We
describe the recent progress in the development of the semiempirical
approach developed by Jain and Khare for the calculations of ionization
cross sections for molecules by electron impact. Along with the state-of-the-art
description of this approach, the emphasis will be on the evaluation
of cross sections for a carbon dimer, C2, and trimer, C3. Single-differential ionization cross sections as a function
of secondary or ejected electron energy and averaged secondary electron
energy for C2 and C3 are calculated at fixed
impinging electron energies of 100 and 200 eV. The integral ionization
cross sections are also derived from ionization threshold to 2000
eV. Extensive comparisons of the presently evaluated direct ionization
cross sections with the only available theoretical binary-encounter-dipole
model calculations of Kim and Rudd, spherical-complex-optical-potential
model calculations of Nagama and Antony, DM model calculations of
Deutsch and Märk, and the calculations of Michelin et al. based
on the combination of the Schwinger variational iterative method and
distorted wave approximation revealed a satisfactory agreement. The
present study also establishes the validity of the semiempirical approaches
and so provides a solid foundation for further applications to the
larger molecules.