Energy of singlet state and triplet state

In summary: However, this explanation doesn't really make sense to me. Electrons with opposite spins can move freely, so why are they supposed to be less likely to stay away from each other in the triplet state?
  • #1
insanul
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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.
 

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  • #2
insanul said:
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.
 
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FAQ: Energy of singlet state and triplet state

What is the difference between the energy of singlet state and triplet state?

The energy of a singlet state is lower than that of a triplet state. This is because in a singlet state, the spins of the two electrons are paired, resulting in a lower overall energy. In a triplet state, the spins of the two electrons are unpaired, resulting in a higher overall energy.

How is the energy of singlet and triplet states affected by external magnetic fields?

The energy of a singlet state is not affected by external magnetic fields, as the paired spins do not interact with the field. However, the energy of a triplet state can be affected by external magnetic fields, as the unpaired spins interact with the field and can undergo energy transitions.

What is the role of electron spin in determining the energy of singlet and triplet states?

The energy of singlet and triplet states is determined by the spin states of the electrons in the system. In a singlet state, the spins are paired and have opposite directions, resulting in a lower overall energy. In a triplet state, the spins are unpaired and have the same direction, resulting in a higher overall energy.

How does the energy of singlet and triplet states affect the physical and chemical properties of molecules?

The energy of singlet and triplet states can affect the physical and chemical properties of molecules in various ways. For example, the difference in energy between the two states can determine the stability of a molecule, as well as its reactivity in different chemical reactions. Additionally, the energy of these states can also affect the color and fluorescence of molecules.

Can the energy of a singlet state be converted to a triplet state, and vice versa?

Yes, the energy of a singlet state can be converted to a triplet state through a process called intersystem crossing. This occurs when an excited electron in a singlet state transfers its energy to another electron, resulting in the formation of a triplet state. The reverse process, known as reverse intersystem crossing, can also occur, converting a triplet state back to a singlet state.

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