Putting everything together, we now have our expression for the total energy,
where 
is some known function, 
is the
potential energy field created by the nuclei, 
is the
simple electron static interaction among the nuclei,
and 
(usually equal to two) is the number of electrons in orbital
i. Note that the expression (12) maps each possible choice
of the set of electronic orbitals 
to a unique
value for the energy of the system and thereby gives the total energy
E as a function of the orbital functions 
. Such an
expression which returns a number as a function of other functions is
called a functional and denoted with square brackets as we do in
Eq. (12).
We now have a functional for the energy in terms of the orbitals, but which orbitals are the right ones to use? The answer is quite sensible: the correct orbitals are those which minimize the total energy E in (12) while obeying the orthonormality constraints (6). Combined with this variational principle, Eq. (12) now gives a complete prescription for computing total energies, and thereby all of the properties mentioned in Sec. 2.
