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

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) 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 HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Processing of high resolution magic angle spinning spectra of breast cancer cells by the filter diagonalization method

Proton nuclear magnetic resonance (H-1 NMR) spectroscopy for detection of biochemical changes in biological samples is a successful technique. However, the achieved NMR resolution is not sufficiently high when the analysis is performed with intact cells. To improve spectral resolution, high resolution magic angle spinning (HR-MAS) is used and the broad signals are separated by a T-2 filter based on the CPMG pulse sequence. Additionally, HR-MAS experiments with a T-2 filter are preceded by a water suppression procedure. The goal of this work is to demonstrate that the experimental procedures of water suppression and T-2 or diffusing filters are unnecessary steps when the filter diagonalization method (FDM) is used to process the time domain HR-MAS signals. Manipulation of the FDM results, represented as a tabular list of peak positions, widths, amplitudes and phases, allows the removal of water signals without the disturbing overlapping or nearby signals. Additionally, the FDM can also be used for phase correction and noise suppression, and to discriminate between sharp and broad lines. Results demonstrate the applicability of the FDM post-acquisition processing to obtain high quality HR-MAS spectra of heterogeneous biological materials.

Calculation of resonances and product state distributions for the unimolecular dissociation of H2S

Resonance phenomena associated with the unimolecular dissociation of H2S --> SH + H have been investigated quantum mechanically by the Lanczos homogeneous filter diagonalization method using a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). Resonance energies, widths (rates), and product state distributions have been obtained. Both dissociation rates and product state distributions of SH show, strong fluctuations, indicating that the dissociation of H2S is essentially irregular. Statistical analysis of neighboring level spacing and width distributions also confirms this behavior. The dissociation rates and product state distributions are compared to the predictions of quantum phase space theory.

Chebyshev real wave packet propagation: H+O-2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrodinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrodinger equation is different from that obtained using the standard Schrodinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O-2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined. (C) 2002 American Institute of Physics.

Quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Future directions in this field are also discussed.

Calculation of bound and resonance states of HO2 for nonzero total angular momentum

Bound and resonance states of HO2 have been calculated quantum mechanically by the Lanczos homogeneous filter diagonalization method [Zhang and Smith, Phys. Chem. Chem. Phys. 3, 2282 (2001); J. Chem. Phys. 115, 5751 (2001)] for nonzero total angular momentum J = 1,2,3. For lower bound states, agreement between the results in this paper and previous work is quite satisfactory; while for high lying bound states and resonances these are the first reported results. A helicity quantum number V assignment (within the helicity conserving approximation) is performed and the results indicate that for lower bound states it is possible to assign the V quantum numbers unambiguously, but for resonances it is impossible to assign the V helicity quantum numbers due to strong mixing. In fact, for the high-lying bound states, the mixing has already appeared. These results indicate that the helicity conserving approximation is not good for the resonance state calculations and exact quantum calculations are needed to accurately describe the reaction dynamics for HO2 system. Analysis of the resonance widths shows that most of the resonances are overlapping and the interferences between them lead to large fluctuations from one resonance to another. In accord with the conclusions from earlier J = 0 calculations, this indicates that the dissociation of HO2 is essentially irregular. (C) 2003 American Institute of Physics.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

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

Bound and resonance states of HO2 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 HO2 are also calculated. (C) 2004 American Institute of Physics.

Iterative quantum computations of HO2 bound states and resonances for J=4 and 5

Bound and resonance states of HO2 have been calculated by both the complex Lanczos homogeneous filter diagonalisation (LHFD) method(1,2) and the real Chebyshev filter diagonalisation method(3,4) for non-zero total angular momentum J = 4 and 5. For bound states, the agreement between the two methods is quite satisfactory; for resonances while the energies are in good agreement, the widths are only in general agreement. The relative performances of the two iterative FD methods have also been discussed in terms of efficiency as well as convergence behaviour for such a computationally challenging problem. A helicity quantum number Ohm assignment (within the helicity conserving approximation) is performed and the results indicate that Coriolis coupling becomes more important as J increases and the helicity conserving approximation is not a good one for the HO2 resonance states.

Recent developments in the quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Recent progresses for non-zero total angular momentum J calculations of resonances including parallel computing models are also included and future directions in this field are discussed.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

Efficient time-independent wave packet scattering calculations within a Lanczos subspace: H+O-2 (J=0) state-to-state reaction probabilities

An efficient Lanczos subspace method has been devised for calculating state-to-state reaction probabilities. The method recasts the time-independent wave packet Lippmann-Schwinger equation [Kouri , Chem. Phys. Lett. 203, 166 (1993)] inside a tridiagonal (Lanczos) representation in which action of the causal Green's operator is affected easily with a QR algorithm. The method is designed to yield all state-to-state reaction probabilities from a given reactant-channel wave packet using a single Lanczos subspace; the spectral properties of the tridiagonal Hamiltonian allow calculations to be undertaken at arbitrary energies within the spectral range of the initial wave packet. The method is applied to a H+O-2 system (J=0), and the results indicate the approach is accurate and stable. (C) 2002 American Institute of Physics.

Lanczos subspace time-independent wave packet calculations of S(D-1)+H-2 reactive scattering

In this paper. we present the results of quantum dynamical simulations of the S (D-1) + H-2 insertion reaction on a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). State-to-state reaction probabilities. product state distributions, and initial-state resolved cumulative reaction probabilities from a given incoming reactant channel are obtained from a time-independent wave packet analysis, performed within a single Lanczos subspace. Integral reaction cross sections are then estimated by J-shifting method and compared with the results from molecular beam experiment and QCT calculations.

Symmetry contaminations in reactive scattering through long-lived collision complexes

We extend our Lanczos subspace time-independent wave packet method [J. Chem. Phys. 116 (2002) 2354] to investigate the issue of symmetry contaminations for the challenging deep-well H + O-2 reaction. Our central objective is to address the issue of whether significant symmetry contamination can occur if a wavepacket initially possessing the correct O-O exchange symmetry is propagated over tens of thousands of recursive steps using a basis which does not explicitly enforce the correct symmetry, and if so how seriously this affects the results. We find that symmetry contamination does exist where the symmetry constraint is not explicitly enforced in the basis. While it affects individual resonances and the associated peak amplitudes, the overall shape of the more averaged quantities such as total reaction probabilities and vibrational branching ratios are not seriously affected. (C) 2004 Elsevier B.V. All rights reserved.