Effect of the long-range portion of coulombic repulsion of electrons on the nature of the ground state of polymers containing conjugated bonds

Conclusions

The variation procedure presented above is equivalent to the summation of only zero-audio diagrams. However, arguments exist based on the theory of perturbation with a small interaction, according to which calculation of the second (superconducting) channel and, consequently, consideration of diagrams of a broader (parquet) class [12] are necessary. The basis for the restrictions accepted by us is first, that we are not examining a small interaction and second, the presence of long-range coulombic repulsion of electrons evidently makes optional the consideration of the superconducting channel even at small γ_mn. Recently it was shown in [13] that for the case of a one-dimensional problem with attraction the accurate spectrum of Fermi excitations coincides in form with the spectrum obtained on the basis of the Bardeen-Cooper-Schrieffer (BCS) approximation and that the slit in the accurate spectrum of a one-dimensional superconductor differs from the BCS slit only in the pre-exponential factor, which makes it possible to look forward to the production of an accurate excitation spectrum in a self-consistent procedure.

It should also be noted that the wave function (3)–(5) for the case of SW is not an eigenfunction of the square of the total spin operator Ŝ² and it is not an eigenfunction of the total pulse operator $\hat P$ of the system of electrons for the case of CW. After projecting to a state with accurate quantum numbers (S=0 for SW states and P=0 for CW states) a new function is obtained, which as previously depends on one variation parameter δ. In this case the new value of δ agrees with the old value with an accuracy to terms ∼1/N. All characteristics of the system calculated with the new and old variation functions including total energy of the excitation spectrum, etc., coincide with this accuracy. Exceptions are spin density, which is equal to zero on each atom of the chain for a singlet component of the SW state [3, 14], and electron density, which is equal to one on each atom of the chain for components with P=0 of the CW state, so that the charge on each atom is equal to zero. Thus, “spin waves” or “charge waves” as such do not exist in the states of type SW or CW with accurate variation functions and only the corresponding correlation functions indicate directly an antiferromagnetic spin structure [3] or a ferroelectric phase.