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The two-body problem of variational electrodynamics possessesdifferential-delay equations of motion with state-dependent delays of neutraltype and solutions that can have velocity discontinuities on countable sets.From a periodic orbit possessing some mild properties at breaking points, wedefine a synchronization function in R x R3, which is further used to constructtwo bounded oscillatory functions vanishing at breaking points and whose firstderivatives are continuous and defined everywhere but at breaking points. Theoscillatory functions are associated with a PDE identity in H2(R3), and wepostulate ordering conditions for the PDE identity to define aFredholm-Schroedinger operator with an O(1/r2) spin-orbit forcing termbelonging to L2(R3). As an application, we introduce the Chemical Principlecriterion to select orbits with asymptotically vanishing far-fields andestimate the Bohr radius parameter of the Fredholm-Schroedinger PDE using theboundary-layer of orbits chosen according to the Chemical Principle criterion.Last, working backward, we derive a Chemical Principle-like condition from theordering conditions.

Chemical Principle and PDE of Variational Electrodynamics