  We present a parametrization within a simplified LCAO model (a type of
Hueckel model) for the description of $\pi$ molecular orbitals in organic
molecules containing $\pi$-bonds between carbon, nitrogen, or oxygen atoms with
$sp^2$ hybridization, which we show to be quite accurate in predicting the
energy of the highest occupied $\pi$ orbital and the first $\pi$-$\pi*$
transition energy for a large set of organic compounds. We provide four
empirical parameter values for the diagonal matrix elements of the LCAO
description, corresponding to atoms of carbon, nitrogen with one $p_z$
electron, nitrogen with two $p_z$ electrons, and oxygen. The bond-length
dependent formula (proportional to $1/d^2$) of Harrison is used for the
non-diagonal matrix elements between neighboring atoms. The predictions of our
calculations have been tested against available experimental results in more
than sixty organic molecules, including benzene and its derivatives,
polyacenes, aromatic hydrocarbons of various geometries, polyenes, ketones,
aldehydes, azabenzenes, nucleic acid bases and others. The comparison is rather
successful, taking into account the small number of parameters and the
simplicity of the LCAO method, involving only $p_z$ atomic orbitals, which
leads even to analytical calculations in some cases.
