  Two-dimensional transition metal carbides and nitrides (MXenes) are a
perspective group of materials with a broad palette of applications. Surface
terminations are a product of the MXene preparation, and post-processing can
also lead to partial coverage. Despite applicability and fundamental properties
being driven by termination patterns, it is not fully clear, how they behave on
MXene surfaces with various degrees of surface coverage. Here, as the first
step, we used density functional theory to predict possible patterns in
prototypic Ti$_2$C MXene, demonstrating the different behavior of the two most
frequent terminal atoms, oxygen, and fluorine. Oxygen (with formal charge
-2$e$) prefers a zigzag line both-side adsorption pattern on bare Ti$_2$C,
attracting the next adsorbent to a minimal distance. Oxygen defects in fully
O-terminated MXene tend to form similar zigzag line vacancy patterns. On the
other hand, fluorine (with a formal charge of -1$e$) prefers one-side flake
(island) adsorption on bare Ti$_2$C and a similar desorption style from fully
fluorinated Ti$_2$C. MXene magnetic behavior is subsequently driven by the
patterns, either compensating locally and holding the global magnetic state of
the MXene until some limit (oxygen case) or gradually increasing total
magnetism by summing of local effects (fluorine case). The systematic
combinatoric study of Ti$_2$CT$_x$ with various coverages ($0 \leq x \leq 2$)
of distinct terminal atoms T = O or F brings encouraging possibilities of
tunable behavior of MXenes and provides useful guidance for its modeling
towards electronic nanodevices.
