 32 kJ/mol) and even more surprisingly as compared to MP2 results for which the reaction is almost athermic. The effect of basis sets were assessed by performing MP2 calculations on B3LYP optimized geometries with four basis sets to compute the activation barriers and reaction energies, as well as DFT with 6-31G+(d) basis (Table S2). It is observed that the variation of the energies with the basis set remains small as it ranges from 1 to at most 4–5 kJ/ mol in most cases (Table 3). This confirms that the basis set used, namely 6-31G(d), is convenient for the calculation of reaction barriers for this class of RAFT molecules, and at MP2 level of theory, a larger basis set does not significantly affect the accuracy of the calculated barriers [37]. Finally, all the results obtained with the M06 method lie between the B3LYP and the range-separated methods, indicating that the M06 functional provides better descriptions of radicals than B3LYP, but significantly worse than CAM-B3LYP or LC-xPBE [15]. The changes in the lengths of Cm-S formed bond between DFT methods in the transition structures for the CH3 addition reactions remain rather small, lying between (0.03–0.04 Å), although the B3LYP method seems to overestimate this distance

3.85 eV) are higher than that of the methyl radical (3.97 eV) thereby indicating that, if any, a charge transfer will take place from nucleophile thiocarbonyl compounds towards the methyl radical here acting as an electron acceptor. Nevertheless, although extremely informative, reactivity index do not give any insights on the pathways followed by the chemical reaction. To this end, an exhaustive exploration of the potential energy surface (PES) for the reactions was performed. 3.1. Addition reactions In all cases a unique transition state corresponding to the H3C–S bond formation has been located (Fig. 2) for the following polymerization reactions:

CH3 þ S@CðOCH2 PhÞSCH3 ! ½CH3  SCðOCH2 PhÞSCH3 



ð4Þ

CH3 þ S@CðOCHPhÞOCHPh ! ½CH3  SCðOCHPhÞOCHPh CH3 þ S@CðOCH2 PhÞOPh ! ½CH3  SCðOCH2 PhÞOPh



ð5Þ



41

ð6Þ

The geometries of the RAFT-adduct radicals are illustrated schematically in Fig. 3. Table 1 shows the thermodynamics parameters for the three reactions of addition, calculated at the B3LYP, M06, CAM-B3LYP, LC-xPBE, and MP2 levels of theory. First of all one can note that all barriers computed at the B3LYP level are lower than those calculated with range-separated functionals, i.e. CAMB3LYP and LC-xPBE. Indeed the inclusion of the range separation approach, from B3LYP to CAM-B3LYP, shows that the differences for the barriers lie between 2 and 3.5 kJ mol1. The inclusion of the range separation seems to allow for a better description of the system and gives a larger energy barrier, although these results are still far from those obtained at MP2, a more reliable level of theory. When the range separation is applied in combination with the PBE exchange functional, the activation barrier still increases in comparison to CAM-B3LYP, by about 4.5–5.5 kJ. However range

Cm C2 1

1 Cβ Cβ

C2

Cm 2

2

C3

Cm

C2 2 1

Fig. 2. B3-LYP/6-31G(d) optimized geometries for the transition structures for addition reactions. The names of important atoms are shown as well as the distance between the carbon of the methyl radicals and the CAF sulfur atom in Å.

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N. Latelli et al. / Computational and Theoretical Chemistry 1027 (2014) 39–45

RCAF 1 RCAF2

RCAF3 Fig. 3. B3LYP/6-31G(d) optimized geometries for the minimum energy conformations of RCAF-adduct radicals.

Table 1 Thermodynamics parameters (barriers (DE–, kJ mol1), activation enthalpies (DH–, kJ mol1) and Gibb’s activation free energies (DG–, kJ mol1) at 298.15 K for the addition-fragmentation reactions, all calculations performed with 6-31G (d) basis set. RAFT agents and RCAF adducts CAF1

