A simple recursion polynomial expansion of the Green`s function with absorbing boundary conditions. Application to the reactive scattering

Journal Article · Tue Aug 22 04:00:00 EDT 1995 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.470477· OSTI ID:83913

Mandelshtam, V A; Taylor, H S ^[1]

---

1. Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)

The new recently introduced [J. Chem. Phys {bold 102}, 7390 (1995)] empirical recursion formula for the scattering solution is here proved to yield an exact polynomial expansion of the operator [{ital E}{minus}({ital {cflx H}}+{cflx @}gG)]{sup {minus}1}, {cflx @}gG being a simple complex optical potential. The expansion is energy separable and converges uniformly in the real energy domain. The scaling of the Hamiltonian is trivial and does not involve complex analysis. Formal use of the energy-to-time Fourier transform of the ABC (absorbing boundary conditions) Green`s function leads to a recursion polynomial expansion of the ABC time evolution operator that is global in time. Results at any energy and any time can be accumulated simultaneously from a single iterative procedure; no actual Fourier transform is needed since the expansion coefficients are known analytically. The approach can be also used to obtain a perturbation series for the Green`s function. The new iterative methods should be of a great use in the area of the reactive scattering calculations and other related fields. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

• DOE Contract Number: FG03-94ER14458
• OSTI ID: 83913
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 8 Vol. 103; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUNDARY CONDITIONS
CHEMICAL REACTIONS
GREEN FUNCTION
HAMILTONIANS
ITERATIVE METHODS
POLYNOMIALS
RECURSION RELATIONS
SCATTERING AMPLITUDES