To illustrate and discuss in details some concepts in this review, we performed computations using ORCA 5.0 program package. The geometries of the polyene carbon chain, as well as 1,3-butadiene and the corresponding α,β-unstaurated carbonyl, have been performed at the restricted Hartree-Fock level (HF) of theory and def2-SVP basis set. To prevent the appearance of charge-density waves in the presented density-difference plots associated with Peierls instability, the final single-point calculations have been performed at the density functional theory (DFT) level with simple LDA approximate functional, along with the def2-SVP basis set.