Why don’t two electrons repel each other in a covalent bond?

This graphic will help you create a bond.

It illustrates the attractive potential of electrons and nuclei, and the repulsive potential of electron-electrons with nuclei-nuclei. This is a function the distance between two atoms.

The atoms at the beginning are separated (at a distance) and have their own energies. As they get closer, both the attractive forces between electrons (lowering their energy) and the repulsive force (increasing their energy) between nuclei and electrons (increasing their energy) start to act. The attractive potential increases until the total potential is exhausted (see the curve at the middle). This is the stable state, where the chemical bond has been formed. Further getting close is impossible because the repulsive potents sharply increase and hence the total energy.

At the minimum, there is no overlap of the valence orbitals

and the energies of the two atoms are split into bonding and anti-bonding energy levels;

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