DFT Calculations of Structure and IR Spectra of Gd₂@C₈₂ Endofullerenes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...

UV–Visible absorption spectra of conjugated dienes arise from the lowest energy π → π* transitions. The light-absorbing part of the molecule is called the chromophore, and the substituents directly attached to the chromophore are called auxochromes. A strong correlation exists between the absorption maxima, λmax, and the structure of a conjugated π system. The Woodward–Fieser rules predict the value of λmax for a given structure by adding the contributions...

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...

Introduction
Conjugated dienes are compounds characterized by the presence of alternating double and single bonds. In a conjugated system like 1,3-butadiene, the unhybridized 2p orbital on each carbon overlaps continuously, allowing the π electrons to be delocalized across the entire molecule. In contrast, this type of overlap does not occur in cumulated and isolated dienes, such as 2,3-pentadiene and 1,4-pentadiene, respectively. Instead, the π electrons remain localized between the double...