This　work　assesses　the　performance　of　seven　exchange-correlation　functionals　(some　with　and　some　without　a　Hubbard　U　correction)　for　their　ability　(i)　to　predict　band　gaps　of　silicon,　diamond,　and　Li-ion　battery　cathode　materials,　(ii)　to　localize　hole　polarons　and　predict　delithiation　energies　in　Li-ion　battery　cathode　materials,　and　(iii)　to　predict　transition　levels　of　charge　carriers　of　doped　silicon　and　diamond.　Both　local　and　hybrid　exchange-correlation　functionals　were　tested.　The　local　functionals　tend　to　underestimate　band　gaps　and　delocalize　polarons.　The　hybrid　functionals　very　often　give　a　good　description　of　both　properties,　but　they　may　not　be　practical　for　calculations　involving　large　unit　cells,　large　ensembles,　or　dynamics,　and　therefore　a　local　functional　with　a　Hubbard　U　correction　is　often　used　(giving　the　method　called　DFT+U),　where　the　value　of　a　parameter　If　is　adjusted　according　to　the　system　and　the　property　being　investigated.　Keeping　in　mind　the　importance　of　computational　cost　and　the　undesirability　of　having　to　adjust　an　empirical　parameter　for　each　system　or　property　of　interest,　we　recently　developed　a　local　functional,　namely　HLE17,　to　try　to　accurately　predict　band　gaps　and　excitation　energies,　and　we　validated　it　using　mostly　main-group　solids　and　molecules.　Here　we　test　the　performance　of　HLE17　for　its　ability　to　predict　band　gaps　and　localize　polarons　in　other　solid-state　materials,　and　we　compare　its　performance　to　that　of　popular　local　functionals　(PBE,　PBEsol,　and　TPSS),　a　range-separated　hybrid　functional　with　screened　exchange　(HSE06),　and　DFT+U.　We　find　that　HLE17　predicts　more　accurate　band　gaps　than　other　local　functionals　and　can　localize　holes　as　polarons,　which　other　local　functionals　usually　fail　to　do,　and　for　a　number　of　cases　it　is　comparable　in　performance　quality　to　Hubbard-corrected　functionals　without　the　need　for　system-specific　parametrization　and　to　hybrid　functionals　without　the　high　cost.　Because　HLE17　does　not　predict　accurate　lattice　constants,　we　use　the　single-point　method　of　quantum　chemistry,　where　the　geometry　is　optimized　with　one　functional　and　the　band　gap　is　calculated　with　HLE17,　or　we　perform　calculations　with　the　lattice　constants　obtained　by　TPSS　and　both　the　fractional　intracell　coordinates　and　the　electronic　structure　obtained　by　HLE17　(a　new　method　denoted　HLE17\\TPSS).　In　particular,　we　performed　calculations　by　HLE17//TPSS,　HLE17//HSE06,　HLE17//DFT+U,　and　HLE17\\TPSS,　and　these　methods　usually　agree　well　with　each　other　and　give　values　similar　to　experiment.