Conformation of bis-nitroxide polarizing agents by multi-frequency EPR spectroscopy

Indirect Detection of the Protons in and around Biradicals and their Mechanistic Role in MAS-DNP

The contribution of protons in or near biradical polarizing agents in Dynamic Nuclear Polarization (DNP) has recently been under scrutiny. Results from selective deuteration and simulations have previously suggested that the role of protons in the biradical molecule depends on the strength of the electron-electron coupling. Here we use the cross effect DNP mechanism to identify and acquire 1H solid-state NMR spectra of the protons that contribute to propagation of the hyperpolarization, via an experimental approach dubbed Nuclear-Nuclear Double Resonance (NUDOR).

Rational Design of a Phosphorus-Centered Disbiradical

Phosphorus-centered disbiradicals, in which the radical sites exist as individual spin doublets with weak spin-spin interaction have not been known so far. Starting from monoradicals of the type [⋅P(μ-NTer)2 P-R], we have now succeeded in linking two such monoradical phosphorus centers by appropriate choice of a linker. To this end, biradical [⋅P(μ-NTer)2 P⋅] (1) was treated with 1,6-dibromohexane, affording the brominated species {Br[P(μ-NTer)]2 }2 C6 H12 (3). Subsequent reduction with KC8 led to the formation of the disbiradical {⋅[P(μ-NTer)]2 }2 C6 H12 (4) featuring a large distance between the radical phosphorus sites in the solid state and formally the highest biradical character observed in a P-centered biradical so far, approaching 100 %. EPR spectroscopy revealed a three-line signal in solution with a considerably larger exchange interaction than would be expected from the molecular structure of the single crystal. Quantum chemical calculations revealed a highly dynamic conformational space; thus, the two radical sites can approach each other with a much smaller distance in solution. Further reduction of 4 resulted in the formation of a potassium salt featuring the first structurally characterized P-centered distonic radical anion (5- ). Moreover, 4 could be used in small molecule activation.

Role of Protons in and around Strongly Coupled Nitroxide Biradicals for Cross-Effect Dynamic Nuclear Polarization

In magic angle spinning dynamic nuclear polarization (DNP), biradicals such as bis-nitroxides are used to hyperpolarize protons under microwave irradiation through the cross-effect mechanism. This mechanism relies on electron-electron spin interactions (dipolar coupling and exchange interaction) and electron-nuclear spin interactions (hyperfine coupling) to hyperpolarize the protons surrounding the biradical. This hyperpolarization is then transferred to the bulk sample via nuclear spin diffusion. However, the involvement of the protons in the biradical in the cross-effect DNP process has been under debate. In this work, we address this question by exploring the hyperpolarization pathways in and around bis-nitroxides. We demonstrate that for biradicals with strong electron-electron interactions, as in the case of the AsymPols, the protons on the biradical may not be necessary to quickly generate hyperpolarization. Instead, such biradicals can efficiently, and directly, polarize the surrounding protons of the solvent. The findings should impact the design of the next generation of biradicals.

AsymPol-TEKs as efficient polarizing agents for MAS-DNP in glass matrices of non-aqueous solvents

Two polarizing agents from the AsymPol family, AsymPol-TEK and cAsymPol-TEK (methyl-free version) are introduced for MAS-DNP applications in non-aqueous solvents. The performance of these new biradicals is rationalized in detail using a combination of electron paramagnetic resonance spectroscopy, density functional theory, molecular dynamics and quantitative MAS-DNP spin dynamics simulations. By slightly modifying the experimental protocol to keep the sample temperature low at insertion, we are able to obtain reproducable DNP-NMR data with 1,1,2,2-tetrachloroethane (TCE) at 100 K, which facilitates optimization and comparison of different polarizing agents. At intermediate magnetic fields, AsymPol-TEK and cAsymPol-TEK provide 1.5 to 3-fold improvement in sensitivity compared to TEKPol, one of the most widely used polarizing agents for organic solvents, with significantly shorter DNP build-up times of ∼1 s and ∼2 s at 9.4 and 14.1 T respectively. In the course of the work, we also isolated and characterized two diastereoisomers that can form during the synthesis of AsymPol-TEK; their difference in performance is described and discussed. Finally, the advantages of the AsymPol-TEKs are demonstrated by recording 2D 13C-13C correlation experiments at natural 13C-abundance of proton-dense microcrystals and by polarizing the surface of ZnO nanocrystals (NCs) coated with diphenyl phosphate ligands. For those experiments, cAsymPol-TEK yielded a three-fold increase in sensitivity compared to TEKPol, corresponding to a nine-fold time saving.

