A uniformly convergent propagation scheme designed for non-Hermitian Hamiltonian operators is presented. The method is based on a Newtonian interpolation polynomial which is created by a recursive application of the Hamiltonian operator on an initial wave function. The interpolation points used to construct the Newtonian polynomial are located in the complex eigenvalue space of the Hamiltonian. A new algorithm is developed to construct the interpolation points. Both time dependent and time independent quantities can be obtained using the same polynomial expansion. The method is particularly useful when negative imaginary potentials are used. The photodissociation dynamics of I-3(-) is studied as an example of the utility of the scheme to gain insight on a dynamical encounter. The bond cleavage is followed in time simultaneously with the calculation of the Raman spectra. The study addresses the role of vibrational excitation of the reactant I-3(-) on the nascent I-2(-) spectral modulations and Raman spectra.