Advanced Charge Extended Hückel (CEH) Model and a Consistent Adaptive Minimal Basis Set for the Elements = 1-103.

The Charge Extended Hückel (CEH) model, initially introduced for adaptive atomic orbital (AO) basis set construction ( , 159, 164108), has been significantly revised to enhance accuracy and robustness, particularly in challenging electronic situations. This revision includes an extension toward -elements, covering actinoids with their -electrons in the valence space. We present a novel noniterative approximation for the electrostatic contribution to the effective Fock matrix, which substantially improves performance in polar or charged systems. Additionally, the training data set for elements = 1-103 has been expanded to encompass even more chemically diverse reference molecules as well as dipole moments and shell populations in addition to atomic charges. It includes a greater variety of "mindless" molecules (MLMs) as well as more complex electronic structures through open-shell and highly charged species. The revised method achieves mean absolute errors for atomic charges of approximately 0.02 for randomly selected (mostly organic) molecules and 0.09 for MLMs, outperforming both classical charge models and established tight-binding methods. Furthermore, the revised CEH model has been validated through density functional theory calculations with the updated adaptive q-vSZP AO basis set on common thermochemical databases. Consistent with the extension of the CEH model, q-vSZP has also been variationally optimized and tested for elements = 58-71 and 87-103. The original versions of both CEH and q-vSZP are now considered deprecated.