Single-spin vector analysis of strongly coupled nuclei in TOCSY NMR experiments

This paper presents a new way to represent the effect of complex radio-frequency (rf) pulse sequences on J-coupled nuclear spin systems. The model uses a vector representation of the single-spin interactions (chemical-shift and rf interactions) and provides a simple route to gain analytical insight into multipulse NMR experiments. The single-spin Hamiltonian is expressed in an interaction representation as Fourier components. These Fourier components are combined for the two spins to establish the averaged coupling term of the Hamiltonian. This effective Hamiltonian is fast to calculate as only single-spin rotations are used and followed by simple summation of numbers for reconstruction of given coupling interactions. The present method is used to gain analytical insight into the performance of the J-coupling transfer sequence DIPSI-2 through two figures of merit (FOM) providing useful information for optimization of such pulse sequences. The first FOM (Ξ_AB) reports the efficiency of the desired total correlation spectroscopy transfer and should be as large as possible, while the second (Ξ_Het) reports the potential leakage of coherence to a heteronuclear spin and should be as small as possible.