▁by ▁additional ▁potential ▁terms ▁which ▁are ▁quadratic ▁in ▁the ▁disp lac ements : ▁▁▁ ▁( from ▁the ▁Taylor ▁expansion ▁above .) ▁ ▁Assuming ▁ ▁the ▁potential ▁is ▁well ▁approxim ated ▁as ▁ ▁, ▁ ▁where ▁ ▁If ▁one ▁assumes ▁that ▁the ▁electron ▁is ▁in ▁the ▁ground ▁state , ▁then ▁the ▁van ▁der ▁Wa als ▁binding ▁energy ▁is ▁essentially ▁the ▁change ▁of ▁the ▁zero - point ▁energy : ▁ ▁This ▁expression ▁also ▁shows ▁the ▁nature ▁of ▁the ▁Z − 3 ▁dependence ▁of ▁the ▁van ▁der ▁Wa als ▁interaction . ▁ ▁Furthermore , ▁by ▁introdu cing ▁the ▁atomic ▁polar iz ability , ▁ ▁the ▁van ▁der ▁Wa als ▁potential ▁can ▁be ▁further ▁simplified : ▁ ▁where ▁ ▁is ▁the ▁van ▁der ▁Wa als ▁constant ▁which ▁is ▁related ▁to ▁the ▁atomic ▁polar iz ability . ▁ ▁Also , ▁by ▁express ing ▁the ▁fourth - order ▁correction ▁in ▁the ▁Taylor ▁expansion ▁above ▁as ▁( a C v Z 0 )   /   ( Z 4 ), ▁where ▁a ▁is ▁some ▁constant , ▁we ▁can ▁define ▁Z 0 ▁as ▁the ▁position ▁of ▁the ▁dynam ical ▁image ▁plane ▁and ▁obtain ▁ ▁The ▁origin ▁of ▁Z 0 ▁comes ▁from ▁the ▁sp illing ▁of ▁the ▁electron ▁wave function ▁out ▁of ▁the ▁surface . ▁ ▁As ▁a ▁result , ▁the ▁position ▁of ▁image ▁plane ▁representing ▁the ▁reference ▁for ▁the ▁space ▁coordinate ▁is ▁different ▁from ▁the ▁substr ate ▁surface ▁itself ▁and ▁modified ▁by ▁Z 0 . ▁ ▁Table ▁ 1 ▁shows ▁the ▁j elli um ▁model ▁calculation ▁for ▁van ▁der ▁Wa als