CAF2

CAF3

RCAF1

RCAF2

RCAF3

20.8 23.4 21.0 60.2

17.5 23.7 21.1 61.4

11.2 29.5 26.9 66.2

88.6 24.5 23.8 27.8

105.4 26.5 26.5 26.4

122.0 9.5 9.5 8.6

-30.2 16.9 9.6 64.0

30.0 18.5 11.2 65.5

21.1 2.5 17.8 69.4

81.8 24.3 20.6 30.2

103.9 36.2 34.7 40.8

114.3 17.1 15.5 20.0

CAM-B3LYP DE 36.2 DE– 25.4 DH – 23.0 DG – 65.1

32.1 26.9 24.3 64.3

22.8 33.0 30.2 72.3

69.5 44.3 43.4 48.5

88.1 51.1 51.1 50.4

98.0 34.8 35.1 32.9

LC-xPBE DE DE– DH – DG –

53.0 29.9 27.6 65.9

49.7 32.3 29.8 69.9

34.3 38.8 36.1 77.2

50.8 64.0 63.1 68.8

74.5 71.9 72.0 71.4

86.1 55.9 56.0 54.2

MP2 DE DE– DH – DG –

7.8 64.6 56.8 119.0

11.6 70.9 67.4 109.7

3.4 72.9 69.1 116.9

6.4 165.0 161.8 176.0

3.1 168.5 161.5 166.8

 

B3LYP DE DE– DH – DG – M06 DE DE– DH – DG –

 

     

Not converged.

(Tables S3–S5). This is in agreement with Coote et al. study [14,16], which showed that B3LYP significantly overestimate the length of the formed bond in the transition state for these types of reaction. On the other hand, the difference in the Cm-S length in the

structures of TSCAF transition states between DFT and MP2 methods is far larger, ranging from 0.15 to 0.10 Å (Table S3–S5). This shows again that the exchange range separation included in DFT methods take into account a part of the dispersion that should be included, and the large difference in energy observed for the reaction barriers may come from these geometry differences. In addition, the distance (S. . .Cm) in the transition states structures, decreases according to the sequence: (S. . .Cm)CAF1 > (S. . .Cm)CAF2 > (S. . .Cm)CAF3. As can be expected this result is correlated with the energy barrier decrease passing from the TSCAF3 to the TSCAF1. However this is contrary to what would be expected from the chemical potential values, from which one can deduce the following electronegativity sequence CAF1 > CAF2 > CAF3 and expect that a bond with the methyl radical would be better formed with CAF1.

3.2. Addition kinetics To explore the effect of substituents on the addition-fragmentation rate coefficients in RAFT polymerization, rate coefficients at 25 °C were calculated at DFT level with the four functionals used for the thermodynamics of the reactions. From the results reported in Table 2, one sees that the addition of carbon-centered radicals to C@S double bonds is a relatively fast reaction. But it is apparent that the addition rate coefficient does not significantly depend on the nature of the RAFT agents used, since they only differ by 1 order of magnitude over the three reactions considered at B3LYP or CAM-B3LYP levels of theories, and 2 orders of magnitude with LC-x functional. This result is important, since it indicates that the driving force acting on the RAFT process lies in the fragmentation kinetics rather the addition step (vide infra). It can be noticed that these rate coefficients lie in the range (104–107) of those reported by Coote [15] for a panel of seven different addition reactions with a methyl radical, calculated by a more sophisticated method (W1-ONIOM). One should be aware that a discrepancy

43

N. Latelli et al. / Computational and Theoretical Chemistry 1027 (2014) 39–45 Table 2 Calculated rate coefficients for addition (kadd), fragmentation (kfrag) and reverse addition (kadd) reactions at 298.15 K. kadd (L mol1 s1) B3LYP

M06

CAM-B3LYP

LC-wPBE

MP2

CAF1 CAF2 CAF3

4.21 103 2.64 103 3.71 102

9.32 102 5.08 102 1.05 102

5.85 102 8.15 102 3.27 101

4.21 102 8.45 101 4.46 100

2.15 107 9.17 106 5.02 107

kfrag (s1) RCAF1 RCAF2 RCAF3

8.17 107 1.47 108 1.93 1011

3.18 107 4.42 105 1.94 109

1.97 104 8.86 103 1.06 107

5.36 100 1.90 100 1.92 103

kadd (s1) CAF1 CAF2 CAF3

6.10 105 3.06 106 8.06 106

6.55 108 2.47 1010 3.17 108

5.45 102 1.55 103 4.63 103

1.57 101 9.30 101 8.21 100

1.14 101 4.15 101 2.16 101

Table 3 Effect of basis set on the barriers heights (kJ mol1) calculated at MP2 level for addition reactions at 298.15 K. TSa

