The Quark--Meson--Coupling (QMC) model self-consistently relates the dynamics of the internal quark structure of a hadron to the relativistic mean fields arising in nuclear matter. It offers a natural explanation to some open questions in nuclear theory, including the origin of many-body nuclear forces and their saturation, the spin-orbit interaction and properties of hadronic matter at a wide range of densities. The QMC energy density functionals QMC-I and QMC$pi$-I have been successfully applied to calculate ground state observables of finite nuclei in the Hartree-Fock + BCS approximation, as well as to predict properties of dense nuclear matter and cold non-rotating neutron stars. Here we report the latest development of the model, QMC$pi$-II, extended to include higher order self-interaction of the $sigma$ meson. A derivative-free optimization algorithm has been employed to determine a new set of the model parameters and their statistics, including errors and correlations. QMC$pi$-II predictions for a wide range of properties of even-even nuclei across the nuclear chart, with fewer adjustable parameters, are comparable with other models. Predictions of ground state binding energies of even-even isotopes of superheavy elements with Z$>$96 are particularly encouraging.
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