A collocation approach for quantum scattering based on the S -matrix version of the Kohn variational principle

Journal Article · Fri Dec 15 04:00:00 EST 1989 · Journal of Chemical Physics; (USA)

DOI:https://doi.org/10.1063/1.457277· OSTI ID:5019703

Yang, W; Peet, A C; Miller, W H ^[1]

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1. Department of Chemistry, University of California, Berkeley, CA (USA) Materials and Chemical Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 (US)

A collocation approach to quantum scattering is presented. The method is based on the {ital S}-matrix version of the Kohn variational principle with a different linear expansion used for the two wave functions---one is a linear combination of basis functions and the other is a pointwise representation with proper asymptotic conditions imposed. The resulting equations are similar in structure to the usual version of the Kohn variational principle, however, in the present approach there are no integrals between the square integrable ({ital L}{sup 2}) basis functions. In addition, the method does not require the knowledge of quadrature weights associated with the collocation points as was the case in a previous pointwise method for quantum scattering. This property means that the method is readily applicable to reactive scattering problems which use different sets of coordinates for reactants and products. Appliction to a simple inelastic test problem (collinear He--H{sub 2} vibrationally inelastic scattering) shows the accuracy of the approach to be comparable to that of the usual variatinal form of the {ital S}-matrix Kohn method.

• OSTI ID: 5019703
• Journal Information: Journal of Chemical Physics; (USA), Journal Name: Journal of Chemical Physics; (USA) Vol. 91:12; ISSN JCPSA; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOM COLLISIONS
ATOM-MOLECULE COLLISIONS
COLLISIONS
ELEMENTS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EXCITED STATES
FLUIDS
FUNCTIONS
GASES
HELIUM
HYDROGEN
INELASTIC SCATTERING
MATRICES
MOLECULE COLLISIONS
NONMETALS
RARE GASES
S MATRIX
SCATTERING
VARIATIONAL METHODS
VIBRATIONAL STATES
WAVE FUNCTIONS