Question

What is orthogonalization energy when two atoms overlap?

Answer 1

In this paper, I read that:

When two atoms overlap, quantum mechanics dictates that they be orthogonal to each other. This drives up the energy and leads to so-called Pauli exclusion. The amount of energy that is driven up is defined as orthogonalization energy.

However, I learned when two atoms come close to each other, some 'molecule' which belongs to a certain point group will form. Thus, proper linear combinations of those atomic orbitals will be the basis of the irreducible invariant subspace of the point group. And these linear combinations are what we called molecular orbitals (MOs). Because of group orthogonality theorem, these MOs are orthogonal.

In this process, it seems there is not some orthogonalization energy, those MOs are orthogonal because of group theory.

On the other hand, I learned that the Pauli exclusion principle comes from the fact that wavefunctions of fermions are antisymmetric. However, it seems the orthogonalization energy is the cause of the Pauli exclusion principle.

Answer 2

$<b>In fact, the equal energy levels split up and become different so instead of one energy level in each atom you obtain two levels of energy of a compound system. It is easily seen in the first order of perturbation theory taking into account the atom interaction operator; thus these two states of the compound system become orthogonal due to belonging to different eigenstates with certain energies.$