BONDING OF HYDROGEN ATOMS

We have reviewed the concepts of energy and position for electrons in isolated Hydrogen atoms. However, atoms seldom exist in isolation. Let’s study the bonding of Hydrogen atoms.

Hydrogen Atom

Let’s consider the two lowest energy levels for an electron in a Hydrogen atom.

The electron is going to be mostly in the lowest energy level.

Two Isolated Atoms

For two atoms that are far from each other and do not interact, the orbitals and energy levels for electrons in each atom are obviously going to stay the same.

Two Interacting Atoms

However, when we consider two atoms together, each energy state splits into two energy states called bonding and anti-bonding states.

See how energy splitting changes as you vary the separation between the two atoms.

Remember Pauli Exclusion principle states that in each energy state only two electrons can stay, one with spin down and one with spin up. This way, the bonding state can accommodate both of the two electrons of the two hydrogen atoms.

Probability Density Function

For an electron in a bonding state, the wavefunctions of the two orbitals interfere constructively in the middle. That means if you conduct many experiments to find the electron, in many cases you will find the electron between the two atoms.

This is the bonding state between the two 1s orbitals.

Antibonding

For an electron in an antibonding state, the wavefunctions of the two orbitals interfere destructively in the middle. That means if you conduct many experiments to find the electron you will rarely find the electron between the two atoms.

Energy Components

In a Hydrogen molecule, both electrons can be in the 1s bonding state whose energy decreases as the two atoms become closer. What about the total energy?





The attractions and repulsions between the charges also contribute to the total Energy.