The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Donald J Kouri - One of the best experts on this subject based on the ideXlab platform.
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distributed Approximating Function approach to time dependent wavepacket propagation in 3 dimensions atom surface scattering
Computer Physics Communications, 1994Co-Authors: Youhong Huang, Thomas L Marchioro, Mark Arnold, Donald J Kouri, David K HoffmannAbstract:Abstract The theoretical formalism of the distributed Approximating Functions (DAF) is applied to solve accurately 3D-atom-surface scattering problems. Formulated in coordinate space, the DAF approach starts from an entirely new idea: providing a “uniform” approximation everywhere to a wavepacket, and results naturally in a near-local or banded free propagator. The banded Toeplitz structure of the DAF free propagator matrix on a uniform grid makes possible the application of the most efficient codes in the matrix-vector multiplication in evolving the waveFunction of a quantum system in time, and with extremely small memory requirements. The numerical study conducted in this paper demonstrates that the DAF method outperforms the most powerful available FFT method both in CPU time and storage requirements. The DAF approach gives the same accurate results as the FFT does, and, in some cases, yields more accurate results.
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Distributed Approximating Function Approach to Atom-Diatom Reactive Scattering: Time-Dependent and Time-Independent Wavepacket Treatments
The Journal of Physical Chemistry, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K. HoffmanAbstract:The recently developed distributed Approximating Function (DAF) method for evaluating the action of the kinetic energy evolution operator, and the kinetic energy portion of the Hamiltonian, is applied to treat collinear reactive scattering. The DAF approach yields highly banded representations of these operators, while permitting the relevant matrix-vector multiplications to be done by fast convolution. Both time-dependent and time-independent wavepacket propagation schemes are employed, along with the DAFs, and accurate results obtained for the standard H+H 2 collinear reactive scattering system
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Distributed Approximating Function approach to time‐dependent wave‐packet propagation in more than one dimension: Inelastic collinear atom–diatom collisions
Journal of Chemical Physics, 1993Co-Authors: Youhong Huang, Thomas L Marchioro, Mark Arnold, Donald J Kouri, David K. HoffmanAbstract:The distributed Approximating Function (DAF) approach to time‐dependent wave‐packet propagation in the coordinate representation is utilized to treat collinear, inelastic atom–diatom collisions. The resulting discretized DAF (DDAF) 2D‐propagator is highly banded, leading to an extremely efficient computational strategy. The approach is illustrated with application to the atom–harmonic oscillator collision system treated earlier by Secrest and Johnson [J. Chem. Phys. 45, 4556 (1966)].
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Interacting distributed Approximating Functions for real‐time quantum dynamics
Journal of Chemical Physics, 1993Co-Authors: David K. Hoffman, Mark Arnold, Donald J KouriAbstract:The distributed Approximating Function (DAF) approach to quantum real‐time dynamics is generalized to include the effects of the potential. The ‘‘interacting’’ DAF (IDAF) is introduced as the identity for a certain class of Functions that can be chosen to approximate as closely as desired any wave packet of interest. Free propagation of the IDAF yields the free propagator for the IDAF class in the coordinate representation, and substitution of this result into the Trotter form for the short‐time full propagator, G(x,x’‖τ), yields the IDAF class full propagator, G(x,x’;{p}‖τ), in the coordinate representation. Here {p} denotes the set of parameters that determine the IDAF class. The IDAF class full propagator can be used to develop discretized path integral‐based algorithms for real‐time quantum dynamics. Use of G(x,x’;{p}‖τ) in the Feynman path integral formalism leads to a new result with interesting features compared to the standard path integral. Specifically, the IDAF class full propagator incorporate...
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Distributed Approximating Function theory for an arbitrary number of particles in a coordinate system-independent formalism
The Journal of Physical Chemistry, 1993Co-Authors: David K. Hoffman, Donald J KouriAbstract:A general, multidimensional distributed Approximating Function theory is developed that applies to any system which has one possible configurational representation in Cartesian variables. That is, the configuration of the system can be expressed as a generalized N-dimensional vector which has the usual transformation properties under multidimensional rotations. In particular, the theory is applicable to a scattering system with an arbitrary number, A, of scattering centers and projectiles (atoms), for which N=3A. The approach makes possible the realization of distributed Approximating Functions (DAFs) in any orthogonal, curvilinear coordinates including spherical polar, cylindrical polar, and hyperspherical, as well as elliptic and parabolic coordinates
David K. Hoffman - One of the best experts on this subject based on the ideXlab platform.
