Density functional perturbation theory with DFT+U in the mixed-basis framework
DFT+U is a viable tool to improve description of materials, where the standard DFT exchange-correlation potentials fail to catch essential properties of electronic correlation. While phenomenological in nature, it is numerically efficient and also gives access to energy derivatives,
e.g. forces and force constants. Most applications to lattice dynam- ics properties have been based on the direct method (supercells and forces), while the linear response approach has been rarely used.
Here I describe a combination of DFT+U and density functional perturbation theory (DFPT) in the framework of the mixed-basis approach, an efficient method based on norm-conserving pseudopo- tentials employing a combination of plane waves and tailored local functions for the expansion of the valence states. The DFPT ex- tension of the mixed-basis method [1,2] has been extensively applied in the past. The present DFT+U implementation employs the fully rotationally invariant form  in its relativistic extension . Its use- fulness is demonstrated for compounds containing 3d or 4f/5f elements.