Analytic banded approximation for the discretized free propagator

Hoffman, David K.; Nayar, Naresh; Sharafeddin, Omar A.; Kouri, Donald J.

doi:10.1021/j100174a052

Cited by 155 publications

(142 citation statements)

References 2 publications

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“…97,98,137,138 The banded Toeplitz representation of the DAF propagator renders a great deal of efficiency to quantum propagation. 59,97,98,137 The evolution of {R C ,P C } is given by the velocity Verlet integrator, 139 which is also obtained through a third-order Trotter factorization of the classical Liouville form of the AIMD equations.…”

Section: Quantum Wavepacket Ab Initio Molecular Dynamics Enhancedmentioning

confidence: 99%

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

2007

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We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantumclassical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl] -, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.

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Section: Quantum Wavepacket Ab Initio Molecular Dynamics Enhancedmentioning

confidence: 99%

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

2007

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“…for wave propagations [23]. Further discussion of its connections to wavelets and the DSC algorithm can be found in Ref.…”

Section: A Dsc-hermite Algorithm and Cfor Schemementioning

confidence: 99%

High resolution conjugate filters for the simulation of flows

Zhou

Wang

2003

Journal of Computational Physics

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This paper proposes a Hermite-kernel realization of the conjugate filter oscillation reduction (CFOR) scheme for the simulation of fluid flows. The Hermite kernel is constructed by using the discrete singular convolution (DSC) algorithm, which provides a systematic generation of low-pass filter and its conjugate high-pass filters. The high-pass filters are utilized for approximating spatial derivatives in solving flow equations, while the conjugate low-pass filter is activated to eliminate spurious oscillations accumulated during the time evolution of a flow. As both low-pass and high-pass filters are derived from the Hermite kernel, they have similar regularity, time-frequency localization, effective frequency band and compact support. Fourier analysis indicates that the CFOR-Hermite scheme yields a nearly optimal resolution and has a better approximation to the ideal low-pass filter than previously CFOR schemes.Thus, it has better potential for resolving natural high frequency oscillations from a shock. Extensive one-and two-dimensional numerical examples, including both incompressible and compressible flows, with or without shocks, are employed to explore the utility, test the resolution, and examine the stability of the present CFOR-Hermite scheme. Extremely small ratio of point- * Corresponding author 1 per-wavelength (PPW) is achieved in solving the Taylor problem, advancing a wavepacket and resolving a shock/entropy wave interaction. The present results for the advection of an isentropic vortex compare very favorably to those in the literature.

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“…in the H, representation, so that the entire calculation could be done without changing representations (62)(63)(64). Since these operators depend only on the time step size (65), rather than on the time itself, they may be evaluated once and stored, thereby saving computational effort if a number of wavepacket propagations are to be done.…”

Section: General Referenced Modified Cayley Methodsmentioning

confidence: 99%

Time-dependent treatment of scattering: potential referenced and kinetic energy referenced modified Cayley approaches to atom–diatom collisions and time-scale separations

Sharafeddin¹,

Kouri²,

Hoffman³

1992

Can. J. Chem.

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. Can. J. Chem. 70, 686 (1992). The time-dependent Lippmann-Schwinger equation describing atom-diatom collisions is expressed in terms of a general reference Hamiltonian, H,, whose dynamics are easily solved in one representation, and a corresponding disturbance Hamiltonian, H,, whose dynamics are easily solved in a different representation. The wavefunction at time t + T is then expressed in terms of its value at a previous time r by means of a simple quadrature approximation. The resulting expression for +(t + T) has a form similar to that occurring in earlier numerical unitary solutions to the time-dependent Schrodinger equation via a Cayley transformation. The structure of the new equations is made explicit for (a) the choice where H , is taken to be the kinetic energy and H, is the potential energy and (b) the choice where H , is taken to be the potential energy and H, is the kinetic energy. In addition, we also deal with several alternatives for treating the binding potential of the diatom. Several alternatives for choosing representations are then explored for reducing the equations to a form amenable to computation. The short time structure of the equations is discussed in terms of a multiple time-scales analysis.Key words: molecular collisions, multiple time scales, quantum dynamics.

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Analytic banded approximation for the discretized free propagator

Cited by 155 publications

References 2 publications

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

High resolution conjugate filters for the simulation of flows

Time-dependent treatment of scattering: potential referenced and kinetic energy referenced modified Cayley approaches to atom–diatom collisions and time-scale separations

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