  An unambiguous crystallographic structure solution for the observed phases
II-VI of high pressure hydrogen does not exist due to the failure of standard
structural probes at extreme pressure. In this work we propose that nuclear
magnetic resonance spectroscopy provides a complementary structural probe for
high pressure hydrogen. We show that the best structural models available for
phases II, III, and IV of high pressure hydrogen exhibit markedly distinct
nuclear magnetic resonance spectra which could therefore be used to
discriminate amongst them. As an example, we demonstrate how nuclear magnetic
resonance spectroscopy could be used to establish whether phase III exhibits
polymorphism. Our calculations also reveal a strong renormalisation of the
nuclear magnetic resonance response in hydrogen arising from quantum
fluctuations, as well as a strong isotope effect. As the experimental
techniques develop, nuclear magnetic resonance spectroscopy can be expected to
become a useful complementary structural probe in high pressure experiments.
