New Strategies in Modeling Electronic Structures and Properties …
123
In actinide elements, the 5f electrons strongly interact with the remaining valence
electrons as well as with each other. This interaction implicates an electronic structure composed of many quasi-degenerate electronic configurations. Examples are
the 5f
n 7s
2 or 5f
n−1 6d7s
2 series of electronic configurations, where n represents
the number of electrons in the 5f shell and is defined as Z − 88, with Z being the
atomic number. These numerous energetically close-lying electronic configurations
are, however, of different character across the actinide series, which causes irregularities in the electronic ground and excited state energies of actinide elements.
Similar to transition metals, the highest (formal) oxidation state of the early
actinides equals the total number of electrons that can be removed from the valence
shell, that is, from the 6d and 5f atomic orbitals. Furthermore, the early actinides
resemble transition metals also in terms of orbitals and valence properties. The
main reason for the close resemblance of actinides and transition metals is that
the actinide 6d orbitals do participate in chemical bonding with other elements [102,
137]. Recently, Wilson et al. [164] observed the energetic crossing of the 5f and
6d atomic states for protactinium, making the protactinium atom a potential crossing point of valence properties that are characteristic for either transition metals or
actinides. Using quantum chemistry methods, the authors provided numerical evidence that both the 5f and 6d orbitals participate in the chemistry of Pa and that the
participation of the 5f orbitals increases for the middle actinides.
Unfortunately, experimental manipulations with actinide species are very limited,
primarily because most actinide atoms are unstable, feature a large number of various
oxidation states, or are radiotoxic. Despite these technical difficulties, experimental
actinide chemistry remains an active field of research that mainly focuses on molecular synthesis of compounds containing thorium and uranium as well as spectroscopic
studies of such compounds [5, 34, 42, 52, 53]. Due to these difficulties, theoretical
modeling of actinide-containing compounds can complement experimental studies
and provide the much sought-after insights into the physico-chemical properties of
actinide complexes and clusters, their reaction mechanisms, and thermochemistry.
However, theoretical modeling of actinide chemistry is challenging for present-day
quantum chemistry as our theoretical model has to account for (i) relativistic effects
and (ii) the correlated motion of electrons.
Due to the large atomic number present in actinide atoms, relativistic effects considerably affect the electronic structure of actinide-containing compounds and may
change the character of the principle configuration compared to calculations where
relativistic effects are ignored. For instance, the relativistic mass correction to the
core electrons causes the contraction of their corresponding orbital radii, while the
valence orbitals are expanded leading to elongated chemical bonds [6]. Furthermore,
spin-orbit interactions, which are comparable in magnitude to the electron-electron
repulsion energy, reduce the degeneracies of states with non-zero angular momentum [86]. To appropriately model the correlated motion of the electrons, our electronic
structure method has to include all degenerate or quasi-degenerate, low-lying elec-
123
In actinide elements, the 5f electrons strongly interact with the remaining valence
electrons as well as with each other. This interaction implicates an electronic structure composed of many quasi-degenerate electronic configurations. Examples are
the 5f
n 7s
2 or 5f
n−1 6d7s
2 series of electronic configurations, where n represents
the number of electrons in the 5f shell and is defined as Z − 88, with Z being the
atomic number. These numerous energetically close-lying electronic configurations
are, however, of different character across the actinide series, which causes irregularities in the electronic ground and excited state energies of actinide elements.
Similar to transition metals, the highest (formal) oxidation state of the early
actinides equals the total number of electrons that can be removed from the valence
shell, that is, from the 6d and 5f atomic orbitals. Furthermore, the early actinides
resemble transition metals also in terms of orbitals and valence properties. The
main reason for the close resemblance of actinides and transition metals is that
the actinide 6d orbitals do participate in chemical bonding with other elements [102,
137]. Recently, Wilson et al. [164] observed the energetic crossing of the 5f and
6d atomic states for protactinium, making the protactinium atom a potential crossing point of valence properties that are characteristic for either transition metals or
actinides. Using quantum chemistry methods, the authors provided numerical evidence that both the 5f and 6d orbitals participate in the chemistry of Pa and that the
participation of the 5f orbitals increases for the middle actinides.
Unfortunately, experimental manipulations with actinide species are very limited,
primarily because most actinide atoms are unstable, feature a large number of various
oxidation states, or are radiotoxic. Despite these technical difficulties, experimental
actinide chemistry remains an active field of research that mainly focuses on molecular synthesis of compounds containing thorium and uranium as well as spectroscopic
studies of such compounds [5, 34, 42, 52, 53]. Due to these difficulties, theoretical
modeling of actinide-containing compounds can complement experimental studies
and provide the much sought-after insights into the physico-chemical properties of
actinide complexes and clusters, their reaction mechanisms, and thermochemistry.
However, theoretical modeling of actinide chemistry is challenging for present-day
quantum chemistry as our theoretical model has to account for (i) relativistic effects
and (ii) the correlated motion of electrons.
Due to the large atomic number present in actinide atoms, relativistic effects considerably affect the electronic structure of actinide-containing compounds and may
change the character of the principle configuration compared to calculations where
relativistic effects are ignored. For instance, the relativistic mass correction to the
core electrons causes the contraction of their corresponding orbital radii, while the
valence orbitals are expanded leading to elongated chemical bonds [6]. Furthermore,
spin-orbit interactions, which are comparable in magnitude to the electron-electron
repulsion energy, reduce the degeneracies of states with non-zero angular momentum [86]. To appropriately model the correlated motion of the electrons, our electronic
structure method has to include all degenerate or quasi-degenerate, low-lying elec-