The extension of the CEH model to accommodate f -elements, alongside the introduction of a novel non-iterative approximation for electrostatic interactions and further param- The updated adaptive q-vSZP basis set benefits from a more consistent optimization using reference charges and extends the variationally optimized minimal basis to cover the entire periodic table up to lawrencium (Z = 103). With its combination of generality, consistency, and the minimal basis approach to alleviate the diagonalization bottleneck, q-vSZP stands as an optimal basis set choice for future SQM methods.