Semiempirical electronic structure methods have been experiencing a resurgence, as highlighted by a recent special issue on this topic. Modern advancements aim to enhance accuracy, broaden applicability to more elements and applications, and further improve efficiency for large systems. These developments are significantly influenced by the rise of machine learning (ML) techniques, leading to potential mutual enhancements. Many low-cost or semiempirical quantum mechanical (SQM) electronic structure methods are limited by their use of unpolarized minimal atomic orbital (AO) basis sets. To address this issue, we recently introduced a density functional theory (DFT) variationally optimized, atom-in-molecule adaptive minimal basis (MB) set, which has been made available consistently for elements up to radon (Z = 86, excluding the lanthanides (Lns)) and termed charge-dependent (polarized) valence single-ζ (q-vSZP). The key innovation is the introduction of a linear dependence for the primitive Gaussian coefficients in a contracted AO on the effective atomic charge of the atom within the molecule. Each symmetry-unique atom thus acquires specifically adapted basis functions. This approach enables the "breathing" of the AOs with both the atomic charge (expansion/contraction for anionic/cationic states) and the number of nearby bonded atoms within a molecule ("Pauli"-type contraction/expansion with more/less neighbors). The q-vSZP basis underpins our current development of an improved tight-binding (TB) SQM method, intended as a successor to the established GFN2-xTB model (working title: g-xTB).