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There is a special class of crystalline structures which, in the first-order perturbation theory, allow for the electronic system to be decoupled from the phonon degrees of freedom. Such systems and electronic states are identified on the basis of symmetry and group theory. To arise such electron–phonon decoupling, three general symmetry-based conditions are to be satisfied. By giving clear formulation of these criteria, a recipe for engineering the configurations with electron–phonon coupling deficiency is presented. The Jahn–Teller theorem validity is also discussed and it is shown that breakdown of the theorem in any dimension is possible, that is, there are specific configurations of molecules, polymers, layers, and 3D crystals, whose total energy is optimized by hosting a ground electronic state that is orbitally degenerate. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim