Linear and sublinear scaling computation of the electronic g-tensor at the density functional theory level

We present an efficient and low-scaling implementation of a density functional theory based method for the computation of electronic g-tensors. It allows for an accurate description of spin-orbit coupling effects by employing the spin-orbit mean-field operator. Gauge-origin independence is ensured by the use of gauge-including atomic orbitals. Asymptotically linear scaling with molecule size is achieved with an atomic orbital based formulation, integral screening methods, and sparse linear algebra. In addition, we introduce an ansatz that exploits the locality of the contributions to the g-tensor for molecules with local spin density. For such systems, sublinear scaling is obtained by restricting the magnetic field perturbation to the relevant subspaces of the full atomic orbital space; several criteria for selecting these subspaces are discussed and compared. It is shown that the computational cost of g-tensor calculations with the local approach can fall below the cost of the self-consistent field calculation for large molecules. The presented methods thus enable efficient, accurate, and gauge-origin independent computations of electronic g-tensors of large molecular systems.