Crystal field Hamiltonians of molecular qubits from generalized spin-orbital DFT

Quantitative descriptions of spin-orbit coupling and crystal field interactions are crucial for the chemical design of single-molecule magnets (SMM) with enhanced magnetic anisotropy and molecular spin qubits with long coherence time. However, an effective spin Hamiltonian that models such interactions contains too many independent crystal field parameters to extract from experimental observables. Additionally, accurate multi-reference ab initio methods, such as CASPT2, for calculating these parameters are prohibitively expensive for many realistic systems. To address this challenge, we have developed a density functional theory (DFT)-based methodology to derive crystal field parameters for any total angular momentum J at the mean-field cost. By sampling generalized spin-orbital Kohn-Sham DFT wavefunctions and their energies of different J orientations, we fitted the crystal field parameters and constructed effective Hamiltonians that model the ground J spin-orbit manifold. The method has been applied to lanthanide SMM and molecular qubits, resulting in low-energy excit­­ed states of quantitative agreement with the experimental energy spectra. The derived model Hamiltonians further provide the foundation for simulating spin-phonon relaxations to enhance the resilience of molecular qubits against decoherence.