Earlier quoted context omitted.
The vast majority of useful things cannot be computed with QED from fundamental principles. You cannot compute even simple atomic energy spectra. The fundamental laws of chemistry have not been changed much by quantum physics, they just became better understood and less mysterious. Quantum mechanics has explained various cases of unusual chemical bonds that appeared to contradict the simpler rules that were believed…
What are you talking about? The spectra of hydrogen is very well understood and a text book example for students to calculate. We use spectra to test QED calculations to something like 14 digits.
The spectrum of hydrogen (ignoring the fine structure) could be computed with the empirical rules of Rydberg before the existence of quantum physics. Quantum physics has just explained it in terms of simpler assumptions.
Quantum physics explains a great number of features of the atomic spectra, but it is unable to compute anything for complex atoms with an accuracy comparable with the experimental measurements.
The QED calculations with "14 digits" of precision are for things that are far simpler than atomic spectra, e.g. for the gyromagnetic ratio of the electron, and even for such things the computations are extremely difficult and error-prone.