Denis Sh. Sabirov

Polarizability as a landmark property for fullerene chemistry and materials science

The review summarizes data on dipole polarizability of fullerenes and their derivatives, covering the most widespread classes of fullerene-containing molecules (fullerenes, fullerene exohedral derivatives, fullerene dimers, endofullerenes, fullerene ions, and derivatives with ionic bonds). These are currently presented by experimental and mainly theoretical works. Particular attention is paid to the analysis of the computational data in terms of additive schemes that assist in understanding the changes in polarizability upon fullerene functionalization and provide a general formula for calculation of polarizability for certain classes of the exohedral derivatives. Additionally, application of polarizability to the physical and chemical problems of fullerene science is discussed. It includes aspects of fullerene reactivity, physicochemical processes in carbon nanostructures (quenching of electronically-excited states, nanocapillarity, etc.) as well as use of fullerene adducts as electron-acceptor materials for organic solar cells and molecular switch devices.

Polarizability of C60 fullerene dimer and oligomers: the unexpected enhancement and its use for rational design of fullerene-based nanostructures with adjustable properties

The high polarizabilities of fullerene and its derivatives cause peculiarities in various physical and chemical processes in fullerene-containing systems. Their polarizabilities have been found to be efficient parameters for the design of nanostructures with desirable behavior. Unfortunately, the appropriate experimental data are scarce for most of the fullerene derivatives, due to their low availability or possible dissociation. At the same time, such information may be useful for C60-based nanotechnologies. We point our attention to the fullerene dimer and oligomers, which are novel and very promising compounds for nano-applications. We have performed the first density-functional theory study on the polarizability of fullerene derivatives (C60)n (n = 1–5) to elucidate how their structure affects the polarizability. In contrast to the concept of additivity, common in physical chemistry, the mean polarizability of (C60)n nonlinearly depends on the number of fullerene cores in their molecules, i.e. it violates the additivity. Similar to the other positive deviations from additive schemes, it has been called exaltation of polarizability. This effect is a result of the interaction of the π-electronic systems of fullerene cores in (C60)n and increases with their maximal remoteness. Experimental evidence of the exaltation is discussed. Thus, it agrees well with the enhancement of the polarizability of crystalline forms of C60 compared to molecular ones measured previously. Also, we have found a strong correlation between the calculated exaltations and the chemical properties of isomeric (C60)3, (C60)2 and its derivatives observed experimentally. The predicted enhancement has not been described previously and may be widespread among various nanostructures (for example, dimers of bowl-shaped hydrocarbons or other fullerenes). Insights into possible applications of the polarizability and its anisotropy to the molecular design and molecular machinery have been provided.

Polarizability of fullerene [2+2]-dimers: a DFT study

Currently, the exaltation of polarizability of (C60)2 dimers has been predicted with DFT-methods (D. Sh. Sabirov, RSC Adv., 2013, 3(42), 19430). It consists of an increase in the polarizability when two C60 molecules are united, forming a [2+2]-dimer. In the present work, we point attention to the bicage structures of the other fullerenes, which are promising compounds for nano-applications. We have performed the first density-functional theory study on the polarizability of fullerene [2+2]-dimers (Cn)2 (n = 20, 24, 30, 36, 50, and 70) and shown that the exaltation of polarizability is typical for all the members of the fullerenes family.

Influence of the charge on the volumes of nanoscale cages (carbon and boron-nitride fullerenes, Ge9z− Zintl ions, and cubic Fe4S4 clusters)

An algorithm for the calculation of the volume of polyhedral ions has been worked out. It is based on the partition of polyhedra into disjoint simplexes (triangular pyramids). The algorithm allows us to perform state-of-the-art calculations on the volumes of carbon and boron-nitride fullerenes and their ions. The general dependence of the volume of fullerene ions on their charge has been determined and described by quadratic correlations. Upon ion formation, carbon fullerenes (C60 and C70), obeying the isolated pentagon rule, show no dependence of the volumes change on the type of fullerene. Using this fact, we have predicted the volumes of giant C540 fullerene ions. Our approach is applicable to cage ions of another type that has been proved by analogous calculations of the volumes of Ge9z− ions and Fe4S4 clusters of the active sites of a ferredoxin protein. The present theoretical study demonstrates that general regularity of charges and volumes of nanoscale cages exists. It should be taken into account in the design of nanodevices and nanomaterials.

What Fullerene Is More Reactive Toward Peroxyl Radicals? A Comparative DFT Study on ROO• Addition to C60 and C70 Fullerenes

The structures of transition states and activation parameters of radical addition of tBuOO• and Ph(CH3)2COO• to the C60 and C70 fullerenes have been found by density functional theory method PBE/3ζ. Calculated by Eyring equation, the rate constants of the tBuOO• addition to C60 and C70, equal to 100 and 18.9 L mol−1 s−1, respectively; in the case of the Ph(CH3)2COO• addition, these are 14.5 and 17.7 L mol−1 s−1 (all reactions are in gas phase). The estimated inhibitor capacity of C60 equals to 3.7–5.3. According to calculated rate constants, C60 is more sensitive toward the structure of the peroxyls added. The calculated values agree with available experimental data on the reactions of these radicals with fullerenes. As follows from the calculated data, rate constants depend both on the nature of the fullerene and radical. The obtained data may be applied as reference values to the analysis of fullerene inhibition effect on the oxidation of organic compounds.

