▁approxim ations . ▁ ▁General izations ▁ ▁While ▁Ko op mans ' ▁theorem ▁was ▁originally ▁stated ▁for ▁calculating ▁ion ization ▁energ ies ▁from ▁restricted ▁( closed - shell ) ▁Hart ree – F ock ▁wave functions , ▁the ▁term ▁has ▁since ▁taken ▁on ▁a ▁more ▁generalized ▁meaning ▁as ▁a ▁way ▁of ▁using ▁orb ital ▁energ ies ▁to ▁calculate ▁energy ▁changes ▁due ▁to ▁changes ▁in ▁the ▁number ▁of ▁electrons ▁in ▁a ▁system . ▁ ▁Gr ound - state ▁and ▁excited - state ▁ ions ▁ ▁Ko op mans ’ ▁theorem ▁applies ▁to ▁the ▁removal ▁of ▁an ▁electron ▁from ▁any ▁occupied ▁mole cular ▁orb ital ▁to ▁form ▁a ▁positive ▁ion . ▁Rem oval ▁of ▁the ▁electron ▁from ▁different ▁occupied ▁mole cular ▁orbit als ▁leads ▁to ▁the ▁ion ▁in ▁different ▁electronic ▁states . ▁The ▁lowest ▁of ▁these ▁states ▁is ▁the ▁ground ▁state ▁and ▁this ▁often , ▁but ▁not ▁always , ▁ar ises ▁from ▁removal ▁of ▁the ▁electron ▁from ▁the ▁H OM O . ▁The ▁other ▁states ▁are ▁excited ▁electronic ▁states . ▁ ▁For ▁example , ▁the ▁electronic ▁configuration ▁of ▁the ▁H 2 O ▁mole c ule ▁is ▁( 1 a 1 ) 2 ▁( 2 a 1 ) 2 ▁( 1 b 2 ) 2 ▁( 3 a 1 ) 2 ▁( 1 b 1 ) 2 , ▁ ▁where ▁the ▁symbols ▁a 1 , ▁b 2 ▁and ▁b 1 ▁are ▁orb ital ▁labels ▁based ▁on ▁mole cular ▁symmetry . ▁From ▁Ko op mans ’ ▁theorem ▁the ▁energy ▁of ▁the ▁ 1 b 1 ▁H OM