Correlation functions and thermal rate constants

Thermal rate constants k(T) and cumulative reaction probabilities N(E) can be computed as a sum of correlation functions C-nm = <<phi>(n)/f((H) over t ilde/phi (m)). In this paper we discuss the use of two different Krylov sub space methods to compute these correlation functions for large systems. The first approach is based on the Lanczos algorithm to transform the Hamilton ian to tridiagonal form. As shown by Mandelshtam (J. Chem, Phys. 1998, 108, 9999) and Chen and Guo (J, Chem. Phys. 1999, 111, 9944), ail correlation f unctions can be computed from a single recursion. The second approach treat s a number of linear systems of equations using a Krylov subspace solver. H ere the quasiminimal residual (QMR) method was used. For the first approach , we found that we needed the same number of Lanczos recursions as the size of the matrix. If Ilo re-orthogonalization is used, the number of recursio ns grows further. The linear solver approach, on the other hand, converges fast for each linear system, but many systems must be solved.