Simultaneous DNP enhancements of ¹H and ¹³C nuclei: Theory and experiments

DNP on heteronuclear spin systems often results in interesting phenomena such as the polarization enhancement of one nucleus during MW irradiation at the "forbidden" transition frequencies of another nucleus or the polarization transfer between the nuclei without MW irradiation. In this work we discuss the spin dynamics in a four-spin model system of the form {e_a-e_b-(¹H,¹³C)}, with the Larmor frequencies ω_a, ω_b, ω_H and ω_C, by performing Liouville space simulations. This spin system exhibits the common ¹H solid effect (SE), ¹³C cross effect (CE) and in addition high order CE-DNP enhancements. Here we show, in particular, the "proton shifted ¹³C-CE" mechanism that results in ¹³C polarization when the model system, at one of its ¹³C-CE conditions, is excited by a MW field at the zero quantum or double quantum electron-proton transitions ω_MW = ω_a ± ω_H and ω_MW = ω_b ± ω_H. Furthermore, we introduce the "heteronuclear" CE mechanism that becomes efficient when the system is at one of its combined CE conditions |ω_a - ω_b| = |ω_H ± ω_C|. At these conditions, simulations of the four-spin system show polarization transfer processes between the nuclei, during and without MW irradiation, resembling the polarization exchange effects often discussed in the literature. To link the "microscopic" four-spin simulations to the experimental results we use DNP lineshape simulations based on "macroscopic" rate equations describing the electron and nuclear polarization dynamics in large spin systems. This approach is applied based on electron-electron double resonance (ELDOR) measurements that show strong ¹H-SE features outside the EPR frequency range. Simulated ELDOR spectra combined with the indirect ¹³C-CE (iCE) mechanism, result in additional "proton shifted ¹³C-CE" features that are similar to the experimental ones. These features are also observed experimentally in ¹³C-DNP spectra of a sample containing 15 mM of trityl in a glass forming solution of ¹³C-glycerol/H₂O and are analyzed by calculating the basic ¹³C-SE and ¹³C-iCE shapes using simulated ELDOR spectra that were fitted to the experimental ones.