ized ▁version ▁of ▁ ▁the ▁internal ▁coordinate ▁q t ▁is ▁denoted ▁by ▁St . ▁ ▁The ▁P ES ▁V ▁can ▁be ▁Taylor ▁expanded ▁around ▁its ▁minimum ▁in ▁terms ▁of ▁the ▁St . ▁ ▁The ▁third ▁term ▁( the ▁H ess ian ▁of ▁V ) ▁evaluated ▁in ▁the ▁minimum ▁is ▁a ▁force ▁derivative ▁matrix ▁F . ▁In ▁the ▁harm onic ▁approximation ▁the ▁Taylor ▁series ▁is ▁ended ▁after ▁this ▁term . ▁The ▁second ▁term , ▁containing ▁first ▁derivatives , ▁is ▁zero ▁because ▁it ▁is ▁evaluated ▁in ▁the ▁minimum ▁of ▁V . ▁The ▁first ▁term ▁can ▁be ▁included ▁in ▁the ▁zero ▁of ▁energy . ▁Thus , ▁ ▁The ▁classical ▁v ibr ational ▁kin etic ▁energy ▁has ▁the ▁form : ▁ ▁where ▁g st ▁is ▁an ▁element ▁of ▁the ▁metric ▁tensor ▁of ▁the ▁internal ▁( cur vil ine ar ) ▁coordinates . ▁The ▁d ots ▁indicate ▁time ▁derivatives . ▁M ixed ▁terms ▁ ▁generally ▁present ▁in ▁cur vil ine ar ▁coordinates ▁are ▁not ▁present ▁here , ▁because ▁only ▁linear ▁coordinate ▁transformations ▁are ▁used . ▁E valu ation ▁of ▁the ▁metric ▁tensor ▁g ▁in ▁the ▁minimum ▁q 0 ▁of ▁V ▁gives ▁the ▁positive ▁definite ▁and ▁symmetric ▁matrix ▁G ▁= ▁g ( q 0 ) − 1 . ▁One ▁can ▁solve ▁the ▁two ▁matrix ▁problems ▁ ▁simultaneously , ▁since ▁they ▁are ▁equivalent ▁to ▁the ▁generalized ▁eigen value ▁problem ▁ ▁where ▁ ▁where ▁fi ▁is ▁equal ▁to ▁ ▁( ▁is ▁the ▁frequency ▁of ▁normal ▁mode ▁i ); ▁ ▁is ▁the ▁unit ▁matrix . ▁The ▁matrix ▁L − 1 ▁contains ▁the