A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

A COMPARATIVE STUDY OF ITERATIVE CHEBYSHEV AND LANCZOS IMPLEMENTATIONS OF THE BOUNDARY INHOMOGENEITY METHOD FOR QUANTUM SCATTERING

We have recently developed a scaleable Artificial Boundary Inhomogeneity (ABI) method [Chem. Phys. Lett.366, 390–397 (2002)] based on the utilization of the Lanczos algorithm, and in this work explore an alternative iterative implementation based on the Chebyshev algorithm. Detailed comparisons between the two iterative methods have been made in terms of efficiency as well as convergence behavior. The Lanczos subspace ABI method was also further improved by the use of a simpler three-term backward recursion algorithm to solve the subspace linear system. The two different iterative methods are tested on the model collinear H+H 2 reactive state-to-state scattering.

CALCULATION OFHO2DENSITY OF STATES ON THREE POTENTIAL ENERGY SURFACES

Density of states (DOS) in both bound and unimolecular dissociation regime for HO2system have been calculated quantum mechanically by Lanczos homogeneous filter diagonalization (LHFD) method. Three potential energy surfaces are explored and the results are contrasted for the total angular momentum J = 0 density of states. While two ab initio potential energy surfaces (PESs) (TU PES, J Chem Phys, 115:3621 and XXZLG PES, J Chem Phys122:244) produce the DOSs which are in fairly good agreement, the semi-empirical double many-body expansion (DMBE) IV PES (J Phys Chem94:8073) generates the much higher DOSs in higher energy range. The quantum mechanical DOSs are also compared with Troe et al.'s results from harmonic density, semiclassical density and their early density of states on the same TU ab initio surface.

HOCl Ro-Vibrational Bound-State Calculations for Nonzero Total Angular Momentum

The Lanczos homogeneous filter diagonalization method has been employed to compute the HOCl ro-vibrational states for a range of total angular momenta (J = 0, 1, 5, 10, 11, 20, 30) on a newly developed ab initio potential energy surface by Nanbu et al. (J. Theor. Comput. Chem. 2002, 1, 263). For such computationally challenging calculations, a parallel computing strategy has been incorporated into our method to perform the matrix-vector multiplications. For the computed low bound states, a spectroscopic assignment has been made and the widely used approximate adiabatic rotation method has been tested for the broad range of total angular momenta for this deep-well system. Comparison of experimental results with exact quantum mechanical calculations for the selected far-infrared transitions involving the range of total angular momenta has been made possible for the first time.

HO2 Ro-Vibrational Bound-State Calculations for Large Angular Momentum: J = 30, 40, and 50

The Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization scheme incorporating doubling of the autocorrelation functions have been employed to compute the HO2 ro-vibrational states for high total angular momenta, J = 30, 40, and 50. For such computationally challenging calculations, we have adopted a parallel computing strategy to perform the matrix-vector multiplications. Low-lying bound states and high-lying bound states close to the dissociation threshold are reported. For low-lying bound states, a spectroscopic assignment has been attempted and the widely used approximate J-shifting method has been tested for this deep-well system. For high-lying bound states, the attempted spectroscopic assignments as well as the J-shifting approximation fail because of very strong Coriolis mixing, indicating that the Coriolis couplings are important for this system.

Unimolecular rovibrational bound and resonance states for large angular momentum: J=20 calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-->H+O2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.

Converged quantum calculations of HO2 bound states and resonances for J=6 and 10

Bound and resonance states of HO(2) are calculated quantum mechanically using both the Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization method for nonzero total angular momentum J=6 and 10, using a parallel computing strategy. For bound states, agreement between the two methods is quite satisfactory; for resonances, while the energies are in good agreement, the widths are in general agreement. The quantum nonzero-J specific unimolecular dissociation rates for HO(2) are also calculated.