Hybrid quantum scattering algorithms for long-range potentials

We investigate hybrid scattering codes which combine the log-derivative integrator (LOGD) of Johnson at short range with one of the three following integrators at moderate to long range: the multichannel WKB algorithm of Johnson, the variable-interval-variable-step (VIVS) algorithm of Parker, Schmalz, and Light, or a new algorithm (AIRY) based on the linear reference potential algorithm of Gordon modified to propagate the log-derivative matrix directly without determination of perturbation corrections. In calculations of S matrices for the collision of two HF molecules, where the off-diagonal coupling decreases only as R−3, the AIRY integrator is found to be 3 times faster than the WKB integrator, at least 5 times faster than the VIVS integrator, and 19 times faster than direct application of the LOGD integrator in the long-range region.