New Strategies in Modeling Electronic Structures and Properties …
147
3. Select those orbitals where I i| j is above the threshold
4. Optimize the wave function for this correlation-based active space
5. Determine the corresponding orbital-pair mutual information
6. Compare the values of I i| j to those of the reference calculation in step 1. If the
small active space calculation can accurately reproduce the orbital-pair correlation
profile, the small active space can be considered as one optimal choice, otherwise
the acceptance threshold for I i| j has to be further reduced (for instance, to 10
−3 )
and steps 3–5 have to be repeated until convergence.
Although, such correlation-based active orbital spaces represent a step towards true
black-box MCSCF-type calculations, the selection criteria might have to be extended
so that they allow us to consider all orbitals important for bond-breaking processes
at all points of the dissociation pathway as the magnitude of orbital-pair correlations
might change along the reaction coordinate. However, technical limitations, like
stability of active space calculations, cannot be excluded and will restrict all automatic
active space selection protocols.
4 Challenging Examples in Computational Actinide
Chemistry
In the following, we briefly review some challenging case studies where computational chemistry allowed us to explain some peculiar or unexpected properties of
actinide-containing compounds.
4.1 Symmetric Dissociation of UO
2+
2
The uranyl cation is a small building block of plenty uranium-containing compounds [34, 51, 58]. This molecule is characterized by a linear geometry and a
singlet ground-state electronic structure. The energetically close lying 5f, 6d, and 7s
orbitals are crucial to describe the strongly-correlated valence electrons. In addition,
the uranium 6p orbitals are “pushed from below” by oxygen 2p electrons and thus
complicate the electronic structure as 6p orbitals are easily polarizable and mix with
5f orbitals [32, 33, 69, 100, 116, 117, 121, 122, 151, 152]. While the bonding
mechanism in UO
2+
2 is well described by single-reference CC theory for molecular
structures close to the equilibrium, conventional quantum chemistry methods, like
CCD, CCSD, CCSD(T), and DFT, usually fail for elongated U–O bonds. Furthermore, the CASSCF method does not allow us to define stable and consistent active
spaces along the whole dissociation pathway. Specifically for UO
2+
2 , a minimal active
space (CAS(12,12)SCF) around the equilibrium should contain all σ -, σ
∗ -, π -, and
π
∗ -orbitals as shown in Fig. 1a. For stretched U–O bonds, however, the φ u and δ u
orbitals become partially occupied and should be included in the active space (see
147
3. Select those orbitals where I i| j is above the threshold
4. Optimize the wave function for this correlation-based active space
5. Determine the corresponding orbital-pair mutual information
6. Compare the values of I i| j to those of the reference calculation in step 1. If the
small active space calculation can accurately reproduce the orbital-pair correlation
profile, the small active space can be considered as one optimal choice, otherwise
the acceptance threshold for I i| j has to be further reduced (for instance, to 10
−3 )
and steps 3–5 have to be repeated until convergence.
Although, such correlation-based active orbital spaces represent a step towards true
black-box MCSCF-type calculations, the selection criteria might have to be extended
so that they allow us to consider all orbitals important for bond-breaking processes
at all points of the dissociation pathway as the magnitude of orbital-pair correlations
might change along the reaction coordinate. However, technical limitations, like
stability of active space calculations, cannot be excluded and will restrict all automatic
active space selection protocols.
4 Challenging Examples in Computational Actinide
Chemistry
In the following, we briefly review some challenging case studies where computational chemistry allowed us to explain some peculiar or unexpected properties of
actinide-containing compounds.
4.1 Symmetric Dissociation of UO
2+
2
The uranyl cation is a small building block of plenty uranium-containing compounds [34, 51, 58]. This molecule is characterized by a linear geometry and a
singlet ground-state electronic structure. The energetically close lying 5f, 6d, and 7s
orbitals are crucial to describe the strongly-correlated valence electrons. In addition,
the uranium 6p orbitals are “pushed from below” by oxygen 2p electrons and thus
complicate the electronic structure as 6p orbitals are easily polarizable and mix with
5f orbitals [32, 33, 69, 100, 116, 117, 121, 122, 151, 152]. While the bonding
mechanism in UO
2+
2 is well described by single-reference CC theory for molecular
structures close to the equilibrium, conventional quantum chemistry methods, like
CCD, CCSD, CCSD(T), and DFT, usually fail for elongated U–O bonds. Furthermore, the CASSCF method does not allow us to define stable and consistent active
spaces along the whole dissociation pathway. Specifically for UO
2+
2 , a minimal active
space (CAS(12,12)SCF) around the equilibrium should contain all σ -, σ
∗ -, π -, and
π
∗ -orbitals as shown in Fig. 1a. For stretched U–O bonds, however, the φ u and δ u
orbitals become partially occupied and should be included in the active space (see