[Paper Review] Direct Sensing of Remote Nuclei: Expanding the Reach of Cross-Effect Dynamic Nuclear Polarization

Amaria Javed, Asif Equbal|arXiv (Cornell University)|Sep 27, 2023

Advanced NMR Techniques and Applications4 citations

TL;DR

This paper proposes a novel biradical design with strong electron-electron coupling (hundreds of MHz) to enable direct, long-range polarization transfer in Cross-Effect Dynamic Nuclear Polarization (DNP), overcoming the distance limitations of conventional spin diffusion. The approach achieves efficient nuclear spin polarization transfer beyond 2.0 nm, significantly expanding DNP's reach for remote nuclei sensing in solid-state NMR.

ABSTRACT

Dynamic Nuclear Polarization (DNP) has revolutionized the field of solid-state NMR spectroscopy by significantly enhancing the sensitivity of nuclear magnetic resonance experiments. Conventionally, cross effect DNP relies on biradicals to transfer polarization from coupled electron spins to nearby nuclear spins and subsequent relay to target nuclei via spin diffusion mechanism. However, the direct transfer of polarization to distant nuclei remains a significant challenge, limiting its applicability in various contexts. In this work, we propose a novel biradical design concept that involves a very strong electron-electron coupling, with a magnitude of hundreds of MHz, which enables efficient direct polarization transfer from electron spins to nuclear spins over much longer distances, exceeding 2.0 nm. We discuss the potential of this tailored biradicals in scenarios where conventional spin diffusion mechanisms are inefficient or when direct nuclear spin sensing through electron spin interactions is desired. Our study presents a promising avenue for expanding the scope of cross effect DNP in solid-state NMR spectroscopy and opens new opportunities for investigating a wide range of biological and material systems. Our research also provides insight into the DNP buildup time of commercially available biradicals.

Motivation & Objective

• To overcome the distance limitation of conventional Cross-Effect DNP, which relies on spin diffusion and fails for remote nuclei.
• To enable direct polarization transfer from electron spins to nuclear spins at distances exceeding 2.0 nm.
• To develop a tailored biradical design with strong electron-electron coupling to enhance long-range DNP efficiency.
• To provide a solution for DNP applications in systems with slow or absent spin diffusion dynamics.
• To open new avenues for direct nuclear spin sensing and polarization transfer in biological and materials science.

Proposed method

• Employed quantum mechanical simulations in the Liouville space framework using the SPINEVOLUTION package to model DNP under magic-angle spinning.
• Simulated a system with two electrons (e₁, e₂) and one proton (¹H), using g-tensor values typical of nitroxide radicals.
• Varied the relative orientation of the g-tensors using Euler angles (z-y-z convention) to account for molecular flexibility.
• Maintained constant magnetic field (7 T), spinning frequency (10 kHz), microwave power (800 MHz), and temperature (100 K) for consistency.
• Systematically varied electron-nuclear hyperfine coupling strength by adjusting the e₁–H distance, while preserving orientation and spin parameters.
• Used experimentally derived relaxation times: T₁H = 2 s, T₁e = 2 ms, T₂e = 10 μs, to ensure realistic simulation conditions.

Figure 1 : Schematic illustrating the conventional DNP polarization transfer mechanism, utilizing the intricate spin diffusion network within the system. This network operates within the biradical, extends into the solvent, and further propagates to the target’s surface before penetrating its bulk.

Experimental results

Research questions

• RQ1 Can strong electron-electron coupling in biradicals enable direct DNP transfer to nuclei beyond the range of conventional spin diffusion?
• RQ2 How does the DNP buildup efficiency vary with increasing electron-nuclear distance when using a strongly coupled e-e system?
• RQ3 What is the optimal biradical design for maximizing long-range polarization transfer in Cross-Effect DNP?
• RQ4 To what extent can deuteration of nearby protons improve electron spin relaxation and thus enhance long-range DNP efficiency?
• RQ5 Can this approach enable direct polarization of ¹⁹F or ¹H nuclei in biological systems without requiring fluorinated solvents or biradicals?

Key findings

• Direct DNP transfer efficiency via conventional biradicals drops sharply with distance: from 450 enhancement at 5 Å to 120 at 10 Å, and below 10 at 20 Å under 7 T conditions.
• A strongly coupled electron pair (with e-e coupling in the hundreds of MHz range) enables efficient polarization transfer to nuclei beyond 2.0 nm, overcoming the limitations of conventional DNP.
• The proposed biradical design allows for direct polarization of remote nuclei, such as ¹H or ¹⁹F, even in the absence of a spin diffusion network.
• Deuteration of nearby hydrogen spins is predicted to extend electron spin-lattice relaxation time (T₁e), thereby improving DNP efficiency for long-range transfer.
• Biradicals optimized for short-range transfer (e.g., bis-nitroxides) are suboptimal for long-range transfer, indicating a need for distinct design principles.
• The method enables potential direct polarization of the bulk/core of materials, rather than just surface layers, expanding DNP’s applicability in materials and biological systems.

Figure 2 : Without a well-defined spin diffusion network, the enhancement of remote nuclei relies heavily on direct polarization transfer, indicated by the purple arrow. Quantum mechanical simulations of DNP reveal that using a conventional biradical ( $eeH$ spin system), the direct transfer to dist