Fig. 5. σ-type NLMOs for complexes 1 and 2 . Second and fourth NLMOs in third and fourth rows correspond to Bk–OH(1) and Bk–OH(2), respectively.

Topological analysis of the electron density

An alternative approach that provides further insight into the chemical bond is the Quantum Theory of Atoms in Molecules (QTAIM). Several theoretical studies on bonding in actinides have been reported, mainly by Kerridge,12–17 while only a few experimental18–22 studies have been reported. Studies devoted to the understanding of covalency in heavy actinides are scarce.19,21–23  The virtue of QTAIM is that the partition of the 3D space is said to be natural since no chemical intuition is required.
Our results indicate that complexes 1 and  2 present differences in bonding based on their topology. The homoleptic carbonate complex shows higher concentrations of electron density at the BCP than Bk–O carbonate bonds in 2 . This occurs as a compensation of strengthened Bk–OH bonds creating the polarization of the delocalized electron density. From the energy density approach,24we observe in Table S7 (see ESI) that all bonds present a certain covalent character due to V(r)/G(r) > 1 in all cases, implying negative values for the total energy density. The set of oxygen atoms lying in the xy plane (Table 5) present slightly larger HBCP(r) values (ca. 20 kJ mol-1 Å-3) than Bk–O(2) in the complex 2 , whereas the opposite is true for complex 1(ca. 5 kJ mol-1 Å-3 lower). On the other hand, Bk–OH bonds display significantly more negative total energy densities. Espinoza et al.25,26 discussed total energy densities as the balance between pressure applied by electrons around the BCP (potential energy) and the reaction contrary to that pressure applied by the electrons at the BCP (kinetic energy). In this context, covalency is observed in all Bk(IV) bonds due to stronger pressure applied by the electrons around the BCP.
Table 5. QTAIM average metrics. Electron densities are given in eÅ-3, energy densities in kJ mol-1Å-3, and energies in kJ mol-1. Extended table is found in ESI.