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Distributed Approximating Function Approach to Atom-Diatom Reactive Scattering: Time-Dependent and Time-Independent Wavepacket Treatments
The Journal of Physical Chemistry, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K. HoffmanAbstract:The recently developed distributed Approximating Function (DAF) method for evaluating the action of the kinetic energy evolution operator, and the kinetic energy portion of the Hamiltonian, is applied to treat collinear reactive scattering. The DAF approach yields highly banded representations of these operators, while permitting the relevant matrix-vector multiplications to be done by fast convolution. Both time-dependent and time-independent wavepacket propagation schemes are employed, along with the DAFs, and accurate results obtained for the standard H+H 2 collinear reactive scattering system
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Distributed Approximating Function approach to time‐dependent wave‐packet propagation in more than one dimension: Inelastic collinear atom–diatom collisions
Journal of Chemical Physics, 1993Co-Authors: Youhong Huang, Thomas L Marchioro, Mark Arnold, Donald J Kouri, David K. HoffmanAbstract:The distributed Approximating Function (DAF) approach to time‐dependent wave‐packet propagation in the coordinate representation is utilized to treat collinear, inelastic atom–diatom collisions. The resulting discretized DAF (DDAF) 2D‐propagator is highly banded, leading to an extremely efficient computational strategy. The approach is illustrated with application to the atom–harmonic oscillator collision system treated earlier by Secrest and Johnson [J. Chem. Phys. 45, 4556 (1966)].
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Interacting distributed Approximating Functions for real‐time quantum dynamics
Journal of Chemical Physics, 1993Co-Authors: David K. Hoffman, Mark Arnold, Donald J KouriAbstract:The distributed Approximating Function (DAF) approach to quantum real‐time dynamics is generalized to include the effects of the potential. The ‘‘interacting’’ DAF (IDAF) is introduced as the identity for a certain class of Functions that can be chosen to approximate as closely as desired any wave packet of interest. Free propagation of the IDAF yields the free propagator for the IDAF class in the coordinate representation, and substitution of this result into the Trotter form for the short‐time full propagator, G(x,x’‖τ), yields the IDAF class full propagator, G(x,x’;{p}‖τ), in the coordinate representation. Here {p} denotes the set of parameters that determine the IDAF class. The IDAF class full propagator can be used to develop discretized path integral‐based algorithms for real‐time quantum dynamics. Use of G(x,x’;{p}‖τ) in the Feynman path integral formalism leads to a new result with interesting features compared to the standard path integral. Specifically, the IDAF class full propagator incorporate...
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Distributed Approximating Function theory for an arbitrary number of particles in a coordinate system-independent formalism
The Journal of Physical Chemistry, 1993Co-Authors: David K. Hoffman, Donald J KouriAbstract:A general, multidimensional distributed Approximating Function theory is developed that applies to any system which has one possible configurational representation in Cartesian variables. That is, the configuration of the system can be expressed as a generalized N-dimensional vector which has the usual transformation properties under multidimensional rotations. In particular, the theory is applicable to a scattering system with an arbitrary number, A, of scattering centers and projectiles (atoms), for which N=3A. The approach makes possible the realization of distributed Approximating Functions (DAFs) in any orthogonal, curvilinear coordinates including spherical polar, cylindrical polar, and hyperspherical, as well as elliptic and parabolic coordinates
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Traveling distributed Approximating Function approach to wave packet propagation: explicit inclusion of a local wave velocity
The Journal of Physical Chemistry, 1993Co-Authors: David K. Hoffman, Mark Arnold, Donald J KouriAbstract:The distributed Approximating Function (DAF) approach to wave packet propagation, designed to treat a restricted class of wave packets which can be approximated to a specified level of accuracy by a polynomial of degree M under the envelope of the DAF, is modified to take explicit account of the group velocity of the specific wave packet describing the collision system of interest. Because the DAFs are exactly and analytically freely propagatible, they yield an accurate analytical fit of the freely propagated wave packet also, which expression can be used to obtain the coordinate representation «traveling» DAF (TDAF) class free propagator
Mark Arnold - One of the best experts on this subject based on the ideXlab platform.
