Density Functional Theory Study on the Decay of Fullerenyl Radicals

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A DFT Study on the Decay of Fullerenyl Radicals RC60•, ROC60•, and ROOC60• (R = tert-Butyl and Cumyl) and Polarizability of the Formed Fullerene Dimers Denis Sh. Sabirov, Ralia R. Garipova, and Ramil G. Bulgakov J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 22 Nov 2013 Downloaded from http://pubs.acs.org on November 24, 2013

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The Journal of Physical Chemistry

A DFT Study on the Decay of Fullerenyl Radicals RC60•, ROC60•, and ROOC60• (R = tert-Butyl and Cumyl) and Polarizability of the Formed Fullerene Dimers Denis Sh. Sabirov*, Ralia R. Garipova, Ramil G. Bulgakov Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, 450075 Ufa, Russia

ACS Paragon Plus Environment

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ABSTRACT. Currently, there are no comparative studies on the possible routes of decay of fullerenyl radicals. Such information is required for development of new synthetic ways to the fullerene derivatives, obtained via radical reactions, and understanding mechanisms of oxidative destruction of fullerene-containing materials. In the present work, we have performed a theoretical study on the possible reactions of the selected fullerenyl radicals, generated in the well-known experimental systems. We consider three main routes for the radical decay: formation of fullerene bisadducts via XC60● + X● reactions, dimerization of XC60●, and their interaction with molecular oxygen. The calculated heat effects explain the experimental regularities of fullerene radical reactions (e.g., the reversibility of the dimerization and low reactivity of fullerenyls toward molecular oxygen). We have found that the heat effects are maximal for the dimerization of ROOC60●, so the interaction of C60 with peroxy radicals may provide more effective synthetic routes to the single-bonded C60 dimers compared to the known ones. Moreover, the exothermicity of ROO● addition to C60 is increased during the subsequent addition that allows reconsidering the reasons underlying C60 antioxidant activity. Additionally, polarizability and its non-additivity of fullerene dimers XC60–C60X have been found. Guided by the calculated polarizabilities, we assume a new bistable system “fullerenyl ↔ dimer” for molecular machinery. Depending on the conditions, such a system can exist in two states differing by their response to external electric fields. Keywords: fullerenyl radicals, fullerene dimers, polarizability, computational thermochemistry.


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Introduction Since the discovery of fullerenyl radicals by Krusic et al. in 1991,1 radical chemistry of fullerenes has been rapidly developed (See the recent exhaustive review2 and several key works in this field3–9). Being an electron-deficient molecule with a strong system of the conjugated double bonds, the C60 fullerene readily attaches diverse usual (non-fullerene) radicals, including C-, Si-, O-, S-, P- and metal-centered species. Numerous reaction sites in the C60 molecule cause its high effectiveness as a radical scavenger (e.g., it is able to capture up to 34 methyls1 or 16 perfluoroalkyl radicals9). Therefore, the C60 fullerene is metaphorically called a radical sponge.1 Moreover, radical reactions of fullerenes underlie syntheses of novel functional derivatives C60Xn.2,10 Type, number and positional relationship of the radicals, tethered to the C60 core, open wide opportunities for production of fullerene derivatives with the desirable physicochemical properties. Another important issue of fullerene radical chemistry deals with ability of C60 and its derivatives to inhibit radical processes in chemical and biochemical systems.2,6 For example, effects of fullerene on the liquid-phase oxidation of hydrocarbons11–13 and lipids,14 radical polymerization (See Ref. 15 and references therein), and thermo-oxidative destruction of the fullerene-containing polymers16,17 have been previously studied. Different radical particles can act as intermediates of the processes listed above: these are alkyl R•, alkoxy RO• and peroxy radicals ROO•. The last one is a result of the reaction between alkyl radicals and oxygen. Generally, each of R•, RO•, or ROO• are able to attach to fullerenes (though with different rates),2,18–22 so it is experimentally difficult to study these radical processes separately. Experimental investigations23–25 have shown that formation of fullerenyl radicals XC60• is the first step of the C60 radical reactions: C60 + X• → XC60•

(1)


