Abstract
This paper is a detailed differential geometrical study of chemically reacting systems. In particular the following coordinate-free properties of chemically reacting systems are obtained: 1) the general solution of the intrinsic reaction coordinate (IRC) (henceforth referred to as meta-IRC), 2) “extended” definitions of the Hessian matrix and normal vibrations at any non-equilibrium point on the surface, and 3) clarification of the close connection between the geometry of meta-IRC and the geography of the surface at a transition point. The theory is elucidated using a model potential surface.
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Glasstone, S., Laidler, K., Eyring, H.: The theory of rate processes. New York: McGraw-Hill 1941
Pearson, R. G.: Accounts Chem. Res.4, 152 (1971)
Stanton, R. E., McIver, Jr., J. W.: J. Am. Chem. Soc.97, 3632 (1975)
Mezey, P. G., in: Application of MO theory in organic chemistry, Csizmadia, LG., Ed. Elsevier 1977
Fukui, K.: J. Phys. Chem.74, 4161 (1970)
Fukui, K., in: The world of quantum chemistry, Daudel, R., Pullman, B. Eds. Holland: D. Reidel Publ. Co. 1974
Fukui, K., Kato, S., Fujimoto, H.: J. Am. Chem. Soc.97, 1 (1975)
Kato, S., Fukui, K.: J. Am. Chem. Soc.98, 6395 (1976)
Ishida, K., Morokuma, K., Komornicki, A.: J. Chem. Phys.66, 2153 (1977)
Joshi, B. D., Morokuma, K.: J. Chem. Phys.67, 4880 (1977)
McCullough, E. A., Wyatt, R. E.: J. Chem. Phys.54, 3578 (1971);54, 3592 (1971)
Polanyi, J. C., Wong, W. H.: J. Chem. Phys.51, 1439 (1969)
Polanyi, J. C.: Accounts Chem. Res.5, 161 (1972)
Laugwitz, D.: Differential and Riemannian geometry. New York: Academic Press 1965
Flanders, H.: Differential forms. New York: Academic Press 1963
Eisenhart, L. P.: Riemannian geometry. Princeton: Princeton Univ. Press 1963
Synge, J. L., Schild, A.: Tensor calculus. Toronto: Univ. of Toronto Press 1962
Thom, R.: Structural stability and morphogenesis. New York: Benjamin 1975
Hirsch, M. W., Smale, S.: Differential equations, dynamical systems, and linear algebra. New York: Academic Press 1974
Krivoshey, I. V., Sleta, L. A.: Theoret. Chim. Acta (Berl.)43, 165 (1976)
Collard, K., Hall, G. G.: Intern. J. Quantum Chem.12, 623 (1977)
Bader, R. F. W.: Accounts Chem. Res.8, 34 (1975)
Srebrenik, S., Bader, R. F. W.: J. Chem. Phys.63, 3945 (1975)
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Tachibana, A., Fukui, K. Differential geometry of chemically reacting systems. Theoret. Chim. Acta 49, 321–347 (1978). https://doi.org/10.1007/BF00552483
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DOI: https://doi.org/10.1007/BF00552483