Sajith V Sadasivan (New York University Abu Dhabi, United Arab Emirates)
LinkedIn: @Sajith V Sadasivan; X: @v_sadasivan
Abstract: Nuclear Magnetic Resonance (NMR) spectroscopy, a key tool for probing molecular structure and dynamics, is fundamentally limited by the intrinsically low thermal polarization of nuclear spins, resulting in weak signal intensities. Dynamic Nuclear Polarization (DNP) enhances NMR sensitivity by transferring polarization from electron spins via microwave irradiation, yet it often demands cryogenic conditions and complex instrumentation. Photochemically induced DNP (photo-CIDNP) offers a promising, microwave-free alternative by exploiting optically generated spin polarization, with recent work using synthetic donor–chromophore–acceptor systems demonstrating significant 1H and 13C hyperpolarization in the solid state. Building on these advances, our present study expands the three-spin mixing (TSM) framework by establishing a generalized resonance condition valid across coupling regimes of radical pairs under both static and magic angle spinning (MAS) conditions. Through an operator-based effective Hamiltonian approach, it is shown that coherent singlet–triplet mixing, driven by hyperfine interactions, is central to the hyperpolarization mechanism through photo-CIDNP. Additionally, a Landau–Zener treatment captures the periodic level anti-crossings enabled by MAS, providing mechanistic insight into polarization transfer pathways. These findings offer critical guidance for optimizing photo-CIDNP transfer and rationally designing photoactive molecular systems for next-generation applications in biomedical imaging and materials characterization.
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Questions:
1. How do the polarization levels and build-up times you are seeing with photo-CIDNP compare to what’s typically achieved using microwave-driven DNP? Are there any trade-offs or unexpected advantages in Photo-CIDNP?
2. In developing the operator-based effective Hamiltonian model, what kinds of assumptions or simplifications did you have to make? And how do those choices affect the accuracy of your predictions?-
Dear Kshama,
Hope you are doing well. Thanks for your questions.
Please find the responses to your questions below.
1. How do the polarization levels and build-up times you are seeing with photo-CIDNP compare to what’s typically achieved using microwave-driven DNP? Are there any trade-offs or unexpected advantages in Photo-CIDNP?
Response: Photo-CIDNP achieves moderate polarization enhancements but offers faster build-up and the possibility of operating towards room temperature with simpler hardware and high‐field compatibility.
In De Biasi et al.’s experiments, the ¹H polarization builds up within seconds under continuous 450 nm laser irradiation. Please refer to https://doi.org/10.1021/jacs.4c06151 (Fig. 3). They obtained bulk NMR signal enhancements by factors of ∼100 at both 9.4 and 21.1 T for the 1H signal under MAS at 100 K. Since this is a non-thermal polarization, it’s not limited as in DNP (by a factor of ~660). It can be improved depending on radical chromophore efficiency and experimental conditions. Microwave DNP achieves larger enhancements but has slower build-up, higher complexity, and requires cryogenics.We have mentioned this in our article (Sec. III B): https://doi.org/10.1063/5.0265957. The perturbation strength, E1, responsible for three-spin mixing (TSM) at level crossings and net transition probabilities in photo-CIDNP can be compared to the three-spin flip process in the cross-effect DNP under MAS using Landau-Zener model. In photo-CIDNP, the corresponding perturbation term, which drives TSM, can be derived from the coefficients of the ZQ and DQ effective TSM Hamiltonian. For the cross-effect (CE), E1 is given by E1 = d*B/ωn. Please refer to https://doi.org/10.1063/1.4747449. E1 in CE DNP is weaker than in photo-CIDNP because, in CE, it is scaled down by the nuclear Larmor frequency, which increases significantly at high magnetic fields.
2. In developing the operator-based effective Hamiltonian model, what kinds of assumptions or simplifications did you have to make? And how do those choices affect the accuracy of your predictions?
Response: Our approach employs an operator-based theoretical framework to model the photo-CIDNP process in a three-spin system. This framework unifies Zeeman, hyperfine, and electron–electron (e–e) coupling interactions into a single effective Hamiltonian that governs the coherent dynamics driving three-spin mixing (TSM) and, ultimately, photo-CIDNP under zero- and double-quantum (ZQ/DQ) matching conditions.
