Using the PBE0/cc-pVDZ quantum chemical method, we calculated structural parameters, dipole moments, polarizabilities and the first hyperpolarizabilities beta of derivatives of dodecahedrane and buckminsterfullerene including two neighboring ethynyl groups in vacuum and in tetrahydrofuran (THF). The hyperpolarizability along the direction of the dipole moment is positive for C20H18(CCH)(2) and C20H18C(CCH)(2), but negative and relatively large for C-60(CCH)(2), C60C(CCH)(2), Kr@C-60(CCH)(2), and Kr@C60C(CCH)(2). Calculations by the PCM method predict increasing of dipole moments for C20H18(CCH)(2) and C20H18C(CCH)(2) molecules in polarizable medium and decreasing of the dipole moments for C-60(CCH)(2), C60C(CCH)(2), Kr@C-60(CCH)(2), and Kr@C60C(CCH)(2) in THF. Wavenumbers that characterize C-H bond vibrations after molecule transfer from vacuum into THF decrease by 16-17 cm(-1), while the corresponding intensities in the IR spectrum increase by factor 1.5.