Potential Function Construction

1
Potential Function Construction

• van der Waals Potential from Molecular
  Polarizability Calculations

2
Potential Function Basic Form

• Source
• Harris, J. Feibelman, P.J. Surface Science 115,
  L133(1982).
• Tensor generalization for dipole-induced van der
  Waals force
• Integration is over all sorption frequencies
• Requires
• Molecular polarizability tensor for dipole source
• Dipole-induced electrical field in the bulk

3
Potential Function Polarizability Tensor

• Polarizability tensor which depends on
  orientation of diatomic relative to surface
  plane
• Surface normal aligned with z-axis
• q0, diatomic perpendicular to surface
• qp, diatomic parallel to surface
• Alphas are longitudinal and transverse
  polarizability components for diatomic

4
Potential Function Induced Field Equation

• Use image-charge theory to project dipole image
  from the vacuum into the medium1
• On-diagonal derivatives are thus

1 Jackson, J. D. Classical Electrodynamics.
John Wiley Sons, 1962, 1975.
5
Potential Function Dielectric Function

• Frequency-dependent dielectric function is needed
• Metals/low-frequency dielectrics2

2 Mavroyannis, C. Mol Phys, 6, 593 (1963)..
6
Potential Function Eliminate Frequency Dependence

• Integration over imaginary frequency domain is
• Assume polarizability to be real and independent
  of sorption frequency

7
Potential Function Coefficient of the VDW
Potential

• Coefficient is a constant times a functional of
  the orientation-dependent polarization tensor

8
Potential Function Polarization Functional

• Exact form of the polarization functional
• Using the orientation-dependent tensor and the
  diatomic polarizability coefficients yields

9
Potential Function Final Form

• At a given displacement from the surface and
  angular displacement of the diatomics axis from
  the surface normal
• Parameterized by the directional polarizability
  coefficients of the diatomic in question

10
Potential Function N2 versus O2 on Ag
Shown is the potential difference VN2-VO2