Schatz, George C. (1976) The quantum dynamics of atom plus diatom chemical reactions. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-09012006-080950
PART 1: The results of accurate quantum dynamical calculations on one, two and three dimensional atom plus diatomic molecule electronically adiabatic chemical reactions are presented. In papers 1 and 2, comparisons between quantum, quasi-classical and semi-classical results for the collinear F + H2 and F + D2 reactions, are examined. Paper 3 discusses the role of reactive and nonreactive collisions in producing vibrational deactivation in the collinear H + FH, D + FD, H + FD and D + FH systems. The extension of reactive scattering calculational methods to atom diatom collisions on a plane and in three dimensions is presented in papers 4 and 6, respectively. In both applications, the Schrodinger equation is solved by a coupled equation method in each of the three equation arrangement channel regions. This is followed by a matching procedure in which the wave function is made smooth and continuous at the boundaries of these regions, In the three dimensional case, the use of body fixed coordinates is crucial to obtaining an efficient coordinate transformation between arrangement channels. Applications of these 2D and 3D methods to the H + H2 exchange reaction are presented in papers 5 and 7. Integral and differential cross sections, reaction probabilities, product and reagent state rotational distributions, and other dynamical information are discussed in the papers, and these results are extensively compared with those of previous quasi-classical, semi-classical and approximate quantum calculations. The results of a very simple angular momentum decoupling approximation are considered in paper 7. In papers 8 and 9 the relative importance of direct versus resonant (shape or Feshbach) mechanisms for several atom diatom reactions is examined. A number of techniques for characterizing both mechanisms are discussed, including time delays, eigenphase shifts, Argand diagrams and the collision lifetime matrix. Extension of these 1D resonances to the 2D and 3D reactions is examined in paper 10 for the simple case of H + H2. PART 2: A method is presented for accurately solving the Schrodinger equation for the reactive collision of an atom with a diatomic molecule in three dimensions on a single Born-Oppenheimer potential energy surface. The Schrodinger equation is first expressed in body fixed coordinates. The wave function is expanded in a set of vibration-rotation functions, and the resulting coupled equations are integrated in each of the three arrangement channel regions to generate primitive solutions. These are then smoothly matched to each other on three matching surfaces which appropriately separate the arrangement channel regions. The resulting matched solutions are linearly combined to generate wave functions which satisfy the reactance and scattering matrix boundary conditions, from which the corresponding R and S matrices are obtained. The scattering amplitudes in the helicity representation are easily calculated from the body fixed S matrices, and from these scattering amplitudes, several types of differential and integral cross sections are obtained. Simplifications arising from the use of parity symmetry to decouple the close coupled equations, the matching procedures and the asymptotic analysis are discussed in detail. Relations between certain important angular momentum operators in body fixed coordinate systems are derived and the asymptotic solutions to the body fixed Schrodinger equation are analyzed extensively. Application of this formalism to the three-dimensional H + H2 reaction is considered including the use of arrangement channel permutation symmetry, even-odd rotational decoupling and post-antisymmetrization. The range of applicability and limitations of the method are discussed.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Chemistry and Chemical Engineering|
|Awards:||The Herbert Newby McCoy Award, 1975|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||8 September 1975|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||15 Sep 2006|
|Last Modified:||26 Dec 2012 02:58|
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