Stellar clusters in the inner Galaxy and their correlation with cold
  dust emission
  Stars are born within dense clumps of giant molecular clouds, constituting
young stellar agglomerates known as embedded clusters, which only evolve into
bound open clusters under special conditions. We statistically study all
embedded clusters (ECs) and open clusters (OCs) known so far in the inner
Galaxy, investigating particularly their interaction with the surrounding
molecular environment and the differences in their evolution. We first compiled
a merged list of 3904 clusters from optical and infrared clusters catalogs in
the literature, including 75 new (mostly embedded) clusters discovered by us in
the GLIMPSE survey. From this list, 695 clusters are within the Galactic range
|l| < 60 deg and |b| < 1.5 deg covered by the ATLASGAL survey, which was used
to search for correlations with submm dust continuum emission tracing dense
molecular gas. We defined an evolutionary sequence of five morphological types:
deeply embedded cluster (EC1), partially embedded cluster (EC2), emerging open
cluster (OC0), OC still associated with a submm clump in the vicinity (OC1),
and OC without correlation with ATLASGAL emission (OC2). Together with this
process, we performed a thorough literature survey of these 695 clusters,
compiling a considerable number of physical and observational properties in a
catalog that is publicly available. We found that an OC defined observationally
as OC0, OC1, or OC2 and confirmed as a real cluster is equivalent to the
physical concept of OC (a bound exposed cluster) for ages in excess of ~16 Myr.
Some observed OCs younger than this limit can actually be unbound associations.
We found that our OC and EC samples are roughly complete up to ~1 kpc and ~1.8
kpc from the Sun, respectively, beyond which the completeness decays
exponentially. Using available age estimates for a few ECs, we derived an upper
limit of 3 Myr for the duration of the embedded phase... (Abridged)
