Fig. 4. Occupation numbers for the active orbitals in molecules (A) 1 and (B) 2 . Black, blue, and red numbers correspond to CAS(7,7), CAS(11,9), and CAS(13,10) active spaces.

Natural Localized Molecular Orbitals (NLMOs)

Natural bond orbitals (NBO) is a well-known method to obtain the localized picture of the wavefunction. With the aid of NLMOs and bond orders the nature of the bond can be revealed. The Wiberg bond order, which does not recover differences between bonding and antibonding contributions in the natural atomic orbital (NAO) basis, is predicted to be 2.61 for both 1 and 2 complexes. The decomposition of this value into individual Bk–O contributions for each complex reveals that these two complexes are different (Table S5, ESI). Bk–OH bonds in complex 2 display the largest bond orders (ca.0.4), which implies that Bk–OCO3 bond orders are decreased in this complex with respect to complex 1 .
Further insight into these differences can be obtained through analysis of localized molecular orbital (LMO) bond orders because they allow the decomposition of the bond order into NLMOs contributions. Table 4 (decomposition per bond in Table S6, ESI) summarizes LMO bond orders including the main contributor to the bond order that corresponds to the σ-NLMO (Fig. 5). The overall values for Bk are 1.476 and 1.548 for 1 and 2 , respectively. Unlike Wiberg bond orders, these values differ from each other because LMO bond orders can discriminate between bonding and antibonding contributions, which make them more insightful into the strength of the bond. Nonetheless, the insight given by both is essentially the same, i.e. Bk–OH bonds display larger bond orders than Bk–OCO3. This picture agrees with the optimized bond distances (Table S1, ESI).
Table 4. Natural localized bond orders with the main σ-NLMOs contribution and their compositions.