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Due to delocalization of the unpaired electron on the carbon framework, addition of the next Х• to any of 59 carbon atoms, remained available in XC60•, is possible. However, the maximal spin density is concentrated on carbon atoms in positions 2 and 4, relative to the site of the first X• addition.23–26 It leads to 1,2- and 1,4-bisadducts, the simplest molecular products of the fullerene radical reactions. Their formation has been experimentally detected.2 The bisadducts are formed according to the following equation: XC60• + X• → C60X2 (2) Addition of the next X• to fullerenyl radicals is not the only way of XC60• decay. Their reaction with oxygen presents another alternative. As is known, fullerene is not oxidized by oxygen (in the absence of light irradiation or a catalyst27), i.e. the fullerene core is rather stable toward O2. Usually, C60 reactivity is changed essentially when the unpaired electron appears on the fullerene cage28 but not in the case of fullerenyl radicals and especially with respect to oxygen. As shown in non-numerous works,29,30 reactivity of fullerenyls toward oxygen is surprisingly low. Indeed, ESR signals of (tBuO)nC60• radicals decay slowly in the presence of oxygen due to the reaction leading to O-centered fullerene-based radicals:29 XC60• + O2 → XC60OO•

(3)

Our previous ESR study30 on the interaction between EtC60• and O2 has shown that the ESR signal intensity is not changed in air atmosphere (compared to its intensity in argon) and only a broadening of the ESR line is observed. It means that the complex EtC60•…O2 is formed whereas no chemical reaction between EtC60• and O2 takes place. As is known,31 hydrocarbon radicals facilely react with oxygen (e.g., in the case of alkyl radicals, the diffusion rate constants are ~109 L /(mol s)). In this aspect, low reactivity of fullerenyl radicals toward O2 seems unusual.


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Dimerization of fullerenyl radicals is the third route of their decay. The reversible formation of the single-bonded dimers is typical for alkyl- and fluoroalkylfullerenyl radicals:2,4,9,32,33 XC60• ↔ XC60–C60X

(4)

Dimers XC60–C60X with X = R have been studied experimentally but the formation of the analogous structures with RO or ROO moieties attached has not been discussed. The interest in such compounds is caused by the opportunity of their use for generation of free radicals in fullerene-containing systems.34 In addition, theoretical studies predict that C60 dimers should demonstrate outstandingly high values of the first35 and the second36 polarizabilities. It makes these chemicals prospective for optical applications and nanodevices. Thus, there are at least three alternative routes of fullerenyl radicals’ decay. For simplification, we have excluded reactions of cross-addition, when different radicals are attached to one fullerene core, and reactions of fullerenyl radicals with the solvent (this is close to the experimental fullerene-containing systems with non-reactive medium, e.g., benzene11). We can propose that formation of 1,2- and 1,4-bisadducts in “C60 + X•” systems should be thermodynamically more favorable than the dimerization due to the observed reversibility of the last one. However, the comparative thermodynamic advantages of the aforementioned reactions have not been studied both theoretically and experimentally. At the same time, such data on the reactivity of fullerenyl radicals may be important to developing the effective synthetic methods, directed to the obtainment of the only one desired product (only XC60–C60X or only C60X2). Withal, thermochemical parameters of these reactions can be applied to a study on the mechanism of oxidative destruction of the fullerene-containing materials. Reactions of radical addition usually have low activation barriers, so they are successfully described by heat effects, facilely calculated in terms of the modern DFT methods. Such an approach to estimation of fullerene reactivity has been widespread.37–39 For example, a DFT


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study on H•, F•, and CH3• addition to the diverse fullerenes (from C20 to C84) allowed obtaining a linear correlation between the heat effects of the addition and the curvature indices of reaction sites in the fullerene molecules.26 In the present theoretical work, we have studied three main routes of decay for RC60•, ROC60•, and ROOC60• fullerenyls (R = tBu• and Ph(CH3)2C•). This set of radicals has been chosen due to the following reasons. Radicals tBuC60•, tBuOC60•, and tBuOOC60• are intermediates of the reactions underlying the modern synthetic strategies for production of oxygen-rich fullerene derivatives.21–23,40 The analogous cumyl-containing fullerenyl radicals (R = Ph(CH3)2C) are generated in the model systems of the liquid-phase oxidation of hydrocarbons.12,13,18,19 In addition, various fullerenyls ROC60• and ROOC60• are generated in different reactions in fullerene-containing systems, such as photolysis of peroxides ROOR20 and dialkoxy disulfides ROSSOR22 in the presence of C60 or catalytic fullerene alkoxylation.41 Computational details The potential energy surface scanning and all optimizations have been performed by density functional theory method PBE/3ζ42,43 implemented in the Priroda program.44 The 3ζ basis set describes electronic configurations of molecular systems by the orbital basis sets of contracted Gaussian-type functions (5s,1p)/[3s,1p] for H, (11s,6p,2d)/[6s,3p,2d] for C and O, which have been used in combination with the density-fitting basis sets of uncontracted Gaussian-type functions (5s,2p) for H, (10s,3p,3d,1f) for C and O atoms. The PBE/3ζ method reproduces structures and physicochemical characteristics of fullerenes and their derivatives with high accuracy, as shown in numerous theoretical works.26,35,37,38,45–49 In addition, it correctly reproduces the experimental data on the distribution of spin density in hydro-, fluoro-, and methylfullerenyl radicals.26


