The relationships between the electronic structures and the normal and inverse isotope effects in the electron–phonon interactions in charged cubane

Abstract

Electron–phonon coupling and possible normal and inverse isotope effects in the monoanion and cation of fully deuterated cubic cluster such as deutero-cubane (CD)8 are studied. The calculational results for charged deutero-cubane are compared with those for charged cubane. The calculated total electron–phonon coupling constants for the monoanion (lLUMO) and cation (lHOMO) of deutero-cubane are 0.631 and 0.777 eV, respectively. The lLUMO value increases much more significantly than the lHOMO value as a consequence of deuteration in cubane. Our calculational results show that inverse (normal) isotope effects as a consequence of full deuteration can be expected in the monoanion (monocation) of cubane. Significant phase patterns difference between the t1u lowest unoccupied molecular orbitals (LUMO) rather localized on carbon atoms and delocalized t2g highest occupied molecular orbitals (HOMO), and the larger displacements of carbon atoms in the Eg mode of 1072 cm−1 (ωD6) as a consequence of deuteration are the main reason for these results. The general relationships between the electronic structures and the normal and inverse isotope effects in superconductivity in charged molecular systems are discussed. We find from our calculations that inverse and no isotope effects as well as normal isotope effects are possible to be observed in molecular superconductivity if we assume that molecular superconductivity is caused by the electron–phonon interactions; the normal isotope effect in superconductivity would be observed when the atoms, the electron density on which is higher, are substituted by their heavier isotopes, while inverse and no isotope effects as well as normal isotope effects would be observed when the atoms, the electron density on which is lower, are substituted by their heavier isotopes. But the possibility that inverse isotope effect is observed is high in the latter case. Therefore, the electronic structures as well as the molecular weights are closely related to the isotope effects.