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.