  A smooth sphere-to-cube transition is experimentally, computationally and
theoretically studied in plasmonic Au nanoparticles, including retardation
effects. Localized surface plasmon-polariton resonances were described with
precision, discriminating among the influences of shape statistics, particle
polydispersity, electrochemistry of excess (surface) charges. Sphere, cube and
semicubes in between all show well-defined secular electrostatic eigenvalues,
producing a wealthy of topological modes afterwards quenched by charge
relaxation processes. The way both eigenvalues and plasmon wavelength vary as a
function of a shape descriptor, parametrizing the transition, is explained by a
minimal model based on the key concepts of crystal (or ligand) field theory
(CFT), bringing for the first time to an {\em electromagnetic analog of crystal
field splitting}. For any orbital angular momentum, eigenvalues evolve as in a
Tanabe-Sugano correlation diagram, relying on the symmetry set by particle
topology and a charge defect between cube and sphere. Expressions for
non-retarded and retarded plasmon wavelengths are given and succeffully applied
to both experimental UV-Vis and numerically simulated values. The CFT analogy
can be promising to delve into the role of shape in nanoplasmonics and
nanophotonics.
