Journal ArticleDOI
Time dependent variational approach to semiclassical dynamics
TLDR
The Dirac-Frenkel-McLachlan variational principle for the time dependent Schrodinger equation and a variational correction procedure for wavefunctions and transition amplitudes are reviewed in this paper.Abstract:
Explicitly time dependent methods for semiclassical dynamics are explored using variational principles. The Dirac–Frenkel–McLachlan variational principle for the time dependent Schrodinger equation and a variational correction procedure for wavefunctions and transition amplitudes are reviewed. These variational methods are shown to be promising tools for the solution of semiclassical problems where the correspondence principle, classical intuition, or experience suggest reasonable trial forms for the time dependent wavefunction. Specific trial functions are discussed for several applications, including the curve crossing problem. The useful semiclassical content of the time dependent Hartree approximation is discussed. Procedures for the variational propagation of density matrices are also derived.read more
Citations
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The multi-configurational time-dependent Hartree approach
TL;DR: In this article, a multi-configurational approach to the time-dependent Schrodinger equation is proposed, which can be used for n degrees of freedom and for any choice of the number of configurations.
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The semiclassical way to molecular spectroscopy
TL;DR: In this paper, a new perspective on the interaction of light with molecules is presented, which deals with a new viewpoint on the interactions between light and molecules and shows that light can be used as a probe of molecular structure and dynamics, and sometimes light acts as a reagent or product in a chemical reaction.
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Mixed quantum–classical dynamics
TL;DR: In this article, a unified derivation of the mean-field and surface-hopping approaches to mixed quantum-classical dynamics is presented, which elucidates the underlying approximations of the methods and their strengths and weaknesses.
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Theoretical Insights into Photoinduced Charge Transfer and Catalysis at Oxide Interfaces
TL;DR: In this article, the authors focus on processes that are essential in terms of photovoltaic and photocatlytic cells, and focus on the processes that can be improved.
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Wigner phase space method: Analysis for semiclassical applications
TL;DR: In this article, the suitability of the Wigner method as a tool for semiclassical dynamics is investigated, and qualitatively introduced the difficulties encountered in some applications, and derive quantitative means of surmounting these difficulties.
References
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TL;DR: In this paper, the crossing of a polar and homopolar state of a molecule with stationary nuclei has been studied, and the essential features may be illustrated in the crossing.
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Description of States in Quantum Mechanics by Density Matrix and Operator Techniques
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Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H+ with D2
John C. Tully,Richard K. Preston +1 more
TL;DR: In this article, an extension of the classical trajectory approach is proposed that may be useful in treating many types of nonadiabatic molecular collisions, where nuclei are assumed to move classically on a single potential energy surface until an avoided surface crossing or other region of large NDE coupling is reached.
Journal ArticleDOI
Time‐dependent approach to semiclassical dynamics
TL;DR: In this paper, a wave packet is decomposed into time-dependent wave packets, which spread minimally and which execute classical or nearly classical trajectories, assuming a Gaussian form for the wave packets and equations of motion for the Gaussians.
Journal ArticleDOI
Semiclassical description of scattering
TL;DR: In this article, the quantum-mechanical scattering amplitude can be simply related to the classical deflection function when the conditions for a semiclassical analysis of the quantum mechanics are met.