2.2 Origin of the Work Function
15
E VAC (im)
V XC
E F
E VAC (im)
V XC
E F
(a)
(b)
inside a solid vacuum
surface
Fig. 2.9 a Potential diagram without taking into account image force. b Potential diagram with
image force taken into account. c Potential diagram with surface term and without taking image
force into account. d Potential diagram with surface term and with image force taken into account.
See text for explanation
gradual, as shown in Fig. 2.9b. Because the physical origin of the image potential in
the bulk is exactly the same as that of V XC , the potentials in the bulk and at an infinite
distance do not change upon introducing the image force. When the surface term
is considered but not the image force, the bulk-related potential changes abruptly,
as shown in Fig. 2.9a, but the potential related to the surface electrostatic potential
changes smoothly near the surface. Thus, the resulting potential diagram is similar
to that shown in Fig. 2.9c. Now, we consider the most realistic case in which both
the surface potential and the image force are taken into account (Fig. 2.9d). Because
the consideration of the image force changes the curve near the surface but not the
potential in the bulk and vacuum, the potential curve in Fig. 2.9d is not so different
from the potential without the image force (dotted curve in Fig. 2.9d) except for very
near the surface.