If an atom such as hydrogen is able to form a covalent bond describe what happens when the electron shells of two atoms overlap?

Answer 1

Assuming both hydrogen atoms are in a singlet state (normal conditions for bonding):

The potential energy as the atoms are far away from each other is almost zero. As they approach each other, the potential energy decreases until it eventually reaches a minimum at about 0.746 Angstroms (7.46x10-11m) of separation with an energy of about -4.52eV. If they continue to approach each other, the potential energy increases steeply, and tends to infinite as the separation distance approaches zero.

For a triplet state, the potential energy is nearly zero at large separations, and increases as the separation distance decreases. It also tends to infinite as the separation distance approaches zero, more rapidly than the case above.

Answer 2

When the hydrogen atoms are far apart, the energy of their interaction is zero.

The potential energy required for bond formation is equal in magnitude to the bond-dissociation energy.

When the two atoms of approach each other, the two nuclei repel each other.