Question

I'm currently working on quantum chemistry with quantum machine learning and one of the operations considered for the calculation is the excitation (and desexcitation) of an electron from an orbital to the other (which corresponds mathematically to a Givens rotation).

So far, these excitations have been taken as spin-preserving, meaning that : say I have initially two electrons in the ground state orbital, if I excite one of them to the excited state, its spin won't be change. Apparently this is something common in quantum chemistry and I wanted to know why.

An argument I thought of was that the necessary energy to flip the spin of the electron is way higher than the typical electronic energy scale of the atom/molecule, hence making it impossible to flip.

Thank you for your response!

Answer 1

In quantum chemistry, excitations of electrons from one orbital to another are usually spin-preserving. This is because the necessary energy to flip the spin of an electron is usually higher than the typical electronic energy scale of atoms or molecules. The Pauli exclusion principle also supports this behavior, preventing two electrons in the same orbital from having the same set of quantum numbers.

Step-by-step explanation:

In quantum chemistry, the excitations of electrons from one orbital to another are usually taken as spin-preserving. This means that if one electron is excited to a higher energy state, its spin remains the same. This is because the necessary energy to flip the spin of an electron is typically higher than the typical electronic energy scale of atoms or molecules. Therefore, the spin of the electron remains unchanged during these excitations.

This spin-preserving behavior is a consequence of the Pauli exclusion principle, which states that no two electrons in the same atom can have exactly the same set of quantum numbers. The spin quantum number, which describes the intrinsic electron property called spin, can only have two values: +1/2 and -1/2. By having opposite spins, two electrons in the same orbital satisfy the Pauli exclusion principle. As a result, spin-flip excitations are energetically unfavorable and not commonly observed in quantum chemistry calculations.