Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Abstract

Articles you may be interested inResonance phenomena associated with the unimolecular dissociation of HO 2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization ͑LHFD͒ method. The calculated resonance energies, rates ͑widths͒, and product state distributions are compared to results from an autocorrelation function-based filter diagonalization ͑ACFFD͒ method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O 2 show strong fluctuations, indicating the dissociation of HO 2 is essentially irregular.

A complex guided spectral transform Lanczos method for studying quantum resonance states

“…Its bound and resonance energies and widths have been extensively studied. 12,63,65,66,68,82,83 As in our previous study, 63 we used the Jacobi coordinates (R H−OO , R OO , θ) with zero total angular momentum J = 0. Thus the system Hamiltonian is written aŝ…”

“…5,59 Therefore, the algorithm is inefficient to study resonances in dense regions, for example, those resonances that appear above a deep potential well, as in molecules HO 2 , NO 2 and HOCO etc. A combined filter diagonalization and Lanczos iteration approach 7,40,63,65 has been proposed to improve the convergence of calculations. On the other hand, if one is interested only in resonance energies and widths, there are several efficient algorithms based on the real (damped) Chebyshev propagation methods [33][34][35][66][67][68][69][70][71] in addition to the Lanczos, 7,63,73 Newton, [74][75][76][77] and Faber 20, 78 polynomial expansions.…”

CALCULATION OFHO2DENSITY OF STATES ON THREE POTENTIAL ENERGY SURFACES

“…In the LHFD method, 24,26 we first project the augmented Hamiltonian into a Krylov subspace using the Lanczos method. 14 Inside the subspace, the Hamiltonian (represented as a tridiagonal matrix, T M ) can be used to perform filter diagonalization (FD) calculations for various energy windows.…”

“…Lanczos methods exploit the sparsity of the tridiagonal subspace Hamiltonian generated by the iterative Lanczos algorithm. 14 While the Lanczos algorithm has commonly been used for matrix diagonalization 13 and short-time propagations, 16 recent work in the Brisbane lab has focused on exploring more general applications of the Lanczos representation, including spectral densities, [17][18][19] filter diagonalization for bound states and resonances, [20][21][22][23][24][25] partial resonance widths in unimolecular decay, 26 and state-tostate reactive scattering. 27,28 An important feature of these newer Lanczos implementations is that all physically relevant information is extracted from within the Lanczos representation.…”

Using <i>ScalIT</i> for Performing Accurate Rovibrational Spectroscopy Calculations for Triatomic Molecules: A Practical Guide

“…Much of the basis set reduction was achieved through the use of the PSODVR in radial dofs. Moreover, approximately 1500 total iterations were required to reach the above accuracy, compared to 6 10 required by Smith [31]- [35]. As one moves up the energy spectrum, the number of iterations required for convergence is increased, regardless of the iterative method employed.…”