  When the first four spectral moments are considered, spectral features
missing in standard Kohn-Sham (KS) density-functional theory (DFT), such as
upper and lower Hubbard bands, as well as spectral satellite peaks, can be
described, and the bandwidths can be corrected. Therefore, we have devised a
\textit{moment-functional based spectral density functional theory} (MFbSDFT)
recently. However, many computational tools in theoretical solid state physics,
such as the construction of maximally localized Wannier functions (MLWFs), have
been developed for KS-DFT and require modifications if they are supposed to be
used in MFbSDFT. Here, we show how generalized Wannier functions may be
constructed from the first four spectral moment matrices. We call these
functions \textit{maximally localized spectral moment Wannier functions}
(MLSMWFs). We demonstrate how MLSMWFs may be used to compute the anomalous Hall
effect (AHE) in fcc Ni by Wannier interpolation. More generally, MLSMWFs may be
computed from the first $2P$ moments ($P=1,2,3,\dots$). Using more than 4
moments opens the perspective of reproducing all spectral features accurately
in MFbSDFT.

Strongly Correlated Electrons