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Quantum mechanical calculations for rearrangement collisions of electrons, atoms, and molecules

Truhlar, Donald G. (1970) Quantum mechanical calculations for rearrangement collisions of electrons, atoms, and molecules. Dissertation (Ph.D.), California Institute of Technology.


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Quantum mechanical calculations are presented of approximate scattering cross sections for elastic and inelastic collisions, including rearrangements, for several processes involving electrons, hydrogen (H), helium (He), and potassium (K) atoms, and hydrogen (H[subscript 2]) and hydrogen halide (HX) molecules. In addition to their interest in terms of the processes themselves, the results are intercompared and compared with previous experimental and theoretical results in such a way as to provide tests of the general usefulness of the various methods used.

Electron scattering is treated using the Born, polarized Born, and Vainshtein-Presnyakov-Sobelman approximations for the direct scattering and thirteen different methods for the exchange scattering. The transitions treated are 1s-1s, 1s-2s, and 2s-2s in H, 1 […]S - 2 […]P, 1 […]S - 3 […]P, and 1 […]S- 2 […]S in He, and elastic scattering and rovibrational excitation of the ground state of H[subscript 1]. Most emphasis is placed on impact energies less than about 100 eV but higher energies are also treated. We draw conclusions concerning the accuracy of the various methods for treating the exchange scattering and for calculating integral cross sections and the angular dependences of differential cross sections for small and medium scattering angles. A version of the distorted wave approximation which should often be useful is presented. Some of the results and discussions for scattering off H and for excitation of the 2 […]P state of He have been presented in two articles and a long abstract which are summarized and referred to in the text.

The statistical phase space theory of Light, Pechukas, and Nikitin is used to calculate cross sections and rate constants for the reactions H + HX (including two isotopes of H) and K + HC1. The H + HX calculations presented here supplement those already published. The probability of reaction is studied as a function of the incident translational energy and impact parameter and the internal states of the products. A generalized nonstatistical phase space theory is presented which is adiabatic in one limit and equivalent to the statistical theory of Light, Pechukas, and Nikitin in another. Some sample calculations using the new theory on H + HBr reactions are also given.

We present numerical solutions of the three-body Schroedinger equation for the collinear H + H[subscript 2] and D + D[subscript 2] chemical reactions on an assumed potential energy surface. The parametrized analytic surface is based on the calculations of Shavitt and coworkers and is thought to be the most accurate surface available. Calculations are performed in one mathematical dimension by the conservation-of-vibrational-energy and vibrational-adiabaticity models. Calculations are presented in two mathematical dimensions which are essentially exact for the collinear collision. The calculations include vibrationally excited reactants and products. The calculations are compared and their relation to and implications for the usual tunneling approximations are discussed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:chemical reactions; electron scattering; quantum mechanical scattering theory; rearrangement collisions
Degree Grantor:California Institute of Technology
Major Option:Chemistry
Thesis Committee:
  • Kuppermann, Aron (chair)
  • McKoy, Vincent
  • Goddard, William A.
Defense Date:1 December 1969
Author Email:truhlar (AT)
Record Number:etd-01082009-135357
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72
Deposited By: Imported from ETD-db
Deposited On:08 Jan 2009
Last Modified:25 Dec 2012 14:57

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