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†.