CAF1 CAF2 CAF3

MP2/6-31G(d)

MP2/6-311G(d)

MP2/cc-PVTZ

MP2/6-31+G(d)

DEZPE

DE–ZPE

DEZPE

DE–ZPE

DEZPE

DE–ZPE

DEZPE

DE–ZPE

7.7 10.8 3.5

57.9 58.9 62.1

8.6 13.5 1.9

54.9 56.2 59.8

12.9 17.27 2.95

50.7 51.2 53.9

7.5 12.9 4.2

54.5 55.1 59.4

a Barrier heights were calculated at the MP2/6-31G(d), MP2/6-311G(d), MP2/cc-PVTZ and MP2/6-31+G(d) levels of theory using B3LYP/6-31G(d) optimized geometries and including B3LYP/6-31G(d) zero-point vibrational energy corrections.

of 1 or 2 orders of magnitude is not so severe because of the exponential form present in the rate constant Eq. (3), one order of magnitude corresponding to less than 6 kJ mol1. 3.3. Fragmentation reactions The fragmentation is the important step of the polymerization reaction mechanism, the reaction is described for the three types of monomers CAF1 to CAF3 in reactions (7) to (9). 

½CH3  SCðOCH2 PhÞSCH3  !  CH2 Ph þ CH3 SðC@OÞSCH3

ð7Þ



½CH3  SCðOCH2 PhÞOCHPh ! CH3  SðC@OÞ  ðOCHPhÞ CH2 Ph 

½CH3  SCðOCH2 PhÞOPh !  CH2 Ph þ CH3 SðC@OÞOPh

ð8Þ ð9Þ

For each reaction, the thermodynamics and kinetics of the fragmentation reaction of the RCAFx have been computed at 25 °C using the four DFT exchange–correlation functionals and MP2 methods (see Tables 1 and 2). The transition state structures obtained at B3LYP/6-31G⁄ for the three reactions are displayed in Fig. 4. One observes that the reactions are significantly more exothermic from the DFT calculations as compared to MP2 ones for which the formation of RCAF1 and RCAF2 is endothermic. For the fragmentation, the results show that the B3LYP functional leads to larger reaction stabilization by more than 20 kJ/mol as compared to CAM-B3LYP and by about 30 to 40 kJ/mol as compared to LC-xPBE. This shows that the range separated DFT functionals are better tools to describe radical molecules as compared to standard hybrid functionals. This can also be observed from the energy barriers for which the hybrid methods seem to completely fail, while the correction via Hartree–Fock exchange inclusion through a range separation approach leads to results closer to those obtained with MP2. Although the results remain far from MP2, the LC-xPBE functional is the one that performs the best (Table 1).

It has to be underlined that, whatever the basis set retained, MP2 calculations lead to highly spin contaminated wavefunctions (>1.1) for fragmentation transition states and products, contrarily to those of reactants, or addition transition states (< 0.76). (Table S6) Therefore the MP2 energy barriers for fragmentation reaction have not been retained. Such bad features for similar calculations were already observed by Coote for similar RAFT systems [14]. These results and the discrepancy between DFT and the MP2 methods are quite surprising and similar to the results for the addition. Again the inclusion of the range-separation of DFT methods tends to give results approaching those obtained at the MP2 level, when available. However such differences do not only lie in the lack of DFT methods to accurately describe the electron localization and dispersion. The MP2 results may also be that different, as already said, because of an overestimation of the dispersion due intrinsically to the MP2 method which error may be broaden be the use of relatively large basis sets [38]. In addition, the known difficulty of MP2 to accurately describe the radical molecules may also be the source of additional errors [39,40]. As can be seen in Table 1, when comparing the activation energies computed for RCAF1 and RCAF2 to RCAF3 the latter values are always lower, the fragmentation is thus easier for CAF3. Then, considering the complete polymerization process, (addition and fragmentation), the whole polymerization reaction appears to be easier for the CAF3 monomer. 3.4. Fragmentation kinetics To explore the effect of substituents on the fragmentation rate coefficients in RAFT polymerization, rate coefficients at 25 °C were calculated at the three levels of theory already used for the thermodynamics of the reactions (See Table 2). From the results reported in Table 2, we can see that the fragmentation reaction is relatively fast, the fragmentation rate coefficients spanning 4 orders of magnitude over the three reactions considered at B3LYP level of theory and 3 orders with CAM-B3LYP or LC-xPBE

