Quantum Wave Packet Dynamics with Trajectories

Lopreore, Courtney L.; Wyatt, Róbert E.

doi:10.1103/physrevlett.82.5190

Cited by 435 publications

(374 citation statements)

References 15 publications

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“…An analysis of errors is provided by comparing the classical and quantum-classical nuclear dynamics formalisms utilizing the Bohmian quantum potential. 34,105,106,[119][120][121][122][123][124][125][126] Conclusions are given in section VI.…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…In both cases a linear evolution equation is replaced by a nonlinear one to reduce the computational effort. In the first case, the solutions of Schrödinger equation for a complex system are modeled as arising from a motion of particles of the "probability fluid" subjected to the quantum potential arising in the Bohmian interpretation of quantum mechanics (see, for example, [28]. This procedure is computationally more effective than solving the multidimensional Schrödinger equation on a grid.…”

Section: Linear Vs Nonlinearmentioning

confidence: 99%

On the linearity of the Schrödinger equation

Bialynicki‐Birula¹

2005

Braz. J. Phys.

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“…The computation of the transition probabilities within the frame work of quantum trajectories appears to be quite straightforward, 17,23 while an accurate description of the reflected wave function presents a challenge. The reason for this is that the reflected component of the wave function interferes with the slow incoming component creating a ''rippled'' density profile.…”

Section: A Scattering On the Eckart Barriermentioning

confidence: 99%

Bohmian dynamics on subspaces using linearized quantum force

Rassolov

Garashchuk

2004

The Journal of Chemical Physics

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In the de Broglie-Bohm formulation of quantum mechanics the time-dependent Schrödinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the dominant quantum-mechanical effects in the semiclassical scattering problems of nuclear dynamics. In this paper we formulate the Bohmian dynamics on subspaces and define the energy-conserving approximate quantum potential in terms of optimized nonclassical momentum, extended to include the domain boundary functions. This generalization allows a better description of the non-Gaussian wave packets and general potentials in terms of simple fitting functions. The optimization is performed independently for each domain and each dimension. For linear fitting functions optimal parameters are expressed in terms of the first and second moments of the trajectory distribution. Examples are given for one-dimensional anharmonic systems and for the collinear hydrogen exchange reaction.

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Quantum Wave Packet Dynamics with Trajectories

Cited by 435 publications

References 15 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

On the linearity of the Schrödinger equation

Bohmian dynamics on subspaces using linearized quantum force

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