Fig. 3. Qualitative electronic states diagram considering ligand field (LF) effect after and before spin orbit coupling (SOC) in [Bk(CO3)4]4-.
However, for molecules 1 and 2 , our calculations show significant mixing between symmetry adapted molecular orbitals of the ligands and the 5f shell, and therefore the electronic structure for both compounds should be discussed in terms of molecular states instead. If the ligand field effect is considered first, the 2L+1 degenerate free-ion states split the ground 8A1that is then split again by spin orbit coupling giving rise to four E1/2 Kramer’s doublets. These states, additionally, have contributions from the 6A1 and4A1 states, which arise from the6P and 4D atomic states, respectively. Fig. 3 shows a qualitative diagram of the electronic states in which both analyses explained above are summarized.
The calculations considering the minimal active space CAS(7,7) partially reproduce the nature of the molecular electronic states and are more similar to a single-ion behavior. We also performed full relativistic 4-compontent multiconfigurational calculations (GRASP2018)8  on the Bk(IV) ion showing that the ground state of the unbound ion is composed by 85% 8S7/2(8S) + 13% 6P7/2(6P), and small contributions (less than 1%) from the 4D7/2.  A similar behavior is obtained by ligand-field DFT (LFDFT) (see Computational Details) with a wavefunction composed by 82% 8S7/2 + 16% 6P7/2 + 2% 4D7/2.  On the other hand, the ground state configuration of the free-ion was 90% 8S + 10% 6P at SOC-NEVPT2 with CAS(7,7) level of theory. The differences can be attributed to the limit of the NEVPT2 approach which can miss about 15-30% of the dynamical correlation effects9 (Table S2, ESI). It is important to note that 4-component multiconfiguration calculations also lack dynamical correlation.
For complexes 1 and 2 , at the same level of theory, the ground state configuration was 87% 8A1(8S) + 13% 6A1(6P) (Table S3). The difference with respect to the free ion can be related with a direct effect of the ligand field, which stabilizes the first spin-free excited sextet by ~1900 cm-1increasing the contribution of 6A1(6P) in the ground configuration.  A significant reduction in the octuplet nature of the ground state is seen within LFDFT, but similar in the stabilization of the sextet multiplet; with a composition of 69% 8A1(8S) + 23% 6A1(6P) + 4% 4A1(4D). In parallel, it is helpful to establish differences between the lanthanide analog isoelectronic to Bk(IV), Gd(III). The calculations of [Gd(CO3)4]5-reveal that the ground state 8S7/2 is almost degenerate (1.7 cm-1) because the mixing of the excited states into the ground term is negligible (100% 8S7/2) (Table S2, ESI). On the other hand, Bk(IV) either as a free-ion or as a complex, shows a totally different picture because of the stronger spin-orbit coupling that mixes the 6P7/2 with the 8S7/2 in the ground state (Table 2, and Tables S2-S5 in ESI). Additionally, the ligand field interaction produces a significant change of the ground state of the actinide ion. Because of the electron correlation, CAS(13,10), the ground spin-free 8A1 state is stabilized, and the four E1/2 Kramer’s doublets experience a reduction in their energies.  The configuration of the ground electronic state for 1  and 2 are 89% 8A1(8S) + 11% 6A1(6P) and 86% 8A1(8S) + 14% 6A1(6P), respectively (Table 2).
Table 2. Energies (cm-1) and composition of the electronic ground multiplet J = 7/2 relative to the ground state from a CAS(13,10) calculation. SO-CASSCF and SO-NEVPT2 differ in the dynamical energy correction by perturbation theory.