An atom-in-molecule adaptive polarized valence single-ζ atomic orbital basis for electronic structure calculations.

The article presents the development of a novel atom-in-molecule adaptive atomic orbital (AO) minimal basis set termed q-vSZP (charge-dependent valence single-ζ, polarized), designed to improve the accuracy of low-cost or semiempirical quantum mechanical (SQM) methods. This basis set uniquely adapts the contraction coefficients of primitive Gaussian functions based on the effective atomic charge and coordination number of each atom in a molecule, enabling the "breathing" (expansion/contraction) of orbitals in response to their chemical environment. Atomic charges are efficiently obtained via a newly introduced Charge Extended Hückel (CEH) model, which provides robust, QM-based charge estimates across elements up to radon (Z=86). Benchmarking with the ωB97X-D4 density functional shows that q-vSZP outperforms standard minimal basis sets with added polarization functions and approaches the quality of double-ζ basis sets like def2-SVP, particularly in thermochemical accuracy, molecular structures, and reduced basis set superposition errors. The work highlights q-vSZP’s potential as an optimal, computationally efficient basis set for future SQM and simplified DFT methods, with ongoing efforts to implement analytical gradients and extend its application.