▁and ▁its ▁image ▁charge , ▁and ▁the ▁second ▁term ▁is ▁due ▁to ▁the ▁interaction ▁of ▁the ▁electron ▁and ▁its ▁image ▁charge . ▁ ▁The ▁rep uls ive ▁interaction ▁is ▁shown ▁in ▁the ▁third ▁and ▁fourth ▁terms ▁ar ising ▁from ▁the ▁interaction ▁of ▁nucle us - image ▁electron ▁and ▁electron - image ▁nucle us , ▁respectively . ▁ ▁By ▁Taylor ▁expansion ▁in ▁powers ▁of ▁| r |   /   | R | , ▁this ▁interaction ▁energy ▁can ▁be ▁further ▁expressed ▁as : ▁ ▁One ▁can ▁find ▁from ▁the ▁first ▁non - van ishing ▁term ▁that ▁the ▁phys is or ption ▁potential ▁depends ▁on ▁the ▁distance ▁Z ▁between ▁ad s or bed ▁atom ▁and ▁surface ▁as ▁Z − 3 , ▁in ▁contrast ▁with ▁the ▁r − 6 ▁dependence ▁of ▁the ▁mole cular ▁van ▁der ▁Wa als ▁potential , ▁where ▁r ▁is ▁the ▁distance ▁between ▁two ▁di pol es . ▁ ▁Model ing ▁by ▁quantum - me chan ical ▁oscill ator ▁ ▁The ▁van ▁der ▁Wa als ▁binding ▁energy ▁can ▁be ▁analyz ed ▁by ▁another ▁simple ▁physical ▁picture : ▁model ing ▁the ▁motion ▁of ▁an ▁electron ▁around ▁its ▁nucle us ▁by ▁a ▁three - dimensional ▁simple ▁harm onic ▁oscill ator ▁with ▁a ▁potential ▁energy ▁Va : ▁ ▁where ▁me ▁and ▁ ω ▁are ▁the ▁mass ▁and ▁v ibr ational ▁frequency ▁of ▁the ▁electron , ▁respectively . ▁ ▁As ▁this ▁atom ▁approaches ▁the ▁surface ▁of ▁a ▁metal ▁and ▁forms ▁ad s or ption , ▁this ▁potential ▁energy ▁Va ▁will ▁be ▁modified ▁due ▁to ▁the ▁image ▁charges