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β-Scission of thioimidoyl radicals (R1–N–CS–R2): A theoretical scale of radical leaving group ability
Chemical Physics Letters 443 (2007) 383–388 www.elsevier.com/locate/cplett
b-Scission of thioimidoyl radicals (R1–N–C@S–R2): A theoretical scale of radical leaving group ability D. Guerra a
a,*
, P. Fuentealba b, A. Aizman c, R. Contreras
d
Departamento de Ciencias Quı´micas, Facultad de Ecologı´a y Recursos Naturales, Universidad Andre´s Bello, Av. Repu´blica, 275, Santiago, Chile b Departamento de Fı´sica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile c Departamento de Quı´mica, Universidad Federico Santa Marı´a, Casilla 110-V, Valparaı´so, Chile d Departamento de Quı´mica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile Received 25 January 2007; in final form 4 June 2007 Available online 17 June 2007
Abstract A theoretical study of the b-scission reactions for some thioimidoyl radicals (R1–N@C–S–R2) using a recently introduced homofugality index, m is presented. This index, that was defined as a descriptor of the leaving group ability in homolytic substitution reactions, predicts that S–R2 fragmentation is always favoured compared to the N–R1 scission, in agreement with the experimental data. This result can be explained on the basis of the regional spin softness of the leaving radical group at the transition state during the homolytic fragmentation. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Thiomidoyl radicals (R1–N@C–S–R2) are a class of intermediates with synthetic interest in cyclation reactions of a variety of heterocycles [1–4] and cascade syntheses of benzothienoquinoxalines [5], benzothienoquinolines [6] and thiochromenoindoles [7]. The ring closure compete with the b-scission of the C–R2 bond to produce isothiocyanates, and the corresponding alkyl radical R2 [8,9]. Both cyclation and dissociation reactions have been recently reviewed by Walton et al. [10,11]. Based on studies by electron paramagnetic resonance (EPR) on S-but-3-enylsubstituted thioimidoyl radicals, they found that for unsubstituted systems, the ring closure is the preferred reaction channel at low temperatures. However, dissociation predominates at temperatures above ca. 300 K. Thioimidoyl radicals can undergo two fragmentation processes described in Scheme 1. Scission of the S–R2 bond yields isothiocyanate (2) and a C-centered radical R2 (scission
*
Corresponding author. Fax: +56 2 6618269. E-mail address: [email protected] (D. Guerra).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.06.053
S). On the other hand, the thioimidoyl radicals may form thiocyanate (3) and a C-centered radical R1 by scission of the R1–N bond (scission N). In the EPR study reported by Walton et al. [10] the authors found that, for a representative series of thiomidoyl radicals, the b-scission underwent exclusively fragmentation of the S–R2 bond. They also found that the b-scission of the R1–N bond did not compete in any case. These experiments prompted us to perform a theoretical analysis using a recently introduced homofugality index [12], which is obtained as the group spin-philicity [13,14] of the leaving group in a homolytic bond cleavage process. This definition is similar to that of nucleofugality associated with the departure of the leaving group bearing the bond electron pair [15]. The homofugality index, m, was recently defined in the context of the spin polarized density functional theory (SP-DFT) [16–18] to describe the leaving group ability in homolytic substitution reactions [12]. In this work we intend to quantitatively describe the leaving group ability of R2 and R1 moieties in the thioimidoyl radicals and to compare the b-scission modes observed in these systems (Scheme 1).
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D. Guerra et al. / Chemical Physics Letters 443 (2007) 383–388
should be probably framed on Ayers et al. [19] pioneering work regarding heterolytic bond cleavage processes). The spin-hardness can be calculated from the spin potentials as follows: þ l S lS : ð4Þ 2 The homofugality index was evaluated at the transition state structures for the two modes of fragmentation involving the radical species t-butyl-N@C–S–R2 and ethylN@C–S–R2 whit R2: n-butyl, i-propyl, ciclopentyl, t-butyl and 2-pentinyl (Tables 1 and 2). The transition state of a chemical reaction is the bottleneck of the process and therefore, the evaluation of reactivity indexes is better suited at this stage of the reaction than at the ground state of reactants. All the structures were fully optimized at the (U)B3LYP level of theory [20–22] using the 6-31 + G(2d, p) basis set implemented in the Gaussian 03 program [23]. Analytical second derivative calculations were performed to ensure that all the stationary points were real minima on the potential energy surface. All the transition states were characterized by a unique imaginary frequency corresponding to each bond scission mode. The activation energies were calculated for the two b-fragmentation modes, total energies were corrected for zero-point vibrational energies and for thermal effects at 298 K. All reactivity indices required to evaluate the homofugality index were obtained by single points calculations on the optimized geometries at the HF/6-31G(d) level of theory, following a prescription recently proposed by Vargas et al. þ [24]. The spin Fukui function (fSS Þ [16] needed to evaluate þ the regional spin-philicity xS;k through the expression of Eq. (2) was evaluated following a computational scheme described elsewhere [25,26]. The spin Fukui function þ fSS ðrÞ can be computed using the approximations proposed by Galvan et al. [16]:
g0SS ¼
Scheme 1.
