  Context. The properties of hydrogenated amorphous carbon (a-C:H) dust evolve
in response to the local radiation field in the interstellar medium and the
evolution of these properties is particularly dependent upon the particle size.
Aims. A model for finite-sized, low-temperature amorphous hydrocarbon
particles, based on the microphysical properties of random and defected
networks of carbon and hydrogen atoms, with surfaces passivated by hydrogen
atoms, has been developed. Methods. The eRCN/DG and the optEC(s) models have
been combined, adapted and extended into a new optEC(s)(a) model that is used
to calculate the optical properties of hydrocarbon grain materials down into
the sub-nanometre size regime, where the particles contain only a few tens of
carbon atoms. Results. The optEC(s)(a) model predicts a continuity in
properties from large to small (sub-nm) carbonaceous grains. Tabulated data of
the size-dependent optical constants (from EUV to cm wavelengths) for a-C:H
(nano-)particles as a function of the bulk material band gap [Eg(bulk)], or
equivalently the hydrogen content, are provided. The effective band gap
[Eg(eff.)] is found to be significantly larger than Eg(bulk) for hydrogen-poor
a-C(:H) nano-particles and their predicted long-wavelength ({\lambda} >
30{\mu}m) optical properties differ from those derived for interstellar
polycyclic aromatic hydrocarbons (PAHs). Conclusions. The optEC(s)(a) model is
used to investigate the size-dependent structural and spectral evolution of
a-C(:H) materials under ISM conditions, including: the IR-FUV extinction, the
217 nm bump and the infrared emission bands. The model makes several
predictions that can be tested against observations.
