A pictorial representation for multispin evolutions

Abstract

AbstractModern NMR techniques involve keeping track of the evolutions of two or more coupled spins. A new multivector representation adequate for visualizing such evolutions is presented. This representation can be put in one‐one correspondence with product operators, and has the advantage that it retains all possible orientations of each spin in the product operator. Thus, as the spins evolve, faithful pictures can be drawn both to indicate the directional change of the spins magnetizations and to deduce the detailed signals that arise from their evolution. The results are in full agreement with density matrix calculations. In particular, one can visualize multiple‐quantum coherence transfer. Evolutions due to chemical shift, J coupling, and the effect of radio frequency (rf) pulses are pictured. A simple heteronuclear chemical shift correlation pulse sequence is used to illustrate how the multivector representation can follow through a combination of spin evolutions and how the signals can be correctly deduced entirely from pictures without the need to refer to density matrix or operator algebra calculations.