C-Pol: Point charge perturbation scheme for mapping tensor moment surfaces

Abstract

We present an efficient moment-based perturbation scheme for evaluating polarizability tensors of small molecules at a fraction of the computational cost of conventional energy-based approaches. Rather than applying explicit electric fields, the method perturbs the molecular charge density using strategically arranged external point charges, as in QM/MM simulations, and extracts polarizability tensors from finite differences of multipole moments extrapolated to the zero-perturbation limit. C-Pol is implemented as a backend-agnostic Python package requiring only that the host quantum chemistry code support external point-charge potentials. We demonstrate interfaces with three codes spanning complementary numerical approaches: GPAW (real-space grids), NWChem, and PySCF (atom-centered basis sets with complete basis set extrapolation). Validation against Gaussian 16 energy-based reference calculations across molecules representing all 19 commonly occurring point groups yields agreement within 3%, with the largest deviations confined to tensor components that are numerically small and contribute negligibly to the electrostatic potential. Finite-difference polarizabilities computed via C-Pol are further shown to agree with analytic coupled-perturbed Hartree-Fock values to within 0.02 a.u. across all tested basis sets, at comparable computational cost for medium-sized systems and with more favorable scaling for larger ones. The package provides a practical and transferable route to high-quality multipole polarizability data for force field development, polarizable embedding, and machine-learning training sets.