In frozen-solution samples each molecule will have a different alignment with respect to the external magnetic field and a unique molecular conformation, leading to a distribution of coupling frequencies across the ensemble. As a result, the coherences generated by the DFHE entangling gate with a specific value of 𝜏 will represent the average over a distribution of coupling frequencies. The simplest model of inter-spin coupling is that of an isotropic interaction, corresponding to physical systems in which the inter-spin coupling is dominated by super-exchange interactions, or equivalently those in which only specific orientations of the molecule with respect to the external magnetic field are sampled. The coupling distribution was modelled as a normal distribution centred at 𝜇 + !" = 2 MHz, corresponding to the maximum of the inter-spin coupling in compound 1, with standard deviations 𝜎 + !" . As expected, first maximum in the simulated fidelity decreases as the distribution of inter-spin couplings is broadened (Figure ). Through the DEER experiment, we can estimate the distribution of couplings exhibited by the sub-population probed by our experiments; the standard deviation of the inter-spin coupling was determined to be approximately 0.244 MHz (Figure , Table ), corresponding to a fidelity of 0.989. For the coupling between two spins to be detectable by pulse dipolar spectroscopy, the interspin distance must be greater than around 1.5 nm. In this distance regime isotropic exchange coupling tends to be negligible, and the inter-spin interaction is generally dominated by the anisotropic dipolar interaction. Assuming all non-secular terms are negligible the strength of the dipolar coupling is given by 𝜔 BB = 𝜔 C (3 cos $ 𝜃 -1), where 𝜃 is the angle between the inter-spin vector and the external magnetic field and 𝜔 C is the coupling frequency when 𝜃 = 90°. While each orientation of the molecule is equally likely to be present in the sample, leading to a Pake pattern of inter-spin coupling frequencies, the orientations do not contribute equally to the recorded data due to the inherent orientation selectivity of microwave pulses (Figure ). As such we can generate two models of dipolar coupling: one with uniform weights representing the sample as a whole, and one in which each orientation is weighted by the overlap of the nitroxide spectrum with the microwave pulses. The simulated fidelities of the entangling gate with 𝜔 C = 2 MHz for the uniform and weighted models are 0.749 and 0.821, respectively, significantly lower than the corresponding simulations considering an isotropic interaction. This decrease in fidelity is caused by interference between systems with different coupling frequencies, which diminishes the expectation values of the anti-phase coherences. The uniformly weighted simulation is more impacted by this interference as its frequency distribution is a complete Pake pattern, whereas the frequency distribution of the spectrally weighted simulation corresponds to a partial Pake pattern.