The transition temperature $T_textrm{c}$ of unconventional superconductivity is often tunable. For a monolayer of FeSe, for example, the sweet spot is uniquely bound to titanium-oxide substrates. By contrast for La$_{2-mathrm{x}}$Sr$_mathrm{x}$CuO$_4$ thin films, such substrates are sub-optimal and the highest $T_textrm{c}$ is instead obtained using LaSrAlO$_4$. An outstanding challenge is thus to understand the optimal conditions for superconductivity in thin films: which microscopic parameters drive the change in $T_mathrm{c}$ and how can we tune them? Here we demonstrate, by a combination of x-ray absorption and resonant inelastic x-ray scattering spectroscopy, how the Coulomb and magnetic-exchange interaction of La$_2$CuO$_4$ thin films can be enhanced by compressive strain. Our experiments and theoretical calculations establish that the substrate producing the largest $T_textrm{c}$ under doping also generates the largest nearest neighbour hopping integral, Coulomb and magnetic-exchange interaction. We hence suggest optimising the parent Mott state as a strategy for enhancing the superconducting transition temperature in cuprates.
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