Energy of singlet state and triplet state

[insanul]

Homework Statement

Energy of singlet state and triplet state

Relevant Equations

none

The picture shown below is one triplet state and one singlet excited state of molecular orbitals. According to Hund's Law, the triplet state, which has 2 electrons with parallel spin, has lower energy than the singlet state. I went through some papers, only to be told that the triplet state has lower energy because the electrons in triplet state tend to stay away from each other thus lessen the repulsion between them. However, none of the papers gave a clear explanation of why electrons with parallel spin are likely to stay away from each other while those with opposite spins can move freely, which I am very curious about.

 

[PeroK]

Homework Statement: Energy of singlet state and triplet state
Homework Equations: none

The picture shown below is one triplet state and one singlet excited state of molecular orbitals. According to Hund's Law, the triplet state, which has 2 electrons with parallel spin, has lower energy than the singlet state. I went through some papers, only to be told that the triplet state has lower energy because the electrons in triplet state tend to stay away from each other thus lessen the repulsion between them. However, none of the papers gave a clear explanation of why electrons with parallel spin are likely to stay away from each other while those with opposite spins can move freely, which I am very curious about.

The triplet state is symmetric, which implies that the spatial wavefunction associated with the electron pair is anti-symmetric.

The singlet state is anti-symmetric, which implies a symmetric spatial wavefunction.

(This is because the overall wavefunction + spin of a fermion must be anti-symmetric.)

If you look up "exchange forces", you will find that a symmetric spatial wavefunction leads to particles being closer together, and an anti-symmetric spatial wavefunction leads to particles being further apart.

That's why electrons in the singlet state are expected to be closer together than those in the triplet state.