  Context. The properties of hydrogenated amorphous carbon (a-C:H) dust are
known to evolve in response to the local conditions. Aims. We present an
adaptable model for the determination of the optical properties of
low-temperature, interstellar a-C:H grains that is based on the fundamental
physics of their composition. Methods. The imaginary part of the refractive
index, k, for a-C:H materials, from 50 eV to cm wavelengths, is derived and the
real part, n, of the refractive index is then calculated using the
Kramers-Kronig relations. Results. The formulated optEC(s) model allows a
determination of the complex dielectric function, epsilon, and refractive
index, m(n, k), for a-C:H materials as a continuous function the band gap, Eg ,
which is shown to lie in the range = -0.1 to 2.7 eV. We provide expressions
that enable a determination of their optical constants and tabulate m(n, k, Eg
) for 14 different values of Eg . We explore the evolution of the likely
extinction and emission behaviours of a-C:H grains and estimate the relevant
transformation time-scales. Conclusions. With the optEC(s) model we are able to
predict how the optical properties of an a-C:H dust component in the
interstellar medium will evolve in response to, principally, the local
interstellar radiation field. The evolution of a-C:H materials appears to be
consistent with many dust extinction, absorption, scattering and emission
properties, and also with H2 molecule, daughter PAH and hydrocarbon molecule
formation resulting from its photo-driven decomposition.
