On the Convergence of the Perturbation Method (Journal of by Tosio Kato

By Tosio Kato

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Extra resources for On the Convergence of the Perturbation Method (Journal of the Faculty of Science, University of Tokyo. Section 1. Mathematics, Astronomy, Physics, Chemistry. vol. 6. part 3, pp. 145 - 226, March 31, 1951)

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36 CHAPTER 1 CHEMICAL BONDING AND STRUCTURE Fig. 13. Energy level diagrams for C3H3 and C5H5 systems. Monocyclic conjugated polyenes are referred to as annulenes, and there exists ample experimental evidence to support the conclusions based on application of HMO theory to neutral and charged annulenes. The relationship between stability and structure in cyclic conjugated systems will be explored more fully in Chapter 9. While HuÈckel's 4n ‡ 2 rule applies only to monocyclic systems, HMO theory is applicable to many other systems.

G. M. N. Glukhovtsev and S. Laiter, Theor. Chim. Acta 92:327 (1995). h. A. Nicolaides and L. Radom, J. Phys. Chem. 98:3092 (1994). Substituent effects on intermediates can also be analyzed by MO methods. Take, for example, methyl cations where adjacent substituents with lone pairs of electrons can form p bonds, as can be expressed in either valence bond or MO terminology. δ+ H :X C+ H δ+ H +X C H X H C H Fig. 9. Total energy as a function of distortion from planarity for methyl cation, methyl radical, and methyl anion.

Fortunately, the absolute errors for compounds of similar structure are likely to be comparable so that the errors will cancel in calculation of the energy differences between related molecules. Calculation of heats of formation and heats of reaction is frequently done on the basis of isodesmic reactions51 in order to provide for maximum cancellation of errors in total binding energies. 10. 6207 a. The orbital energies (eigenvalues) are not given. The lowest-energy orbital is c1 ; the highest-energy orbital, c7 .

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