Journal ArticleDOI
Multilayer formulation of the multiconfiguration time-dependent Hartree theory
Haobin Wang,Michael Thoss +1 more
TLDR
In this paper, a multilayer formulation of the multiconfiguration time-dependent Hartree (MCTDH) theory is presented, where the single-particle (SP) functions in the original MCTDH method are further expressed employing a timedependent multi-figurational expansion, and the Dirac-Frenkel variational principle is applied to optimally determine the equations of motion.Abstract:
A multilayer (ML) formulation of the multiconfiguration time-dependent Hartree (MCTDH) theory is presented. In this new approach, the single-particle (SP) functions in the original MCTDH method are further expressed employing a time-dependent multiconfigurational expansion. The Dirac–Frenkel variational principle is then applied to optimally determine the equations of motion. Following this strategy, the SP groups are built in several layers, where each top layer SP can contain many more Cartesian degrees of freedom than in the previous formulation of the MCTDH method. As a result, the ML-MCTDH method has the capability of treating substantially more physical degrees of freedom than the original MCTDH method, and thus significantly enhances the ability of carrying out quantum dynamical simulations for complex molecular systems. The efficiency of the new formulation is demonstrated by converged quantum dynamical simulations for systems with a few hundred to a thousand degrees of freedom.read more
Citations
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Journal ArticleDOI
Multilayer multiconfiguration time-dependent Hartree method: implementation and applications to a Henon-Heiles hamiltonian and to pyrazine.
Oriol Vendrell,Hans-Dieter Meyer +1 more
TL;DR: In this article, the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive MCTDH algorithm given by Manthe [J. Phys.
Journal ArticleDOI
O(dlog N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling
TL;DR: From numerical examples presented here, it is observed that the quantics tensor method has proved its value in application to various function related tensors/matrices arising in computational quantum chemistry and in the traditional finite element method/boundary element method (FEM/BEM).
Journal ArticleDOI
Quantum dynamics simulations using Gaussian wavepackets: the vMCG method
Gareth W. Richings,Iakov Polyak,Kaite Spinlove,Graham A. Worth,Irene Burghardt,Benjamin Lasorne +5 more
TL;DR: In this paper, the authors present a variational multi-configurational Gaussian (vMCG) method to solve the time-dependent Schrodinger equation (TDSE).
Journal ArticleDOI
Using the MCTDH wavepacket propagation method to describe multimode non-adiabatic dynamics
TL;DR: The MCTDH method has been used successfully to treat the non-adiabatic dynamics of a number of systems as discussed by the authors, and is able to treat larger systems than other quantum dynamics methods.
Journal ArticleDOI
Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances
TL;DR: A survey of the recent results and future prospects of the tensor-structured numerical methods in applications to multidimensional problems in scientific computing and focuses on the recent quantics-TT tensor approximation method that allows to represent N-d tensors with log-volume complexity.
References
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Light-Induced Redox Reactions in Nanocrystalline Systems
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TL;DR: In this paper, the authors present a survey of the various approaches to Quantum-Statistical metastability, including Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic System-Plus-Reservoir Models Linear and Nonlinear Quantum Environments Ohmic, Super-Ohmic, and Sub-ohmic Dissipation Quantum Decoherence and Relaxation Correlation Functions, Response Functions, and Fluctuation-Dissipation Theorem Damped Quantum Mechanical Harmonic Oscillator Quantum Brownian Motion Thermodynamic Variational
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The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets
TL;DR: In this article, a review of the multiconfiguration time-dependent Hartree (MCTDH) method for propagating wavepackets is given, and the formal derivation, numerical implementation, and performance of the method are detailed.
Journal ArticleDOI
Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H+ with D2
John C. Tully,Richard K. Preston +1 more
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