Configuration interaction (CI) is a method for solving the
nonrelativistic Schrödinger equation
where i,j denote electrons and A,B denote nuclei,
with 
, 
, and 
.
Typical applications of the CI method employ the
Born-Oppenheimer approximation, whereby the the motions of the
electrons are treated as uncoupled from those of the nuclei.
Thus the ``electronic'' Shrödinger equation is solved at discrete
sets of fixed nuclear positions
The Born-Oppenheimer approximation is invoked so often in computational
quantum chemistry that the subscripts in the preceeding equation are
usually suppressed and the equation is written simply as 
. However, it is important to remember that the electronic
energy 
is an artifact of the Born-Oppenheimer approximation
and is not as physically meaningful as the total energy
of a system. Within the Born-Oppenheimer approximation, we estimate
the total energy by adding the
nuclear-nuclear repulsion energy and the nuclear kinetic energy to the
total electronic energy of equation (2.7).
While the CI method can be extended to incorporate some relativistic effects (e.g. spin-orbit terms), this is not generally done; these notes will be concerned only with the nonrelativistic Hamiltonian (2.7).