  We investigate nuclear magnetic resonance (NMR) in near-zero-field, where the
Zeeman interaction can be treated as a perturbation to the electron mediated
scalar interaction (J-coupling). This is in stark contrast to the high field
case, where heteronuclear J-couplings are normally treated as a small
perturbation. We show that the presence of very small magnetic fields results
in splitting of the zero-field NMR lines, imparting considerable additional
information to the pure zero-field spectra. Experimental results are in good
agreement with first-order perturbation theory and with full numerical
simulation when perturbation theory breaks down. We present simple rules for
understanding the splitting patterns in near-zero-field NMR, which can be
applied to molecules with non-trivial spectra.
