Peierls distortion in linear chains. In linear molecules with three or more atoms there may be PJTE distortions that do not violate the linearity but change the interatomic distances. For instance, as a result of the PJTE a centrosymmetric linear system may become non-centrosymmetric in the equilibrium configurations, as, for example, in the BNB molecule (see in ). An interesting extension of such distortions in sufficiently long (infinite) linear chains was first considered by Peierls. In this case the electronic states, combinations of atomic states, are in fact band states, and it was shown that if the chain is composed by atoms with unpaired electrons, the valence band is only half filled, and the PJTE interaction between the occupied and unoccupied band states leads to the doubling of the period of the linear chain (see also in the books ).