We have measured the total electron scattering cross sections of several NMR shift reagent molecules X(hfc)(3), where X = Yb, Er, Eu and Pr, by means of electron transmission spectroscopy (ETS) to determine their vertical attachment energies. A strong low-energy resonance (<1 eV) is observed in all of the compounds except for Yb(hfC)(3). We explain this anomaly in terms of the ground-state electron configuration of each molecule. Also, with the aid of restricted open-shell Hartree-Fock (ROHF) calculations on analogous molecules with truncated fluorocarbon chains, we have assigned specific normally unoccupied orbitals to the resonances observed in ETS. To our knowledge, these molecules are the largest for which this procedure has been successfully completed. Nolting et al. (J. Phys. B 1997, 30, 5491) have demonstrated that the above NMR shift reagents exhibit electron circular dichroism (ECD) between I and 10 eV. Using our new total cross section data, we comment on the possibility of resonance involvement in the generation of ECD.