2. Model equations and computational details The homofugality index is defined as the regional spinphilicity of the leaving group (LG) as follows [12]: X m x þ xþ ð1Þ S ðLGÞ ¼ S;k ; k2LG
xþ S;k
the quantity philicity [14]:
is the regional (condensed to atom) spin-
þ þ xþ S;k ¼ xS fSS;k ;
ð2Þ
þ where fSS is the generalized spin Fukui function introduced by Galvan et al. [16], as the derivative of the spin density with respect to the spin number, NS = Na Nb. xþ S is the spin-philicity index introduced [13] to describe the stabilization in energy in the direction of increasing multiplicity: 2
xþ S
ðlþ SÞ ; 2g0SS
ð3Þ
lþ S is the spin potential in the direction of increasing multiplicity and g0SS is the global spin hardness of the system. The present approach just completes the formulation of the leaving group ability description of molecular fragments in radical processes where the bond cleavage corresponds this time to an homolytic process (it would be certainly of interest to derive it from a formal model which
Table 1 Experimental and theoretical activation energies, Fukui function, spin-philicity and homofugality indexes of the leaving group (R2, R1) calculated at the cis transition states structure for the b-scission of the S–R2 and R1–N bonds, respectively, of some R1–N@C–S–R2 radicalsa R2
Scission S
Scission N
Ea (kcal/mol)
þ fSS
xþ S
m
Ea (kcal/mol)
þ fSS
xþ S
m
Exp.
Theo.
n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
11.9 10.2 9.2 5.9 66.7
10.1 7.9 7.5 5.2 3.5
0.0512 0.0637 0.0839 0.0864 0.1359
4.67 4.70 4.72 4.71 4.69
R1 = t-butyl 0.24 17.6 0.30 17.6 0.40 17.5 0.41 16.9 0.64 19.0
0.0459 0.0486 0.0480 0.0487 0.0373
5.64 5.68 5.64 5.67 5.30
0.26 0.28 0.27 0.28 0.20
n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
12.0 8.6 8.9 6.4 –
10.1 7.9 7.8 5.5 3.4
0.0504 0.0605 0.0854 0.0873 0.1343
4.65 4.68 4.66 4.68 4.67
R1 = ethyl 0.23 22.9 0.28 22.4 0.40 22.3 0.41 21.7 0.63 23.9
0.0279 0.0283 0.0312 0.0287 0.0201
5.58 5.59 5.57 5.59 5.36
0.16 0.16 0.17 0.16 0.11
a
Experimental activation energy for identical (R1 = t-butyl) and analogous (R1 = ethyl) thioimidoyl radicals from Ref. [10]. Theoretical activation þ energy calculated at UB3LYP/6-31 + G(2d, p) level of theory. The indexes fSS , xþ S and m calculated at UB3LYP/6-31 + G(2d, p) i UHF/6-31G(d) level of theory. xþ and m values are given in eV units. S
D. Guerra et al. / Chemical Physics Letters 443 (2007) 383–388
385
Table 2 Theoretical activation energies, Fukui function, spin-philicity and homofugality indexes of the leaving group (R2, R1) calculated at the trans transition states structure for the b-scission of the S–R2 and R1–N bonds, respectively, of some R1–N@C–S–R2 radicalsa R2
Scission S
Scission N
Ea (kcal/mol)
þ fSS
xþ S
m
n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
12.1 10.8 10.3 9.4 7.6
0.0682 0.0884 0.1654 0.1311 0.2198
4.92 4.81 4.48 4.66 4.88
R1 = t-butyl 0.34 20.7 0.43 21.1 0.74 21.1 0.61 20.6 1.07 20.0
n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
11.9 10.2 9.7 8.3 7.3
0.0646 0.0832 0.1566 0.1683 0.2202
4.87 4.76 4.91 4.95 4.89
0.31 0.40 0.77 0.83 1.08
Ea (kcal/mol)
þ fSS
xþ S
m
0.0533 0.0473 0.0512 0.0464 0.5006
5.64 5.49 5.48 5.50 5.21
0.24 0.26 0.28 0.25 1.92
0.0328 0.0332 0.0406 0.0315 0.0212
5.42 5.72 5.74 5.57 5.24
0.18 0.19 0.23 0.18 0.11
R1 = ethyl 24.3 24.9 24.9 24.2 23.9
a þ Theoretical activation energy calculated at UB3LYP/6-31 + G(2d, p) level of theory. The indexes fSS , xþ S and m calculated at UB3LYP/6-31 + and m values are given in eV units. G(2d, p) i UHF/6-31G(d) level of theory. xþ S
1 h a 2 b 2 i uL ðrÞ þ uH ðrÞ ; ð5Þ 2 /aL ðrÞ and /bH ðrÞ are the a and b LUMO and HOMO spin– orbitals, respectively. The spin potentials lþ S and lS needed to evaluate the 0 spin hardness gSS were calculated using the finite difference formulas proposed by Galvan et al. [17,18], namely:
þ fSS ðrÞ
lþ S
eaL ðMÞ ebH ðMÞ 2
and l S
eaH ðM 0 Þ ebL ðM 0 Þ ; 2
ð6Þ
in terms of the one-electron energies of the HOMO and LUMO orbitals for the system in the lower (M) and upper (M 0 ) spin multiplicities, respectively. 3. Results and discussion EPR parameters are consistent with the idea that thioimidoyls are r-radicals [8–10]. Based on these EPR data and theoretical calculations at the UB3LYP/6-31 + G(2d, p) level of theory performed on the R1–N@C–S– R2 (R1 = R2 = ethyl, i-propyl and t-butyl) radicals, Walton et al. [10] concluded that thioimidoyls are r-radicals with a bent structure and a trans conformation about the C@N double bond (Scheme 2). Since thioimidoyls prefer an strans conformation, they concluded that for these radicals, the actual scission pathway should be preceded by rotation of the S–C bond followed by fragmentation. We relay on the results of these authors to accordingly select the two conformational minima corresponding to the cis and trans
Scheme 2.
