interactions which can explain the peculiarity of the AtO
+ hydrolysis constant. The
structure of the AtO(OH) species, optimized at the 2c-B3LYP/aug-cc-pVTZ-PP-2c
level of theory, is presented in Fig. 20.7.
The At-O 1 distance, 1.953 Å, is close to the predicted bond length in the bare
AtO
+ cation, 1.930 Å [104], while the At-O 2 distance, 2.150 Å, is notably longer
and closer to the AtO bond length calculated for the AtOH species, 2.156 Å [25].
The At atom seems divalent and the α(O 1 AtO 2 ) valence angle, about 107.5°, argue
for a AX 2 E 2 type in VSEPR theory. Figure 20.7 also displays the ELF localization
domains. In addition to core basins, the ELF topology yields seven valence basins,
two V(At) basins accounting for At lone pairs, four V(O) valence basins and one
protonated basin, V(O, H). As in the case of the AtOH species [25], no V(At, O)
bonding basins were found. This outcome is usual for mainly ionic bonds. The
integrated ELF and QTAIM properties are presented in Table 20.4.
q(At) and q(O) atomic charges deserve a special attention: they are large (about
one unity or larger) and of opposite signs, as it could be expected for mainly ionic
bonds. The QTAIM descriptors at At-O BCPs, reported in Table 20.5, shows large
positive ∇
2
ρ b values consistent with closed-shell interactions between At and O
atoms.
Fig. 20.7 Optimized structure (left, distances in angstroms and angle in degrees) and ELF
localization domains (right, ELF = 0.8) of the AtO(OH) species at the 2c-B3LYP/
aug-cc-pVTZ-PP-2c level of theory. Color code magenta for core C(At) basin, red for valence
V(At) and V(O) basins and cyan for the protonated bonding V(O, H) basin
Table 20.4 ELF population analysis and QTAIM charges (e) calculated at various levels of
theory for the AtO(OH) species
C(At) + V(At) V(O 1 ) V(O 2 ) V(O 2 , H) q(At) q(O 1 ) q(O 2 )
2c-B3LYP/aug-cc-pVTZ-PP-2c
23.18
7.07
5.66
1.80
1.46 −0.91 −1.15
ΔSO
+0.08
−0.08 −0.08 +0.06
+0.01
0.00 −0.01
2c-B3LYP/aug-cc-pVQZ-PP-2c
23.07
7.17
5.65
1.82
1.49 −0.95 −1.13
2c-M06-2X/aug-cc-pVTZ-PP-2c 22.91
7.22
5.77
1.80
1.61 −1.01 −1.22
2c-PBE0/aug-cc-pVTZ-PP-2c
23.09
7.16
5.63
1.83
1.53 −0.97 −1.17
20 Quantum Chemical Topology in the Field …
571
+ hydrolysis constant. The
structure of the AtO(OH) species, optimized at the 2c-B3LYP/aug-cc-pVTZ-PP-2c
level of theory, is presented in Fig. 20.7.
The At-O 1 distance, 1.953 Å, is close to the predicted bond length in the bare
AtO
+ cation, 1.930 Å [104], while the At-O 2 distance, 2.150 Å, is notably longer
and closer to the AtO bond length calculated for the AtOH species, 2.156 Å [25].
The At atom seems divalent and the α(O 1 AtO 2 ) valence angle, about 107.5°, argue
for a AX 2 E 2 type in VSEPR theory. Figure 20.7 also displays the ELF localization
domains. In addition to core basins, the ELF topology yields seven valence basins,
two V(At) basins accounting for At lone pairs, four V(O) valence basins and one
protonated basin, V(O, H). As in the case of the AtOH species [25], no V(At, O)
bonding basins were found. This outcome is usual for mainly ionic bonds. The
integrated ELF and QTAIM properties are presented in Table 20.4.
q(At) and q(O) atomic charges deserve a special attention: they are large (about
one unity or larger) and of opposite signs, as it could be expected for mainly ionic
bonds. The QTAIM descriptors at At-O BCPs, reported in Table 20.5, shows large
positive ∇
2
ρ b values consistent with closed-shell interactions between At and O
atoms.
Fig. 20.7 Optimized structure (left, distances in angstroms and angle in degrees) and ELF
localization domains (right, ELF = 0.8) of the AtO(OH) species at the 2c-B3LYP/
aug-cc-pVTZ-PP-2c level of theory. Color code magenta for core C(At) basin, red for valence
V(At) and V(O) basins and cyan for the protonated bonding V(O, H) basin
Table 20.4 ELF population analysis and QTAIM charges (e) calculated at various levels of
theory for the AtO(OH) species
C(At) + V(At) V(O 1 ) V(O 2 ) V(O 2 , H) q(At) q(O 1 ) q(O 2 )
2c-B3LYP/aug-cc-pVTZ-PP-2c
23.18
7.07
5.66
1.80
1.46 −0.91 −1.15
ΔSO
+0.08
−0.08 −0.08 +0.06
+0.01
0.00 −0.01
2c-B3LYP/aug-cc-pVQZ-PP-2c
23.07
7.17
5.65
1.82
1.49 −0.95 −1.13
2c-M06-2X/aug-cc-pVTZ-PP-2c 22.91
7.22
5.77
1.80
1.61 −1.01 −1.22
2c-PBE0/aug-cc-pVTZ-PP-2c
23.09
7.16
5.63
1.83
1.53 −0.97 −1.17
20 Quantum Chemical Topology in the Field …
571