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N. Latelli et al. / Computational and Theoretical Chemistry 1027 (2014) 39–45

1

Cβ

Cβ

C2

1

2 C2

2

C2

Cβ

Fig. 4. B3LYP/6-31G(d) optimized geometries for the transition structures for fragmentation reactions. The names of important atoms are shown as well as the distance between the carbon of the leaving group and the CAF oxygen atom in Å.

functionals. It is worth noting that only the LC-xPBE rate coefficients lie in the range (104–102) of those reported by Coote [15] for a panel of seven different fragmentation reactions with a methyl radical, our results with B3LYP, M06, and CAM-B3LYP functionals leading to significantly larger rate constants. More important, in contrast to the reactions studied by Coote [15], we find considerably larger rate constants for the fragmentation reactions than for the addition reactions. In order to understand the changes in the spin densities and bond lengths during the fragmentation of RCAF agents, spin densities of the relevant atoms involved in the transition state TSRCAF are compared in Table 4 with those of Table 4 Spin densities (a.u.) of Cb and C2 atoms along the fragmentation reaction for RCAFs.

RCAF1 TSRCAF1 RCAF1-FRAG RCAF2 TSRCAF2 RCAF2-FRAG RCAF3 TSRCAF3 RCAF3-FRAG

dspin

B3LYP

CAM-B3LYP

Lc-wPBE

MP2

Cb C2 Cb C2 Cb C2 Cb C2 Cb C2 Cb C2 Cb C2 Cb C2 Cb C2

0.73 0.00 0.52 0.34 0.00 0.78 0.73 0.00 0.45 0.33 0.00 0.74 0.54 0.34 0.54 0.34 0.00 0.78

0.76 0.00 0.51 0.42 0.00 0.82 0.75 0.00 0.45 0.42 0.00 0.79 0.52 0.46 0.52 0.46 0.00 0.83

0.79 0.00 0.51 0.50 0.00 0.89 0.78 0.00 0.46 0.50 0.00 0.86 0.53 0.53 0.53 0.53 0.00 0.89

0.98 0.00 0.90 0.55 0.00 1.09 0.94 0.00 0.57 0.82 0.00 1.08 0.89 0.42 0.89 0.42 0.00 1.09

the reactants, RCAF, and products, RCAF-FRAG. A more exhaustive report of values, including bond distances, is given in Tables S6–S8. The representation of the spin density, condensed to atoms, is used to locate the atom(s) carrying the radical character. Then, following the addition, the radical is localized primarily on the b carbon (0.73–0.79 for RCAF1 according to all methods) (Table 4), the rest of the density is distributed over the sulfur and oxygen (0.05– 0.10). In the transition state structures (TSRCAF1) the spin density is split between the b carbon and C2 (Table 4). After fragmentation, the product RCAF1-FRAG holds a highly localized radical in C2 carbon of CH2Ph radicals. Compared to RCAF1, RCAF3 has a lower density at the carbon b (0.69–0.74 according to all methods) (Table 4), oxygen (ca. 0.05– 0.10) and sulfur (0.06–0.09) atoms, whereas its stability is greater than that of RCAF1. This stabilization promotes the fragmentation, in agreement with the fact that the computed rate coefficient of RCAF1 is always 3 orders of magnitude higher than that of RCAF3 for each of the three levels of theory considered. Using the MP2 calculation, the radical is always localized primarily on the b carbon (0.98, 0.87) for RCAF1 and RCAF2, respectively. The rest of the density is spread, over the sulfur and oxygen (0.01–0.04). This is expected, knowing the trend of DFT methods to overestimate the electronic delocalization contrarily to Hartree–Fock and MP2 methods. This trend, which is higher at LDA level, is reduced with hybrid functionals (e.g. B3LYP) and furthermore by range separated functionals, as can be observed in Table 4 and S7–S9. In the transition state structures (TSRCAF1) the spin density is split about two thirds for b carbon and one third for C2 carbon (Table 4). After fragmentation, the products RCAF1FRAG and RCAF3-FRAG holds a highly localized radical in C2 carbon of CH2Ph radicals (1.09) (Table 4).

