  Improved computation of the dielectric function considering excitonic effects
and long wavelength is performed and compared with the nearly free electron
band approximation, similarly with the Penn's model case. New expressions for
the real and imaginary part of the dielectric function are presented and the
real part compared with the Penn's result. The obtained functions satisfy the
Kramers-Kr\"onig relations, in contrast with earlier results in the literature.
In addition, our improved dielectric function presents a coeficient of 2/3 for
small gap approximation (different from the value of 1 in the original Penn
model) is very close to the value 0.62 obtained in [Can. J. Phys.53,(1975)
p.2549] from pure numerical procedures. The obtained dielectric function also
is used in a rough and stimative analysis of the metal-insulator transition in
molecular hydrogen being the critical densities determined near the
experimental values for the hydrogen coming from other approach. The
approximated expressions and critical values are given and the usefulness of
the rough methods involved in the determination of the critical points briefly
discussed.
