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The instabilities of the Hartree–Fock solutions and the lattice instabilities for conjugated hydrocarbons: The bond‐order and bond‐length alternations
Author(s) -
Toyota A.,
Tanaka T.,
Nakajima T.
Publication year - 1976
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560100520
Subject(s) - pentalene , instability , singlet state , chemistry , bond order , conjugated system , lattice (music) , excited state , annulene , molecular physics , bond length , chemical physics , atomic physics , computational chemistry , physics , molecule , quantum mechanics , organic chemistry , acoustics , polymer
The instabilities, especially the singlet instabilities, of the conventional Hartree–Fock ( HF ) solutions for a variety of alternant and nonalternant hydrocarbons, some of which have been known to show lattice instabilities (bond‐length alterations), are examined. The HF solutions for nonalternant hydrocarbons in the pentalene series larger than heptalene and [4 n + 2]‐annulenes larger than C 22 H 22 are found to be singlet unstable and there appear new solutions lower in energy than the conventional HF solutions and characterized by charge‐density waves exhibiting bond‐order alterations. It is found that such symmetry‐breaking solutions are energetically further stabilized by distorting the nuclear framework so that it may match up with the distribution of bond‐order matrix elements of the charge‐density wave, which means that in conjugated systems the singlet instability of the HF solution is always accompanied with the lattice instability. Further, it is shown that in conjugated systems, even when the HF solution is singlet stable, if it is not sufficiently stable as, for example, in pentalene and heptalene, there is every possibility for the occurrence of lattice instability. It is also shown that the singlet instability as well as the lattice instability arises from the existence of a sufficiently low‐lying singlet excited state.