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A smooth sphere-to-cube transition is experimentally, computationally andtheoretically studied in plasmonic Au nanoparticles, including retardationeffects. Localized surface plasmon-polariton resonances were described withprecision, discriminating among the influences of shape statistics, particlepolydispersity, electrochemistry of excess (surface) charges. Sphere, cube andsemicubes in between all show well-defined secular electrostatic eigenvalues,producing a wealthy of topological modes afterwards quenched by chargerelaxation processes. The way both eigenvalues and plasmon wavelength vary as afunction of a shape descriptor, parametrizing the transition, is explained by aminimal model based on the key concepts of crystal (or ligand) field theory(CFT), bringing for the first time to an {\em electromagnetic analog of crystalfield splitting}. For any orbital angular momentum, eigenvalues evolve as in aTanabe-Sugano correlation diagram, relying on the symmetry set by particletopology and a charge defect between cube and sphere. Expressions fornon-retarded and retarded plasmon wavelengths are given and succeffully appliedto both experimental UV-Vis and numerically simulated values. The CFT analogycan be promising to delve into the role of shape in nanoplasmonics andnanophotonics.

Shape Plasmonics and Geometric Eigenvalues: The Crystal Field Plasmon Splitting in a Sphere-to-Cube Continuous Transition