Simulation of coherence selection by pulsed field gradients in liquid-state NMR using an auxiliary matrix formalism

An algorithm for simulating coherence selection due to a pulse sequence element consisting of two pulsed field gradients separated by a short collection of pulses and delays is introduced. This algorithm involves computation of the matrix exponential of an auxiliary matrix twice the size of the system Liouvillian, a dimensional increase smaller than is required with other known computational methods. Approximations valid for most simulations of liquid-state NMR spectra are involved in the derivation. Diffusion is omitted, but could be treated in an approximate way as a damping over the pulse sequence element. Several NMR pulse sequences using gradients for coherence selection have been implemented, making use of the functionality of Spinach (http://spindynamics.org/Spinach.php). Example simulations testing these implementations are presented, and the extent to which the formal dimensional reduction can lead to a speedup in simulation time discussed. It is found that the previously known methods can be made competitive with the auxiliary matrix method by making use of their embarrassingly parallel nature. Cases where the relative dimensional reduction of the auxiliary matrix method is very large, or where efficient parallelization of the simulation independent of the nature of the algorithm used exists, are found to lead to situations beneficial for the auxiliary matrix algorithm in this comparison.