The Shrödinger Equation & Hydrogen Molecule Bonding

In summary, the conversation discusses the possibility of a single electron creating multiple bonds in a molecule and the theoretical implications of this scenario. It is concluded that while multiple bonds can exist with multiple electrons, removing all but one electron would likely make the molecule unstable. This can be proven theoretically by solving the Schrödinger equation or noting the absence of solutions in this case.
  • #1
Higgsono
93
4
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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  • #2
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.
 
  • #3
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?
 
  • #4
By solving the Schrödinger equation - or noting the absence of solutions in this case.

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

1. What is the Schrödinger Equation and how does it relate to the Hydrogen Molecule Bonding?

The Schrödinger Equation is a fundamental equation in quantum mechanics that describes the behavior and properties of a quantum system. It is used to determine the wave function, which contains all the information about the system's energy, position, and momentum. The equation is used to study the bonding of two Hydrogen atoms to form a Hydrogen molecule.

2. How does the Schrödinger Equation explain the stability of the Hydrogen molecule?

The Schrödinger Equation predicts that the electrons in a Hydrogen molecule will have lower energy levels when they are bonded together compared to when they are separated. This lower energy state makes the Hydrogen molecule more stable, resulting in the formation of a covalent bond between the two atoms.

3. Can the Schrödinger Equation be used to study other molecules besides Hydrogen?

Yes, the Schrödinger Equation can be applied to any quantum system, including more complex molecules. However, as the number of atoms in a molecule increases, the mathematical complexity of the equation also increases, making it difficult to solve. Therefore, approximations and simplifications are often used to study larger molecules.

4. What is the significance of the quantum numbers in the Schrödinger Equation for Hydrogen molecule bonding?

The quantum numbers in the Schrödinger Equation for Hydrogen molecule bonding represent the energy levels and spatial distribution of the electrons in the molecule. These numbers determine the shape and stability of the molecule, as well as the energy required to break the covalent bond.

5. How does the Schrödinger Equation account for the repulsion of the two positively charged Hydrogen nuclei?

The Schrödinger Equation includes a term for the Coulomb repulsion between the two positively charged nuclei. This term contributes to the overall energy of the molecule, and its magnitude depends on the distance between the two nuclei. As the two nuclei move closer together, the repulsion term increases, making the molecule less stable. This is why there is a preferred distance between the two nuclei in a Hydrogen molecule.

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