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 $B_0$ is held constant while the oscillating field $B_1$ is varied, it seems like we can just calculate the eigenvalues of $H(B_0)$. Then, the resonant frequencies at which $B_1$ is observed will correspond to transitions between these energy eigenvalues.
- If the oscillating field $B_1$ 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 $H(B_0)$ for every possible field strength $B_0$, 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?
Best Answer
Yes in theory, while varying $B_0$ might initially seem more computationally intensive than varying B₁, modern EPR equipment and software have made both approaches relatively straightforward. The actual computational effort will often depend more on the sample's complexity and the desired precision than on the experimental convention chosen. EPR spectrometers use FPGAs which are specifically designed to do the mathematics quickly.
So in any EPR experiment we have two magnetic fields to consider:
$B_0$ is used to split the energy levels of the unpaired electrons due to the Zeeman effect. And since $B_1$ is applied perpendicular to $B_0$, it is used to induce the transitions between these energy levels of the electrons.
Considering $B_0$ is held constant while $B_1$ is varied:
You had this one correct. if $B_0$ is held constant, then we can calculate the eigenvalues of the spin Hamiltonian with that particular $B_0$. Once these energy levels are determined, $B_1$ is applied, and if its frequency matches resonance occurs and is detected as absorption in the EPR spectrum.
Considering $B_0$ is varied while $B_1$ is held constant:
In this case, as you vary $B_0$, the energy levels of the unpaired electrons change. If at any particular $B_0$ value, the energy difference between the two levels matches the frequency of the constant $B_1$, resonance will occur. The method of varying $B_0$ while keeping $B_1$ constant can be seen as a 'sweep' across different possible energy level differences, looking for a match with B₁.
This approach requires calculating the eigenvalues of the spin Hamiltonian for every value of $B_0$ to determine the corresponding resonant frequencies. Since you're "sweeping" through a range of B₀ values, this method might appear computationally intensive. But, in practice, modern EPR spectrometers and software tools are optimized for this, making the process efficient.
The complexity of the sample being studied usually matters more at influencing the computational effort. For instance, samples with multiple interacting spins or those where additional interactions (like spin-orbit coupling) are significant and can require more sophisticated computational models.