Supplementary Material

See Supplementary Material for (1) the description of the generalized cluster correlation expansion method, (2) the computational details, (3) tests of convergence with respect to the gCCE order, and (4) a derivation of the evolution of the full electron-nuclei spin pure state in the Hahn-echo experiment and the electron spin coherence functions expressed in terms of the pure state, for both isotropic exchange and dipolar interactions between the two electron spins.