Activation energies and information entropies of helium penetration through fullerene walls. Insights into the formation of endofullerenes nX@C60/70 (n = 1 and 2) from the information entropy approach

In the present study, we calculate the activation barriers and information entropies of helium penetration into the C60 and C70 fullerenes resulting in the singly and doubly filled endofullerenes Hen@C60/70 (n = 1 and 2). The activation barriers of hexagon penetration of C60 and C70 are very high (∼900 kJ mol−1) and they slightly increase for the second insertion as compared to the first step. The activation parameters are linearly correlated with the squares of the penetrated hexagons. This allows the proposal that the other fullerene cages should reveal almost the same penetrability because the size of the hexagons do not significantly vary from one fullerene to another. We have found that the experimental ratios of the yields of He@C60/70 and He2@C60/70 (and the other related endofullerenes Nen@C70, (H2)n@C70, and NHe@C60/70) may be qualitatively described in terms of the information entropy approach using the respective changes in information entropy upon the formation of singly and doubly filled endofullerenes. This approach stresses the probabilistic nature of the penetration processes and may be used for qualitative prediction of the expected yields of endofullerenes with two encapsulated species.

Positional isomerism, stability, and polarizability of C20(CH2)n (n = 1–10), the cyclopropane adducts of the smallest fullerene: General formula for calculation of mean polarizability of fullerene derivatives C20XnYm and C60XnYm with fixed (n + m) number of different addends

ABSTRACT All regioisomers of fullerene adducts C20(CH2)n have been found and their stability and polarizability have been studied by the PBE/3ζ method. As in the case of the C60 and C70 adducts, mean polarizability of C20(CH2)n quadratically depends on the number of addends and demonstrates the depression, viz. negative deviation of polarizability from the linear additive scheme. Another, linear formula is proposed for calculating mean polarizability of the C20 and C60 fullerene adducts with mixed functionalization C20(CH2)nOm and C60(CH2)nOm and fixed number of addends. The obtained results will be further used to work out the algorithm for counting all possible C60Xn cycloadducts and searching a general formula for calculation of the C60XnYm polarizability with variable (n + m) number of addends.

Compression of Methane Endofullerene CH4@C60 as a Potential Route to Endohedral Covalent Fullerene Derivatives: A DFT Study

Two modes of CH4@C60 endofullerene compression have been studied by the PBE/3ζ method. According to the performed calculations, its compression in the direction of opposite hexagons or pentagons should lead to new endohedral covalent derivatives with methyl group or cyclopropane moiety respectively. Possibility of tuning the activation parameters by varying the trapped molecule has been shown theoretically. Endohedral covalent derivatives of C60 should have longer (and weaker) chemical bonds between the fullerene cage and endohedral addends in comparison with exohedral analogues. The obtained data may be used for the searching of synthetic paths to endohedrally functionalized fullerene derivatives, currently unknown.

A mechanistic study of manganese(III) acetate-mediated phosphonyl group additions to [60]- and [70]-fullerenes: the oxidative-ion-transfer mechanism vs. free radical addition

The phosphonylation of C60 with HP(O)(OAlk)2 and Mn(OAc)3·2H2O has been considered to occur via a free radical (FR) path involving intermediate radicals ˙P(O)(OAlk)2. The present study provides evidence in support of another mechanism for the reactions, oxidative-ion-transfer (OIT). The mechanism involves the change of an acetate group in Mn(OAc)3 for the phosphonate group and oxidation of C60 by the Mn(OAc)2P(O)(OAlk)2 formed to a pair: (C60˙+, Mn(OAc)2P(O)(OAlk)2˙-) followed by the transfer of the phosphonate anion to give the monophposphonylfullerenyl radical. It undergoes reversible dimerization. The polyaddition occurs analogously. Moreover, the compounds Mn(OAc)2P(O)(OAlk)2 (Alk = Et and i-Pr) obtained make novel reagents for phosphonylation of fullerenes working by the OIT mechanism. The reactions of C60 in benzene with equimolar amounts of Mn(OAc)2P(O)(OPr-i)2 or Hg[P(O)(OPr-i)2]2 which is known as working by the FR mechanism since it produces radical ˙P(O)(OPr-i)2 under UV-irradiation, furnished the same radical ˙C60P(O)(OPr-i)2. However, at a 20-fold molar excess of the reagent toward C60, a single derivative C60[P(O)(OPr-i)2]4 and a mixture of derivatives bearing between two and eight phosphonyls were obtained in the former and latter cases, respectively. With C70, the change of the mechanism produced a change in the regioselectivity: 5 and 3 isomers of ˙C70P(O)(OPr-i)2 were obtained, respectively. DFT-calculations provided the hyperfine coupling (hfc) constants of the isomers and explained the regioselectivity change.