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.

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.

Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

A study of the interaction between operator style and machine capability for a hydraulic mining excavator

This paper presents a case study that explores how operator digging style juxtaposes with mechanical capability for a class of hydraulic mining excavators. The relationships between actuator and digging forces are developed and these are used to identify the excavator's capability to apply forces in various directions. Two distinct modes of operation are examined to see how they relate to the mechanical capabilities of the linkage and to establish if one has merit over the other. It is found that one of these styles results in lower loading of the machine.

X-ray scattering studies of mixed langmuir monolayers and Langmuir-Blodgett films of a noncentrosymmetric porphyrin with cadmium arachidate

The structures of mixed Langmuir (floating) monolayers and Langmuir-Blodgett (LB) films of a phenanthroline-porphyrin with cadmium arachidate (PhenPor + CdAr) have been investigated by synchrotron X-ray grazing incidence diffraction (GIXD) and specular X-ray reflectivity (SXR). GIXD measurements of the floating monolayers showed only one peak, arising from the CdAr domains in the films, at a scattering angle of 21.5 degrees. This is consistent with a hexagonal structure (alpha = 4.77 Angstrom). The correlation length in these domains is 250 Angstrom. GMD measurements of the LB films, however, show two sets of diffraction features: one arises from CdAr domains with a rectangular in-plane structure (alpha = 7.44 Angstrom and b = 4.90 Angstrom) and a correlation length of 85 Angstrom; the other is from porphyrin domains with an oblique in-plane structure (alpha (p) 15.2 Angstrom, b(p) = 8.86 Angstrom, and gamma (p) = 80 degrees) and a correlation length of 105 Angstrom. These dimensions are consistent with the surface pressure-area isotherm measurements and indicate that the two components are immiscible. The thickness of the bilayer is 57 Angstrom, and there is no correlation between the bilayers. Introduction of a trigger compound does not alter the structure of the films but slightly increases the bilayer thickness. The SXR measurements of the floating monolayers also support the suggested immiscibility of the two components in the films.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

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.

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.

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.

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+H2 reactive state-to-state scattering.