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distributed Approximating Function approach to time dependent wavepacket propagation in 3 dimensions atom surface scattering
Computer Physics Communications, 1994Co-Authors: Youhong Huang, Thomas L Marchioro, Mark Arnold, Donald J Kouri, David K HoffmannAbstract:Abstract The theoretical formalism of the distributed Approximating Functions (DAF) is applied to solve accurately 3D-atom-surface scattering problems. Formulated in coordinate space, the DAF approach starts from an entirely new idea: providing a “uniform” approximation everywhere to a wavepacket, and results naturally in a near-local or banded free propagator. The banded Toeplitz structure of the DAF free propagator matrix on a uniform grid makes possible the application of the most efficient codes in the matrix-vector multiplication in evolving the waveFunction of a quantum system in time, and with extremely small memory requirements. The numerical study conducted in this paper demonstrates that the DAF method outperforms the most powerful available FFT method both in CPU time and storage requirements. The DAF approach gives the same accurate results as the FFT does, and, in some cases, yields more accurate results.
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Distributed Approximating Function approach to time‐dependent wave‐packet propagation in more than one dimension: Inelastic collinear atom–diatom collisions
Journal of Chemical Physics, 1993Co-Authors: Youhong Huang, Thomas L Marchioro, Mark Arnold, Donald J Kouri, David K. HoffmanAbstract:The distributed Approximating Function (DAF) approach to time‐dependent wave‐packet propagation in the coordinate representation is utilized to treat collinear, inelastic atom–diatom collisions. The resulting discretized DAF (DDAF) 2D‐propagator is highly banded, leading to an extremely efficient computational strategy. The approach is illustrated with application to the atom–harmonic oscillator collision system treated earlier by Secrest and Johnson [J. Chem. Phys. 45, 4556 (1966)].
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Interacting distributed Approximating Functions for real‐time quantum dynamics
Journal of Chemical Physics, 1993Co-Authors: David K. Hoffman, Mark Arnold, Donald J KouriAbstract:The distributed Approximating Function (DAF) approach to quantum real‐time dynamics is generalized to include the effects of the potential. The ‘‘interacting’’ DAF (IDAF) is introduced as the identity for a certain class of Functions that can be chosen to approximate as closely as desired any wave packet of interest. Free propagation of the IDAF yields the free propagator for the IDAF class in the coordinate representation, and substitution of this result into the Trotter form for the short‐time full propagator, G(x,x’‖τ), yields the IDAF class full propagator, G(x,x’;{p}‖τ), in the coordinate representation. Here {p} denotes the set of parameters that determine the IDAF class. The IDAF class full propagator can be used to develop discretized path integral‐based algorithms for real‐time quantum dynamics. Use of G(x,x’;{p}‖τ) in the Feynman path integral formalism leads to a new result with interesting features compared to the standard path integral. Specifically, the IDAF class full propagator incorporate...
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Traveling distributed Approximating Function approach to wave packet propagation: explicit inclusion of a local wave velocity
The Journal of Physical Chemistry, 1993Co-Authors: David K. Hoffman, Mark Arnold, Donald J KouriAbstract:The distributed Approximating Function (DAF) approach to wave packet propagation, designed to treat a restricted class of wave packets which can be approximated to a specified level of accuracy by a polynomial of degree M under the envelope of the DAF, is modified to take explicit account of the group velocity of the specific wave packet describing the collision system of interest. Because the DAFs are exactly and analytically freely propagatible, they yield an accurate analytical fit of the freely propagated wave packet also, which expression can be used to obtain the coordinate representation «traveling» DAF (TDAF) class free propagator
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Properties of the optimum distributed Approximating Function class propagator for discretized and continuous wave packet propagations
The Journal of Physical Chemistry, 1992Co-Authors: David K. Hoffman, Mark Arnold, Donald J KouriAbstract:A new, more concise derivation of the continuous and discretized distributed Approximating Function (CDAF and DDAF) class free propagators and a detailed explication of their properties are presented. The DAF class propagators are characterized by three factors: namely, a real Gaussian, a unimodulator oscillatory factor, and a {open_quotes}shape polynomial{close_quotes} of degree M (with M even) which has complex coefficients. For the continuous version of the theory, these factors are solely a Function of the time step {tau} and take the forms exp[-m(x{prime}-x){sup 2}/4{h_bar}{tau}{tau}], and g{sub M}(x-x1{sigma}(0)=({h_bar}{tau}/m){sup {1/2}},{tau}), respectively, where {sigma}(0) = ({h_bar}{tau}/m){sup {1/2}} is the width of the Gaussian envelope of the CDAF. The discrete version of the theory requires slightly different forms for these factors, because of the choice of {sigma}(0) depends also on the grid spacing. The relationship {sigma}(0) = ({h_bar}{tau}/m){sup {1/2}}, which gives the optimum choice of the Gaussian envelope of the CDAF for minimizing its spread in time {tau}, is derived. The relationship between the Gaussian width {sigma}(0) and the degree of the shape polynomial is given, and it is shown that the specification of the time step {tau} is sufficient to fix all other parameters. The time step {tau} is determined by the characteristics ofmore » the propagator algorithm being used. 11 refs., 10 figs.« less
Youhong Huang - One of the best experts on this subject based on the ideXlab platform.
