repulsion between the bonding electrons and the lone pairs, adjacent to the bond,
that have the same symmetry (σ in dihalogen molecules). It has been rationalized
that CSB originates primarily from LPBWE [99, 100]. Therefore, SOC leads to a
rise of CSB in the At 2 bond. The QTAIM analysis at the BCP provided in
Table 20.3 confirms these findings. When comparing scalar-relativistic and
quasirelativistic B3LYP/aug-cc-pVTZ-PP-2c calculations, ρ b is lowered by SOC
(−0.015 e bohr
−3 ), ∇
2
ρ b is slightly increased (+0.008 e bohr
−5 ) and the |V b |/G b ratio
decreases (−0.21). Each of these observations supports a weakening of the magnitude of covalency in the At 2 bond. Another striking example is the experimentally
identified AtCH 3 compound where spin-orbit coupling effects are able to increase
the CSB character of the At-C bond [25].
The robustness of QCT analyzes of the 2c-B3LYP/aug-cc-pVTZ-PP-2c wave
function has also been checked. Basis set incompleteness effects have been evaluated by replacing the aug-cc-pVTZ-PP-2c basis set by the much more flexible
aug-cc-pVQZ-PP-2c one. The effects related to the description of the electron
correlation have also been tested by changing the DFT functional for the M06-2X
and PBE0 ones. At first, we notice that the equilibrium distance, R e , is not much
modified (at most 3 % with M06-2X functional). Regarding the calculated values
reported in Tables 20.2 and 20.3, it is obvious that the populations of ELF basins
and QTAIM indicators are quite similar and the SOC effects on these properties (i.e.
ΔSO values) appear especially stable regardless of the computational model
(functional, basis set) used. No exception has been noticed. But more importantly
are the trends drawn from the numbers. Whatever is the retained level of theory,
previously outlined trends regarding the bond in At 2 are not changed at all by the
results of the further ELF and QTAIM analyzes. Thus, all our results lead to
non-ambiguous conclusions: the QCT methodology appears quite suitable to
underline SOC effects on the At 2 electronic structure.
20.3.2 AtO(OH) Species
At is a rare radioelement, i.e. it has no stable isotopes, and the longest-lived isotopes
can only be produced in trace quantities (<10
−8 g). Therefore, no spectroscopic
tools can be used and structural information lack in the literature for characterizing
the nature of At-bonds. Thus, quantum chemical methods represent a valuable tool
to shed light, at the molecular scale, on the chemistry of this “invisible” element.
The case of the closed-shell AtO(OH) species highlights this situation. This species
was recently identified as the product of the hydrolysis reaction of the AtO
+ cation.
The measured equilibrium constant, 10
−1.9 [30], is particularly impressive (indicating a strong interaction between AtO
+ and the involved water molecule). As
previously discussed [30], the hydrolysis constants published for other monocharged cations appear, in comparison, very weak. For instance, the values range
from 10
−13.21 for the spherical Tl
+ cation to 10
−4.65 for the much bigger MeHg
+
molecular cation. Does the bonding scheme in AtO(OH) can disclose strong
570
M. Amaouch et al.
that have the same symmetry (σ in dihalogen molecules). It has been rationalized
that CSB originates primarily from LPBWE [99, 100]. Therefore, SOC leads to a
rise of CSB in the At 2 bond. The QTAIM analysis at the BCP provided in
Table 20.3 confirms these findings. When comparing scalar-relativistic and
quasirelativistic B3LYP/aug-cc-pVTZ-PP-2c calculations, ρ b is lowered by SOC
(−0.015 e bohr
−3 ), ∇
2
ρ b is slightly increased (+0.008 e bohr
−5 ) and the |V b |/G b ratio
decreases (−0.21). Each of these observations supports a weakening of the magnitude of covalency in the At 2 bond. Another striking example is the experimentally
identified AtCH 3 compound where spin-orbit coupling effects are able to increase
the CSB character of the At-C bond [25].
The robustness of QCT analyzes of the 2c-B3LYP/aug-cc-pVTZ-PP-2c wave
function has also been checked. Basis set incompleteness effects have been evaluated by replacing the aug-cc-pVTZ-PP-2c basis set by the much more flexible
aug-cc-pVQZ-PP-2c one. The effects related to the description of the electron
correlation have also been tested by changing the DFT functional for the M06-2X
and PBE0 ones. At first, we notice that the equilibrium distance, R e , is not much
modified (at most 3 % with M06-2X functional). Regarding the calculated values
reported in Tables 20.2 and 20.3, it is obvious that the populations of ELF basins
and QTAIM indicators are quite similar and the SOC effects on these properties (i.e.
ΔSO values) appear especially stable regardless of the computational model
(functional, basis set) used. No exception has been noticed. But more importantly
are the trends drawn from the numbers. Whatever is the retained level of theory,
previously outlined trends regarding the bond in At 2 are not changed at all by the
results of the further ELF and QTAIM analyzes. Thus, all our results lead to
non-ambiguous conclusions: the QCT methodology appears quite suitable to
underline SOC effects on the At 2 electronic structure.
20.3.2 AtO(OH) Species
At is a rare radioelement, i.e. it has no stable isotopes, and the longest-lived isotopes
can only be produced in trace quantities (<10
−8 g). Therefore, no spectroscopic
tools can be used and structural information lack in the literature for characterizing
the nature of At-bonds. Thus, quantum chemical methods represent a valuable tool
to shed light, at the molecular scale, on the chemistry of this “invisible” element.
The case of the closed-shell AtO(OH) species highlights this situation. This species
was recently identified as the product of the hydrolysis reaction of the AtO
+ cation.
The measured equilibrium constant, 10
−1.9 [30], is particularly impressive (indicating a strong interaction between AtO
+ and the involved water molecule). As
previously discussed [30], the hydrolysis constants published for other monocharged cations appear, in comparison, very weak. For instance, the values range
from 10
−13.21 for the spherical Tl
+ cation to 10
−4.65 for the much bigger MeHg
+
molecular cation. Does the bonding scheme in AtO(OH) can disclose strong
570
M. Amaouch et al.