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In this work, we describe essential tools of linear algebra necessary forcalculating the effect of chemical exchange on spin dynamics and polarizationtransfer in various nuclear magnetic resonance (NMR) experiments. We show howto construct Hamiltonian, relaxation, and chemical exchange superoperators inthe Liouville space, as well as demonstrate corresponding code in Python.Examples of applying the code are given for problems involving chemicalexchange between NH3 and NH4+ at zero and high magnetic field and polarizationtransfer from parahydrogen relevant in SABRE (signal amplification byreversible exchange) at low magnetic field (0-20 mT). The presented methodologyfinds utility for describing the effect of chemical exchange on NMR spectra andcan be extended further by taking into account non-linearities in the masterequation.

Essential Tools of Linear Algebra for Calculating Nuclear Spin Dynamics of Chemically Exchanging Systems