ated ▁hydro car bon ▁system ▁which ▁does ▁not ▁possess ▁an ▁odd - member ed ▁ring . ▁For ▁such ▁systems ▁it ▁is ▁possible ▁to ▁undert ake ▁a ▁st arring ▁process , ▁in ▁which ▁the ▁carbon ▁atoms ▁are ▁divided ▁into ▁two ▁sets : ▁all ▁the ▁car b ons ▁in ▁one ▁set ▁are ▁marked ▁with ▁a ▁star ▁such ▁that ▁no ▁two ▁star red ▁or ▁un star red ▁atoms ▁are ▁bond ed ▁to ▁each ▁other . ▁Here ▁the ▁star red ▁set ▁contains ▁the ▁highest ▁number ▁of ▁atoms . ▁When ▁this ▁condition ▁is ▁met , ▁the ▁sec ular ▁determin ant ▁in ▁the ▁H ück el ▁approximation ▁has ▁a ▁simpler ▁form , ▁since ▁cross - di ag onal ▁elements ▁between ▁atoms ▁in ▁the ▁same ▁set ▁are ▁necessarily ▁ 0 . ▁ ▁Altern ant ▁hydro car b ons ▁display ▁three ▁very ▁interesting ▁properties : ▁The ▁mole cular ▁orb ital ▁energ ies ▁for ▁the ▁ π ▁system ▁are ▁pa ired , ▁that ▁is ▁for ▁an ▁orb ital ▁of ▁energy ▁ ▁there ▁is ▁one ▁of ▁energy ▁. ▁The ▁coefficients ▁of ▁two ▁pa ired ▁mole cular ▁orbit als ▁are ▁the ▁same ▁at ▁the ▁same ▁site , ▁except ▁for ▁a ▁sign ▁change ▁in ▁the ▁un star red ▁set . ▁The ▁population ▁or ▁electron ▁density ▁at ▁all ▁sites ▁is ▁equal ▁to ▁unity ▁in ▁the ▁ground ▁state , ▁so ▁the ▁distribution ▁of ▁ π ▁electrons ▁is ▁uniform ▁across ▁the ▁whole ▁mole c ule . ▁ ▁Moreover , ▁if ▁the ▁altern ant ▁hydro car bon ▁contains ▁an ▁odd ▁number ▁of ▁atoms ▁then ▁there ▁must ▁be ▁an ▁un