Computational Insights into Electronic Excitations, Spin-Orbit Coupling Effects, and Spin Decoherence in Cr(IV)-based Molecular Qubits

The great success of point defects and dopants in semiconductors for quantum information processing has invigorated a search for molecules with analogous properties. Flexibility and tunability of desired properties in a large chemical space have great advantages over solid-state systems. The properties analogous to point defects were demonstrated in Cr(IV)-based molecular family, Cr(IV)(aryl)$_4$, where the electronic spin states were optically initialized, read out, and controlled. Despite this kick-start, there is still a large room for enhancing properties crucial for molecular qubits. Here we provide computational insights into key properties of the Cr(IV)-based molecules aimed at assisting chemical design of efficient molecular qubits. Using the multireference ab-initio methods, we investigate the electronic states of Cr(IV)(aryl)$_4$ molecules with slightly different ligands, showing that the zero-phonon line energies agree with the experiment, and that the excited spin-triplet and spin-singlet states are highly sensitive to small chemical perturbations. By adding spin-orbit interaction, we find that the sign of the uniaxial zero-field splitting (ZFS) parameter is negative for all considered molecules, and discuss optically-induced spin initialization via non-radiative intersystem crossing. We quantify (super)hyperfine coupling to the $^{53}$Cr nuclear spin and to the $^{13}$C and $^1$H nuclear spins, and we discuss electron spin decoherence. We show that the splitting or broadening of the electronic spin sub-levels due to superhyperfine interaction with $^1$H nuclear spins decreases by an order of magnitude when the molecules have a substantial transverse ZFS parameter.