N. Latelli et al. / Computational and Theoretical Chemistry 1027 (2014) 39–45

Finally, it is interesting to compare the reaction rate of the reversed addition kadd (i.e. the dissociation of the methyl group) to those of the addition, and to that of the dissociation leading to the products. The ratio kfrag/kadd, easily obtained from the constants in Table 2, indicates clearly that the efficiency of the RAFT mechanism follows the trend CAF3 > CAF1 > CAF2, whereas it was CAF1 > CAF2 > CAF3 for the addition only (kadd/kadd). 4. Concluding remarks DFT molecular orbital calculations have been used to study the thermodynamics and kinetics of the addition-fragmentation reaction of thiocarbonyl compounds. The use of DFT range-separated functionals improves the description of the radical reactions leading to larger energy barrier, and also the reaction becomes more exothermic as compared to B3LYP level. It is noticeable that the addition rate coefficients calculated using three DFT functionals, are found to vary by approximately one order of magnitude while the fragmentation rate coefficients vary by 3 orders of magnitude. Therefore, the efficiency of the RAFT mechanism is mainly controlled by the fragmentation step, for which the structure of the reactant is important. This is in full agreement of the experimental work of Arotçarena [10]. Acknowledgments The authors gratefully acknowledge the GENCI/CINES for HPC resources/computer time (Project cpt2130). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.comptc.2013. 10.018. References [1] C.J. Hawker, A.W. Bosman, E. Harth, New polymer synthesis by nitroxide mediated living radical polymerizations, Chem. Rev. 101 (2001) 3661–3688. [2] J.S. Wang, K.J. Matyjaszewski, Control1ed ‘‘living’’ radical polymerization. Atom transfer radical polymerization in the presence of transition-metal complexes, J. Am. Chem. Soc. 117 (1995) 5614–5615. [3] J. Chiefari, Y.K.B. Chong, F. Ercole, J. Krstina, J. Jeffery, T.P.T. Le, R.T.A. Mayadunne, G.F. Meijs, C.L. Moad, E. Rizzardo, S.H. Thang, Living free-radical polymerization by reversible addition-fragme, Macromolecules 31 (1998) 5559–5562. [4] A. Ah Toy, H. Chaffey-Millar, T.P. Davis, M.H. Stenzel, E.I. Izgorodina, M.L. Coote, C. Barner-Kowollik, Thioketone spin traps as mediating agents for free radical polymerization processes, Chem. Commun. (2006) 835–837. [5] H. Chaffey-Millar, E.I. Izgorodina, C. Barner- Kowollik, M.L. Coote, Radical addition to thioketones: computer-aided design of spin traps for controlling free-radical polymerization, J. Chem. Theor. Comput. 2 (2006) 1632–1645. [6] A. Debuigne, Y. Champouret, R. Jerome, R. Poli, C. Detrembleur, Mechanistic insights into the cobalt-mediated radical polymerization (CMRP) of vinyl acetate with cobalt (III) adducts as initiators, Chem. Eur. J. 14 (2008) 4046– 4059. [7] P. Delduc, C. Tailhan, S. Zard, A convenient source of alkyl and acyl radicals, J. Chem. Soc. Chem. Commun. (1988) 308–310. [8] G. Moad, E. Rizzardo, S.H. Thang, Radical addition-fragmentation chemistry in polymer synthesis, Polymer 49 (2008) 1079–1131. [9] C. Barner-Kowollik (Ed.), Handbook of RAFT Polymerization, Wiley-VCH, Weinheim, Germany, 2007. [10] M. Arotçarena, PhD thesis, Lyon, France (2000). [11] M.L. Coote, D.J. Henry, Effect of substituents on radical stability in reversible addition fragmentation chain transfer polymerization: an ab initio study, Macromolecules 38 (2005) 1415–1433. [12] M.L. Coote, Ab initio study of the additionfragmentation equilibrium in raft polymerization: when is polymerization retarded?, Macromolecules 37 (2004) 5023–5031

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