0 0   cm − 1 ▁▁ β ▁= ▁ 0 . 0 0 0 7 ▁for ▁ Δ E ▁= ▁ 1 5 0 0   cm − 1 . ▁( The ▁reci pro cal ▁cent imeter ▁is ▁an ▁energy ▁unit ▁that ▁is ▁commonly ▁used ▁in ▁inf ra red ▁spect ro sc opy ; ▁▁ 1   cm − 1 ▁corresponds ▁to ▁). ▁When ▁an ▁exc itation ▁energy ▁is ▁ 5 0 0   cm − 1 , ▁then ▁about ▁ 8 . 9 ▁percent ▁of ▁the ▁mole cules ▁are ▁therm ally ▁excited ▁at ▁room ▁temperature . ▁To ▁put ▁this ▁in ▁perspective : ▁the ▁lowest ▁exc itation ▁v ibr ational ▁energy ▁in ▁water ▁is ▁the ▁b ending ▁mode ▁( about ▁ 1 6 0 0   cm − 1 ). ▁Thus , ▁at ▁room ▁temperature ▁less ▁than ▁ 0 . 0 7 ▁percent ▁of ▁all ▁the ▁mole cules ▁of ▁a ▁given ▁amount ▁of ▁water ▁will ▁v ibr ate ▁faster ▁than ▁at ▁absolute ▁zero . ▁ ▁As ▁stated ▁above , ▁rotation ▁hardly ▁influ ences ▁the ▁mole cular ▁geometry . ▁But , ▁as ▁a ▁quantum ▁mechanical ▁motion , ▁it ▁is ▁therm ally ▁excited ▁at ▁relatively ▁( as ▁compared ▁to ▁v ibration ) ▁low ▁temper atures . ▁From ▁a ▁classical ▁point ▁of ▁view ▁it ▁can ▁be ▁stated ▁that ▁at ▁higher ▁temper atures ▁more ▁mole cules ▁will ▁rotate ▁faster , ▁which ▁implies ▁that ▁they ▁have ▁higher ▁angular ▁velocity ▁and ▁angular ▁momentum . ▁In ▁quantum ▁mechanical ▁language : ▁more ▁eigen states ▁of ▁higher ▁angular ▁momentum ▁become ▁therm