chemical bonds may vanish depending on the nature of the bonds. Here, trifling
effects were noticed on the mainly ionic At-O bonds of the AtO(OH) species, while
it was previously found in the AtCH 3 species that spin-orbit coupling effects are
able to increase the CSB character of the At-C bond [25]. Furthermore, the simplicity of the methodology is highlighted via another emblematic case. It is
acknowledged that all relativistic contributions must be included into calculations
on systems like the uranyl cation (i.e. containing heavy elements), but currently all
investigations on the UO 2
2+ chemical bonding are at best switched to a
scalar-relativistic level. This inconsistency is now over.
Beyond practical considerations regarding the understanding of heavy-elements
chemistry, this study has also demonstrated the robustness of QTAIM and ELF
topological analyzes in the quasirelativistic framework. Only small modifications
on the investigated descriptors, among which ELF basin populations, QTAIM
atomic charges, ρ b and ∇
2
ρ b , were found when changing between B3LYP, PBE0
and M06-2X functionals, or when moving from triple zeta basis sets to quadruple
ones. Future works will focus on extending the topological analyzes of other
functions of the electron density (Fukui functions, Non Covalent Index), as well as
the distributed electrostatic moments based on the ELF partition (DEMEP) analysis
[114], to the field of quasirelativistic quantum calculations.
Acknowledgements This work has been supported by grants funded by the French National
Agency for Research (ANR-2010-BLAN-0807), with “Investissements d’Avenir” (ANR-11EQPX-0004, ANR-11-LABX-0018).
References
1. Lewis GN (1916) The atom and the molecule. J Am Chem Soc 38(4):762–785
2. Linnett JW (1961) A modification of the Lewis-Langmuir octet rule. J Am Chem Soc
83(12):2643–2653
3. Bader RFW (1991) A quantum theory of molecular structure and its applications. Chem Rev
91(5):893–928
4. Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of
electron localization functions. Nature 371(6499):683–686
5. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and
molecular systems. J Chem Phys 92(9):5397–5403
6. Weinhold F (2002) Natural bond orbital methods. In: Encyclopedia of computational
chemistry, John Wiley & Sons, Ltd
7. Gillespie RJ, Bayles D, Platts J, Heard GL, Bader RFW (1998) The Lennard-Jones function:
a quantitative description of the spatial correlation of electrons as determined by the
exclusion principle. J Phys Chem A 102(19):3407–3414
8. Roos BO, Borin AC, Gagliardi L (2007) Reaching the maximum multiplicity of the covalent
chemical bond. Angew Chem Int Ed Engl 46(9):1469–1472
9. Visscher L, Dyall KG (1996) Relativistic and correlation effects on molecular properties.
I. The dihalogens F2, Cl2, Br 2, I2, and At2. J Chem Phys 104(22):9040–9046
10. Saue T, Faegri K, Gropen O (1996) Relativistic effects on the bonding of heavy and
superheavy hydrogen halides. Chem Phys Lett 263(3–4):360–366
20 Quantum Chemical Topology in the Field …
577
effects were noticed on the mainly ionic At-O bonds of the AtO(OH) species, while
it was previously found in the AtCH 3 species that spin-orbit coupling effects are
able to increase the CSB character of the At-C bond [25]. Furthermore, the simplicity of the methodology is highlighted via another emblematic case. It is
acknowledged that all relativistic contributions must be included into calculations
on systems like the uranyl cation (i.e. containing heavy elements), but currently all
investigations on the UO 2
2+ chemical bonding are at best switched to a
scalar-relativistic level. This inconsistency is now over.
Beyond practical considerations regarding the understanding of heavy-elements
chemistry, this study has also demonstrated the robustness of QTAIM and ELF
topological analyzes in the quasirelativistic framework. Only small modifications
on the investigated descriptors, among which ELF basin populations, QTAIM
atomic charges, ρ b and ∇
2
ρ b , were found when changing between B3LYP, PBE0
and M06-2X functionals, or when moving from triple zeta basis sets to quadruple
ones. Future works will focus on extending the topological analyzes of other
functions of the electron density (Fukui functions, Non Covalent Index), as well as
the distributed electrostatic moments based on the ELF partition (DEMEP) analysis
[114], to the field of quasirelativistic quantum calculations.
Acknowledgements This work has been supported by grants funded by the French National
Agency for Research (ANR-2010-BLAN-0807), with “Investissements d’Avenir” (ANR-11EQPX-0004, ANR-11-LABX-0018).
References
1. Lewis GN (1916) The atom and the molecule. J Am Chem Soc 38(4):762–785
2. Linnett JW (1961) A modification of the Lewis-Langmuir octet rule. J Am Chem Soc
83(12):2643–2653
3. Bader RFW (1991) A quantum theory of molecular structure and its applications. Chem Rev
91(5):893–928
4. Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of
electron localization functions. Nature 371(6499):683–686
5. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and
molecular systems. J Chem Phys 92(9):5397–5403
6. Weinhold F (2002) Natural bond orbital methods. In: Encyclopedia of computational
chemistry, John Wiley & Sons, Ltd
7. Gillespie RJ, Bayles D, Platts J, Heard GL, Bader RFW (1998) The Lennard-Jones function:
a quantitative description of the spatial correlation of electrons as determined by the
exclusion principle. J Phys Chem A 102(19):3407–3414
8. Roos BO, Borin AC, Gagliardi L (2007) Reaching the maximum multiplicity of the covalent
chemical bond. Angew Chem Int Ed Engl 46(9):1469–1472
9. Visscher L, Dyall KG (1996) Relativistic and correlation effects on molecular properties.
I. The dihalogens F2, Cl2, Br 2, I2, and At2. J Chem Phys 104(22):9040–9046
10. Saue T, Faegri K, Gropen O (1996) Relativistic effects on the bonding of heavy and
superheavy hydrogen halides. Chem Phys Lett 263(3–4):360–366
20 Quantum Chemical Topology in the Field …
577