# Can we have molecular transitions that change multiplicity?

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• BillKet
In summary, the conversation discusses the possibility of molecular transitions that change the multiplicity of the electronic level, specifically for electric dipole and magnetic dipole. The Wigner-Eckart theorem can be used to study matrix elements of the spin tensor, and it shows that transitions between different multiplicities are possible if the spins differ by one. The possibility of transitions between different electronic terms of different multiplicities is also mentioned, with the mechanism for such transitions depending on the symmetries of the relevant molecular states.
BillKet
Hello! Can we have molecular transitions (not restricted to electric dipole) that change the multiplicity of the electronic level i.e. ##2S+1##. For electric dipole that is strictly forbidden. For magnetic dipole, we have a term in the operator of the form ##S\cdot B## and assuming the B is along the z-axis of the lab frame and after a bit of math we get a matrix element for this of the form:

$$<S' \Sigma'|T_q^1(S)|S \Sigma>$$
where I assumed Hund case a, and ##T_q^1(S)## is the spherical tensor representation of the operator S in the molecule frame. However this operator seem to act only on ##\Sigma##, while leaving S unchanged, which would imply that we can't change S by a dipole transition either. Is this the case? How can we change S? Thank you!

Even if the operator "seems to act" only on the projection quantum numbers ##\Sigma##, you still have the all-powerful Wigner-Eckart theorem at your disposal to study matrix elements of the form that you've written. For each spherical ##q##-component of the spin tensor ##\text{T}^{(1)}_{q}(\mathbf{S})## you have
$$\langle S' \Sigma'| \text{T}^{(1)}_{q}(\mathbf{S})|S \Sigma \rangle = (-1)^{S'-\Sigma'} \begin{pmatrix} S' & 1 & S\\ -\Sigma' & q & \Sigma \end{pmatrix} \langle S'|| \text{T}^{(1)}(\mathbf{S})||S \rangle \rm{,}$$
where the quantity on the rightmost hand-side is the reduced matrix element of the tensor, and due to the symmetry conditions imposed on the Wigner ##3j## symbol (namely, that the quantum numbers in its upper row satisfy the triangle rule for addition of angular momenta) you obtain that, in this case,
$$\Delta S \equiv S - S' = \pm 1 \rm{,}$$
which shows you that your tensor can connect multiplicity manifolds whose spins differ by one.

As for your first question regarding the possibility of transitions between different electronic terms of different multiplicities - of course such transitions are possible (one example is the oxygen ##A##-band - look it up if you want), but the mechanisms which "allow" for the change in multiplicity in the general case depend on the symmetries of the wave functions of the relevant molecular states between which such transitions can occur.

## 1. Can molecular transitions change the multiplicity of a molecule?

Yes, molecular transitions can change the multiplicity of a molecule. Multiplicity refers to the spin state of a molecule, which can be altered through various processes such as electron excitation or nuclear spin relaxation.

## 2. How do molecular transitions affect the properties of a molecule?

Molecular transitions can alter the electronic and magnetic properties of a molecule, which can have significant impacts on its chemical and physical behavior. For example, changes in multiplicity can affect the molecule's reactivity and stability.

## 3. What factors influence the likelihood of a molecular transition changing multiplicity?

The likelihood of a molecular transition changing multiplicity depends on several factors, including the molecule's electronic structure, the energy of the transition, and the presence of external influences such as magnetic fields or collisions with other molecules.

## 4. Can we control molecular transitions to change the multiplicity of a molecule?

Yes, we can control molecular transitions to change the multiplicity of a molecule through various techniques such as manipulating the molecule's environment or using external stimuli such as light or electric fields.

## 5. Are there any applications of molecular transitions changing multiplicity?

Yes, there are several applications of molecular transitions changing multiplicity, including in fields such as materials science, quantum computing, and spectroscopy. Understanding and controlling these transitions can also aid in the development of new technologies and materials.

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