q-vSZPs: A polarized, adaptive minimal Gaussian basis set for the elements Z = 1-86 designed for efficient mean-field electronic structure calculations.

We present q-vSZPs, a polarized, environment-adaptive minimal Gaussian basis set parameterized for elements Z = 1-86 (excluding lanthanides) and designed for efficient mean-field quantum-mechanical calculations on large molecular systems. Building on the previously introduced q-vSZP basis set, the number of primitive functions is substantially reduced while retaining the key feature of charge- and coordination-number-dependent contraction coefficients, which enable environment-dependent "breathing" of the atomic orbitals. The effective atomic charges required for the basis set setup are obtained from the bond-capacity electronegativity equilibration model (EEQBC), which accurately reproduces density functional theory (DFT)-level Hirshfeld charges at negligible computational cost. Comprehensive benchmarking on the GMTKN55 database demonstrates that q-vSZPs incurs only a moderate loss in accuracy relative to q-vSZP (WTMAD-2 increase of 2.9 kcal⋅mol-1), while substantially outperforming conventional non-adaptive minimal basis sets (MBs). For non-covalent interactions, the performance even surpasses that of the double-ζ def2-SVP basis set, owing to a substantially lower basis set superposition error as a consequence of the molecular optimization strategy. A non-adaptive variant using averaged charges and coordination numbers (qavg-vSZPs) is additionally provided as a drop-in minimal basis for any quantum-chemical program. For a representative 4108-atom system, q-vSZPs achieves a twofold reduction in both SCF wall time and memory consumption for DFT calculations relative to q-vSZP, placing it in the efficiency range of other MBs. The utility of q-vSZPs is further demonstrated through a mixed-basis application for the computation of the Raman spectrum of adenine in water.