While seminal works intended to reveal SOC effects on the bonding schemes
were discussed in term of spinors [9–13], canonical molecular spinors are not suited
for the bonding analysis in complex systems, as opposed to small and/or symmetric
model systems. Some have promoted the use of localized spinors [14], and in order
to recover some chemical significance in terms of bonding, lone pairs and core
orbitals, natural spinors similar to natural orbitals in the non-relativistic frameworks
have been derived and implemented [15, 16]. It is worth noting that the concept of
bond order in the context of multiconfigurational wave functions have been
extended recently to two-step spin-orbit coupling approaches [17].
Alternative strategies belonging to the Quantum Chemical Topology (QCT)
methodology are known for a long time in the field of non-relativistic quantum
calculations. They aim to answer general questions about the nature of chemical
bonds, the characterization of bonding schemes, reactivity and chemical reactions.
Among them, both the Quantum Theory of Atoms In Molecules (QTAIM) and the
topological analysis of the Electron Localization Function (ELF) have been
reviewed in numerous articles and books [3, 18–23]. Recently, some of us have
notably extended ELF and QTAIM analyzes in the field of quasirelativistic quantum
calculations [24, 25]. These tools should allow computational chemists to study
complex molecular systems for which the consideration of SOC is crucial. The
current chapter aims to demonstrate their power for probing the bonding in
heavy-atom systems. It is not only of fundamental interest, but it is also crucial for
applications of societal interest (e.g. nuclear medicine, energy production), or may
be related to environmental issues (e.g. in the context of nuclear waste management).
Indeed, in order to illustrate the originality of the proposed methodology, two
emblematic test cases have been selected: the At 2 species and the uranyl dication.
Astatine (At, Z = 85) is the heaviest naturally occurring halogen and one of its
longest-lived isotopes,
211 At, is of considerable interest in oncology as a radiotherapeutic agent for targeted alpha therapy [26]. While hypothetical, the At 2 species
is known for displaying spectacular SOC effects [9, 27–29]. In contrast, the second
selected At-species, AtO(OH) [30], might be involved in some of the labeling
protocols, if one looks closely at the experimental conditions (pH, E h ) [31], which
are currently developed for using
211 At in alpha-immunotherapy. Others interesting
systems are actinides complexes and especially those involving multiple bonds
[32–37]. The chemistry of the uranyl dication, UO 2
2+ , is to date more widely studied
by computational chemists than that of any other actinide. Indeed, the crucial role of
the uranyl dication during the uranium conversion stage in the nuclear fuel cycle has
brought for some decades the researchers attention on this species. Nevertheless,
much remains to be said about the bonding in UO 2
2+ . Among the various questions
that arise, regarding the selected systems, we focus especially on the following:
(1) What types of bond tend to establish heavy atoms and what are the factors
affecting the chemical bonding?
(2) How are depicted the SOC effects by means of QCT methodology?
(3) What is the influence of the selected computational model (methods, basis
sets) on QCT results when wave functions are built from spinors?
20 Quantum Chemical Topology in the Field …
555
were discussed in term of spinors [9–13], canonical molecular spinors are not suited
for the bonding analysis in complex systems, as opposed to small and/or symmetric
model systems. Some have promoted the use of localized spinors [14], and in order
to recover some chemical significance in terms of bonding, lone pairs and core
orbitals, natural spinors similar to natural orbitals in the non-relativistic frameworks
have been derived and implemented [15, 16]. It is worth noting that the concept of
bond order in the context of multiconfigurational wave functions have been
extended recently to two-step spin-orbit coupling approaches [17].
Alternative strategies belonging to the Quantum Chemical Topology (QCT)
methodology are known for a long time in the field of non-relativistic quantum
calculations. They aim to answer general questions about the nature of chemical
bonds, the characterization of bonding schemes, reactivity and chemical reactions.
Among them, both the Quantum Theory of Atoms In Molecules (QTAIM) and the
topological analysis of the Electron Localization Function (ELF) have been
reviewed in numerous articles and books [3, 18–23]. Recently, some of us have
notably extended ELF and QTAIM analyzes in the field of quasirelativistic quantum
calculations [24, 25]. These tools should allow computational chemists to study
complex molecular systems for which the consideration of SOC is crucial. The
current chapter aims to demonstrate their power for probing the bonding in
heavy-atom systems. It is not only of fundamental interest, but it is also crucial for
applications of societal interest (e.g. nuclear medicine, energy production), or may
be related to environmental issues (e.g. in the context of nuclear waste management).
Indeed, in order to illustrate the originality of the proposed methodology, two
emblematic test cases have been selected: the At 2 species and the uranyl dication.
Astatine (At, Z = 85) is the heaviest naturally occurring halogen and one of its
longest-lived isotopes,
211 At, is of considerable interest in oncology as a radiotherapeutic agent for targeted alpha therapy [26]. While hypothetical, the At 2 species
is known for displaying spectacular SOC effects [9, 27–29]. In contrast, the second
selected At-species, AtO(OH) [30], might be involved in some of the labeling
protocols, if one looks closely at the experimental conditions (pH, E h ) [31], which
are currently developed for using
211 At in alpha-immunotherapy. Others interesting
systems are actinides complexes and especially those involving multiple bonds
[32–37]. The chemistry of the uranyl dication, UO 2
2+ , is to date more widely studied
by computational chemists than that of any other actinide. Indeed, the crucial role of
the uranyl dication during the uranium conversion stage in the nuclear fuel cycle has
brought for some decades the researchers attention on this species. Nevertheless,
much remains to be said about the bonding in UO 2
2+ . Among the various questions
that arise, regarding the selected systems, we focus especially on the following:
(1) What types of bond tend to establish heavy atoms and what are the factors
affecting the chemical bonding?
(2) How are depicted the SOC effects by means of QCT methodology?
(3) What is the influence of the selected computational model (methods, basis
sets) on QCT results when wave functions are built from spinors?
20 Quantum Chemical Topology in the Field …
555