C-Pol: Point-Charge Perturbation Scheme for Mapping Tensor Moment Surfaces

Molecular polarizability tensors beyond the dipole-dipole level are key inputs to polarizable force fields, polarizable embedding, and machine-learned response models, yet routines to compute them exist in few quantum chemistry codes and are largely confined to atom-centered Gaussian basis sets. We present a general, backend-agnostic implementation of moment-based point-charge perturbation that removes this restriction. The molecular charge density is perturbed by external point charges available in any QM/MM-capable code, whether real-space-grid, plane-wave, or atom-centered, and the dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole tensors are recovered from finite differences of the perturbed multipole moments extrapolated to the zero-perturbation limit. The accuracy and generality of the method are established through three independent implementations spanning complementary numerical representations: GPAW (real-space grids), NWChem, and PySCF (atom-centered basis sets). Energy-based reference values (Gaussian 16) for all 19 commonly occurring point groups are reproduced within 3%. Furthermore, the finite-difference values agree with analytic coupled-perturbed Hartree-Fock results to within 4%, at comparable cost for medium-sized systems and more favorable scaling for larger ones. Relative to conventional energy-based schemes that require basis set extrapolation, the method reduces the number of SCF evaluations by a factor of 27. It is distributed as the open-source package C-Pol.