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After DFT-optimizations and vibration modes solving (to prove that all the stationary points, respective to the radicals/molecules under study, are minima of the potential energy surfaces) by standard techniques, the heat effects of the reactions have been calculated as the differences between the total energies E of the products and the reactants with inclusion of zero-point vibrational energy corrections εZPV and the temperature corrections Hcorr (T = 298 K):

∆H r ° =

∑ (E

tot

+ ε ZPV + H corr ) −

products

∑ (E

tot

+ ε ZPV + H corr )

(5)

reac tan ts

Components of polarizability tensors have been calculated in terms of finite field approach as the second order derivatives of the total energy E with respect to the homogenous external electric field. They have been calculated in the arbitrary coordinate system and then diagonalized. Eigenvalues of polarizability tensors αxx, αyy, αzz have been used for the calculation of the mean polarizabilities of the molecules:

α=

1 (α xx + α yy + α zz ) 3

(6)

The PBE/3ζ-based finite field approach allows reproducing the measured mean polarizabilitites of C60 and C70 fullerenes.35,49–51 The mathematical operations on polarizability tensors have been performed by POLARIZ program,52 worked out by us for the fast data processing upon calculations of polarizability.

Results and discussion Formation of fullerenyl radicals XC60• at the reaction (1) is exothermic, regardless of the type of X• (Table 1). The formed fullerenyl radicals XC60• are characterized by almost the same distribution of spin density: its maximal values correspond to carbon atoms in positions 2 and 4 (relative to the site of the first X added) (Figure 1, Table 2). That is why we have scrutinized the


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possibility of reactions (2–4) (bisadduct formation, O2 addition or dimerization) for the mentioned reaction sites. Additionally, we have considered the 1,16-bisadducts and 1,16,1´,16´dimers as the products of reactions (2) and (4). In spite of the lower spin density in this position compared to 2 and 4 sites, the 1,16-bisadduts have been identified among the products of addition of bulky radicals to C60.10 Table 1 Heat effects of R•, RO•, and ROO• addition to C60 (reaction (1), kJ/mol) R

t

Bu

Ph(CH3)2C

R•

–64.4

–11.9

RO•

–59.4

–59.0

ROO•˙

–8.4

–13.0

•

X

Figure 1 Fullerenyl radicals RC60•, ROC60•, and ROOC60• with R = tBu. Reaction sites of the further additions are designated; key bond lengths are shown in Å for R = tBu and R = Ph(CH3)2C (in parentheses).


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Table 2 Spin densities of different reaction sites in XC60• fullerenyls (Mulliken population analysis) X Position R

RO

ROO

2

0.444 (0.444)*

0.430 (0.432)

0.419 (0.423)

4

0.211 (0.210)

0.220 (0.217)

0.214 (0.216)

16

0.090 (0.090)

0.087 (0.086)

0.088 (0.088)

*Values for R = tBu are given; values for R = Ph(CH3)2C are given in parentheses. Heat effects of fullerene bisadducts formation via reactions (2). Interaction of fullerenyls XC60• with the same X• is a paramount route to the diverse fullerene bis- and polyadducts.1,2 In the case of alkyl radicals (X = R), formation of 1,16- and 1,4-bisadducts is thermodynamically more favorable according to the calculations performed (Table 3). Note that absolute values of the heat effects are decreased two times from tBu• to Ph(CH3)2C•, a more voluminous radical. Due to the sterical hindrances, formation of 1,2-C60R2 is endothermic in both tert-buthyl and cumyl cases. Table 3 Heat effects of isomeric bisadducts С60Х2 formation via reaction (2); the highest ∆Hrº values in each row are shown in bold (kJ/mol) Reaction