configurations about the C@N double bond (Scheme 2) to evaluate the performance of our homofugality index to describe both fragmentation modes (S and N) as well as the leaving group ability of radical fragments ðR1 and R2 Þ in b-scission reactions of thioimidoyl radicals. The activation energies, homofugality indexes, as well as the generalized spin Fukui functions and the regional spinphilicity values calculated for both fragmentation modes (S and N) for the cis radicals are compiled in Table 1. The values corresponding to the trans radicals are shown in Table 2. The calculated activation energies for the fragmentation of the S–R2 bond on cis structures are in good qualitative agreement with the experiment (Table 1) measured by EPR spectroscopy [10] for identical (R1 = t-butyl) or analogous (R1 = ethyl) thioimidoyls. It may be seen that the activation energy for the b-scission of S–R2 bond has an inverse relationship with the homofugality index: low barriers are consistently related to high values of homofugality of the departing radical. The same pattern is obtained for the scission of S–R2 bond in trans structures (Table 2). Note that the substitution of t-butyl by ethyl at R1 (Scheme 1) has little effect on the scission of the S–R2 bond. The experimental and calculated activation energies as well as homofugality of the R2 radicals (columns 2, 3 and 6 in Table 1 and columns 2 and 5 in Table 2) change little with N-alkyl substituents for both cis and trans structures. The same behaviour is observed for the scission of the N–R1 bond for the S-alkyl derivatives which show a little influence on the departure of the t-butyl and ethyl radicals (see columns 7 and 10 in Table 1 and columns 6 and 9 in Table 2). From these results we may conclude that the homofugality index provides information about the intrinsic homofugality pattern of radicals. The comparison between the homofugality of the R2 radical and the experimental rate coefficients for the b-scission of the S–R2 bond, for the cis structures, are depicted in Fig. 1. It may be seen that a significant correlation between
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D. Guerra et al. / Chemical Physics Letters 443 (2007) 383–388
Fig. 1. Plot of the homofugality index versus the logarithm of observed rate constants for the b-scission of the S–R2 bond of t-butyl-N@C–S–R2 and ethyl-N@C–S–R2 radicals. Experimental rate constants were obtained from Ref. [10]. The homofugality index is calculated at the cis transition state at B3LYP/6-31 + G(2d, p) i UHF/6-31G(d) level of theory. R is the regression coefficient.
the homofugality index and the logarithm of the experimental rate constant [10] is obtained (R2 = 0.97). Since rate coefficient values are only available for fragmentation at the S–R2 bond at the cis configuration, we performed a comparison between the homofugality index and the theoretical activation energies for the b-scission at the S–R2 bond at the trans conformation (see Fig. 2). The comparison shows that the trans conformation yields similar results.
The general reactivity trends in terms of the homofugality index is: n-butyl < i-propyl < c-C5H9 < t-butyl < 2-pentinyl, which is in qualitative agreement with the experimental rate constants [10]. These results show that the information encompassed in the homofugality index is consistent with the idea that a greater branching at the C-atom attached to sulphur and nitrogen atoms dramatically increases the rate of fragmentation of the radicals R2 and R1 , respectively (i.e., m (n-butyl) = 0.24 and m (t-butyl) = 0.41 for the scission at the S end of the t-butyl-N@C–S–R2 and m (ethyl) = 0.16 and m (t-butyl) = 0.26 for the scission at the N side of the R1–N@C–S–n-butyl), in agreement with the experiment [10]. In order to evaluate with more detail the usefulness of the homofugality index, a theoretical study was carried out on the two fragmentation modes, scission S and scission N, on thiomidoyl radical with the same substituent at both nitrogen and sulphur centres. The calculations were carried out for the cis conformation of thioimidoyl radicals bearing primary, secondary and tertiary alkyl groups as well as cyclic groups on both nitrogen and sulphur ends (Table 3). In all cases the homofugality at the sulphur side was found to be greater than that at the nitrogen side. Table 3 clearly shows that the departure of the radical at the sulphur side is predicted to be always favoured compared to the homofugality at the nitrogen side, independent of the substituent patterns. Note that this effect may also be observed from Tables 1 and 2, except when the primary radical n-butyl was released in competition with the t-butyl radical (Table 1) and when the 2-pentinyl radical is released with a tertiary radical (Table 1). The departure of the radical at the sulphur side is always favoured compared to the homofugality at the nitrogen side a result that can be traced to the regional spin softness [14,27], which is greater in sulphur derivatives than nitrogen derivatives. This pattern of reactivity is similar to that obtained previously for bimolecular homolytic substitution reactions involving methyl, silyl, germyl and stannyl radicals, where the observed leaving group order of this series [12] was þ C < Si < Ge Sn. The generalized Fukui function fSS ðrÞ required to evaluate the homofugality index is a normalized spin softness [27] and as such, it may be viewed as a measure of the distortion of the spin density (polarizability) Table 3 Fukui function, spin-philicity and homofugality indexes for the leaving group R calculated at the cis transition states structure for fragmentation at the R–N and S–R bonds of R–N@C–S–R radicalsa R
Fig. 2. Comparison between homofugality index and theoretical activation energy for the reaction of b-scission of the S–R2 bond for t-butylN@C–S–R2 and ethyl-N@C–S–R2 radicals. Values calculated at the trans transition state, the homofugality index was evaluated at B3LYP/631 + G(2d, p) i UHF/6-31G(d) level of theory and the activation energy was obtained at B3LYP/6-31 + G(2d, p) level of theory. R is the regression coefficient.
