  We define the normal Hochschild cohomology of an admissible subcategory of
the derived category of coherent sheaves on a smooth projective variety $X$ ---
a graded vector space which controls the restriction morphism from the
Hochschild cohomology of $X$ to the Hochschild cohomology of the orthogonal
complement of this admissible subcategory. When the subcategory is generated by
an exceptional collection, we define its new invariant (the height) and show
that the orthogonal to an exceptional collection of height $h$ in the derived
category of a smooth projective variety $X$ has the same Hochschild cohomology
as $X$ in degrees up to $h - 2$. We use this to describe the second Hochschild
cohomology of quasiphantom categories in the derived categories of some
surfaces of general type. We also give necessary and sufficient conditions of
fullness of an exceptional collection in terms of its height and of its normal
Hochschild cohomology.
