  The interfacial structure of a silicon grain boundary (Si-GB) plays a
decisive role on its chemical functionalization and has implications in diverse
physical-chemical properties of the material. Therefore, GB interface is
particularly relevant when the material is employed in high performance
technological applications. Here, we studied from first principles the role of
GB interface by providing an atomistic understanding of two different
$\Sigma$3\{112\} Si-GB models. These models are (1$\times$1) and (1$\times$2)
$\Sigma$3\{112\} Si-GBs which lead to different structural reconstruction.
Starting from these two models, we have shown that geometry optimization has an
important role on the structural reconstruction of the GB interface and
therefore on its properties. For this reason, we discussed different
methodologies to define an optimal relaxation protocol. The influence of the
local structures in (1$\times$1) and (1$\times$2) models have also been
investigated in the presence of vacancies where different light impurities of
different valency (C, N, H, O) can segregate. We studied how local structures
in (1$\times$1) and (1$\times$2) models are modified by the presence of
vacancies and impurities. These structural modifications have been correlated
with the changes of the energetics and electronic properties of the GBs. The
behavior of (1$\times$1) and (1$\times$2) models demonstrated to be
significantly different. The interaction with vacancies and the segregation of
C, N, H and O are significantly different depending on the type of local
structures present in $\Sigma$3\{112\} Si-GB.