Ethyl n-Butyl i-Propyl t-Butyl c-C5H9
Scission S
Scission N
þ fSS
xþ S
m
þ fSS
xþ S
m
0.0486 0.0635 0.0864 0.0530 0.0880
4.68 4.67 4.72 4.65 4.74
0.2273 0.2464 0.2965 0.4069 0.4166
0.0269 0.0425 0.0487 0.0296 0.0483
5.56 5.68 5.68 5.58 5.73
0.1495 0.1651 0.2415 0.2764 0.2765
a þ The indexes fSS , xþ S and m calculated at UB3LYP/6-31 + G(2d, p)// UHF/6-31G(d) level of theory. xþ S and m values are given in eV units.
D. Guerra et al. / Chemical Physics Letters 443 (2007) 383–388
that seems to play an important role in homolytic cleavage processes. In summary, the results show that the homofugality index provides useful information about the quality of a leaving group for these radical processes. The homofugality evaluated at the transition state structures for the N and S scission processes correctly describes the observed scission pattern. As in the case of the homolytic substitution reactions, the homofugality order appears again driven by the spin Fukui function, which is related to the regional spin softness of the leaving radical group at the transition state. Here again an interesting parallel with the parent heterolytic cleavage observed in polar processes which depends on the regional electronic softness evaluated at the nucleofuge moiety may be established. 4. Concluding remarks A theoretical study of the b-scission reactions for some thioimidoyl radicals (R1–N@C–S–R2) using a recently introduced homofugality index, m, has been presented. To evaluate the performance of our homofugality index, the study was carried out on the two fragmentation modes: scission at the S–R2 and R1–N bonds, for two conformational minima corresponding to the cis and trans configurations about the C@N double bond. The homofugality evaluated at the transition state (TS) structures for the N and S scission processes correctly describes the observed scission pattern. Following a suggestion by a reviewer, we have evaluated the performance of the proposed reactivity index at the ground state of molecules, and we have verified that the description of the scission pattern is better described at the TS stage of the reaction. The results of these calculations are compiled in Table 4. The departure of the radical at the sulphur side ðR2 Þ is predicted to be always favoured compared to the homofugality at the nitrogen side ðR1 Þ that can be traced to the regional spin softness, which is greater in sulphur derivaTable 4 Global spin-philicity, Fukui function and homofugality indexes of the leaving groups (R2, R1) calculated at the cis ground state structure of some R1–N@C–S–R2 radicalsa R2
xþ S
þ fSS ðR2 Þ
m (R2)
þ fSS ðR1 Þ
m (R1)
R1 = t-butyl n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
4.71 4.66 4.66 4.71 5.47
0.0307 0.0477 0.0814 0.0428 0.2724
0.14 0.22 0.38 0.20 1.49
0.0659 0.0651 0.0608 0.0658 0.0366
0.31 0.30 0.28 0.31 0.20
R1 = ethyl n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
4.71 4.70 4.66 4.72 5.47
0.0318 0.0458 0.0796 0.0414 0.2750
0.15 0.21 0.37 0.20 1.51
0.0601 0.0565 0.0533 0.0561 0.0239
0.28 0.27 0.25 0.26 0.13
tives than nitrogen derivatives. As in the case of the bimolecular homolytic substitution reactions involving methyl, silyl, germyl and stannyl radicals, the homofugality order appears again driven by the spin Fukui function, which is related to the regional spin softness of the leaving radical group at the transition state. Here again an interesting parallel with the parent heterolytic cleavage observed in polar processes which depends on the regional electronic softness evaluated at the nucleofuge moiety may be established. The general reactivity trends in terms of the homofugality index, for the radical species t-butyl-N@C–S–R2 and ethylN@C–S–R2, is: n-butyl < i-propyl
a
þ The indexes xþ fSS and m calculated at UB3LYP/6S, 31 + G(2d, p) i UHF/6-31G(d) level of theory. xþ S and m values are given in eV units.
