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We discuss the adiabatic self-trapping of small polarons within the densityfunctional theory (DFT). In particular, we carried out plane-wavepseudo-potential calculations of the triplet exciton in NaCl and found noenergy minimum corresponding to the self-trapped exciton (STE) contrary to theexperimental evidence and previous calculations. To explore the origin of thisproblem we modelled the self-trapped hole in NaCl using hybrid densityfunctionals and an embedded cluster method. Calculations show that thestability of the self-trapped state of the hole drastically depends on theamount of the exact exchange in the density functional: at less than 30% of theHartree-Fock exchange, only delocalized hole is stable, at 50% - bothdelocalized and self-trapped states are stable, while further increase of exactexchange results in only the self-trapped state being stable. We argue that themain contributions to the self-trapping energy such as the kinetic energy ofthe localizing charge, the chemical bond formation of the di-halogen quasimolecule, and the lattice polarization, are represented incorrectly within theKohn-Sham (KS) based approaches.Comment: 6 figures, 1 tabl

Modeling charge self-trapping in wide-gap dielectrics: Localization problem in local density functionals