  From ultraviolet to mid-infrared region, light-matter interaction mechanisms
in semiconductors progressively shift from electronic transitions to phononic
resonances and are affected by temperature. Here, we present a parallel
temperature-dependent treatment of both electrons and phonons entirely from
first principles, enabling the prediction of full-spectrum optical responses.
At elevated temperatures, $\textit{ab initio}$ molecular dynamics is employed
to find thermal perturbations to electronic structures and construct effective
force constants describing potential landscape. Four-phonon scattering and
phonon renormalization are included in an integrated manner in this approach.
As a prototype ceramic material, cerium dioxide (CeO$_2$) is considered in this
work. Our first-principles calculated refractive index of CeO$_2$ agrees well
with measured data from literature and our own temperature-dependent
ellipsometer experiment.
