  Epitaxial strain offers an effective route to tune the physical parameters in
transition metal oxides. So far, most studies have focused on the effects of
strain on the bandwidths and crystal field splitting, but recent experimental
and theoretical works have shown that also the effective Coulomb interaction
changes upon structural modifications. This effect is expected to be of
paramount importance in current material engineering studies based on
epitaxy-based material synthesization. Here, we perform constrained random
phase approximation calculations for prototypical oxides with a different
occupation of the d shell, LaTiO3 (d1), LaVO3 (d2), and LaCrO3 (d3), and
systematically study the evolution of the effective Coulomb interactions
(Hubbard U and Hund's J) when applying epitaxial strain. Surprisingly, we find
that the response upon strain is strongly dependent on the material. For
LaTiO3, the interaction parameters are determined by the degree of localization
of the orbitals, and grow with increasing tensile strain. In contrast, LaCrO3
shows the opposite trends: the interactions parameters shrink upon tensile
strain. This is caused by the enhanced screening due to the larger electron
filling. LaVO3 shows an intermediate behavior.
