We develop a model for calculating the optical difference frequency generat
ion (DFG) spectra of adsorbate covered surfaces, and apply it to analyze re
cently obtained results for CN- covered Au. We split the surface nonlinear
susceptibility of the system into separate contributions from the noncentro
symmetric adsorbate layer and from the substrate. The former has a dipolar
susceptibility given by a product of the Raman and infrared responses of it
s stretch mode. To account for the virtual interband transitions of the sub
strate we employ a continuous dipolium model immersed within a semiinfinite
jellium which allows for the intraband screening. The resulting DFG line s
hape depends on the relative phase between the adsorbate and the substrate
responses and yields information on the orientation of the molecule and on
the strength of its effective dipole moment.