DNPSOUP: A simulation software package for dynamic nuclear polarization

Non-perturbative treatment of the solid effect of dynamic nuclear polarization

In the solid effect of dynamic nuclear polarization (DNP), the concerted flips of the electronic and nuclear spins, which are needed for polarization transfer, are induced by the microwaves. Commonly, the effect of the microwaves is modeled by a rate process whose rate constant is determined perturbatively. According to quantum mechanics, however, the coherent microwave excitation leads to Rabi nutation, which corresponds to a rotation rather than a rate process. Here we reconcile the coherent effect of the microwaves with the description by rate equations by focusing only on the steady state of the spin dynamics. We show that the phenomenological rate constants describing the synchronous excitation of the electronic and nuclear spins can be selected such that the description by rate equations yields the same steady state as the exact quantum-mechanical treatment. The resulting non-perturbative rates differ from the classical, perturbative ones and remain valid also at the high microwave powers used in modern-day DNP. Our treatment of the solid effect highlights the role of the coherences in the mechanistic steps of polarization transfer and reveals the importance of the dispersive (i.e., out-of-phase) component of the EPR line. Interestingly, the multiplicative dependence of the DNP enhancement on the dispersive EPR component was intuited in the very first report of the solid effect in liquids . The time-domain description of the solid effect developed here is extendable to liquids, where the dipolar interaction changes randomly in time due to molecular diffusion.

Time domain DNP at 1.2 T

We present the results of an experimental pulsed DNP study at 1.2 T (33.5 GHz/51 MHz electron and 1H Larmor frequencies, respectively). The results include a comparison of constant-amplitude NOVEL (CA-NOVEL), ramped-amplitude NOVEL (RA-NOVEL) and the frequency-swept integrated solid effect (FS-ISE) experiments all of which were performed at the NOVEL matching condition, ω1S=ω0I, where ω1S is the electron Rabi frequency andω0I the proton Larmor frequency. To the best of our knowledge, this is the first pulsed DNP study carried out at field higher than X-band (0.35 T) using the NOVEL condition. A combination of high microwave power (∼150 W) and a microwave cavity with a high Q (∼500) allowed us to satisfy the NOVEL matching condition. We also observed stretched solid effect (S2E) contributions in the Zeeman field profiles when chirped pulses are applied. Furthermore, the high quality factor of the cavity limits the concentration of the radical to ∼5 mM and generates a hysteresis in the FS-ISE experiments. Nevertheless, we observe very high DNP enhancements that are comparable to the results at X-band. These promising outcomes suggest the importance of further studies at even higher fields that delineate the instrumentation and methods required for time domain DNP.