Rieper, Anders and Vedral modelled the electron clouds of nucleic acids in a single strand of DNA as a chain of coupled quantum harmonic oscillators with dipole-dipole interaction between nearest neighbours. As a main result, the entanglement contained in the chain coincides with the binding energy of the molecule. Derived in the limit of long distances and periodic potentials analytic expressions linking the entanglement witnesses to the energy reduction due to the quantum entanglement in the electron clouds.