### Chemical Bonding and Interpretation of Time-Dependent Electronic
Processes with Maximum Probability Domains

### Andreas SAVIN

*Laboratoire de Chimie Théorique, CNRS, and Sorbonne Université, UPMC Univ Paris 06, 4 place Jussieu, F 75252 Paris cedex 05,
France.*

**Abstract:**

Tools have been designed obtain information about chemical bonds from quantum mechanical calculations.They work well for solutions of the stationary Schrödinger equation, but it is not clear whether Lewis electron pairs they aim to reproduce survive in time-dependent processes, in spite of the underlying Pauli principle being obeyed in this regime.
A simple model of two same-spin non-interacting fermions in a one-dimensional box with an opaque wall, is used to study this problem, because it allows presenting the detailed structure of the wave function. It is shown that
i) oscillations persisting after the Hamiltonian stopped changing produce for certain time intervals states where Lewis
electron pairs are spatially separated, and
ii) methods (like density analysis, or the electron localization function) that are widely used for describing bonding in the stationary case, have limitations in such situations. An exception is provided by
the maximum probability domain (the spatial domain that maximizes the probability to find a given number of particles in
it). It is conceptually simple, and satisfactorily describes the phenomenon.