387
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b-Scission of thioimidoyl radicals (R1–N–C@S–R2): A theoretical scale of radical leaving group ability D. Guerra a
a,*
, P. Fuentealba b, A. Aizman c, R. Contreras
d
Departamento de Ciencias Quı´micas, Facultad de Ecologı´a y Recursos Naturales, Universidad Andre´s Bello, Av. Repu´blica, 275, Santiago, Chile b Departamento de Fı´sica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile c Departamento de Quı´mica, Universidad Federico Santa Marı´a, Casilla 110-V, Valparaı´so, Chile d Departamento de Quı´mica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile Received 25 January 2007; in final form 4 June 2007 Available online 17 June 2007
Abstract A theoretical study of the b-scission reactions for some thioimidoyl radicals (R1–N@C–S–R2) using a recently introduced homofugality index, m is presented. This index, that was defined as a descriptor of the leaving group ability in homolytic substitution reactions, predicts that S–R2 fragmentation is always favoured compared to the N–R1 scission, in agreement with the experimental data. This result can be explained on the basis of the regional spin softness of the leaving radical group at the transition state during the homolytic fragmentation. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Thiomidoyl radicals (R1–N@C–S–R2) are a class of intermediates with synthetic interest in cyclation reactions of a variety of heterocycles [1–4] and cascade syntheses of benzothienoquinoxalines [5], benzothienoquinolines [6] and thiochromenoindoles [7]. The ring closure compete with the b-scission of the C–R2 bond to produce isothiocyanates, and the corresponding alkyl radical R2 [8,9]. Both cyclation and dissociation reactions have been recently reviewed by Walton et al. [10,11]. Based on studies by electron paramagnetic resonance (EPR) on S-but-3-enylsubstituted thioimidoyl radicals, they found that for unsubstituted systems, the ring closure is the preferred reaction channel at low temperatures. However, dissociation predominates at temperatures above ca. 300 K. Thioimidoyl radicals can undergo two fragmentation processes described in Scheme 1. Scission of the S–R2 bond yields isothiocyanate (2) and a C-centered radical R2 (scission
*
Corresponding author. Fax: +56 2 6618269. E-mail address: [email protected] (D. Guerra).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.06.053
S). On the other hand, the thioimidoyl radicals may form thiocyanate (3) and a C-centered radical R1 by scission of the R1–N bond (scission N). In the EPR study reported by Walton et al. [10] the authors found that, for a representative series of thiomidoyl radicals, the b-scission underwent exclusively fragmentation of the S–R2 bond. They also found that the b-scission of the R1–N bond did not compete in any case. These experiments prompted us to perform a theoretical analysis using a recently introduced homofugality index [12], which is obtained as the group spin-philicity [13,14] of the leaving group in a homolytic bond cleavage process. This definition is similar to that of nucleofugality associated with the departure of the leaving group bearing the bond electron pair [15]. The homofugality index, m, was recently defined in the context of the spin polarized density functional theory (SP-DFT) [16–18] to describe the leaving group ability in homolytic substitution reactions [12]. In this work we intend to quantitatively describe the leaving group ability of R2 and R1 moieties in the thioimidoyl radicals and to compare the b-scission modes observed in these systems (Scheme 1).
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D. Guerra et al. / Chemical Physics Letters 443 (2007) 383–388
should be probably framed on Ayers et al. [19] pioneering work regarding heterolytic bond cleavage processes). The spin-hardness can be calculated from the spin potentials as follows: þ l S lS : ð4Þ 2 The homofugality index was evaluated at the transition state structures for the two modes of fragmentation involving the radical species t-butyl-N@C–S–R2 and ethylN@C–S–R2 whit R2: n-butyl, i-propyl, ciclopentyl, t-butyl and 2-pentinyl (Tables 1 and 2). The transition state of a chemical reaction is the bottleneck of the process and therefore, the evaluation of reactivity indexes is better suited at this stage of the reaction than at the ground state of reactants. All the structures were fully optimized at the (U)B3LYP level of theory [20–22] using the 6-31 + G(2d, p) basis set implemented in the Gaussian 03 program [23]. Analytical second derivative calculations were performed to ensure that all the stationary points were real minima on the potential energy surface. All the transition states were characterized by a unique imaginary frequency corresponding to each bond scission mode. The activation energies were calculated for the two b-fragmentation modes, total energies were corrected for zero-point vibrational energies and for thermal effects at 298 K. All reactivity indices required to evaluate the homofugality index were obtained by single points calculations on the optimized geometries at the HF/6-31G(d) level of theory, following a prescription recently proposed by Vargas et al. þ [24]. The spin Fukui function (fSS Þ [16] needed to evaluate þ the regional spin-philicity xS;k through the expression of Eq. (2) was evaluated following a computational scheme described elsewhere [25,26]. The spin Fukui function þ fSS ðrÞ can be computed using the approximations proposed by Galvan et al. [16]:
g0SS ¼
Scheme 1.
