A minimal machine-learning correction of DFTB Mulliken charges towards DFT-level MBIS populations

Density-functional tight binding (DFTB) enables efficient quantum-based simulations for large molecular systems, but atomic charges are typically reported via Mulliken population analysis and often deviate from density-based charge definitions at the density functional theory (DFT) level. Minimal basis iterative stockholder (MBIS) charges are attractive due to numerical stability and reduced basis-set sensitivity, yet MBIS is not available in standard DFTB workflows due to the lack of an explicit real-space electron density. Here we develop a minimal, physics-informed machine-learning (ML) correction that maps DFTB Mulliken charges to DFT reference MBIS charges at the atom-wise level. The model uses only atomic identity, DFTB Mulliken charge, and inexpensive local-geometry descriptors derived from the molecular structure, while enforcing exact molecular charge conservation at inference by a per-molecule shift. Using 5000 molecules from the QM9 database split into 4000/500/500 for training, validation, and testing, we show that nonlinearity alone provides limited improvement over an element-wise linear baseline, whereas incorporating local geometric descriptors yields a substantial accuracy gain, particularly for carbon and nitrogen. The proposed correction provides DFT-level charge quality at a computational cost comparable to standard DFTB calculations and can be readily integrated into existing DFTB-based workflows.