A Comment on the Paper by Hideo Fukutome: Spin Density Wave and Charge Transfer Wave in Long Conjugated Molecules

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Abstract
The relationship is pointed out between the paper by Fukutome [H. Fukutome, Prog. Theor. Phys. 40 (1968), 998, 1227] and our paper on stabilities of the solutions of HF equations [J. Čížek and J. Paldus, J. Chem. Phys. 47 (1967), 3976]. It is shown that in the case of the singlet instabilities [J. Čížek and J. Paldus, op. cit.] (instabilities to number density fluctuations [H. Fukutome, op. cit.]) of π-electronic models of cyclic polyenes, two cases must be distinguished, namely the instability to the atomic charge density fluctuations, as well as the instability to the bond-order fluctuations. The HF equations in Bogoliubov form for the solutions having alternating bond orders are given. The results of the actual calculations of the HF solutions for both types of singlet instabilities in cyclic polyenes are briefly mentioned. These calculations show that for all semiempirical parametrizations currently used the HF solutions with alternating atomic charge density are not only higher in energy than the bond-order alternating HF solutions, but are also singlet unstable.

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