A simple recursion polynomial expansion of the Green`s function with absorbing boundary conditions. Application to the reactive scattering
- 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, Vol. 103, Issue 8; Other Information: PBD: 22 Aug 1995
- Country of Publication:
- United States
- Language:
- English
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