Abstract
This review is devoted to the basic problem in quantum theory of quasi-one-dimensional electron systems like polyenes (Part 1) and cumulenes (Part 2) – physical origin of the forbidden zone in these and analogous 1D electron systems due to two possible effects – Peierls instability (bond alternation) and Mott instability (electron correlation). Both possible contradiction and coexistence of the Mott and Peierls instabilities are summerized on the basis of the Kiev quantum chemistry team research projects.
Highlights
This review gives detailed results and thorough discussion of basic results in quantum theory of quasione-dimensional electron systems like Polyenes (Part 1 [1]) and Cumulenes (Part 2), including partly Polyacetylenes, Polydiacetylenes, and some organic crystalline conductors obtained by Kiev quantum chemistry team with my direct and consultive or conductive participation in some of the research projects below
The EHF method gives zero value of the torsion barrier for long cumulenes with equal bond lengths. These results once more suggest the necessity for taking account of electron correlation when large conjugated systems are treated. We think that these results provide some further evidence for the correlation nature of the forbidden zone in spectra of long cumulene chains and, long polyene chains
Conclusions & Perspectives Advances in physics and chemistry of lowdimensional electron systems have been magnificent in the last few dacades
Summary
This review gives detailed results and thorough discussion of basic results in quantum theory of quasione-dimensional electron systems like Polyenes (Part 1 [1]) and Cumulenes (Part 2), including partly Polyacetylenes, Polydiacetylenes, and some organic crystalline conductors obtained by Kiev quantum chemistry team with my direct and consultive or conductive participation in some of the research projects below. If the long cumulene chain in the conformation A (D2d ) involving the odd number of π-electrons in each of the two subsystems a and b is treated by means of the Huckel or the RHF methods, in the spectrum of such chain there are two levels in the ground state which correspond to the zero values of one-electron energies, whether the bond alternation is introduced or not. Equation (69) shows that ˆ is proportional to the overall difference in the number of electrons with spin σ at the even and odd atoms of the chain and differs from zero only if spin alternation at the neighbouring sites of the chain take place Retaining this term makes it possible to account for the correlation contribution to the energy gap or, in other words, to treat the Mott-type semiconductors, while, as it has been mentioned, the second term in (65) allows ua to consider the Peierls instability. Which is merely a correction to the Hartree-type term discussed above, and in the ground state assumbed to be replacable by the C number N 12 ;
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