Multi Electron Spin Cluster Enabled Dynamic Nuclear Polarization with Sulfonated BDPA

Dynamic nuclear polarization (DNP) can amplify the solid-state nuclear magnetic resonance (NMR) signal by several orders of magnitude. The mechanism of DNP utilizing α,γ-bisdiphenylene-β-phenylallyl (BDPA) variants as Polarizing Agents (PA) has been the subject of lively discussions on account of their remarkable DNP efficiency with low demand for microwave power. We propose that electron spin clustering of sulfonated BDPA is responsible for its DNP performance, as revealed by the temperature-dependent shape of the central DNP profile and strong electron-electron (e-e) crosstalk seen by Electron Double Resonance. We demonstrate that a multielectron spin cluster can be modeled with three coupled spins, where electron J (exchange) coupling between one of the e-e pairs matching the NMR Larmor frequency induces the experimentally observed absorptive central DNP profile, and the electron T1e modulated by temperature and magic-angle spinning alters the shape between an absorptive and dispersive feature. Understanding the microscopic origin is key to designing new PAs to harness the microwave-power-efficient DNP effect observed with BDPA variants.

Polarizing agents for efficient high field DNP solid-state NMR spectroscopy under magic-angle spinning: from design principles to formulation strategies

Dynamic Nuclear Polarization (DNP) has recently emerged as a cornerstone approach to enhance the sensitivity of solid-state NMR spectroscopy under Magic Angle Spinning (MAS), opening unprecedented analytical opportunities in chemistry and biology. DNP relies on a polarization transfer from unpaired electrons (present in endogenous or exogenous polarizing agents) to nearby nuclei. Developing and designing new polarizing sources for DNP solid-state NMR spectroscopy is currently an extremely active research field per se, that has recently led to significant breakthroughs and key achievements, in particular at high magnetic fields. This review describes recent developments in this area, highlighting key design principles that have been established over time and led to the introduction of increasingly more efficient polarizing sources. After a short introduction, Section 2 presents a brief history of solid-state DNP, highlighting the main polarization transfer schemes. The third section is devoted to the development of dinitroxide radicals, discussing the guidelines that were progressively established to design the fine-tuned molecular structures in use today. In Section 4, we describe recent efforts in developing hybrid radicals composed of a narrow EPR line radical covalently linked to a nitroxide, highlighting the parameters that modulate the DNP efficiency of these mixed structures. Section 5 reviews recent advances in the design of metal complexes suitable for DNP MAS NMR as exogenous electron sources. In parallel, current strategies that exploit metal ions as endogenous polarization sources are discussed. Section 6 briefly describes the recent introduction of mixed-valence radicals. In the last part, experimental aspects regarding sample formulation are reviewed to make best use of these polarizing agents in a broad panel of application fields.

Designing broadband pulsed dynamic nuclear polarization sequences in static solids

Dynamic nuclear polarization (DNP) is a nuclear magnetic resonance (NMR) hyperpolarization technique that mediates polarization transfer from unpaired electrons with large thermal polarization to NMR-active nuclei via microwave (mw) irradiation. The ability to generate arbitrarily shaped mw pulses using arbitrary waveform generators allows for remarkable improvement of the robustness and versatility of DNP. We present here novel design principles based on single-spin vector effective Hamiltonian theory to develop new broadband DNP pulse sequences, namely, an adiabatic version of XiX (X-inverse X)-DNP and a broadband excitation by amplitude modulation (BEAM)-DNP experiment. We demonstrate that the adiabatic BEAM-DNP pulse sequence may achieve a ¹H enhancement factor of ∼360, which is better than ramped-amplitude NOVEL (nuclear spin orientation via electron spin locking) at ∼0.35 T and 80 K in static solids doped with trityl radicals. In addition, the bandwidth of the BEAM-DNP experiments (~50 MHz) is about three times the ¹H Larmor frequency. The generality of our theoretical approach will be helpful in the development of new pulsed DNP sequences.

