A spectral transform Krylov subspace iteration approach to quantum scattering

A spectral transform Lanczos iteration method is suggested to find the eigenvalues and eigenvectors of the coupling matrix appearing in quantum scattering calculations. Three main attributes which improve previous implementations are (a) partial reorthogonalization, (b) exponential filter, and (c) discrete variable representation basis. The method is applied to the 3D rotating line umbrella calculations of the reaction Cl+CH4⇌ HCl+CH3 which shows that it is substantially faster than the direct diagonalization method. Calculated state-to-state reaction probabilities as well as adiabats are in good agreement with previous results.