Linking Chemical Structure and Coherence Times of Molecular Spin Qubits

The electron spin is a natural qubit platform whose properties, when embedded in a molecule, can be tuned by synthetic chemistry. However, the quantum properties can be exploited only over a limited time scale, and lengthening the coherence time remains a significant challenge. Nuclear spin diffusion is one of the principal sources of decoherence, but a complete removal of spin-bearing nuclei is hardly feasible in practice, and therefore, strategies to mitigate their impact are essential. Despite considerable efforts to screen the chemical space for improved molecular spin qubits (MSQs) as well as advances in simulation techniques to understand the physical details of the decoherence processes, a broader picture bringing together the chemical and physical views of this phenomenon is still lacking. In this work, we fill this gap by analyzing the decoherence induced by a nuclear spin bath of protons through a parameter space screening approach based on the analytic pair product approximation. As specific cases, we discuss [Cu-(dbm)₂] (H-dbm = dibenzoylmethane) and (PPh₄)₂[Cu-(mnt)₂] (mnt^2- = maleonitriledithiolate) diluted into a nonmagnetic crystalline matrix. The analysis reveals the geometric and statistical conditions that lead to strong contributions to decoherence and enables us to identify the nuclear pairs that are most relevant to decoherence effects. This allows formulating new design rules for proton-containing MSQs and systematically reveals potential avenues for their improvement. Most importantly, our analysis emphasizes that long coherence times require a proper design of the environment in which the MSQ is embedded, while nuclear spins on the MSQ itself are less important.