A simple recursion polynomial expansion of the Green’s function with absorbing boundary conditions. Application to the reactive scattering
10.1063/1.470477
Crossref journal-article
AIP Publishing
The Journal of Chemical Physics (317)
Abstract

The new recently introduced [J. Chem. Phys 102, 7390 (1995)] empirical recursion formula for the scattering solution is here proved to yield an exact polynomial expansion of the operator [E−(Ĥ+Γ̂)]−1, Γ̂ 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.

Bibliography

Mandelshtam, V. A., & Taylor, H. S. (1995). A simple recursion polynomial expansion of the Green’s function with absorbing boundary conditions. Application to the reactive scattering. The Journal of Chemical Physics, 103(8), 2903–2907.

Authors 2
  1. Vladimir A. Mandelshtam (first)
  2. Howard S. Taylor (additional)
References 18 Referenced 305
  1. 10.1063/1.469051 / J. Chem. Phys. (1995)
  2. 10.1063/1.452459 / J. Chem. Phys. (1987)
  3. 10.1063/1.465450 / J. Chem. Phys. (1993)
  4. 10.1039/ft9908601641 / J. Chem. Soc. Faraday Trans. (1990)
  5. 10.1016/0010-4655(93)90142-Y / Comput. Phys. Commun. (1993)
  6. 10.1016/0009-2614(93)85523-Q / Chem. Phys. Lett. (1993)
  7. 10.1016/0009-2614(94)00590-7 / Chem. Phys. Lett. (1994)
  8. 10.1063/1.468481 / J. Chem. Phys. (1994)
  9. 10.1063/1.466354 / J. Chem. Phys. (1994)
  10. 10.1063/1.456755 / J. Chem. Phys. (1989)
  11. 10.1063/1.463088 / J. Chem. Phys. (1992)
  12. 10.1063/1.448462 / J. Chem. Phys. (1985)
  13. 10.1016/0009-2614(89)87328-2 / Chem. Phys. Lett. (1989)
  14. 10.1021/j100319a003 / J. Phys. Chem. (1988)
  15. 10.1063/1.448136 / J. Chem. Phys. (1984)
  16. 10.1016/0021-9991(86)90199-3 / J. Comput. Phys. (1986)
  17. 10.1088/0953-4075/26/23/021 / J. Phys. B (1993)
  18. 10.1146/annurev.pc.45.100194.001045 / Annu. Rev. Phys. Chem. (1994)
Dates
Type When
Created 23 years, 1 month ago (July 26, 2002, 8:14 a.m.)
Deposited 2 years, 1 month ago (July 9, 2023, 10:33 a.m.)
Indexed 1 month, 1 week ago (July 24, 2025, 7:42 a.m.)
Issued 30 years ago (Aug. 22, 1995)
Published 30 years ago (Aug. 22, 1995)
Published Print 30 years ago (Aug. 22, 1995)
Funders 0

None

@article{Mandelshtam_1995, title={A simple recursion polynomial expansion of the Green’s function with absorbing boundary conditions. Application to the reactive scattering}, volume={103}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.470477}, DOI={10.1063/1.470477}, number={8}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Mandelshtam, Vladimir A. and Taylor, Howard S.}, year={1995}, month=aug, pages={2903–2907} }