Fullerenes, polycyclic aromatic hydrocarbons and their derivatives are carbon-rich compounds, whose molecules are constructed with sp2-carbon atoms [1]. The latter means their richness with remarkably responsive pi electrons. This feature makes fullerenes and PAHs promising for diverse nanotechnology and materials science applications. Meanwhile, the title compounds are currently known as one of the most widespread and survivable molecules of interstellar media. Thus, there is a fundamental interest in studying their properties. In this talk, we discuss computational studies on carbon-rich compounds focusing on their molecular properties, especially dipole polarizability. The corresponding numerical estimates allows predicting efficiency of the fullerene-containing organic solar cells, screening endo-atoms of endofullerene-implemented qubits, abundances of carbon-rich compounds under laboratory and environmental (space) conditions [2, 3]. A part of the report deals with the reactivity of the interiors of the endofullerenes under high pressures that might lead to a novel, currently unknown compounds [4]. The results obtaining with molecular dynamics simulations and quantum chemical methods are compared. Quantum chemical techniques and models of polarizability used in computational chemistry of fullerenes and PAHs, such as additive schemes and site-specific analysis, are discussed [5]. In the report, we focus on the minimum-polarizability principle that allows studying chemical dynamics beyond the energy estimates. This allowed us predicting non-planar helicenes under space conditions [6], which were further identified as the main compounds formed in circumstellar envelops of carbon stars. The found regularities are discussed in a tight conjunction with relevant experiments [2, 5, 7]. The current works of the authors are financially supported with the Russian Science Foundation (project number 22-13-20095). References 1. Sabirov D.Sh., Osawa E. J. Chem. Inf. Model. 2015, 55, 1576. 2. Sabirov D.Sh. RSC Adv. 2014, 4, 44996 (review). 3. Sabirov D.Sh. Fullerene Nanotube Carbon Nanostruct. 2020, 28, 71 (review). 4. Sabirov D.Sh. J. Phys. Chem. C 2013, 117, 1178. 5. Sabirov D.Sh., Tukhbatullina A.A. Nanomaterials 2022, 12, 4404. 6. Sabirov D.Sh., Garipova R.R., Cataldo F. Mol. Astrophys. 2018, 12, 10. 7. Sabirov D.Sh., Tukhbatullina A.A., Shepelevich I.S. ACS Earth Space Chem. 2022, 6, 1 (review).