To facilitate analytical treatment, we analyze the Hamiltonian within the separate α and β manifolds of the nuclear spin using polarization (or polar) operators. A fictitious zero-quantum operator is introduced for the electron spins (radical pair) to simplify the spin dynamics. We also perform a transformation into a tilted frame, aligning the effective rotation axis with the quantization (z) axis. This allows us to extract effective precession frequencies for the nuclear spin in the α and β manifolds, which appear on the right-hand side of the ZQ/DQ matching conditions. To further analyze nuclear hyperpolarization, we transform the tilted-frame Hamiltonian into the interaction frame, following the strategy used in CP and DNP frameworks. This yields generalized resonance conditions for both ZQ and DQ transitions.
Our model establishes these generalized matching conditions in a form that remains valid across all regimes of spin parameters, including variations in the g-tensor isotropic shift (Δ), electron–electron coupling strength (d), and hyperfine coupling constants (A and B). The resulting effective Hamiltonians introduce a dipolar scaling factor, which directly governs the rate of polarization transfer. An analytical solution for the time evolution of the density matrix under the effective Hamiltonian, along with the corresponding expression for the trace of the nuclear spin polarization ⟨Iz(t)⟩, reveals an intensity factor that defines the maximum achievable polarization. The total efficiency of nuclear hyperpolarization is determined by the interplay between this dipolar scaling and intensity factor, providing key insights into the rational design of photoactive sensitizer molecules and the optimization of experimental conditions for efficient photo-CIDNP. The excellent agreement between numerical simulations and analytical predictions under three distinct electron–electron coupling regimes—strong, intermediate, and weak—relative to Δ supports the reliability of our model and its ability to identify optimal conditions for three-spin mixing and photo-CIDNP. Overall, this study lays a robust theoretical foundation for optimizing nuclear polarization transfer in diverse photo-CIDNP applications.
For more detailed information, please refer to https://doi.org/10.1063/5.0265957 or contact us.
Thank you.
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Dear Sajith,
Yes, I’m doing well and hope you’re doing great too! Thank you for answering all the questions so thoroughly.-
Good to know! I’m also doing good.
You’re welcome.
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Hi Sajith, nice talk! I am excited to see Photo-CIDNP is improved under MAS conditions. I was wondering, how high in magnetic field can you do this technique, whether that is modified by going from static to MAS conditions, and what fields it is optimal.
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Hi Raj,
Thank you for the nice comment and thoughtful question.
Photo-CIDNP transfer under MAS relies on periodic anti-level crossings, which are governed by the matching conditions mentioned. MAS modulates the Hamiltonian terms periodically, which helps drive matching conditions repeatedly per rotor cycle, leading to better build-up and more uniform polarization (as compared to CE DNP as explained in Sec. IIIB, https://doi.org/10.1063/5.0265957). Under MAS, the effective fields can transiently match the conditions for efficient TSM, even if the static field would otherwise be unfavorable.
At low fields, nuclear Larmor frequencies (ωₙ) are small, so matching conditions are relatively easy to satisfy. At higher fields, ωₙ becomes large, and achieving the matching becomes more stringent. The efficiency of polarization transfer can drop if the anti-level crossings shift away from optimal conditions. Having said this, it’s not just B₀, but also the relative g-shift (Δg), e-e coupling, and anisotropic hyperfine terms that matter (which are the important factors appearing in the matching condition). With proper molecular design (e.g., adjusting Δg and couplings), photo-CIDNP can still work efficiently even at 9.4 T, 21.1 T, or possibly higher fields.
In De Biasi et al.’s recent experiments, they obtained bulk 1H NMR signal enhancements by factors of ~100 at both 9.4 and 21.1 T under MAS at 100 K using PhotoPol-S (as compared to their experiments at 0.3 T, yielding enhancement ~ 16 fold under STATIC conditions using Photopol). Please refer to https://doi.org/10.1021/jacs.4c06151 (Fig. 2) and https://doi.org/10.1021/jacs.3c03937 (Fig. 3). In this case, the matching conditions at 21.1 T are achieved by significantly increasing the e-e coupling from 5.5 MHz in PhotoPol to 570 MHz in PhotoPol-S by eliminating the spacer segment. Since the 1H hyperfine couplings in PhotoPol and PhotoPol-S are expected to be less than 50 MHz, there is less flexibility to adjust this as compared to e-e couplings towards higher fields.
Hope this answers your question.
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Thank you for your detailed response! That is very interesting, and makes sense to me–so it is harder to make it work at higher fields, but better molecular design can improve it. It’s very interesting to know that already there are some designs that work at 9.4 and even at 21.1 T up to 100x enhancement. I am excited to see such optimized molecular designs in the future!
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Same here!
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