Towards an e cient implementation of the eigenstateexpansion method for quantum molecular

We investigate the eecient computation of a few of the lowest eigenvalues of a symmetric eigenvalue problem occurring in quantum dynamical molecular simulations. The systems of equations that arise when applying subspace iteration or the Jacobi-Davidson algorithm with the shift-and-invert spectral transformation are solved by the preconditioned conjugate gradient method. We propose and analyze a new eeective ADI-type preconditioner that exploits the special structure of the matrix which is the sum of Kronecker products of Toeplitz matrices. The theoretical convergence behavior is veriied by numerical experiments.