2. Model equations and computational details The homofugality index is defined as the regional spinphilicity of the leaving group (LG) as follows [12]: X m x þ xþ ð1Þ S ðLGÞ ¼ S;k ; k2LG
xþ S;k
the quantity philicity [14]:
is the regional (condensed to atom) spin-
þ þ xþ S;k ¼ xS fSS;k ;
ð2Þ
þ where fSS is the generalized spin Fukui function introduced by Galvan et al. [16], as the derivative of the spin density with respect to the spin number, NS = Na Nb. xþ S is the spin-philicity index introduced [13] to describe the stabilization in energy in the direction of increasing multiplicity: 2
xþ S
ðlþ SÞ ; 2g0SS
ð3Þ
lþ S is the spin potential in the direction of increasing multiplicity and g0SS is the global spin hardness of the system. The present approach just completes the formulation of the leaving group ability description of molecular fragments in radical processes where the bond cleavage corresponds this time to an homolytic process (it would be certainly of interest to derive it from a formal model which
Table 1 Experimental and theoretical activation energies, Fukui function, spin-philicity and homofugality indexes of the leaving group (R2, R1) calculated at the cis transition states structure for the b-scission of the S–R2 and R1–N bonds, respectively, of some R1–N@C–S–R2 radicalsa R2
Scission S
Scission N
Ea (kcal/mol)
þ fSS
xþ S
m
Ea (kcal/mol)
þ fSS
xþ S
m
Exp.
Theo.
n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
11.9 10.2 9.2 5.9 66.7
10.1 7.9 7.5 5.2 3.5
0.0512 0.0637 0.0839 0.0864 0.1359
4.67 4.70 4.72 4.71 4.69
R1 = t-butyl 0.24 17.6 0.30 17.6 0.40 17.5 0.41 16.9 0.64 19.0
0.0459 0.0486 0.0480 0.0487 0.0373
5.64 5.68 5.64 5.67 5.30
0.26 0.28 0.27 0.28 0.20
n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
12.0 8.6 8.9 6.4 –
10.1 7.9 7.8 5.5 3.4
0.0504 0.0605 0.0854 0.0873 0.1343
4.65 4.68 4.66 4.68 4.67
R1 = ethyl 0.23 22.9 0.28 22.4 0.40 22.3 0.41 21.7 0.63 23.9
0.0279 0.0283 0.0312 0.0287 0.0201
5.58 5.59 5.57 5.59 5.36
0.16 0.16 0.17 0.16 0.11
a
Experimental activation energy for identical (R1 = t-butyl) and analogous (R1 = ethyl) thioimidoyl radicals from Ref. [10]. Theoretical activation þ energy calculated at UB3LYP/6-31 + G(2d, p) level of theory. The indexes fSS , xþ S and m calculated at UB3LYP/6-31 + G(2d, p) i UHF/6-31G(d) level of theory. xþ and m values are given in eV units. S
D. Guerra et al. / Chemical Physics Letters 443 (2007) 383–388
385
Table 2 Theoretical activation energies, Fukui function, spin-philicity and homofugality indexes of the leaving group (R2, R1) calculated at the trans transition states structure for the b-scission of the S–R2 and R1–N bonds, respectively, of some R1–N@C–S–R2 radicalsa R2
Scission S
Scission N
Ea (kcal/mol)
þ fSS
xþ S
m
n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
12.1 10.8 10.3 9.4 7.6
0.0682 0.0884 0.1654 0.1311 0.2198
4.92 4.81 4.48 4.66 4.88
R1 = t-butyl 0.34 20.7 0.43 21.1 0.74 21.1 0.61 20.6 1.07 20.0
n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
11.9 10.2 9.7 8.3 7.3
0.0646 0.0832 0.1566 0.1683 0.2202
4.87 4.76 4.91 4.95 4.89
0.31 0.40 0.77 0.83 1.08
Ea (kcal/mol)
þ fSS
xþ S
m
0.0533 0.0473 0.0512 0.0464 0.5006
5.64 5.49 5.48 5.50 5.21
0.24 0.26 0.28 0.25 1.92
0.0328 0.0332 0.0406 0.0315 0.0212
5.42 5.72 5.74 5.57 5.24
0.18 0.19 0.23 0.18 0.11
R1 = ethyl 24.3 24.9 24.9 24.2 23.9
a þ Theoretical activation energy calculated at UB3LYP/6-31 + G(2d, p) level of theory. The indexes fSS , xþ S and m calculated at UB3LYP/6-31 + and m values are given in eV units. G(2d, p) i UHF/6-31G(d) level of theory. xþ S
1 h a 2 b 2 i uL ðrÞ þ uH ðrÞ ; ð5Þ 2 /aL ðrÞ and /bH ðrÞ are the a and b LUMO and HOMO spin– orbitals, respectively. The spin potentials lþ S and lS needed to evaluate the 0 spin hardness gSS were calculated using the finite difference formulas proposed by Galvan et al. [17,18], namely:
þ fSS ðrÞ
lþ S
eaL ðMÞ ebH ðMÞ 2
and l S
eaH ðM 0 Þ ebL ðM 0 Þ ; 2
ð6Þ
in terms of the one-electron energies of the HOMO and LUMO orbitals for the system in the lower (M) and upper (M 0 ) spin multiplicities, respectively. 3. Results and discussion EPR parameters are consistent with the idea that thioimidoyls are r-radicals [8–10]. Based on these EPR data and theoretical calculations at the UB3LYP/6-31 + G(2d, p) level of theory performed on the R1–N@C–S– R2 (R1 = R2 = ethyl, i-propyl and t-butyl) radicals, Walton et al. [10] concluded that thioimidoyls are r-radicals with a bent structure and a trans conformation about the C@N double bond (Scheme 2). Since thioimidoyls prefer an strans conformation, they concluded that for these radicals, the actual scission pathway should be preceded by rotation of the S–C bond followed by fragmentation. We relay on the results of these authors to accordingly select the two conformational minima corresponding to the cis and trans
Scheme 2.
