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A. Łachma´ nska et al.
also excited state) electronic structure, we have to account for both relativistic and
correlation effects on an equal footing. This poses a particular challenge for conventional electronic structure methods primarily because we have to deal with two
heavy-element centers.
The strong multi-reference nature of the neptunyl CCIs becomes evident when
we perform an orbital correlation analysis. The orbital-pair mutual information for
the ground-state of the diamond-shaped neptunyl CCI [NpO 2 ]
2+
2 is shown in Fig. 3b.
The correlation between orbital pairs is indicated by lines, while its strength is colorcoded: strong correlations are shown in blue, medium-sized correlations in red, etc.
Specifically for the diamond-shaped [NpO 2 ]
2+
2 , the σ g - and σ
∗
g -type orbitals are as
important as δ u - and φ u -type orbitals. Note that π -type orbitals are only moderately
correlated with each other. The orbital-correlation analysis, thus, suggests that a
balanced active space for neptunyl-containing CCIs that allows us to describe both
nondynamic and static correlation (or moderately and strongly correlated orbitals)
should contain approximately 30 orbitals (δ u -, φ u -, bonding and antibonding combinations of σ g -, σ u -, π u -, and π g -type orbitals of each monomer). However, such large
active spaces are difficult to handle with conventional multi-reference methods. In a
first approximation, we can consider active spaces where only the strongest orbitalpair correlations are accounted for, while the remaining correlations are treated a
posteriori using, for instance, perturbation theory. Such a study has been presented
recently in [86] and highlights the interplay of relativistic and correlations effects in
neptunyl CCIs.
5 Summary
This chapter reviewed different quantum chemistry approaches applicable to actinide
chemistry. Actinide-containing compounds are particularly challenging as both relativistic effects and correlation effects have to be accounted for on an equal footing.
Specifically, we have focused on the most common relativistic Hamiltonians and
wave-function-based methods that allow us to reliably model actinide chemistry.
Particularly interesting are novel and unconventional methods, like the DMRG algorithm or geminal-based approaches as they allow us to include a large number of
orbitals in active space calculations. This feature is desirable especially for multicentered actinide-containing compounds.
Our numerical examples show the strengths and pitfalls of present-day quantum chemistry methods when the systems under study contain one or more heavyelements. While DFT can accurately provide molecular geometries, wave-functionbased methods have to be applied to describe electronic structures of ground- and
excited-states. Furthermore, conventional methods like CASSCF fail in describing
potential energy surfaces for stretched actinide–ligand bonds. Such calculations can
only be accomplished using modern and unconventional methods like DMRG or
AP1roG.
A. Łachma´ nska et al.
also excited state) electronic structure, we have to account for both relativistic and
correlation effects on an equal footing. This poses a particular challenge for conventional electronic structure methods primarily because we have to deal with two
heavy-element centers.
The strong multi-reference nature of the neptunyl CCIs becomes evident when
we perform an orbital correlation analysis. The orbital-pair mutual information for
the ground-state of the diamond-shaped neptunyl CCI [NpO 2 ]
2+
2 is shown in Fig. 3b.
The correlation between orbital pairs is indicated by lines, while its strength is colorcoded: strong correlations are shown in blue, medium-sized correlations in red, etc.
Specifically for the diamond-shaped [NpO 2 ]
2+
2 , the σ g - and σ
∗
g -type orbitals are as
important as δ u - and φ u -type orbitals. Note that π -type orbitals are only moderately
correlated with each other. The orbital-correlation analysis, thus, suggests that a
balanced active space for neptunyl-containing CCIs that allows us to describe both
nondynamic and static correlation (or moderately and strongly correlated orbitals)
should contain approximately 30 orbitals (δ u -, φ u -, bonding and antibonding combinations of σ g -, σ u -, π u -, and π g -type orbitals of each monomer). However, such large
active spaces are difficult to handle with conventional multi-reference methods. In a
first approximation, we can consider active spaces where only the strongest orbitalpair correlations are accounted for, while the remaining correlations are treated a
posteriori using, for instance, perturbation theory. Such a study has been presented
recently in [86] and highlights the interplay of relativistic and correlations effects in
neptunyl CCIs.
5 Summary
This chapter reviewed different quantum chemistry approaches applicable to actinide
chemistry. Actinide-containing compounds are particularly challenging as both relativistic effects and correlation effects have to be accounted for on an equal footing.
Specifically, we have focused on the most common relativistic Hamiltonians and
wave-function-based methods that allow us to reliably model actinide chemistry.
Particularly interesting are novel and unconventional methods, like the DMRG algorithm or geminal-based approaches as they allow us to include a large number of
orbitals in active space calculations. This feature is desirable especially for multicentered actinide-containing compounds.
Our numerical examples show the strengths and pitfalls of present-day quantum chemistry methods when the systems under study contain one or more heavyelements. While DFT can accurately provide molecular geometries, wave-functionbased methods have to be applied to describe electronic structures of ground- and
excited-states. Furthermore, conventional methods like CASSCF fail in describing
potential energy surfaces for stretched actinide–ligand bonds. Such calculations can
only be accomplished using modern and unconventional methods like DMRG or
AP1roG.