Product 1,2-C60X2

1,4-C60X2

1,16-C60X2

Bu• + tBuC60•

+15.7

–104.9

–114.9

Ph(CH3)2C • + Ph(CH3)2C C60•

+68.5

–52.9

–64.6

t

BuO• + tBuOC60•

–136.6

–144.1

–108.4

Ph(CH3)2CO• + Ph(CH3)2COC60•

–120.66

–145.98

–110.3

t

BuOO• + tBuOOC60•

–102.6

–94.8

–58.9

Ph(CH3)2COO• + Ph(CH3)2COOC60•

–108.4

–102.5

–60.9

t


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In the case of RO• and ROO•, formation of bisadducts is characterized by exothermic heat effects for all the studied reaction sites. However, the reactions resulting in both 1,2- and 1,4bisadducts have the largest ∆Hrº values that proves their equiprobability. For example, the small difference (less than 10 kJ/mol) in the highly exothermic heat effects of 1,2- and 1,4-addition of t

BuOO•, predicted here theoretically, well corresponds to the experimental identification of both

1,4-C60(OOtBu)2 and 1,2-C60(OOtBu)2 among the products of interaction between C60 and tertbutylperoxy radicals.40 The heat effects of the second X• addition to the C60 core (reaction (2)) are significantly higher than the respective values for the first step (reaction (1)). Thus, in the case of 1,4-C60tBu2, 1,4C60(OtBu)2, and 1,4-C60(OOtBu)2, the enthalpies of reactions (2) equal to –104.9, –144.1, and – 102.5 kJ/mol whereas formation of the respective tBuC60•, tBuOC60•, and tBuOOC60• radicals are accompanied by the lower heat effects , being –64.4, –59.4, and –8.4 kJ/mol, respectively (Table 1). It is explained by the fact that decay of one radical occurs on the first step while on the next one, two radicals (X• and XC60•) cease to exist. Obviously, all the subsequent odd steps are characterized by the lower heat effects than the even ones. The latest statement has been demonstrated for the case of the subsequent addition of tert-butylperoxy radicals to C60, a wellknown experimental system, studied by Gan et al.40 (Figure 2).


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Figure 2 Heat effects of the subsequent addition of tBuOO• to C60. Sites and the order of addition are shown on the structural formula. Here, the heat effects of the odd steps describe reactivity of C60 (n = 1) and its adducts C60(OOtBu)2 (n = 3) and C60(OOtBu)4 (n = 5) toward tBuOO• radicals. Figure 2 allows elucidating a trend to the enhancement of the reactivity during the addition of peroxy radicals to C60. Indeed, exothermicity of the radical addition rises almost six times from the intact fullerene to C60(OOtBu)4. This information may be important to understanding the reasons of high efficiency of C60 as an antioxidant and inhibitor of radical processes because most of the known explanations deal with the large number of the reaction sites in its molecule.2 Based on the calculations performed, we can assume that its efficiency, in addition to the reason above, may be explained by the exothermicity increasing with each radical captured. Heat effects of XC60• reactions with molecular oxygen. We pay attention to the reactions between XC60• and O2 because molecular oxygen is always present in both in vitro and in vivo studies of antioxidant activity of C60 and its derivatives. The O-centered radicals XC60OO• should be products of the mentioned interactions.


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Table 4 Heat effects of the reactions between fullerenyls and triplet molecular oxygen (data for the analogous reactions with singlet oxygen are shown in parentheses) (kJ/mol) Reaction

Product 1,2-XC60OO•

1,4-XC60OO•

t

BuC60• + O2

+29.6 (–128.1)

+10 (–147.7)

t

BuOC60• + O2

+5.5 (–152.2)

+13.7 (–144)

t

BuOOC60• + O2

+0.4 (–157.2)

+11.7 (–146)

Ph(CH3)2CC60• + O2

+30.3 (–127.3)

+8.4 (–149.3)

Ph(CH3)2COC60• + O2

–*

+26.8 (–130.8)

Ph(CH3)2COOC60• + O2

+2.6 (–155)

+10.4 (–147.2)

* Localization of the stationary point corresponding to this radical has been failed.

