Question

I have read that rather than holding the static magnetic field constant and varying the frequency of the oscillating field in Electron Paramagnetic Resonance/Electron Spin Resonance (EPR/ESR) spectroscopy, the oscillating field is held constant while the static field varies in strength. I understand why this might be convenient for the purposes of physical implementation, but it seems to be that it would make it much harder to perform theoretically calculations of EPR structure (which is necessary to derive physical meaning from the results of the experiment). Specifically, if the spin Hamiltonian with external magnetic field strength B

is H(B)
, it seems to me that the following things are true:

If the static field B0 is held constant while the oscillating field B1 is varied, it seems like we can just calculate the eigenvalues of H(B0)
. Then, the resonant frequencies at which B1 is observed will correspond to transitions between these energy eigenvalues.
If the oscillating field B1 is held at constant frequency while the strength of the static field is varied, it seems that it would be necessary to find the eigenvalues of H(B0) for every possible field strength B0, so that one can check when the frequency of the oscillating field happens to align with one of the transition energies. This seems like it would require a massive amount of additional computational overhead.
So are my instincts correct - does calculating the frequency of EPR spectra require much more computation as a result of the experimental conventions? Or can anyone explain to me where I am confused?

Answer 1

In EPR/ESR spectroscopy, the oscillating field is held constant while the static field varies. This convention makes theoretical calculations more challenging, as finding eigenvalues of the spin Hamiltonian is required for various field strengths. This leads to additional computational overhead.

Step-by-step explanation:

In Electron Paramagnetic Resonance/Electron Spin Resonance (EPR/ESR) spectroscopy, the oscillating field is held constant while the static field varies in strength. This convention is primarily for the convenience of physical implementation.

However, it does make it more challenging to perform theoretical calculations. When the static field is held constant, one can calculate the eigenvalues of the spin Hamiltonian at that field strength. The resonant frequencies observed when the oscillating field is varied correspond to transitions between these energy eigenvalues.

On the other hand, if the oscillating field is held at a constant frequency while the strength of the static field is varied, it would indeed require finding the eigenvalues of the spin Hamiltonian for every possible field strength. This can introduce a significant amount of computational overhead.

Therefore, your instincts are correct that calculating the frequency of EPR spectra requires more computation when the experimental conventions are followed. However, these conventions are necessary for practical implementation.