The Shrödinger Equation & Hydrogen Molecule Bonding

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Discussion Overview

The discussion revolves around the bonding characteristics of the hydrogen molecule ion and the implications of the Schrödinger equation when applied to systems with varying numbers of protons and electrons. Participants explore the possibility of a single electron forming multiple bonds and the stability of molecular structures under different electron configurations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether a single electron can create two or more bonds, particularly in the context of the hydrogen molecule ion.
  • Another participant suggests that multiple bonds typically require multiple electrons, citing cyclohexane as an example, and expresses skepticism about the stability of a molecule with only one electron.
  • A further reply indicates that the removal of electrons from a molecule could lead to significant charge and instability, raising questions about theoretical proof for a system with one electron and two protons.
  • One participant proposes solving the Schrödinger equation as a method to analyze the stability of such systems, noting that H3+ is stable with two electrons.

Areas of Agreement / Disagreement

Participants express differing views on the ability of a single electron to form multiple bonds, with some skepticism regarding the stability of such configurations. The discussion remains unresolved regarding the theoretical implications of a single electron in bonding scenarios.

Contextual Notes

Participants do not reach a consensus on the stability of molecules with varying electron configurations, and there are unresolved assumptions regarding the application of the Schrödinger equation in these contexts.

Higgsono
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In the hydrogen molecule ion, one electron is responsible for the covalent bond between the atoms. But is it possible for one single elctron to create two bonds or more? What happens if we solve the Shrödinger equation for 3 protons and 1 electron?
 
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Higgsono said:
But is it possible for one single elctron to create two bonds or more?
You can have multiple bonds by multiple electrons, e. g. in cyclohexane. I would be surprised if removing all but one electrons from those bonds works - the molecule gets charged a lot which probably breaks the molecule.
 
mfb said:
You can have multiple bonds by multiple electrons, e. g. in cyclohexane. I would be surprised if removing all but one electrons from those bonds works - the molecule gets charged a lot which probably breaks the molecule.

Yes, I guess the molecule would be unstable. How would one go about proving this theoretically, in the case of one electron and two protons?
 
By solving the Schrödinger equation - or noting the absence of solutions in this case.

##H_3^+## is stable with two electrons.
 

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