The calculated heat effects of reactions (3) with O2 in the ground state (triplet) are endothermic for all the XC60● radicals, regardless of the nature of X (Table 4). It explains the experimental observation of very slow interaction of fullerenyls with oxygen.29,30 Endothermicity of O2 addition to the position 2 decays in the series RC60• > ROC60• > ROOC60•. It explains why RC60• and ROC60• have demonstrated the different reactivity toward oxygen in experiments. Indeed, the slow reaction has been detected in the case of alkoxyfullerenyls (tBuO)nC60• 29 whereas in the case of alkylfullerenyl EtC60•, no chemical reaction has been found, and only the reversible formation of intermolecular complex has been observed.30 We propose that reactivity of XC60• toward oxygen can be enhanced by the use of its excited state (singlet) instead of the ground one. As the calculations indicate, 1O2 addition to carbon atoms 2 and 4 in fullerenyls is highly exothermic. Herewith, 1,4-RC60OO•, 1,2-ROC60OO•, and 1,2-ROOC60OO• are the thermodynamically more favorable products in reactions (3). In the case of RC60•, addition to position 2 is unfavorable due to the steric hindrances: bulky tert-butyl and


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cumyl addends in RC60• screen this reaction site. In the case of ROOC60• and ROC60OO•, the voluminous R moieties are more remote from the site that facilitates oxygen addition to the mentioned position. Wave functions of oxygen and peroxides are multiconfigurational, so investigation of the reasons underlying low reactivity of fullerenyls toward oxygen demands multiconfigurational quantum-chemical methods.53 Unfortunately, these are currently not applicable to such big systems as fullerenes and their derivatives. Nevertheless, we have theoretically justified possibility of a new class of radicals XC60OO•: all the mentioned structures are minima on potential energy surface. Such radicals may be precursors for synthesis of fullerene-contataining polymers, in which С60 cores are linked by peroxide bridges. Scheme 1 Heat effects of reactions between hydrocarbon radicals and molecular oxygen. Spin densities of the reaction sites are shown in red O O

0.979

C

O2

+

-148.6 kJ/mol

O O

0.917

C

+

O2

-93.02 kJ/mol

Ph 0.629

Ph

C Ph

Ph

+

O2

Ph

O O

-14.28 kJ/mol

Ph

Radicals XC60OO• have been almost unstudied both theoretically and experimentally. Only in the work,29 generation of (tBuO)nC60OO• has been confirmed by evolution of ESR signal in aerobic conditions. Usually, interaction of C-centered radicals with molecular oxygen occurs intensively.31 In order to compare, we have calculated heat effects of the analogous reactions of other radicals – 1,3-butadien-2-yl, phehyl (these radicals have the delocalized unpaired electrons


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and can be considered as distant analogues of XC60•) and Gomberg radical (a classic example of a radical with steric hindrances) (Scheme 1). The PBE/3ζ-calculated heat effects are exothermic in all these cases. Thus, XC60• radicals essentially differ from their hydrocarbon analogues in the aspect of their reactivity toward molecular oxygen. Most likely, it is caused by spreading the unpaired electron over the fullerene cage. Indeed, in the mentioned hydrocarbon radicals, the free spins are concentrated mainly on the one reactive site, so the spin densities are much higher (0.629–0.979, Scheme 1) in comparison with fullerenyl radicals (less than 0.450, Table 2). Table 5 Heat effects of dimerization of fullerenyl radicals (kJ/mol) Product Radical

1,2,1ʹ,2ʹ-XC60– C60X

1,4,1ʹ,4ʹ-XC60– C60X

1,16,1ʹ,16ʹ-XC60– C60X

t

BuC60•

–

–3.4

+6.4

t

BuOC60•

+38.1

–52.9

+9

t

BuOOC60•

–10.4

–65.5

+8.6

Ph(CH3)2CC60•

–

–2.7

+2.7

Ph(CH3)2COC60•

–

–40.6

+20.5

Ph(CH3)2COOC60•

+4.9

–58.2

+3.9

Heat effects of fullerenyl dimerization and polarizability of the dimers formed in reactions (4). Dimerization of fullerenyl radicals is another possible process in “fullerene + radical” systems. The calculated heat effects of the dimerization are small (Table 5) that reflects their reversibility, previously found in experimental studies.2,4,9,32,33 Comparison of ∆Hrº shows that the dimerization should result in 1,4,1ʹ,4ʹ-dimers because their formation via reaction (4) is the only exothermic mode. This perfectly agrees with the detection of such dimers among the products of the radical reactions.2,32 Noteworthy, the dimerization is thermodynamically more


