Rotational spectrum and structure of thioborine: HBS
The millimeter-wave spectra of eight isotopic species of thioborine have been observed. This unstable molecule displays the rotational spectrum of a linear rotor. For the most abundant isotopic specie...
The millimeter-wave spectra of eight isotopic species of thioborine have been observed. This unstable molecule displays the rotational spectrum of a linear rotor. For the most abundant isotopic specie...
Raman study of aqueous zinc oxide-alkali metal hydroxide system
Analysis of Raman spectra of concentrated alkali metal hydroxide solutions and the solutions of ZnO in concentrated alkali metal hydroxide solutions has contradicted the tetrahedral structure of zinca...
Analysis of Raman spectra of concentrated alkali metal hydroxide solutions and the solutions of ZnO in concentrated alkali metal hydroxide solutions has contradicted the tetrahedral structure of zinca...
On transition-state theory and the classical mechanics of collinear collisions
J. Chem. Phys. 58, 1622 (1973); doi:10.1063/1.1679404
Issue Date: 15 February 1973
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We consider classical transition-state theory of collinear atom-diatom reactions. There are (many) potential surfaces for which this theory is exact provided all trajectories with energy above some fixed value are disregarded; the energy cutoff of course depends on the surface. We develop a simple criterion for recognizing or constructing such surfaces, and discuss examples. We also show that if a surface has a proper transition state, as defined below, then transition-state theory is exact unless collision complexes exist.
©1973 The American Institute of Physics
| History: | Received 28 September 1972 |
| Permalink: |
http://link.aip.org/link/?JCPSA6/58/1622/1 |
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REFERENCES (6)
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- We use the word “trajectory” indiscriminately, to designate a classical phase path (pt,qt) or its configuration space projection qt.
- This means that the criterion for transition-state theory is purely dynamic: the canonical weighting e−
H is incidental, and if transition-state theory is exact to energy E then integrals (1) and (2) are equal with e−H replaced by any smooth function f(H) that cuts off at H = E. In particular, if canonical transition-state theory is exact to energy E, the microcanonical analogue [f(H) = 
(H−E![[prime]](http://scitation.aip.org/stockgif3/prime.gif)
)] must be exact for almost all E
E. - J. C. Keck, Advances in Chemical Physics (Interscience, New York, 1967), Vol. 13, p. 85.
- The whole trick, in the following two paragraphs, is to prove that this is actually the case. If we require of the various line segments that they not intersect one another in the region V(q)E, the lines can be regarded as belonging to a coordinate grid [much like the “natural collision coordinates” studied extensively by R. A. Marcus, J. Chem. Phys. 45, 4493, 4500 (1966)], and the proof is trivial. But we do not want to require this: it is an annoyance—in constructing a family of straight lines—to worry about intersections, so the modest effort needed to get the stronger result is worthwhile.
- A caution: this map must be in the skewed coordinate frame. The criterion above is not invariant to the transformation from “natural” coordinates to the skewed frame.
- R. N. Porter and M. Karplus, J. Chem. Phys. 40, 1105 (1964).
