20.2.5 Computational Details
Geometry optimizations and frequency calculations have been performed using the
quasirelativistic SODFT method, implemented in the NWChem program package
[44], prior to the topological analyzes. Energy-consistent relativistic PPs generated
by the Stuttgart/Cologne group for At and U atoms, namely ECP60MDF [90, 91],
were used for replacing the 60 core electrons. The explicit treatment of the
remaining electrons involved the aug-cc-pVXZ-PP-2c (X = T, Q) basis sets,
described in Ref. [92], for At and the quadruple zeta ANO basis set, described in
Ref. [91], for U. For the lighter atoms, H and O, we opted for the aug-cc-pVXZ
basis sets [93, 94]. The ANO and aug-cc-pVQZ basis sets were left fully uncontracted in computations on UO 2
2+ species to ensure proper description of the
semi-core atomic spinors. The applied density-functional approximations were the
popular PBE0 and B3LYP hybrid functionals, and the widely used M06-2X
meta-hybrid functional. For the sake of simplicity, the results of B3LYP calculations are first discussed and, if necessary, the deviations with respect to the two
other functionals are highlighted. In order to evaluate SOC effects on the studied
species, geometry optimizations (and frequency calculations) have been also done
at scalar-relativistic level through DFT calculations, in the absence of
spin-dependent potentials ( b
V SO ) into PPs. Afterward, new QTAIM and ELF
topological analyzes have been carried out. The SOC effects, ΔSO, are defined as
the difference between quasirelativistic and scalar-relativistic computed values.
Note that for all computations on linear species, the latters are aligned with the zaxis. All the topological analyses here presented have been carried out using
modified versions of the NWChem [44] and TopMod [89] program packages.
Isovalue curves and surfaces have been drawn using Molekel [95].
20.3 Probing the Nature of At-X Bonds (X = At, O)
20.3.1 At 2 Species
The At 2 species and other species containing At atom have brought the attention
mainly for testing the reliability of relativistic quantum mechanical methods [9, 28,
29, 92, 96, 97]. It came out notably that SOC strongly affects the properties of the
closed-shell At 2 species. Spectroscopic constants calculated at CCSD(T) level using
either the 4c Dirac-Coulomb Hamiltonian or an X2C Hamiltonian [9, 98], are
presented in Table 20.1.
The performances of our 2c-B3LYP/aug-cc-pVTZ-PP-2c computations seem
rather good: the calculated bond length (R e ), harmonic frequency (ω e ) and dissociation energy (D e ) deviate from the ones calculated at 4c-CCSD(T) level by less
than 1.5 % on average. A lesser agreement appears with 2c-CCSD(T) results and
mainly regarding the D e value, but the latter corresponds to an extrapolation to the
566
M. Amaouch et al.
Geometry optimizations and frequency calculations have been performed using the
quasirelativistic SODFT method, implemented in the NWChem program package
[44], prior to the topological analyzes. Energy-consistent relativistic PPs generated
by the Stuttgart/Cologne group for At and U atoms, namely ECP60MDF [90, 91],
were used for replacing the 60 core electrons. The explicit treatment of the
remaining electrons involved the aug-cc-pVXZ-PP-2c (X = T, Q) basis sets,
described in Ref. [92], for At and the quadruple zeta ANO basis set, described in
Ref. [91], for U. For the lighter atoms, H and O, we opted for the aug-cc-pVXZ
basis sets [93, 94]. The ANO and aug-cc-pVQZ basis sets were left fully uncontracted in computations on UO 2
2+ species to ensure proper description of the
semi-core atomic spinors. The applied density-functional approximations were the
popular PBE0 and B3LYP hybrid functionals, and the widely used M06-2X
meta-hybrid functional. For the sake of simplicity, the results of B3LYP calculations are first discussed and, if necessary, the deviations with respect to the two
other functionals are highlighted. In order to evaluate SOC effects on the studied
species, geometry optimizations (and frequency calculations) have been also done
at scalar-relativistic level through DFT calculations, in the absence of
spin-dependent potentials ( b
V SO ) into PPs. Afterward, new QTAIM and ELF
topological analyzes have been carried out. The SOC effects, ΔSO, are defined as
the difference between quasirelativistic and scalar-relativistic computed values.
Note that for all computations on linear species, the latters are aligned with the zaxis. All the topological analyses here presented have been carried out using
modified versions of the NWChem [44] and TopMod [89] program packages.
Isovalue curves and surfaces have been drawn using Molekel [95].
20.3 Probing the Nature of At-X Bonds (X = At, O)
20.3.1 At 2 Species
The At 2 species and other species containing At atom have brought the attention
mainly for testing the reliability of relativistic quantum mechanical methods [9, 28,
29, 92, 96, 97]. It came out notably that SOC strongly affects the properties of the
closed-shell At 2 species. Spectroscopic constants calculated at CCSD(T) level using
either the 4c Dirac-Coulomb Hamiltonian or an X2C Hamiltonian [9, 98], are
presented in Table 20.1.
The performances of our 2c-B3LYP/aug-cc-pVTZ-PP-2c computations seem
rather good: the calculated bond length (R e ), harmonic frequency (ω e ) and dissociation energy (D e ) deviate from the ones calculated at 4c-CCSD(T) level by less
than 1.5 % on average. A lesser agreement appears with 2c-CCSD(T) results and
mainly regarding the D e value, but the latter corresponds to an extrapolation to the
566
M. Amaouch et al.