Under CNDO, only the valence electrons are considered explicitly. Interactions between electrons on the same atom are handled simply. Since the atomic orbital basis is built from orthonormal atomic functions, then the interaction between different orbitals and , , due to their symmetry. The core Hamiltonian elements, , are fitted to experiment. In CNDO/1 these were fitted to atomic ionisation energies, but in CNDO/2 this was modified by fitting to the average of the ionisation potential and electron affinity, making the system more applicable to both electron gain and loss.

In order to overcome the basis dependency of the ZDOA, the remaining two-centre integrals only depend on their host atoms and not on the orbital type. This is achieved by using an average electrostatic repulsion on any atom A caused by atom B, (the `electron repulsion integral'), so that

In CNDO/1, is approximated by *s*-orbital integrals on
the atoms,

Similarly if the core potential (consisting of the nucleus and core
electrons) on an atom *B* is then to maintain rotational
invariance, the interaction between an electron on atom *A* and this
core on atom *B* must be a constant, *V*_{AB} (the `potential
integrals').

Similarly to , in CNDO/1 *V*_{AB} is calculated using an
*s*-orbital on atom *A*:

In CNDO/2, an improved parameterisation, this was replaced with a simple approximation, .

The lack of monatomic differential overlap removes all terms of the form

Next the interaction between an electron and the field of two atoms,
*A* and *B* is simplified (the `resonance integral',
)^{}, by setting it proportional to the overlap integral,
,

where are known as the bonding parameters and
are dependent on the atom types *A* and *B*. Under CNDO/1 these are
approximated to ,and is fitted to *ab initio* calculations for each
species.

The precise parameterisation technique used to determine ,, *V*_{AB}, and varies.
Although I have described the method used for CNDO/1 and CNDO/2 (the
earliest parameterisations), there have been many refinements to these
since. CNDO is extremely fast, and this has meant that when computing
resources were limited, CNDO calculations have been able to perform
pioneering calculations on system sizes inaccessible to their *ab
initio* cousins. Much of the accuracy lost during the above
simplifications is compensated for by the use of parameterisation to
experimental and *ab initio* results. Although CNDO is not as
accurate as *ab initio* methods such as AIMPRO it remains a useful
investigative tool in semiconductor calculations, and a valuable
intermediate between empirical potentials and full *ab initio*
calculations.