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

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

**收稿日期:** 2017-09-1
**接受日期:** 2017-09-25

**Corresponding authors:**

**Received:** 2017-09-1
**Accepted:** 2017-09-25

**摘要**

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.

**关键词：**

**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.

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