  Context: Absorption by molecules in the Earth's atmosphere strongly affects
ground-based astronomical observations. The resulting absorption line strength
and shape depend on the highly variable physical state of the atmosphere, i.e.
pressure, temperature, and mixing ratio of the different molecules involved.
Usually, supplementary observations of so-called telluric standard stars (TSS)
are needed to correct for this effect, which is expensive in terms of telescope
time. We have developed the software package molecfit to provide synthetic
transmission spectra based on parameters obtained by fitting narrow ranges of
the observed spectra of scientific objects. These spectra are calculated by
means of the radiative transfer code LBLRTM and an atmospheric model. In this
way, the telluric absorption correction for suitable objects can be performed
without any additional calibration observations of TSS. Aims: We evaluate the
quality of the telluric absorption correction using molecfit with a set of
archival ESO-VLT X-Shooter visible and near-infrared spectra. Methods: Thanks
to the wavelength coverage from the U to the K band, X-Shooter is well suited
to investigate the quality of the telluric absorption correction with respect
to the observing conditions, the instrumental set-up, input parameters of the
code, the signal-to-noise of the input spectrum, and the atmospheric profiles.
These investigations are based on two figures of merit, I_off and I_res, that
describe the systematic offsets and the remaining small-scale residuals of the
corrections. We also compare the quality of the telluric absorption correction
achieved with moelcfit to the classical method based on a telluric standard
star. (Abridged)
