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 . 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 as a function of the orbital functions . Such an expression which returns a number as a function of other functions is called a function

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 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.

Tomas Arias 2004-01-26