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 and Cumulenes, 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
We begin in Part 1 of the review with local electronic states in long polyene chains in the simple tightbinding approximation [1,2,3,4]
Further we turn to theory of electronic structure of long polyene neutral alternant radicals based on the different orbital for different spins self-consistent field (SCF) method [6]
Summary
This review gives detailed results and thorough discussion of basic results in quantum theory of quasione-dimensional electron systems like Polyenes and Cumulenes, 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 perturbation is localized in the middle of the chain, neglecting terms like exp( n ) in (49) and solving the corresponding equation, one obtains It follows from (50) that an appearance of a pair of local states is possible only when the bond is strengthened. Substituting corresponding Green functions from (10)–(13) into (48), the following equation is obtained for the local levels appearing under the perturbation of the weaker bond An analysis of (56) shows that this solution exists only when | 2 | | 2 | This means that any small strengthening of the weaker bond in the middle of the chain always leads to the appearance of two local states in the forbidden zone. All paragraphs are devoted to different methods for accounting of interaction between electrons
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