Automated Framework for Molecular Multipole Calculations: Benchmarking DFT Methods and Dataset Generation for Azole-Based Materials

Abstract

Molecular electric dipole and quadrupole moments are fundamental descriptors of charge distribution and intermolecular electrostatics, with applications spanning spectroscopy, force-field parametrization, and the design of proton-conducting materials. Despite their importance, extracting multipole moments from DFT typically requires specialized postprocessing, and validated benchmark datasets remain scarce for chemistries of interest. Here, we present an open-source, basis-set-agnostic Python framework that automates the calculation of molecular dipole and quadrupole moments from plane-wave and Gaussian-type-orbital DFT, supporting both total-electron-density and charge-density-difference formulations, and benchmark it against experimental references for 99 dipole and 54 quadrupole moments across five density functional approximations. We further apply the framework to generate a data set of 242 substituted azoles relevant to nonaqueous proton conduction and show that computed dipole and quadrupole moments provide complementary information about molecular charge distribution. As a preliminary exploration of these data as machine-learning targets, an unoptimized random forest baseline trained on identity-based structural descriptors predicts dipole moments to within 0.5 D for weakly perturbing substituents but yields larger errors for strongly electron-withdrawing groups; these errors correlate with the Hammett σp constant, motivating the use of electronically resolved descriptors in future modeling efforts. The framework, benchmark results, and azole data set are released openly to support high-throughput electronic structure data generation, force-field parametrization, and machine-learning studies of multipole-aware materials design.