Quantum mechanical image potential theory

We present a quantum-mechanical image-potential theory by determining analytically the Kohn-Sham (KS) exchange-correlation potential v_xc(z) in the classically forbidden region of the metal-vacuum interface. The asymptotic structure of the image potential is determined to be -(α_KS,x+1/4)/z, where α_KS,x depends upon the Fermi energy and barrier height of the metal. The structure is obtained from exact expressions derived for v_xc(r) in the asymptotic region in terms of the electron self-energy. The KS exchange potential is determined as v_x(z)∼-α_KS,x/z, thereby confirming previous work. The correlation part of the self-energy employed is that of the plasmon-pole approximation, and leads to the KS correlation potential v_c(z)∼-1/(4z). The quantum image potential derived therefore, differs from the commonly accepted classical form of -1/(4z). The import of this result to both the theory of image states and the density-functional theory is also discussed.