Figure 1. Energy‐level diagrams (|m S m I>), transitions (ω i), and relaxation rates W i associated with an SI spin system. (a) The relaxation rates are given for dipolar coupling (W I (nuclear), W 0 (zero quantum), and W 2 (double quantum)) and scalar coupling (W S 0 (zero quantum)). (b) The Overhauser effect is achieved by applying saturating microwaves to the allowed EPR transitions (ω e), while observing the NMR transitions (ω n). In this example we assume that pure scalar relaxation is the dominant relaxation mechanism. (c and d) Solid‐effect, where W S is the electron spin relaxation rate and ω ± are the forbidden transitions. The gray spheres represent the population probabilities (p 1, p 2, p 3, p 4) at the steady state without the application of microwaves (a) and with microwaves (b–d).

Figure 2. Dependence of the coupling factor ξ on the product of electron Larmor frequency and correlation time. Shown are cases of pure rotational and translational diffusion with dipolar coupling (solid lines), and of scalar coupling for various β values (dashed lines). The vertical lines correspond to experimental conditions of 9.8/0.3 and 260 GHz/10 T for a correlation time of 20 ps.

Figure 3. Energy‐level diagram (|m S1 m S2 m I>) associated with a three‐spin SSI spin system (S, I = 1/2). Strong mixing between levels 4> and 5> occurs if the energy difference matches the nuclear Zeeman splitting.

Figure 4. Energy distribution of populations (n(E)) between electronic spin state manifolds m Z = 1/2 and m Z =− 1/2, separated by energy ħω e. The width of each state (ħδ) is determined by electron–electron dipolar broadening. (a) Thermal equilibrium T L = T D = T Z. (b) Application of off‐resonant microwave radiation at ω < ω e “cools” the dipolar bath 0 < T D < T Z. (c) Application of off‐resonant microwave radiation at ω > ω e “heats” the dipolar bath to a negative spin temperature 0 < |T D| < T Z, T D < 0.

Figure 5. Setups for DNP at high magnetic fields.

Figure 6. DNP enhancement and EPR lineshape of 10 mM ‐TEMPOL in water at room temperature as a function of the external magnetic field.