  Signal Amplification By Reversible Exchange (SABRE) creates hyperpolarization
(large spin magnetization) using a transition metal catalyst and parahydrogen,
addressing the sensitivity limitations of magnetic resonance. SABRE and its
heteronuclear variant X-SABRE are simple, fast and general, but to date have
not produced polarization levels as large as more established methods. We show
here that inaccuracies in the theoretical framework for these applications,
which focuses on avoided crossings (also called level anti-crossings or LACs)
steer current SABRE and X-SABRE experiments away from optimal solutions.
Accurate simulations show astonishingly rich and unexpected dynamics in
SABRE/X-SABRE, which we explain with a combination of perturbation theory and
average Hamiltonian approaches. This theoretical picture predicts simple pulse
sequences with field values far from LACs (both instantaneously and on
average), using different terms in the effective Hamiltonian to strategically
control evolution and improve polarization transfer. Significant signal
enhancements under such highly non-intuitive conditions are verified
experimentally.
