Density and wave function analysis of actinide complexes: what can fuzzy atom, atoms-in-molecules, Mulliken, Lowdin, and natural population analysis tell us?

Recent advances in computational methods have made it possible to calculate the wave functions for a wide variety of simple actinide complexes. Equally important is the ability to analyze the information contained therein and produce a chemically meaningful understanding of the electronic structure. Yet the performance of the most common wave function analyses for the calculation of atomic charge and bond order has not been thoroughly investigated for actinide systems. This is particularly relevant because the calculation of charge and bond order even in transition metal complexes is known to be fraught with difficulty. Here we use Mulliken, Lowdin, natural population analysis, atoms-in-molecules (AIM), and fuzzy atom techniques to determine the charges and bond orders of UO(2)(2+), PuO(2)(2+), UO(2), UO(2)Cl(4)(2-), UO(2)(CO)(5)(2+), UO(2)(CO)(4)(2+), UO(2)(CN)(5)(3-), UO(2)(CN)(4)(2-), UO(2)(OH)(5)(3-), and UO(2)(OH)(4)(2-). This series exhibits a clear experimental and computational trend in bond lengths and vibrational frequencies. The results indicate that Mulliken and Lowdin populations and bond orders are unreliable for the actinyls. Natural population analysis performs well after modification of the partitioning of atomic orbitals to include the 6d in the valence space. The AIM topological partitioning is insensitive to the electron donating ability of the equatorial ligands and the relative atomic volume of the formally U(VI) center is counterintuitively larger than that of O(2-) in the UO(2)(2+) core. Lastly, the calibrated fuzzy atom method yields reasonable bond orders for the actinyls at significantly reduced computational cost relative to the AIM analysis.