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favorable for peroxyfullerenyls ROOC60• than for the respective RC60• and ROC60•. This fact can be useful for development of new synthetic strategies to obtain fullerene dimers with higher yields compared to the known methods (current synthetic approaches are commonly based only on the dimerization of RC60• radicals or their derivatives2,32). Moreover, peroxy groups of ROOC60–C60OOR dimers can be facilely involved in the further chemical transformations, similar to one-cage C60 peroxides54, that provide opportunities for the functionalization of such bi-cage fullerene derivatives. Previously, the exaltation of dipole polarizability has been found for [2+2]-dimer (С60)2 and its derivatives.35 Caused by the interaction of π-electronic systems of two C60 cores, this phenomenon is proposed for the application to nanomaterials and nanodevices design. Since the polarizability (α) of [1+1]-dimers, formed at radical reactions, has not been studied, we have calculated the polarizability tensors and the mean polarizabilities of XC60–C60X. Mean polarizabilities of the dimers have been calculated quantum-chemically (αPBE/3ζ) and in terms of the additive scheme based on the polarizability of the respective fullerenyl radicals: • α add ( XC60 − C60 X ) = 2α ( XC60 )

(7)

We have found that the mean polarizabilities of XC60–C60X are much higher compared to the respective values for the original radicals or the C60 fullerene (82.7 Å3, PBE/3ζ calculation) (Table 6). In order to find out how polarizability changes upon the dimerization, we have calculated the deviations from the additive scheme for each [1+1]-dimer:

∆α = α DFT − α add

(8)

Referred to the basic definitions, we have expected that the deviations ∆α, calculated according to equation (8), would be negative because highly-polarizable unpaired electrons of two XC60• radicals vanish upon dimerization. The analogy with the hydrocarbon chemistry is suitable here.


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For example, according to PBE/3ζ calculations, ∆α is negative (–1.5 Å3) for the dimer of CH2=C•–CH=CH2 radical. In contrast, ∆α values for the dimers of fullerenyl radicals are positive, lying in the range 5.8…11.4 Å3. It means that exaltation of polarizability takes place in the case of [1+1]-dimers, analogous to their [2+2]-counterparts. The maximal exaltation ∆α has been found typical for RC60–C60R dimers. It is larger than 10 Å3 that is enough to be detected by the modern experimental techniques for polarizability measurements, e.g., interferometry, previously applied to measuring polarizability of polyfluorofullerenes.55 Probably, the magnitude of ∆α of XC60–C60X can be regulated by variation of X, attached to the C60 core.

Table 6 Components of the diagonalized polarizability tensors (αxx, αyy, and αzz), additive polarizability (αadd), mean polarizability (αPBE/3ζ), and its deviation from the additive scheme (∆α) for 1,4,1ʹ,4ʹ-XC60–C60X dimers (Å3) Dimer

αxx

αyy

αzz

αPBE/3ζ

αadd

∆α

t

BuC60–C60tBu

157.47

177.23

258.00

197.57

2 × 93.63

10.31

t

BuOC60–C60OtBu

158.77

184.00

255.90

199.56

2 × 95.37

8.82

t

BuOOC60–C60OOtBu

160.93

189.79

256.37

202.36

2 × 96.96

8.44

Ph(CH3)2CC60–C60C(CH3)2Ph

186.96

194.43

269.37

216.92

2 × 102.77

11.38

Ph(CH3)2COC60–C60OC(CH3)2Ph

169.48

202.05

272.70

214.74

2 × 104.48

5.78

Ph(CH3)2COOC60– C60OOC(CH3)2Ph

174.18

211.05

271.14

218.79

2 × 105.33

8.13

From a fundamental point of view, the positive deviation of polarizability from the additive scheme is unusual in terms of the minimum polarizability principle.56,57 According to this principle, thermodynamically more stable state of a molecular system should demonstrate lower polarizability. In the systems “dimer (A) – fullerenyl (B)”, state A is more stable and,


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consequently, the deviation ∆α should be negative. However, the contrary situation is observed in the computations. Thus, the single-bonded fullerene dimers are one of the compounds violating the minimum polarizability principle (along with the noted in the previous work58). The calculated polarizabilities of fullerenyl radicals and the respective dimers allow proposing such a system “dimer (A) – fullerenyl (B)” (Scheme 2) for application in molecular machinery, similar to the molecular switch concept.59 The dimerization is reversible and XC60–C60X molecules facilely dissociate (e.g., under the thermal treatment) resulting in the respective radicals, which can be again dimerized under the appropriate conditions. At the same time, states A and B of such a fullerene-containing system significantly differ in mean polarizabilities, i.e. the states differ in the response to external electric fields and this difference is measurable. We believe that the described systems may find an application in nanotechnologies.