configurations about the C@N double bond (Scheme 2) to evaluate the performance of our homofugality index to describe both fragmentation modes (S and N) as well as the leaving group ability of radical fragments ðR1 and R2 Þ in b-scission reactions of thioimidoyl radicals. The activation energies, homofugality indexes, as well as the generalized spin Fukui functions and the regional spinphilicity values calculated for both fragmentation modes (S and N) for the cis radicals are compiled in Table 1. The values corresponding to the trans radicals are shown in Table 2. The calculated activation energies for the fragmentation of the S–R2 bond on cis structures are in good qualitative agreement with the experiment (Table 1) measured by EPR spectroscopy [10] for identical (R1 = t-butyl) or analogous (R1 = ethyl) thioimidoyls. It may be seen that the activation energy for the b-scission of S–R2 bond has an inverse relationship with the homofugality index: low barriers are consistently related to high values of homofugality of the departing radical. The same pattern is obtained for the scission of S–R2 bond in trans structures (Table 2). Note that the substitution of t-butyl by ethyl at R1 (Scheme 1) has little effect on the scission of the S–R2 bond. The experimental and calculated activation energies as well as homofugality of the R2 radicals (columns 2, 3 and 6 in Table 1 and columns 2 and 5 in Table 2) change little with N-alkyl substituents for both cis and trans structures. The same behaviour is observed for the scission of the N–R1 bond for the S-alkyl derivatives which show a little influence on the departure of the t-butyl and ethyl radicals (see columns 7 and 10 in Table 1 and columns 6 and 9 in Table 2). From these results we may conclude that the homofugality index provides information about the intrinsic homofugality pattern of radicals. The comparison between the homofugality of the R2 radical and the experimental rate coefficients for the b-scission of the S–R2 bond, for the cis structures, are depicted in Fig. 1. It may be seen that a significant correlation between
386
D. Guerra et al. / Chemical Physics Letters 443 (2007) 383–388
Fig. 1. Plot of the homofugality index versus the logarithm of observed rate constants for the b-scission of the S–R2 bond of t-butyl-N@C–S–R2 and ethyl-N@C–S–R2 radicals. Experimental rate constants were obtained from Ref. [10]. The homofugality index is calculated at the cis transition state at B3LYP/6-31 + G(2d, p) i UHF/6-31G(d) level of theory. R is the regression coefficient.
the homofugality index and the logarithm of the experimental rate constant [10] is obtained (R2 = 0.97). Since rate coefficient values are only available for fragmentation at the S–R2 bond at the cis configuration, we performed a comparison between the homofugality index and the theoretical activation energies for the b-scission at the S–R2 bond at the trans conformation (see Fig. 2). The comparison shows that the trans conformation yields similar results.
The general reactivity trends in terms of the homofugality index is: n-butyl < i-propyl < c-C5H9 < t-butyl < 2-pentinyl, which is in qualitative agreement with the experimental rate constants [10]. These results show that the information encompassed in the homofugality index is consistent with the idea that a greater branching at the C-atom attached to sulphur and nitrogen atoms dramatically increases the rate of fragmentation of the radicals R2 and R1 , respectively (i.e., m (n-butyl) = 0.24 and m (t-butyl) = 0.41 for the scission at the S end of the t-butyl-N@C–S–R2 and m (ethyl) = 0.16 and m (t-butyl) = 0.26 for the scission at the N side of the R1–N@C–S–n-butyl), in agreement with the experiment [10]. In order to evaluate with more detail the usefulness of the homofugality index, a theoretical study was carried out on the two fragmentation modes, scission S and scission N, on thiomidoyl radical with the same substituent at both nitrogen and sulphur centres. The calculations were carried out for the cis conformation of thioimidoyl radicals bearing primary, secondary and tertiary alkyl groups as well as cyclic groups on both nitrogen and sulphur ends (Table 3). In all cases the homofugality at the sulphur side was found to be greater than that at the nitrogen side. Table 3 clearly shows that the departure of the radical at the sulphur side is predicted to be always favoured compared to the homofugality at the nitrogen side, independent of the substituent patterns. Note that this effect may also be observed from Tables 1 and 2, except when the primary radical n-butyl was released in competition with the t-butyl radical (Table 1) and when the 2-pentinyl radical is released with a tertiary radical (Table 1). The departure of the radical at the sulphur side is always favoured compared to the homofugality at the nitrogen side a result that can be traced to the regional spin softness [14,27], which is greater in sulphur derivatives than nitrogen derivatives. This pattern of reactivity is similar to that obtained previously for bimolecular homolytic substitution reactions involving methyl, silyl, germyl and stannyl radicals, where the observed leaving group order of this series [12] was þ C < Si < Ge Sn. The generalized Fukui function fSS ðrÞ required to evaluate the homofugality index is a normalized spin softness [27] and as such, it may be viewed as a measure of the distortion of the spin density (polarizability) Table 3 Fukui function, spin-philicity and homofugality indexes for the leaving group R calculated at the cis transition states structure for fragmentation at the R–N and S–R bonds of R–N@C–S–R radicalsa R
Fig. 2. Comparison between homofugality index and theoretical activation energy for the reaction of b-scission of the S–R2 bond for t-butylN@C–S–R2 and ethyl-N@C–S–R2 radicals. Values calculated at the trans transition state, the homofugality index was evaluated at B3LYP/631 + G(2d, p) i UHF/6-31G(d) level of theory and the activation energy was obtained at B3LYP/6-31 + G(2d, p) level of theory. R is the regression coefficient.
