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).

Basic applications of the information entropy concept to chemical objects are reviewed. These applications deal with quantifying chemical and electronic structures of molecules, signal processing, structural studies on crystals, and molecular ensembles. Recent advances in the mentioned areas make information entropy a central concept in interdisciplinary studies on digitalizing chemical reactions, chemico-information synthesis, crystal engineering, as well as digitally rethinking basic notions of structural chemistry in terms of informatics.

Currently, the purified higher C 60 fullerene adducts come into use as electron-acceptor materials in organic solar cells. As known, the number of regioisomeric structures grows up rapidly with the increase of the number of addends in C 60 derivatives. To make the computational description of their diversity, an accurate quantum chemical investigation of anisotropy of polarizability of C 60 higher adducts has been performed by the modern density functional theory method. The correlation between the calculated dihydronaphthyl-C 60 bisadducts anisotropies and the key output parameters of organic solar cells, based on them, has been found. The data on the higher fullerene adducts anisotropy may be useful to search for new fullerene-based electon-acceptor materials for organic solar cells.

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 C 60 -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 (C 60 ) 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 (C 60 ) 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 p-electronic systems of fullerene cores in (C 60 ) 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 C 60 compared to molecular ones measured previously. Also, we have found a strong correlation between the calculated exaltations and the chemical properties of isomeric (C 60 ) 3 , (C 60 ) 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.