| Summary: | <p>Simulating NMR experiments may appear mysterious and even
daunting for those who are new to the field. Yet, broken down into pieces,
the process may turn out to be easier than expected. Quite the opposite,
it is in fact a powerful and playful means to get insights into the spin
dynamics of NMR experiments. In this tutorial paper, we show step by step
how some NMR experiments can be simulated, assuming as little prior
knowledge from the reader as possible. We focus on the case of NMR at zero
and ultralow fields, an emerging modality of NMR in which the spin dynamics
are dominated by spin–spin interactions rather than spin–field interactions,
as is usually the case with conventional high-field NMR. We first show how to
simulate spectra numerically. In a second step, we detail an approach to
construct an eigenbasis for systems of spin-<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="4cd212bb5948f97dc54e7e1f631d7969"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mr-4-87-2023-ie00001.svg" width="20pt" height="14pt" src="mr-4-87-2023-ie00001.png"/></svg:svg></span></span> nuclei at
zero field. We then use it to interpret the numerical simulations.</p>
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