We are now prepared to outline a general strategy for finding the
total energy E. To evaluate the various terms in (12), we
need the correct orbitals 
, which we can find from
using a Schrödinger-solver routine to solve
(16). To determine according to (17),
we need the nuclear potential, which we know from
(2); the potential from the electrons, which we get
from a Poisson-solver routine to solve (4) for a given
; and a simple subroutine to evaluate the function
for the values of .
Figure 2: Stages of solving the Kohn-Sham equations
The minimum of E obtains only when all of the above equations hold
simultaneously. In particular, the density must be
self-consistent: the density 
which we input must lead
to a potential which gives rise to a set of orbitals
that sum to a final density 
equal to
the input density. (See Figure 2.) Viewing the
contents of the dashed box in Figure 2 as a function
which takes the density as input and produces a new
density as output, self-consistency is the condition that 
, a set of non-linear equations for the value of the
charge density at each point in space. There are quite power
numerical methods for solving such equations given the capability of
computing 
. Eventually, we shall discuss
these techniques, but first we shall develop the ability to compute
.