A SIMPLE RECURSION POLYNOMIAL EXPANSION OF THE GREENS-FUNCTION WITH ABSORBING BOUNDARY-CONDITIONS - APPLICATION TO THE REACTIVE SCATTERING

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-(($) over cap H+Gamm a)](-1), Gamma 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 compl ex analysis. Formal use of the energy-to-time Fourier transform of the ABC (absorbing boundary conditions) Green's function leads to a recur sion polynomial expansion of the ABC time evolution operator that is g lobal in time. Results at any energy and any time can be accumulated s imultaneously from a single iterative procedure; no actual Fourier tra nsform is needed since the expansion coefficients are known analytical ly. 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 u se in the area of the reactive scattering calculations and other relat ed fields. (C) 1995 American Institute of Physics.