  In this first in a series of articles, we apply effective interactions
derived by the Unitary Correlation Operator Method (UCOM) to the description of
open-shell nuclei, using a self-consistent Hartree-Fock-Bogoliubov framework to
account for pairing correlations. To disentangle the particle-hole and
particle-particle channels and assess the pairing properties of $\VUCOM$, we
consider hybrid calculations using the phenomenological Gogny D1S interaction
to derive the particle-hole mean field. In the main part of this article, we
perform calculations of the tin isotopic chain using $\VUCOM$ in both the
particle-hole and particle-particle channels. We study the interplay of both
channels, and discuss the impact of non-central and non-local terms in
realistic interactions as well as the frequently used restriction of pairing
interactions to the ${}^1S_0$ partial wave. The treatment of the center-of-mass
motion and its effect on theoretical pairing gaps is assessed independently of
the used interactions.
