TRANSITION-STATE RESONANCES BY COMPLEX SCALING - A 3-DIMENSIONAL STUDY OF CLHCL

Four lowest-lying transition state resonance energies and lifetimes in the three-dimensional ClH+Cl<--ClHCl-->Cl+HCl reaction are reported i n this paper. This is the first application of the complex coordinate method to a three-dimensional, triatomic molecule with a double dissoc iation continuum, which has been handled by means of the hyperspherica l coordinates. Two numerical strategies have been considered in order to make the calculations feasible, The first one consists in minimizin g the dimension of the Hamiltonian matrix by prediagonalization of the basis set. This has been achieved in terms of the successive adiabati c reduction method of Bacic and Light [J. Chem, Phys. 85, 4594 (1986)] , holding the hyperradius tired. The second strategy is to compute a r educed set of eigenvalues corresponding to the resonances by using the complex Lanczos algorithm, The number of Lanczos recursions required to achieve convergence is dramatically reduced by applying the iterati ve scheme to the complex scaled resolvant operator (E(0)-(H) over bar) (-1), rather than to the complex scaled Hamiltonian. Inversion of a la rge complex symmetric matrix is avoided by using an LU decomposition o f the complex scaled Hamiltonian matrix (E(0)-(H) over bar) The propos ed numerical approach appears to be very efficient and powerful for th e study of large systems. (C) 1995 American Institute of Physics.