DNPSOUP: A simulation software package for dynamic nuclear polarization

Dynamic Nuclear Polarization Simulation Optimized with a Unified Propagator (DNPSOUP) is an open-source numerical software program that models spin dynamics for dynamic nuclear polarization (DNP). The software package utilizes a direct numerical approach using the inhomogeneous master equation to treat the time evolution of the spin density operator under coherent Hamiltonians and stochastic relaxation effects. Here we present the details of the theory behind the software, starting from the master equation, and arriving at characteristic operators for any section of density operator time-evolution. We then provide an overview of the DNPSOUP software architecture. The efficacy of the program is demonstrated by simulating DNP field profiles on small spin systems exploiting both continuous wave and time-domain DNP mechanisms. Examples include Zeeman field profiles for the solid effect, Overhauser effect, and cross effect, and microwave field profiles for NOVEL, off-resonance NOVEL, the integrated solid effect, the stretched solid effect, and TOP-DNP. The software should facilitate a better understanding of the DNP process, aid in the design of optimized DNP polarizing agents, and allow us to examine new pulsed DNP methods at conditions that are not currently experimentally accessible, especially at high magnetic fields with high-power microwave pulses.

Spin-spin interaction and relaxation in two trityl-nitroxide diradicals

Trityl-nitroxides show substantial promise as polarizing agents in solid state dynamic nuclear polarization. To optimize performance it is important to understand the impact of spin-spin interactions on relaxation times of the diradicals. CW spectra and electron spin relaxation were measured for two trityl-nitroxides that differ in the substituents on the amide linker and have different strengths of the exchange interaction J. Analysis of the EPR spectra in terms of overlapping AB spin-spin splitting patterns explains the impact of J on various regions of the spectra. Even modest values of J are large relative to the separation between trityl and nitroxide resonances for some nitrogen nuclear spin state. Two conformations for each diradical were observed in CW spectra in fluid solution at X-band and Q-band. For one diradical J = 15 G (83%) and 5 G (17%) at 293 K, and J = 27 G (67%) and 3 G (33%) with interspin distances of 16 Å and 12 Å, respectively, at 80 K. For the second diradical the exchange interaction is stronger: the two conformations in fluid solution at 293 K had J = 113 G (67%) and 59 G (33%) and at 80 K the value of J was 43 G and there were two conformations with interspin distances of 13 and 11.5 Å. The observation of two conformations for each diradical, with different values of J, demonstrates the dependence of their exchange interactions on through-bond orbital interactions. X-band values of spin relaxation rates 1/T₁ and 1/T_m at 80 to 120 K for the trityl-nitroxides are similar to values for nitroxide mono-radicals, and faster than for trityl radicals. These observations show that even for a relatively small value of J, the nitroxide is very effective in enhancing the relaxation of the more slowly relaxing trityl.

Role of electron spin dynamics and coupling network in designing dynamic nuclear polarization

Dynamic nuclear polarization (DNP) has emerged as a powerful sensitivity booster of nuclear magnetic resonance (NMR) spectroscopy for the characterization of biological solids, catalysts and other functional materials, but is yet to reach its full potential. DNP transfers the high polarization of electron spins to nuclear spins using microwave irradiation as a perturbation. A major focus in DNP research is to improve its efficiency at conditions germane to solid-state NMR, at high magnetic fields and fast magic-angle spinning. In this review, we highlight three key strategies towards designing DNP experiments: time-domain "smart" microwave manipulation to optimize and/or modulate electron spin polarization, EPR detection under operational DNP conditions to decipher the underlying electron spin dynamics, and quantum mechanical simulations of coupled electron spins to gain microscopic insights into the DNP mechanism. These strategies are aimed at understanding and modeling the properties of the electron spin dynamics and coupling network. The outcome of these strategies is expected to be key to developing next-generation polarizing agents and DNP methods.

