text: The van der Waals binding energy can be analyzed by another simple physical picture: modeling the motion of an electron around its nucleus by a three-dimensional simple harmonic oscillator with a potential energy V:
  where m and &omega; are the mass and vibrational frequency of the electron, respectively.
  As this atom approaches the surface of a metal and forms adsorption, this potential energy V will be modified due to the image charges by additional potential terms which are quadratic in the displacements:
  :  (from the Taylor expansion above.)
  Assuming
  the potential is well approximated as
  where
  If one assumes that the electron is in the ground state, then the van der Waals binding energy is essentially the change of the zero-point energy:
  This expression also shows the nature of the Z dependence of the van der Waals interaction.
  Furthermore, by introducing the atomic polarizability,
  the van der Waals potential can be further simplified:
  where
  is the van der Waals constant which is related to the atomic polarizability.
  Also, by expressing the fourth-order correction in the Taylor expansion above as (aCZ) / (Z), where a is some constant, we can define Z as the position of the dynamical image plane and obtain
  The origin of Z comes from the spilling of the electron wavefunction out of the surface.  As a result, the position of image plane representing the reference for the space coordinate is different from the substrate surface itself and modified by Z.
  Table 1 shows the jellium model calculation for van der Waals constant C and dynamical image plane Z of rare gas atoms on various metal surfaces.  The increasing of C from He to Xe for all metal substrates is caused by the larger atomic polarizability of the heavier rare gas atoms.  For the position of the dynamical image plane, it decreases with increasing dielectric function and is typically on the order of 0.2 Å.