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.

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.

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.

Currently, there is no common conception on the stability and achievability of fullerene isomers under the arc-discharge synthesis conditions. Different approaches operate with energetic, structural, and topological parameters of the fullerene molecules to explain why some fullerene isomers are more preferable than the others. In the present work, we have selected the most appropriate approaches based on topological roundness, information entropy, nuclear volumes, and sphericities and compared their predictions with the relevant experimental data on the C₈₄ fullerene isomers (obeying the isolated pentagon rule) and density functional theory estimates of their stability. We have found that the molecules of most stable (and most abundant) C₈₄ isomers have the minimal extremal roundness, maximal sphericity, and largest volume and vice versa. In the case of the information entropy, no correlation is observed. Interestingly, the found correlation between the volume and the stability of the C₈₄ isomers is unexpectedly inverse, i.e. more stable C₈₄ isomers have larger inner cavities inside, though traditionally large volume is associated with instability of hollow framework molecules. We assume that the large volumes allows enhancing the sphericity of the fullerene cages as we found the last one favoring the stability and the unstable C₈₄ fullerene cages having low volumes are far from the spherical shape. We think that the results obtained may be extrapolated to other fullerene isomeric sets and contribute to the understanding the grounds of the interconnection in the triad “topology – structure – energy” underlying structural chemistry.