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distributed Approximating Function approach to time dependent wavepacket propagation in 3 dimensions atom surface scattering
Computer Physics Communications, 1994Co-Authors: Youhong Huang, Thomas L Marchioro, Mark Arnold, Donald J Kouri, David K HoffmannAbstract:Abstract The theoretical formalism of the distributed Approximating Functions (DAF) is applied to solve accurately 3D-atom-surface scattering problems. Formulated in coordinate space, the DAF approach starts from an entirely new idea: providing a “uniform” approximation everywhere to a wavepacket, and results naturally in a near-local or banded free propagator. The banded Toeplitz structure of the DAF free propagator matrix on a uniform grid makes possible the application of the most efficient codes in the matrix-vector multiplication in evolving the waveFunction of a quantum system in time, and with extremely small memory requirements. The numerical study conducted in this paper demonstrates that the DAF method outperforms the most powerful available FFT method both in CPU time and storage requirements. The DAF approach gives the same accurate results as the FFT does, and, in some cases, yields more accurate results.
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Distributed Approximating Function Approach to Atom-Diatom Reactive Scattering: Time-Dependent and Time-Independent Wavepacket Treatments
The Journal of Physical Chemistry, 1994Co-Authors: Youhong Huang, Donald J Kouri, David K. HoffmanAbstract:The recently developed distributed Approximating Function (DAF) method for evaluating the action of the kinetic energy evolution operator, and the kinetic energy portion of the Hamiltonian, is applied to treat collinear reactive scattering. The DAF approach yields highly banded representations of these operators, while permitting the relevant matrix-vector multiplications to be done by fast convolution. Both time-dependent and time-independent wavepacket propagation schemes are employed, along with the DAFs, and accurate results obtained for the standard H+H 2 collinear reactive scattering system
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Distributed Approximating Function approach to time‐dependent wave‐packet propagation in more than one dimension: Inelastic collinear atom–diatom collisions
Journal of Chemical Physics, 1993Co-Authors: Youhong Huang, Thomas L Marchioro, Mark Arnold, Donald J Kouri, David K. HoffmanAbstract:The distributed Approximating Function (DAF) approach to time‐dependent wave‐packet propagation in the coordinate representation is utilized to treat collinear, inelastic atom–diatom collisions. The resulting discretized DAF (DDAF) 2D‐propagator is highly banded, leading to an extremely efficient computational strategy. The approach is illustrated with application to the atom–harmonic oscillator collision system treated earlier by Secrest and Johnson [J. Chem. Phys. 45, 4556 (1966)].
Naresh Nayar - One of the best experts on this subject based on the ideXlab platform.
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A computational demonstration of the distributed Approximating Function approach to real time quantum dynamics
The Journal of Physical Chemistry, 1992Co-Authors: Naresh Nayar, David K. Hoffman, Xin Ma, Donald J KouriAbstract:The authors report computational applications for the newly developed distributed Approximating Function (DAF) approach to real time quantal wavepacket propagation for several one-dimensional model problems. The DAF is constructed to fit all wavepackets accurately which can be represented, to the same accuracy, by a polynomial of degree M, or less, within the envelope of the DAF. (This defines the {open_quotes}DAF class{close_quotes} of Functions.) By expressing the DAF (and thus the wavepacket to be propagated) in terms of Hermite Functions (each a product of a Hermite polynomial and its Gaussian generating Function), the DAF approximation to the wavepacket is propagated freely and exactly for a short time {tau}. The Hermite Functions are the natural basis states for describing the free evolution of a localized particle and yield a highly banded representation for the free particle propagator. Combining the DAF class free propagation scheme with any of several short time approximations to the full propagator enables one to propagate the wavepacket through a potential. The DAF results for the propagated wavepacket and various scattering amplitudes are shown to be in good agreement with those obtained by more standard methods. 17 refs., 7 figs., 4 tabs.