Level crossing analysis of chemically induced dynamic nuclear polarization: Towards a common description of liquid-state and solid-state cases

Abstract

Chemically Induced Dynamic Nuclear Polarization (CIDNP) is an efficient method of creating non-equilibrium polarization of nuclear spins by using chemical reactions, which have radical pairs as intermediates. The CIDNP effect originates from (i) electron spin-selective recombination of radical pairs and (ii) the dependence of the inter-system crossing rate in radical pairs on the state of magnetic nuclei. The CIDNP effect can be investigated by using Nuclear Magnetic Resonance (NMR) methods. The gain from CIDNP is then two-fold: it allows one to obtain considerable amplification of NMR signals; in addition, it provides a very useful tool for investigating elusive radicals and radical pairs. While the mechanisms of the CIDNP effect in liquids are well established and understood, detailed analysis of solid-state CIDNP mechanisms still remains challenging; likewise a common theoretical frame for the description of CIDNP in both solids and liquids is missing. Difficulties in understanding the spin dynamics that lead to the CIDNP effect in the solid-state case are caused by the anisotropy of spin interactions, which increase the complexity of spin evolution. In this work, we propose to analyze CIDNP in terms of level crossing phenomena, namely, to attribute features in the CIDNP magnetic field dependence to Level Crossings (LCs) and Level Anti-Crossings (LACs) in a radical pair. This approach allows one to describe liquid-state CIDNP; the same holds for the solid-state case where anisotropic interactions play a significant role in CIDNP formation. In solids, features arise predominantly from LACs, since in most cases anisotropic couplings result in perturbations, which turn LCs into LACs. We have interpreted the CIDNP mechanisms in terms of the LC/LAC concept. This consideration allows one to find analytical expressions for a wide magnetic field range, where several different mechanisms are operative; furthermore, the LAC description gives a way to determine CIDNP sign rules. Thus, LCs/LACs provide a consistent description of CIDNP in both liquids and solids with the prospect of exploiting it for the analysis of short-lived radicals and for optimizing the polarization level.

Magnetic field and orientation dependence of solid-state CIDNP

“…The pseudo-secular hyperfine term is required since the high-field approximation is violated for the nuclear spin. As a consequence, we recast the RP Hamiltonian as follows 12,[19][20][21] :…”

“…One should note that transition to the Liouville space requires dealing with matrices of higher dimensionality. Nonetheless, operations with super-matrices are straightforward, and highly optimized algorithms exist for computing matrix exponentials and for matrix inversion, so that the method proposed turns out to be more numerically efficient than the one we used earlier 12 .…”

“…As far as the interpretation of solid-state CIDNP is concerned, it usually considers a number of mechanisms, termed differential relaxation (DR), differential decay (DD) and three-spin mixing (TSM). Our recent paper 12 shows that one can look at CIDNP from a more general perspective of level crossing phenomena by associating the features in the field dependence to specific Level Crossings (LCs) and Level Anti-Crossings (LACs). By using this kind of description, we were able to obtain analytically positions of the features in the CIDNP field dependences and to derive the sign rules for polarization.…”

15N photo-CIDNP MAS NMR on both photosystems and magnetic field-dependent 13C photo-CIDNP MAS NMR in photosystem II of the diatom Phaeodactylum tricornutum

“…For the photo-CIDNP effect in the solid state, up to three mechanisms have been discovered to contribute to the spin-hyperpolarisation (Scheme 1): the three spin mixing (TSM), the differential decay (DD) and the differential-relaxation (DR) mechanisms (Jeschke 1998;McDermott et al 1998;Polenova and McDermott 1999;Prakash et al 2006;Sosnovsky et al 2016). Under typical conditions in bacterial RCs of Rhodobacter (R.) sphaeroides, the TSM mechanism leads to emissive NMR signals reaching their maximum if a matching of the nuclear Zeeman frequency with the coupling of two electron spins as a spin-correlated radical pair (SCRP) and the anisotropic hyperfine coupling with a nucleus occurs (Jeschke 1998).…”

Coherent manipulation of non-thermal spin order in optical nuclear polarization experiments

“…Such a treatment is inspired by the theoretical description of CIDNP (recently developed by some of us). 63 The idea of this method is based on the analysis of the spin dynamics at level crossings. 64 Finally, it is of interest to extend the present methodology from molecular crystals, where there is a single fixed orientation of the spin interaction tensors, to disordered media.…”