Electrostatics Beyond Atomic Charges: A High-Performance Multipole Engine for FFprime

I am applying to build the multipole electrostatics evaluation engine for FFprime, addressing Issue #1 (Electrostatics beyond the atomic charges). FFprime already derives atom-centered multipole moments from quantum-chemical calculations. What it needs is the other half — functions that take those moments and compute the electrostatic potential and field at arbitrary points in space. That is what I will build. My three planned deliverables are: (1) a fully vectorized, convention-unified implementation of monopole, dipole, and quadrupole potential and field functions; (2) a Cartesian-to-spherical conversion layer connecting the Cartesian implementations to the spherical harmonic representation used in the RSC paper; and (3) analysis utilities including field projection and field comparison metrics, as listed in the stretch goal of the issue. Before submitting this proposal I have already made four contributions to the repo: PR #5 implementing dipole and quadrupole functions with 26 unit tests, PR #11 implementing the Cartesian-to-spherical conversion layer, and technical reviews on PRs #2 and #4 identifying vectorization gaps and convention inconsistencies. I am a CS undergraduate at VIT Vellore with strong foundations in linear algebra, NumPy vectorization, and scientific software design. The mathematical framework — tensor decomposition, multipole expansions — is something I have studied independently and already applied in my contributions.