F ock ▁wave function , ▁i . e . ▁a ▁single ▁Sl ater ▁determin ant ▁composed ▁of ▁orbit als ▁that ▁are ▁the ▁eigen functions ▁of ▁the ▁corresponding ▁self - cons istent ▁F ock ▁operator . ▁ ▁Emp ir ical ▁compar isons ▁with ▁experimental ▁values ▁and ▁higher - quality ▁ab ▁init io ▁calculations ▁suggest ▁that ▁in ▁many ▁cases , ▁but ▁not ▁all , ▁the ▁ener get ic ▁corre ctions ▁due ▁to ▁relax ation ▁effects ▁nearly ▁cancel ▁the ▁corre ctions ▁due ▁to ▁electron ▁correlation . ▁ ▁A ▁similar ▁theorem ▁exists ▁in ▁density ▁functional ▁theory ▁( DF T ) ▁for ▁rel ating ▁the ▁exact ▁first ▁vertical ▁ion ization ▁energy ▁and ▁electron ▁aff inity ▁to ▁the ▁H OM O ▁and ▁L UM O ▁energ ies , ▁although ▁both ▁the ▁deriv ation ▁and ▁the ▁precise ▁statement ▁differ ▁from ▁that ▁of ▁Ko op mans ' ▁theorem . ▁I on ization ▁energ ies ▁calculated ▁from ▁D FT ▁orb ital ▁energ ies ▁are ▁usually ▁poor er ▁than ▁those ▁of ▁Ko op mans ' ▁theorem , ▁with ▁errors ▁much ▁larger ▁than ▁two ▁electron ▁vol ts ▁possible ▁depending ▁on ▁the ▁exchange - cor relation ▁approximation ▁employed . ▁The ▁L UM O ▁energy ▁shows ▁little ▁correlation ▁with ▁the ▁electron ▁aff inity ▁with ▁typical ▁approxim ations . ▁The ▁error ▁in ▁the ▁D FT ▁counter part ▁of ▁Ko op mans ' ▁theorem ▁is ▁a ▁result ▁of ▁the ▁approximation ▁employed ▁for ▁the ▁exchange ▁correlation ▁energy ▁functional ▁so ▁that , ▁unlike ▁in ▁H F ▁theory , ▁there ▁is ▁the ▁possibility ▁of ▁improved ▁results ▁with ▁the ▁development ▁of ▁better