Quantum mechanical generalized phase-shift approach to atom-surface scattering: A Feshbach projection approach to dealing with closed channel effects

Journal Article · Mon Mar 28 00:00:00 EDT 2011 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3565426· OSTI ID:21560062

Maji, Kaushik; Kouri, Donald J ^[1]

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1. Departments of Chemistry, Mathematics, Mechanical Engineering, and Physics, University of Houston, Houston, Texas 77204-5006 (United States)

We have developed a new method for solving quantum dynamical scattering problems, using the time-independent Schroedinger equation (TISE), based on a novel method to generalize a ''one-way'' quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N{sup 2} scaling, where N is the number of coupled equations. The full two-way nature of the TISE is included while propagating the wave function in the scattering variable and the full S-matrix is obtained. The new algorithm is based on a ''Modified Cayley'' operator splitting approach, generalizing earlier work where the method was applied to the time-dependent Schroedinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtz-type equation, and for more than one degree of freedom, these are notoriously ill-behaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components.

• OSTI ID: 21560062
• Journal Information: Journal of Chemical Physics, Vol. 134, Issue 12; Other Information: DOI: 10.1063/1.3565426; (c) 2011 American Institute of Physics; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
ALGORITHMS
APPROXIMATIONS
ATOMS
BOUNDARY CONDITIONS
DEGREES OF FREEDOM
NUMERICAL SOLUTION
PHASE SHIFT
PROJECTION OPERATORS
QUANTUM MECHANICS
S MATRIX
SCATTERING
SCHROEDINGER EQUATION
SOLUTIONS
SURFACES
TIME DEPENDENCE
WAVE FUNCTIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DISPERSIONS
EQUATIONS
FUNCTIONS
HOMOGENEOUS MIXTURES
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MATRICES
MECHANICS
MIXTURES
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS