Spin-Dependent Nonorthogonal Generalized Wannier Functions and their Integration with PAW and Hubbard Corrections in Linear-Scaling DFT
We present a spin-dependent extension of the non-orthogonal generalized Wannier function (NGWF) formalism within the framework of linear-scaling density functional theory (LS-DFT) as implemented in the ONETEP code. In traditional LS-DFT representations, both spin channels are constrained to share a common variational basis, which limits the accuracy for systems that are spin-polarized or exhibit magnetic order. Our approach allows NGWFs to vary independently for each spin channel, enabling a more accurate representation of spin-polarization in the electronic density. We demonstrate the efficacy of this method through a series of test cases, including localized magnetic defects in two-dimensional hBN, transition metal complexes, two-dimensional van der Waals magnetic materials, and both bulk and nanocluster ferromagnetic Co. In each scenario, the incorporation of spin-dependent NGWFs results in enhanced accuracy for total energy calculations, improved localization of spin density, and accurate predictions of magnetic ground states. This improvement is particularly notable when combined with DFT+U and DFT+U+J corrections. In this work, we take the opportunity to describe the combination of DFT+U+J and the projector-augmented wave (PAW) formalism within the LS-DFT framework, including how PAW participates in the ionic Pulay force, and in the minimum-tracking linear response approach for computing parameters in situ. Our findings demonstrate that spin-dependent NGWFs are a crucial and computationally efficient advancement in the linear-scaling DFT simulation of spin-polarized materials.