o-Semiquinone radical anion isolated as an amorphous porous solid

The use of metal cations is a commonly applied strategy to create S > 1/2 stable molecular systems containing semiquinone radicals. Persistent mono-semiquinonato complexes of diamagnetic metal ions (S = 1/2) have been hitherto less common and mostly limited to the complexes of heavy metal ions. In this work, a mono-semiquinonato complex of aluminum, derived from 1,2-dihydroxybenzene, is obtained using a surprisingly short and uncomplicated procedure. The isolated product is an amorphous and porous solid that exhibits very good stability under ambient conditions. To characterise its molecular and electronic structure, 9.7, 34 and 406 GHz EPR spectroscopy was used in concert with computational techniques (DFT and DLPNO-CCSD). It was revealed that the radical complex is composed of two chemically equivalent aluminum cations and two catechol-like ligands with the unpaired electron uniformly distributed between the two organic molecules. The good stability and porous structure make this complex applicable in heterogeneous aerobic reactions.

The distance between g-tensors of nitroxide biradicals governs MAS-DNP performance: The case of the bTurea family

Bis-nitroxide radicals are common polarizing agents (PA), used to enhance the sensitivity of solid-state NMR experiments via Magic Angle Spinning Dynamic Nuclear Polarization (MAS-DNP). These biradicals can increase the proton spin polarization through the Cross-Effect (CE) mechanism, which requires PAs with at least two unpaired electrons. The relative orientation of the bis-nitroxide moieties is critical to ensure efficient polarization transfer. Recently, we have defined a new quantity, the distance between g-tensors, that correlates the relative orientation of the nitroxides with the ability to polarize the surrounding nuclei. Here we analyse experimentally and theoretically a series of biradicals belonging to the bTurea family, namely bcTol, AMUPol and bcTol-M. They differ by the degree of substitution on the urea bridge that connects the two nitroxides. Using quantitative simulations developed for moderate MAS frequencies, we show that these modifications mostly affect the relative orientations of the nitroxide, i.e. the length and distribution of the distance between the g-tensors, that in turn impacts both the steady state nuclear polarization/depolarization as well as the build-up times. The doubly substituted urea bridge favours a large distance between the g-tensors, which enables bcTol-M to provide ∊_on/off>200 at 14.1 T/600 MHz/395 GHz with build-up times of 3.8 s using a standard homogenous solution. The methodology described herein was used to show how the conformation of the spirocyclic rings flanking the nitroxide function in the recently described c- and o-HydrOPol affects the distance between the g-tensors and thereby polarization performance.

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.

Application of Multi-Slice Spiral CT in the Evaluation of Diffuse Lung Diseases

This article analyzes the manifestations, characteristics, and significance of multi-slice spiral CT for diffuse lung disease, and evaluates the diagnostic value of multi-slice CT multi-directional reconstruction for diffuse lung disease. After performing multi-slice spiral CT examination on the patient and collecting relevant data, the characteristic multi-slice CT imaging findings of diffuse lung disease were determined by statistical analysis. Diffuse lung disease is representative in multi-slice spiral CT image imaging manifestations of the disease include multiple disseminated small nodules, multiple voids, ground glass shadows, and lung consolidation. And analyze the correlation of image performance, and then use statistical methods to analyze and evaluate the value of multi-slice spiral CT characteristic images in the diagnosis of diffuse lung disease, and analyze the characteristics of these characteristic multi-slice CT image appearances. The use of high-resolution CT to screen the characteristic CT imaging findings of the same research object, and then to perform a statistical analysis of the diagnostic differences with multi-slice spiral CT, further confirmed the importance of multi-slice CT for diffuse lung disease Diagnostic value. Studies have shown that multi-slice CT imaging technology is of great significance in the evaluation of diffuse lung diseases.

