Next, we ignore the matrix elements ! " 𝐴 '± 𝑐𝑜𝑠 𝜃 that slightly mix the nuclear spin states, but not the nuclear and electron spin states, so these terms do not contribute to polarization transfer between the two spins (see Supporting Information) . Thus, the matrix representation reduces to two independent 2 × 2 sub-matrices-one corresponding to zero quantum (ZQ) transitions (the central four elements 22, 23, 32 and 33) and one corresponding to double quantum (DQ) transitions (the outer four elements 11, 14, 41 and 44)-allowing us to solve the Liouville-von Neumann equation analytically. The procedure is straightforward, see for instance the treatment of the solid effect in Wenckebach and similarly for NOVEL and ISE . The ZQ and DQ transitions give different signs of the polarization transfer. Accordingly, we subtract the contribution of the ZQ and DQ transitions and find for the evolution of the nuclear polarization. Here we define (6) and P0 as the electron polarization.