Ligand NMR Chemical Shift Calculations for Paramagnetic Metal Complexes: 5f¹ vs 5f² Actinides

Ligand paramagnetic NMR (pNMR) chemical shifts of the 5f¹ complexes UO₂(CO₃)₃^5- and NpO₂(CO₃)₃^4-, and of the 5f² complexes PuO₂(CO₃)₃^4- and (C₅H₅)₃UCH₃ are investigated by wave function theory calculations, using a recently developed sum-over-states approach within complete active space and restricted active space paradigm including spin-orbit (SO) coupling [J. Phys. Chem. Lett. 2015, 20, 2183-2188]. The experimental ¹³C pNMR shifts of the actinyl tris-carbonate complexes are well reproduced by the calculations. The results are rationalized by visualizing natural spin orbitals (NSOs) and spin-magnetizations generated from the SO wave functions, in comparison with scalar relativistic spin densities. The analysis reveals a complex balance between spin-polarization, spin and orbital magnetization delocalization, and spin-compensation effects due to SO coupling. This balance creates the magnetization due to the electron paramagnetism around the nucleus of interest, and therefore the pNMR effects. The calculated proton pNMR shifts of the (C₅H₅)₃UCH₃ complex are also in good agreement with experimental data. Because of the nonmagnetic ground state of (C₅H₅)₃UCH₃, the ¹H pNMR shifts arise mainly from the magnetic coupling contributions between the ground state and low-energy excited states belonging to the 5f manifold, along with the thermal population of degenerate excited states at ambient temperatures.