Semiclassically optimized complex absorbing potentials of polynomial form. I. Pure imaginary case

We present an optimal, pure imaginary complex absorbing potential (CAP) of polynomial form, for calculating resonance energies and widths, photodissociation cross sections, rate constants, etc. The optimal CAP is derived by minimizing reflection from, and transmission through, the CAP. Reflection and transmission are computed semiclassically. The optimal CAP is general, and can be used at any energy and with any absorbing region width. It significantly reduces the absorbing region width required to compute resonances of the one-dimensional Hazi–Taylor system. We also clearly discuss different types of reflection, and resolve apparent discrepancies relating to optimal CAPs.