Computer simulation of multipulse and Fourier transform NMR experiments. IV. Some simulations including the time development of the off-diagonal density matrix elements

Abstract

The density matrix method has been used to simulate a number of multipulse and Fourier transform NMR experiments in which the time development of the off-diagonal diasity matrix elements (in the basis in which the Hamiltonian is diagonal) is important. The effects of the nonsecular elements in the relaxation matrix have been investigated, and these elements have been included in all the simulations where they are significant. The experiments simulated in this paper are the following. (a) The repetitively pulsed Fourier mode NMR experiment: Off-diagonal density matrix elements have not previously been included in a calculation of this type. As a result, the important phase effects in coupled spin systems are analysed for the first time. (b) The cw mode NMR experiment using a “time share” approximation: Calculations of the “time shared” spectra for coupled spin systems has not been considered before. (c) Carr-Purcell and modified Carr-Purcell pulse sequences, including Fourier transform spin echo spectroscopy and the simulation of J spectra: Realistic relaxation processes are included in the J spectra calculations. (d) The calculation and Fourier transformation of free induction decays. The examples presented in this paper are restricted to two-spin (AB) systems. However, the methods employed and the programs written in connection with this work can be applied to larger spin systems. As in earlier papers in this series the effects of intramolecular dipolar relaxation, external random field relaxation and mutual exchange are included in the relaxation matrices used.