A variational polaron self-interaction corrected total-energy functional for charge excitations in wide-band gap insulators

摘要

We conduct a detailed investigation of the polaron self-interaction (pSI)error in standard approximations to the exchange-correlation (XC) functionalwithin density-functional theory (DFT). The pSI leads to delocalization errorin the polaron wave function and energy, as calculated from the Kohn-Sham (KS)potential in the native charge state of the polaron. This constitutes theorigin of the systematic failure of DFT to describe polaron formation in bandinsulators. It is shown that the delocalization error in these systems is,however, largely absent in the KS potential of the closed-shell neutral chargestate. This leads to a modification of the DFT total-energy functional thatcorrects the pSI in the XC functional. The resulting pSIC-DFT methodconstitutes an accurate parameter-free {\it ab initio} methodology forcalculating polaron properties in insulators at a computational cost that isorders of magnitude smaller than hybrid XC functionals. Unlike approaches thatrely on parametrized localized potentials such as DFT+$U$, the pSIC-DFT methodproperly captures both site and bond-centered polaron configurations. This isdemonstrated by studying formation and migration of self-trapped holes inalkali halides (bond-centered) as well as self-trapped electrons in anelpasolite compound (site-centered). The pSIC-DFT approach consistentlyreproduces the results obtained by hybrid XC functionals parametrized byDFT+$G_0W_0$ calculations. Finally, we generalize the pSIC approach to hybridfunctionals, and show that in stark contrast to conventional hybridcalculations of polaron energies, the pSIC-hybrid method is insensitive to theparametrization of the hybrid XC functional. On this basis, we furtherrationalize the success of the pSIC-DFT approach.