The orthogonalized plane wave (OPW) method Conyers Herring had proposed in 1940 solved the convergence problem, but at a considerable practical cost: each calculation required explicitly handling the complete wave functions of the core electrons, which kept the procedure a powerful but cumbersome tool to apply to real materials. James C. Phillips, a theoretical physicist who had joined in 1956 the Bell Labs group led precisely by Herring, spent those years developing an empirical pseudopotential to fit the covalent energy gaps of silicon and germanium, but sought a version derived from first principles rather than empirically fitted. At Berkeley, together with Leonard Kleinman — then a doctoral student, who according to his own autobiographical account explicitly wondered why not "imitate" the OPW orthogonalization procedure instead of the approximate pseudopotentials circulating in the literature — both proved in 1959 a decisive result: Herring's OPW formalism is mathematically equivalent to solving the Schrödinger equation for a valence electron moving not in the crystal's real potential, but in a much weaker, smoother effective potential — the pseudopotential — in which the repulsive effect of orthogonalization to the core electrons is absorbed as an explicit additional term. The practical consequence was immediate: instead of handling the core functions at every step of the calculation, it suffices to replace them with this effective potential, drastically reducing computational cost with no loss of precision. Phillips and Kleinman's reformulation is the direct basis of the entire modern family of pseudopotential methods (norm-conserving, ultrasoft, etc.) used today together with density functional theory in virtually all industrial-scale materials and semiconductor simulation software.