Transition state resonances by complex scaling: A three-dimensional study of ClHCl

Abstract

Four lowest-lying transition state resonance energies and lifetimes in the three-dimensional ClH+Cl←ClHCl→Cl+HCl reaction are reported in this paper. This is the first application of the complex coordinate method to a three-dimensional, triatomic molecule with a double dissociation continuum, which has been handled by means of the hyperspherical coordinates. Two numerical strategies have been considered in order to make the calculations feasible. The first one consists in minimizing the dimension of the Hamiltonian matrix by prediagonalization of the basis set. This has been achieved in terms of the successive adiabatic reduction method of Bac̆ić and Light [J. Chem. Phys. 85, 4594 (1986)], holding the hyperradius fixed. The second strategy is to compute a reduced 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 iterative scheme to the complex scaled resolvant operator (E0−H̄)−1, rather than to the complex scaled Hamiltonian. Inversion of a large complex symmetric matrix is avoided by using an LU decomposition of the complex scaled Hamiltonian matrix (E0−H̄). The proposed numerical approach appears to be very efficient and powerful for the study of large systems.