Ethyl n-Butyl i-Propyl t-Butyl c-C5H9
Scission S
Scission N
þ fSS
xþ S
m
þ fSS
xþ S
m
0.0486 0.0635 0.0864 0.0530 0.0880
4.68 4.67 4.72 4.65 4.74
0.2273 0.2464 0.2965 0.4069 0.4166
0.0269 0.0425 0.0487 0.0296 0.0483
5.56 5.68 5.68 5.58 5.73
0.1495 0.1651 0.2415 0.2764 0.2765
a þ The indexes fSS , xþ S and m calculated at UB3LYP/6-31 + G(2d, p)// UHF/6-31G(d) level of theory. xþ S and m values are given in eV units.
D. Guerra et al. / Chemical Physics Letters 443 (2007) 383–388
that seems to play an important role in homolytic cleavage processes. In summary, the results show that the homofugality index provides useful information about the quality of a leaving group for these radical processes. The homofugality evaluated at the transition state structures for the N and S scission processes correctly describes the observed scission pattern. As in the case of the homolytic substitution reactions, the homofugality order appears again driven by the spin Fukui function, which is related to the regional spin softness of the leaving radical group at the transition state. Here again an interesting parallel with the parent heterolytic cleavage observed in polar processes which depends on the regional electronic softness evaluated at the nucleofuge moiety may be established. 4. Concluding remarks A theoretical study of the b-scission reactions for some thioimidoyl radicals (R1–N@C–S–R2) using a recently introduced homofugality index, m, has been presented. To evaluate the performance of our homofugality index, the study was carried out on the two fragmentation modes: scission at the S–R2 and R1–N bonds, for two conformational minima corresponding to the cis and trans configurations about the C@N double bond. The homofugality evaluated at the transition state (TS) structures for the N and S scission processes correctly describes the observed scission pattern. Following a suggestion by a reviewer, we have evaluated the performance of the proposed reactivity index at the ground state of molecules, and we have verified that the description of the scission pattern is better described at the TS stage of the reaction. The results of these calculations are compiled in Table 4. The departure of the radical at the sulphur side ðR2 Þ is predicted to be always favoured compared to the homofugality at the nitrogen side ðR1 Þ that can be traced to the regional spin softness, which is greater in sulphur derivaTable 4 Global spin-philicity, Fukui function and homofugality indexes of the leaving groups (R2, R1) calculated at the cis ground state structure of some R1–N@C–S–R2 radicalsa R2
xþ S
þ fSS ðR2 Þ
m (R2)
þ fSS ðR1 Þ
m (R1)
R1 = t-butyl n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
4.71 4.66 4.66 4.71 5.47
0.0307 0.0477 0.0814 0.0428 0.2724
0.14 0.22 0.38 0.20 1.49
0.0659 0.0651 0.0608 0.0658 0.0366
0.31 0.30 0.28 0.31 0.20
R1 = ethyl n-Butyl i-Propyl c-C5H9 t-Butyl 2-Pentinyl
4.71 4.70 4.66 4.72 5.47
0.0318 0.0458 0.0796 0.0414 0.2750
0.15 0.21 0.37 0.20 1.51
0.0601 0.0565 0.0533 0.0561 0.0239
0.28 0.27 0.25 0.26 0.13
tives than nitrogen derivatives. As in the case of the bimolecular homolytic substitution reactions involving methyl, silyl, germyl and stannyl radicals, the homofugality order appears again driven by the spin Fukui function, which is related to the regional spin softness of the leaving radical group at the transition state. Here again an interesting parallel with the parent heterolytic cleavage observed in polar processes which depends on the regional electronic softness evaluated at the nucleofuge moiety may be established. The general reactivity trends in terms of the homofugality index, for the radical species t-butyl-N@C–S–R2 and ethylN@C–S–R2, is: n-butyl < i-propyl
a
þ The indexes xþ fSS and m calculated at UB3LYP/6S, 31 + G(2d, p) i UHF/6-31G(d) level of theory. xþ S and m values are given in eV units.
387
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