▁terms ▁of ▁these ▁coordinates . ▁The ▁G F ▁method ▁gives ▁the ▁linear ▁transformation ▁from ▁general ▁internal ▁coordinates ▁to ▁the ▁special ▁set ▁of ▁normal ▁coordinates . ▁ ▁The ▁G F ▁method ▁ ▁A ▁non - linear ▁mole c ule ▁consisting ▁of ▁N ▁atoms ▁has ▁ 3 N ▁− ▁ 6 ▁ ▁internal ▁degrees ▁of ▁freedom , ▁because ▁position ing ▁a ▁mole c ule ▁in ▁three - dimensional ▁space ▁requires ▁three ▁degrees ▁of ▁freedom , ▁and ▁the ▁description ▁of ▁its ▁orientation ▁in ▁space ▁requires ▁another ▁three ▁degree ▁of ▁freedom . ▁These ▁degrees ▁of ▁freedom ▁must ▁be ▁subtract ed ▁from ▁the ▁ 3 N ▁degrees ▁of ▁freedom ▁of ▁a ▁system ▁of ▁N ▁particles . ▁ ▁The ▁interaction ▁among ▁atoms ▁in ▁a ▁mole c ule ▁is ▁described ▁by ▁a ▁potential ▁energy ▁surface ▁( P ES ), ▁which ▁is ▁a ▁function ▁of ▁ 3 N ▁− ▁ 6 ▁coordinates . ▁The ▁internal ▁degrees ▁of ▁freedom ▁q 1 , ▁... , ▁ ▁q 3 N − 6 ▁describing ▁the ▁P ES ▁in ▁an ▁optimal ▁way ▁are ▁often ▁non - linear ; ▁they ▁are ▁for ▁instance ▁val ence ▁coordinates , ▁such ▁as ▁b ending ▁and ▁t ors ion ▁angles ▁and ▁bond ▁st ret ches . ▁It ▁is ▁possible ▁to ▁write ▁the ▁quantum ▁mechanical ▁kin etic ▁energy ▁operator ▁for ▁such ▁cur vil ine ar ▁coordinates , ▁but ▁it ▁is ▁hard ▁to ▁form ulate ▁a ▁general ▁theory ▁applicable ▁to ▁any ▁mole c ule . ▁This ▁is ▁why ▁Wilson ▁linear ized ▁the ▁internal ▁coordinates ▁by ▁assuming ▁small ▁disp lac ements . ▁The ▁linear