ELF –

The LCT was the first to propose the topological study of the ELF function in the 2000s. The topmod09 suite is offered free of charge to the scientific community.

Bifurcation trees

The topological analysis of the electron localization function ELF provides a partition of the molecular space into basins of attractors which have a clear chemical signification. The hierarchy of these basins is given by the bifurcation of the localization domains.

In the case of π-donor substituents the aromatic domain is first opened close to the substituted carbon and then in the vicinity of the meta carbon; whereas for attractor substituents it is first opened in the ortho and para positions. The orienting effects of the electrophilic substitutions are correlated with these bifurcations. The experimental favored positions always correspond to the locally electronegative carbons (i.e., those which keep their shell structure at the higher ELF values). This suggests that the local Pauli repulsion plays a noticeable role in the orienting effects which are complementary to the charge transfer effect involved in standard quantum chemical pictures.

Isosurface of the ELF function (η(r)=0.65) for le toluene and nitrobenzene.

ELF in the Field of Quasirelativistic Quantum Calculations

It is acknowledged that the relativistic quantum treatments are mandatory when a molecule involves a heavy-element. Although it has been proved that the influence of the spin-orbit coupling (SOC) on the molecular structure or on bonding may be strong, the investigation of this relativistic effect on the electronic structure is rather difficult. Chemists are not familiar with the spinors, resulting from wave equations and that do not lend themselves easily to visualization (as they are complex vector functions). An alternative strategy to analyze quasirelativistic wave functions and bonding schemes have been proposed with the topological analysis of the electron density (QTAIM) and ELF. These approaches, well established in the nonrelativistic field for long time ago, have been recently extented to quasirelativistic field (2012, 2014). The combined density analysis provides a straightforward way to highlight the SOC effects on the classical chemical paradigms.