▁electron ▁aff inity ▁in ▁this ▁sense . ▁ ▁Calcul ations ▁of ▁electron ▁aff in ities ▁using ▁this ▁statement ▁of ▁Ko op mans ' ▁theorem ▁have ▁been ▁critic ized ▁on ▁the ▁grounds ▁that ▁virtual ▁( un occup ied ) ▁orbit als ▁do ▁not ▁have ▁well - f ounded ▁physical ▁interpret ations , ▁and ▁that ▁their ▁orb ital ▁energ ies ▁are ▁very ▁sensitive ▁to ▁the ▁choice ▁of ▁basis ▁set ▁used ▁in ▁the ▁calculation . ▁ ▁As ▁the ▁basis ▁set ▁becomes ▁more ▁complete ; ▁more ▁and ▁more ▁" m ole cular " ▁orbit als ▁that ▁are ▁not ▁really ▁on ▁the ▁mole c ule ▁of ▁interest ▁will ▁appear , ▁and ▁care ▁must ▁be ▁taken ▁not ▁to ▁use ▁these ▁orbit als ▁for ▁estim ating ▁electron ▁aff in ities . ▁ ▁Compar isons ▁with ▁experiment ▁and ▁higher - quality ▁calculations ▁show ▁that ▁electron ▁aff in ities ▁predicted ▁in ▁this ▁manner ▁are ▁generally ▁quite ▁poor . ▁ ▁For ▁open - shell ▁systems ▁ ▁Ko op mans ' ▁theorem ▁is ▁also ▁applicable ▁to ▁open - shell ▁systems . ▁ ▁It ▁was ▁previously ▁believed ▁that ▁this ▁was ▁only ▁in ▁the ▁case ▁for ▁removing ▁the ▁un pa ired ▁electron , ▁but ▁the ▁valid ity ▁of ▁Ko op mans ’ ▁theorem ▁for ▁RO H F ▁in ▁general ▁has ▁been ▁proven ▁ ▁provided ▁that ▁the ▁correct ▁orb ital ▁energ ies ▁are ▁used . ▁The ▁spin ▁up ▁( alpha ) ▁and ▁spin ▁down ▁( beta ) ▁orb ital ▁energ ies ▁do ▁not ▁necessarily ▁have ▁to ▁be ▁the ▁same . ▁ ▁C ounter part ▁in ▁density ▁functional