Using the molecular orbital diagram as shown in the image attached to this answer, the hydrogen molecule anion can exist.
What is a molecular orbital diagram?
We define the molecular orbital diagram as the diagram that shows the way that the atoms of the elements are able to interact to form molecules. We know that the molecules are said to be formed by the combination of the atomic orbitals. The number of atomic orbitals that were combined is equal to the number of molecular orbitals that can be produced by the reaction.
Now we know that the two electrons of the hydrogen molecue woud be found in a bonding molecular orbital. As such, the added electron would have to go into an anti bonding molecular orbital. The bond order of the hydrogen molecule anion is then obtained as;
1/2( 2 - 1) = 0.5
The bond order is above zero thus the specie is able to exist.
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