Scheme 2 The proposed fullerene-containing molecular system with two states differing by their response to external electric fields X

X

heating or hν 2 cooling

X

A enchanced response to electric fields

B lower response to electric fields

Conclusion


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Alternative routes of decay for RC60●, ROC60●, and ROOC60● fullerenyl radicals, generated in “R• + C60” systems under aerobic conditions, have been studied by the density-functional theory method PBE/3ζ. The obtained thermochemical data explain the observed experimental regularities of fullerene radical reactions and allow predicting new chemical and physical properties that may be useful for synthetic organic chemistry and nanotechnology applications. Formation of bisadducts C60X2 is the most exothermic route of decay for the radicals under study. A comparison of the heat effects shows that the most thermodynamically favorable products in these reactions are 1,16- and 1,4-C60R2 in the case of alkyls; 1,4- and 1,2-C60(OR)2 in the case of alkoxyls; and 1,2- and 1,4- C60(OOR)2 in the case of peroxy radicals. Here, we have found that exothermicity of addition of peroxy radicals to the fullerene framework is increased during the subsequent addition. We will apply this interesting fact to a study on the mechanisms of C60 antioxidant activity. Much lower exothermic heat effects are typical for the dimerization of fullerenyls resulting in 1,4,1ʹ,4ʹ-dimers (the other variants of dimerization are endothermic according to the calculations performed). Herewith, the heat effect is maximal for the dimerization of ROOC60● among the other cases. Therefore, the interaction of C60 with peroxy radicals can be recommended as one of the way to increase the yields of the single-bonded C60 dimers instead of the common strategy based on the RC60• dimerization. The interaction with molecular oxygen is the less probable route of decay for fullerenyl radicals due to its endothermicity. Their reactivity toward O2 rises in the series RC60● < ROC60● < ROOC60● and can be enhanced by the use of the singlet molecular oxygen. This way, the Ocentered radicals 1,4-RC60OO●, 1,2-ROC60OO● и 1,2-ROOC60OO● should be generated by highly exothermic addition of 1О2 to XC60●.


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In the context of new materials and nanotechnology, we pay a particular attention to the polarizability of the dimers, formed in the radical reactions of C60. First, these are compounds with outstandingly high mean polarizabilities, i.e. high response to electric fields. Second, the polarizability of such dimers is more than two times higher than the polarizability of the respective fullerenyl radicals. Taking into account the well-known reversibility of the dimerization, we have proposed a fullerene-containing molecular system which can exist in two reversible states (dimer and radical) with different response to external electric field. REFERENCES (1) Krusic, P. J.; Wasserman, E.; Keizer, P. N.; Morton J. R.; Preston K. F. Radical Reactions of C60. Science 1991, 254, 1183–1185. (2) Tzirakis, M. D.; Orfanopoulos, M. Radical Reactions of Fullerenes: From Synthetic Organic Chemistry to Materials Science and Biology. Chem. Rev. 2013, 113, 5262–5321. (3) Morton, J. R.; Preston, K. F.; Krusic, P. J.; Hill, S. A.; Wasserman E. ESR Studies of the Reaction of Alkyl Radicals with C60. J. Phys. Chem. 1992, 96, 3576–3578. (4) Tumanskii, B. L.; Bashilov, V. V.; Bubnov, N. N.; Solodovnikov, S. P.; Sokolov V. I. ESR Study of the Reversible Dimerization of Phosphonylfullerenyl Radicals. Bull. Russ. Acad. Sci. Div. Chem. Sci. 1992, 41, 1519–1520. (5) Tumanskii, B. L.; Bashilov, V. V.; Solodovnikov, S. P.; Sokolov V. I. EPR Investigation of the Adducts of Element-Centered Radicals with Polyhedral Carbon Clusters (Fullerenes). Bull. Russ. Acad. Sci. Div. Chem. Sci. 1992, 41, 1140–1141. (6) Sokolov, V. I. The Problem of Fullerenes. The Chemical Aspect. Russ. Chem. Bull. Int. Ed. 1993, 42, 1–11.


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This work was supported by the Presidium of the Russian Academy of Sciences (program No. 24 “Foundations of Basic Research of Nanotechnologies and Nanomaterials”).

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Density Functional Theory Study on the Decay of Fullerenyl Radicals

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