  In materials like transition metals oxides where electronic Coulomb
correlations impede a description in terms of standard band-theories, the
application of genuine many-body techniques is inevitable. Interfacing the
realism of density-functional based methods with the virtues of Hubbard-like
Hamiltonians, requires the joint ab initio construction of transfer integrals
and interaction matrix elements (like the Hubbard U) in a localized basis set.
In this work, we employ the scheme of maximally localized Wannier functions and
the constrained random phase approximation to create effective low-energy
models for Manganese monoxide, and track their evolution under external
pressure. We find that in the low pressure antiferromagnetic phase, the
compression results in an increase of the bare Coulomb interaction for specific
orbitals. As we rationalized in recent model considerations [Phys. Rev. B 79,
235133 (2009)], this seemingly counter-intuitive behavior is a consequence of
the delocalization of the respective Wannier functions. The change of screening
processes does not alter this tendency, and thus, the screened on-site
component of the interaction - the Hubbard U of the effective low-energy system
- increases with pressure as well. The orbital anisotropy of the effects
originates from the orientation of the orbitals vis-a-vis the deformation of
the unit-cell. Within the high pressure paramagnetic phase, on the other hand,
we find the significant increase of the Hubbard U is insensitive to the orbital
orientation and almost exclusively owing to a substantial weakening of
screening channels upon compression.
