Phonons and electron-phonon coupling in DFT+U from linear response

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 phe­ nomenological in nature, it is numerically efficient and gives access to total energy derivatives and consequently to lattice dynamics properties. Most current applications of DFT+U to phonons utilize the direct method (supercells and force calculations), while the numerically more efficient linear re­ sponse approach has been rarely used [l]. Here, a linear re­ sponse formalism for DFT+U implemented in the framework of the mixed-basis pseudopotentials method is presented. This implementation employs the fully rotationally invariant form in its relativistic extension. lt can be combined with spin­ polarization or spin-orbit interaction, and provides straightfor­ ward access to electron-phonon coupling matrix elements. Its usefulness is demonstrated for several compounds containing 3d or 4f/5f elements.
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