Algorithms for obtaining cumulative reaction probabilities for chemical reactions (Q675193)

Computation of eigenvalues of a quantum chemical Hermitian matrix \(Z\) is discussed. It has a few small physical eigenvalues, while all the other, nonphysical eigenvalues are much larger. The separation is such that all the physical eigenvalues can be considered as one cluster. The implicitly restarted Lanczos algorithm (IRL) with Chebyshev polynomial preconditioning computes one physical eigenvector. Several ways of finding more than one physical eigenvector are compared and it is found that a coarse parallel algorithm, where \(k\) independent runs of IRL find one vector each in the physical subspace, together making up a nonorthogonal approximate basis of this physical eigenvector subspace, performs better than the other variants.