A comprehensive study of NGC 2345, a young open cluster with a low
  metallicity
  NGC 2345 is a young open cluster hosting seven blue and red supergiants, low
metallicity and a high fraction of Be stars which makes it a privileged
laboratory to study stellar evolution.
  We aim to improve the determination of the cluster parameters and study the
Be phenomenon. Our objective is also to characterise its seven evolved stars by
deriving their atmospheric parameters and chemical abundances.
  We performed a complete analysis combining for the first time $ubvy$
photometry with spectroscopy as well as $Gaia$ Data Release 2. We obtained
spectra with classification purposes for 76 stars and high-resolution
spectroscopy for an in-depth analysis of the blue and red evolved stars. We
identify a new red supergiant and 145 B-type likely members within a radius of
18.7$\pm$1.2 arcmin, which implies an initial mass,
$M_{\textrm{cl}}\approx$5200 M$_{\odot}$. We find a distance of 2.5$\pm$0.2 kpc
for NGC 2345, placing it at $R_{\textrm{GC}}$=10.2$\pm$0.2 kpc. Isochrone
fitting supports an age of 56$\pm$13 Ma, implying masses around 6.5 M$_{\odot}$
for the supergiants. A high fraction of Be stars ($\approx$10$\%$) is found.
From the spectral analysis we estimate for the cluster an average
$v_{\textrm{rad}}$=$+58.6\pm0.5$ kms$^{-1}$ and a low metallicity,
[Fe/H]=$-$0.28$\pm$0.07. We also have determined chemical abundances for Li, O,
Na, Mg, Si, Ca, Ti, Ni, Rb, Y, and Ba for the evolved stars. The chemical
composition of the cluster is consistent with that of the Galactic thin disc.
One of the K supergiants, S50, is a Li-rich star, presenting an
A(Li)$\approx$2.1. An overabundance of Ba is found, supporting the enhanced
$s$-process.
  NGC 2345 has a low metallicity for its Galactocentric distance, comparable to
typical LMC stars. It is massive enough to serve as a testbed for theoretical
evolutionary models for massive intermediate-mass stars.
