 Pseudopotential 
Definition:  Approximation of the
Schrödinger equation
exclusively for
valence electrons. 
Explanation:  The pseudopotential
is used to simplify
the mathematical
description of
complex systems and
is constructed to
replace the full
atomic allelectron
potential such that
core states are
eliminated and the
valence electrons of
outer shells are
described by
pseudowave
functions with
significantly fewer
nodes. This allows
the pseudowave
functions to be
described with far
fewer Fourier modes,
thus making
planewave basis
sets practical to
use. In this
approach, only the
chemically
active valence
electrons are
usually explicitly
dealt
with, while the core
electrons are
“frozen”, being
considered together
with the nuclei as
rigid
nonpolarizable ion
cores.
Ab
initio
pseudopotentials are
derived from an
atomic reference
state, requiring
that the pseudo and
allelectron
valence
eigen states have
the
same energies and
amplitude outside a
chosen core cutoff
radius [1]. 
References:  [1] http://en.wikipedia.org/wiki/Pseudopotential See also, e.g. P. Schwerdtfeger, ChemPhysChem 12, 3143 (2011) 