Understanding the g-tensors of perchlorotriphenylmethyl and Finland-type trityl radicals

The 285 GHz EPR spectra of perchlorotriphenylmethyl and tetrathiatriarylmethyl radicals in frozen solution have been accurately measured. The relationship between their molecular structures and their g-tensors has been investigated with the aid of DFT calculations, revealing that the degree of spin density delocalization away from the central methylene carbon is an important determining factor of the g-anisotropy. In particular, the small amount of spin densities on the Cl or S heteroatoms at the 2 and 6 positions with respect to the central carbon have the strongest influence. Furthermore, the amount of spin densities on these heteroatoms and thus the anisotropy can be modulated by the protonation (esterification) state of the carboxylate groups at the 4 position. These results provide unique insights into the g-anisotropy of persistent trityl radicals and how it can be tuned.

High-Field Dynamic Nuclear Polarization

Dynamic nuclear polarization (DNP) is one of the most prominent methods of sensitivity enhancement in nuclear magnetic resonance (NMR). Even though solid-state DNP under magic-angle spinning (MAS) has left the proof-of-concept phase and has become an important tool for structural investigations of biomolecules as well as materials, it is still far from mainstream applicability because of the potentially overwhelming combination of unique instrumentation, complex sample preparation, and a multitude of different mechanisms and methods available. In this review, I introduce the diverse field and history of DNP, combining aspects of NMR and electron paramagnetic resonance. I then explain the general concepts and detailed mechanisms relevant at high magnetic field, including solution-state methods based on Overhauser DNP but with a greater focus on the more established MAS DNP methods. Finally, I review practical considerations and fields of application and discuss future developments.

Optimizing nitroxide biradicals for cross-effect MAS-DNP: the role of g-tensors' distance

Nitroxide biradicals are common polarizing agents used to enhance the sensitivity of solid-state NMR experiments via Magic Angle Spinning Dynamic Nuclear Polarization (MAS-DNP). These biradicals are used to increase the polarization of protons through the cross-effect mechanism, which requires two unpaired electrons with a Larmor frequency difference greater than that of the protons. From their early conception, the relative orientation of the nitroxide rings has been identified as a critical factor determining their MAS-DNP performance. However, the MAS leads to a complex DNP mechanism with time dependent energy level anti-crossings making it difficult to pinpoint the role of relative g-tensor orientation. In this article, a single parameter called "g-tensors' distance" is introduced to characterize the relative orientation's impact on the MAS-DNP field profiles. It is demonstrated for the first time how the g-tensors' distance determines the nuclear hyperpolarization and depolarization properties of a given biradical. This provides a new critical parameter that paves the way for more efficient bis-nitroxides for MAS-DNP.

Balancing dipolar and exchange coupling in biradicals to maximize cross effect dynamic nuclear polarization

Balancing dipolar and exchange coupling is essential for efficient Cross Effect DNP. This explains the complex performance of standard radicals (AMUPOL and HyTek) at high magnetic field and fast spinning.

Pulse-Shaped Dynamic Nuclear Polarization under Magic-Angle Spinning

Dynamic nuclear polarization (DNP) under magic-angle spinning (MAS) is transforming the scope of solid-state NMR by enormous signal amplification through transfer of polarization from electron spins to nuclear spins. Contemporary MAS-DNP exclusively relies on monochromatic continuous-wave (CW) irradiation of the electron spin resonance. This limits control on electron spin dynamics, which renders the DNP process inefficient, especially at higher magnetic fields and non cryogenic temperatures. Pulse-shaped microwave irradiation of the electron spins is predicted to overcome these challenges but hitherto has never been implemented under MAS. Here, we debut pulse-shaped microwave irradiation using arbitrary-waveform generation (AWG) which allows controlled recruitment of a greater number of electron spins per unit time, favorable for MAS-DNP. Experiments and quantum mechanical simulations demonstrate that pulse-shaped DNP is superior to CW-DNP for mixed radical system, especially when the electron spin resonance is heterogeneously broadened and/or when its spin-lattice relaxation is fast compared to the MAS rotor period, opening new prospects for MAS-DNP.

Quo vadis EPR?

Complexity of paramagnetic catalysts and materials increases, and the same applies to systems targeted by integrative structural biology. Hence, EPR spectroscopists must find ways to enhance information content of their data. I argue that a third major wave of method development in EPR spectroscopy, which is triggered by recent advances in digital electronics and computing, can achieve this. Transfer of NMR methods to EPR will go on, but part of the new EPR methodology will depend on completely new concepts.

Biradical rotamer states tune electron J coupling and MAS dynamic nuclear polarization enhancement

Cross Effect (CE) Dynamic Nuclear Polarization (DNP) relies on the dipolar (D) and exchange (J) coupling interaction between two electron spins. Until recently only the electron spin D coupling was explicitly included in quantifying the DNP mechanism. Recent literature discusses the potential role of J coupling in DNP, but does not provide an account of the distribution and source of electron spin J coupling of commonly used biradicals in DNP. In this study, we quantified the distribution of electron spin J coupling in AMUPol and TOTAPol biradicals using a combination of continuous wave (CW) X-band electron paramagnetic resonance (EPR) lineshape analysis in a series of solvents and at variable temperatures in solution - a state to be vitrified for DNP. We found that both radicals show a temperature dependent distribution of J couplings, and the source of this distribution to be conformational dynamics. To qualify this conformational dependence of J coupling in both molecules we carry out Broken Symmetry DFT calculations which show that the biradical rotamer distribution can account for a large distribution of J couplings, with the magnitude of J coupling directly depending on the relative orientation of the electron spin pair. We demonstrate that the electron spin J couplings in both AMUPol and TOTAPol span a much wider distribution than suggested in the literature. We affirm the importance of electron spin J coupling for DNP with density matrix simulations of DNP in Liouville space and under magic angle spinning, showcasing that a rotamer with high J coupling and optimum relative g-tensor orientation can significantly boost the DNP performance compared to random orientations of the electron spin pair. We conclude that moderate electron spin J coupling above a threshold value can facilitate DNP enhancements.

Improved waveguide coupling for 1.3 mm MAS DNP probes at 263 GHz

We consider the geometry of a radially irradiated microwave beam in MAS DNP NMR probes and its impact on DNP enhancement. Two related characteristic features are found to be relevant: (i) the focus of the microwave beam on the DNP MAS sample and (ii) the microwave magnetic field magnitude in the sample. We present a waveguide coupler setup that enables us to significantly improve beam focus and field magnitude in 1.3 mm MAS DNP probes at a microwave frequency of 263 GHz, which results in an increase of the DNP enhancement by a factor of 2 compared to previous standard hardware setups. We discuss the implications of improved coupling and its potential to enable cutting-edge applications, such as pulsed high-field DNP and the use of low-power solid-state microwave sources.

De novo prediction of cross-effect efficiency for magic angle spinning dynamic nuclear polarization

Magic angle spinning dynamic nuclear polarization (MAS-DNP) has become a key approach to boost the intrinsic low sensitivity of NMR in solids. This method relies on the use of both stable radicals as polarizing agents (PAs) and suitable high frequency microwave irradiation to hyperpolarize nuclei of interest. Relating PA chemical structure to DNP efficiency has been, and is still, a long-standing problem. The complexity of the polarization transfer mechanism has so far limited the impact of analytical derivation. However, recent numerical approaches have profoundly improved the basic understanding of the phenomenon and have now evolved to a point where they can be used to help design new PAs. In this work, the potential of advanced MAS-DNP simulations combined with DFT calculations and high-field EPR to qualitatively and quantitatively predict hyperpolarization efficiency of particular PAs is analyzed. This approach is demonstrated on AMUPol and TEKPol, two widely-used bis-nitroxide PAs. The results notably highlight how the PA structure and EPR characteristics affect the detailed shape of the DNP field profile. We also show that refined simulations of this profile using the orientation dependency of the electron spin-lattice relaxation times can be used to estimate the microwave B1 field experienced by the sample. Finally, we show how modelling the nuclear spin-lattice relaxation times of close and bulk nuclei while accounting for PA concentration allows for a prediction of DNP enhancement factors and hyperpolarization build-up times.

ELDOR-detected NMR beyond hyperfine couplings: a case study with Cu(ii)-porphyrin dimers

The pulse EPR method ELDOR-detected NMR gives information about electron–electron couplings in Cu(ii) porphyrin dimers.